ssp.tnw.utwente.nl · The work described in this thesis was performed in the Solid State Physics...

PATTERN FORMATION AND MAGNETICANISOTROPY IN THIN METAL FILMS

Sebastiaan van Dijken

The work described in this thesis was performed in the Solid State Physics divisionof the department of Applied Physics at the University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlands

Dijken, S. vanPattern Formation and Magnetic Anisotropy in Thin Metal Films.Proefschrift Universiteit Twente, Enschede.ISBN 90-365-1459-2

Druk: Printpartners Ipskamp, Enschede.

c° S. van Dijken, 2000

Cover: Structures of sand on the beach at Santpoort (The Netherlands).

PATTERN FORMATION AND MAGNETICANISOTROPY IN THIN METAL FILMS

PROEFSCHRIFT

ter verkrijging vande graad van doctor aan de Universiteit Twente,

op gezag van de rector magni…cus,prof.dr. F.A. van Vught,

volgens besluit van het College voor Promotiesin het openbaar te verdedigen

op vrijdag 16 juni 2000 te 16.45 uur.

door

Sebastiaan van Dijkengeboren op 2 mei 1973

te Velsen

Dit proefschrift is goedgekeurd door de promotor:

prof.dr.ir. B. Poelsema

This thesis is based partly on the following articles:

Steering-enhanced roughening during metal deposition at grazing incidence (Chapter3)S. van Dijken, L.C. Jorritsma, and B. PoelsemaPhys. Rev. Lett. 82, 4038 (1999).

Grazing-incidence metal deposition: Pattern formation and slope selection (Chapter3)S. van Dijken, L.C. Jorritsma, and B. Poelsemaaccepted for publication in Phys. Rev. B.

Line formation during grazing-incidence ion sputtering of Cu(001) (Chapter 4)S. van Dijken, D. de Bruin, and B. Poelsemain preparation.

Growth-induced uniaxial anisotropy in grazing-incidence deposited magnetic …lms(Chapter 6)S. van Dijken, G. Di Santo, and B. Poelsemasubmitted to Appl. Phys. Lett..

The in‡uence of the deposition angle on the magnetic anisotropy in thin Co …lmson Cu(001) (Chapter 6)S. van Dijken, G. Di Santo, and B. Poelsemain preparation.

Spin-reorientation transition in Ni …lms on Cu(001): The in‡uence of H2 adsorp-tion (Chapter 7)R. Vollmer, Th. Gutjahr-Löser, J. Kirschner, S. van Dijken, and B. PoelsemaPhys. Rev. B 60, 6277 (1999).

The in‡uence of CO and H2 adsorption on the spin reorientation transition inNi/Cu(001) (Chapter 7)S. van Dijken, R. Vollmer, B. Poelsema, and J. KirschnerJ. Magn. Magn. Mat. 210, 316 (2000).

Contents

1 Introduction 11.1 This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Homoepitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Adatom di¤usion . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Growth modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.3 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 Island shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Heteroepitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.1 Lattice mis…t . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.2 Alloying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Ion sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 Thin …lm magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5.1 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . 16

2 Experimental 192.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Di¤raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Kinematic approximation . . . . . . . . . . . . . . . . . . . . 202.2.2 Peak pro…les . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.3 Bragg peak intensity . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Helium atom scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4 SPA-LEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.5 Magneto-optic Kerr e¤ect. . . . . . . . . . . . . . . . . . . . . . . . . 302.6 MOKE setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.7 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3 Steering-enhanced roughening 373.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 Normal versus grazing incidence deposition . . . . . . . . . . . . . . . 403.3 Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4 Slope selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.5 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . 543.6 Azimuthal dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 56

vii

viii CONTENTS

3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4 Grazing incidence ion sputtering of Cu(001) 654.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Ion sputtering in the [110]-direction . . . . . . . . . . . . . . . . . . . 684.3 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.4 Ion sputtering in the [100]-direction . . . . . . . . . . . . . . . . . . . 794.5 Ion impact induced surface di¤usion . . . . . . . . . . . . . . . . . . . 884.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5 Co and Co/Cu multilayer growth on Cu(001) 935.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2 Growth modes in Co/Cu(001) . . . . . . . . . . . . . . . . . . . . . . 945.3 Surface alloying during Co/Cu(001) growth . . . . . . . . . . . . . . . 1015.4 Annealing of thin Co …lms . . . . . . . . . . . . . . . . . . . . . . . . 1035.5 Co/Cu multilayer growth on Cu(001) . . . . . . . . . . . . . . . . . . 1065.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6 Magnetic anisotropy in Co/Cu(001) 1116.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.2 Deposition angle dependence . . . . . . . . . . . . . . . . . . . . . . . 1126.3 Surface morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.4 Annealing and Cu adsorption . . . . . . . . . . . . . . . . . . . . . . 1266.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7 Spin reorientation transition in Ni/Cu(001) 1337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.2 H2/Ni/Cu(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.3 CO/Ni/Cu(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.4 Cu/Ni/Cu(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1447.5 Surface anisotropy energy . . . . . . . . . . . . . . . . . . . . . . . . 1467.6 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1487.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Summary 167

Samenvatting 171

Dankwoord 175

Chapter 1

Introduction

1.1 This thesisTo date two approaches to pattern a surface have been pursued. In the top-downapproach, lithography driven methods such as microprinting are used for direct pat-terning, whereas the bottom-up approach relies on self-organizing processes. Com-plex structures of dimensions well below the micrometer range can be obtained byoptical lithography. The minimum lateral size of surface structures which can beachieved with this technologically important technique is limited due to the wave-length of light. To miniaturize electronic and magnetic devices further, other tech-niques such as focused ion-beam nanolithography have been developed. Further-more, scanning probe microscopy tips and cantilevers have been used to engravestructures with nanometer resolution. The drawback of this technique is the lim-ited scan area, typically in the micrometer range, over which the pattern can beobtained. In contrast to serial lithography, self-organization phenomena open theway for the formation of a regular pattern on large areas in a single technologicalprocess step. The lateral size of the surface structures obtained by self-organizingprocesses is typically in the nanometer range. The preparation of nanostructuresby self-organization gains importance with the ongoing miniaturization of devicesand storage media. For example, self-organized well-ordered magnetic nanodots canplay a role in the production of high density storage media in the future.

The preparation of well-de…ned and well-ordered nanostructures by self-organizat-ion strongly depends on the growth and/or sputtering conditions. Parameters suchas surface symmetry, substrate temperature and growth/removal rate determine theshape of structures, the arrangement of structures, the lateral length scale, andthe surface roughness. In heteroepitaxial systems (di¤erent substrate and depositedmaterial), which are of great interest for technological applications, even more pos-sibilities to pattern a surface are available. The lattice mismatch between substrateand deposition material can, for example, be used to obtain well-ordered nanostruc-tures.

In contrast to surface patterning other applications require the growth of very

1

2 CHAPTER 1. INTRODUCTION

smooth …lms. The performance of alternating layered …lms of magnetic and non-magnetic metals exhibiting the giant magnetoresistance (GMR) e¤ect, for example,depends critically on the interface roughness. Kinematic roughening and/or alloyingcan deteriorate the strength of the GMR e¤ect in multilayer devices drastically. Agood knowledge about the mechanisms controlling growth is thus crucial for bothsurface patterning and smooth …lm growth.

From a technological viewpoint magnetic anisotropy is one of the most importantproperties of magnetic materials. Depending on the application, materials with high,medium or low magnetic anisotropy will be required, for respective applications aspermanent magnets, storage media or magnetic cores in transformers and magneticrecording heads. The physical origin of magnetic anisotropy and its strength inultrathin magnetic …lms or magnetic nanodots can be quite di¤erent from that inthe bulk. This makes it possible to tune the magnetic anisotropy by using di¤erentsubstrate and deposition materials and di¤erent growth conditions. The substratesymmetry, …lm thickness, and surface morphology, for example, in‡uence magneticanisotropy.

In this thesis pattern formation during homoepitaxial growth (same substrateand deposition material) and ion sputtering is studied. Special emphasize is laidon the in‡uence the deposition and sputtering geometry have on the shape andarrangement of evolving nanostructures. Furthermore, Co and Co/Cu multilayergrowth on Cu(001) is investigated. This technologically important heteroepitaxialsystem, which shows a tendency to alloy, is studied as a function of growth temper-ature, growth rate, and deposition angle. Finally, the in‡uence of H2, CO and Cuadsorption on the magnetic anisotropy in thin Ni …lms on Cu(001) is analyzed.

This thesis is organized as follows: in the following of this chapter a short intro-duction into the basic concepts of homoepitaxy, heteroepitaxy, ion sputtering, andthin …lm magnetism is given. The experimental details as well as a brief introduc-tion to kinematic di¤raction theory and magneto-optics is presented in Chap. 2.The helium atom scattering and spot pro…le analysis low electron energy di¤rac-tion (SPA-LEED) instrument used to investigate the surface morphology and themagneto-optic Kerr e¤ect (MOKE) used to study the magnetic properties of ultra-thin …lms are described. In Chap. 3, the in‡uence of the deposition geometry on theevolving surface morphology during molecular beam epitaxy (MBE) of Cu/Cu(001)is discussed. It is shown that growth fronts become progressively rougher upon ro-tation of the molecular beam from normal to grazing incidence. The remarkablekinetic roughening observed after growth at grazing incidence is explained by steer-ing. Steering refers to the focussing of incident atom ‡ux on top of protrudingterraces. The origin and consequences of steering are discussed in detail. In Chap.4, ion sputtering of Cu(001) is studied. It is shown that ion sputtering can be usedas a powerful tool to structure a surface on a nanometer scale. Grazing-incidence ionsputtering results in a well-ordered line structure parallel to the plane of incidence.The formation of parallel lines is explained by preferential sputtering of illuminatedstep edge atoms. The in‡uence of the substrate temperature, the azimuthal sputter-

1.2. HOMOEPITAXY 3

ing direction, and the energy of the incident ions are discussed in detail. Chapter 5deals with the growth of Co and Co/Cu multilayers on Cu(001). The measurementsin this chapter reveal that thermally activated exchange of Co adatoms and Cu sub-strate atoms becomes signi…cant around 330 K. The consequences of this exchangemechanism for the growth of the …rst and subsequent monolayers are discussed.Furthermore, the annealing behavior of ultrathin Co …lms on Cu(001) is analyzed.Chapter 6 is devoted to the deposition angle dependence of the in-plane magneticanisotropy in ultrathin Co …lms on Cu(001). It is shown that grazing-incidenceMBE of Co results in an uniaxial magnetic anisotropy, whose strength increaseswith increasing deposition angle. The measured magnetic anisotropy is related tothe formation of elongated structures during growth. The elongation of structuresis explained by the steering phenomenon, which is described in Chap. 3. In thelast chapter, the in‡uence of H2, CO and Cu adsorption on the magnetic anisotropyin thin Ni …lms on Cu(001) is described. Adsorption of H2, CO and Cu reducesthe critical thickness of the spin reorientation transition in Ni/Cu(001) drastically.The shift of the spin reorientation transition is completely attributed to a strongdecrease of the magnetic surface anisotropy energy induced by H2, CO or Cu.

1.2 Homoepitaxy

Growth systems in which substrate and …lm material are of the same kind, i.e.,homoepitaxial growth systems, are the simplest model systems for epitaxial growth.No complicating e¤ects arise due to a di¤erence in the surface free energy or a lat-tice mis…t between substrate and …lm. Thermodynamic considerations impose thathomoepitaxial growth proceeds layer-by-layer. As a consequence, the occurrence ofdi¤erent growth modes in homoepitaxy is a true kinetic e¤ect. A detailed studyof homoepitaxy can therefore lead to a deeper insight in growth kinetics. Subse-quently, this knowledge can be used to improve the growth of technologically moreinteresting heteroepitaxial …lms.

Apart from very low substrate temperatures where thermal di¤usion of singleatoms (adatoms) is negligible, growth modes in homoepitaxy can be characterizedby two di¤usion processes: the di¤usion of adatoms on a ‡at terrace and the di¤u-sion of adatoms across a descending step edge. Furthermore, the terrace di¤usionof adatoms plays an important role in the nucleation process. The nucleation pro-cess determines the intrinsic lateral length scale of a growing …lm, i.e., the distancebetween adatom structures. While the di¤usion of adatoms plays a decisive role inthe evolution of the surface morphology during growth and in particular governsthe distance scale between adatom structures, it is discussed …rst in this section.Thereafter, the di¤erent growth modes are described. Then, the substrate tempera-ture and deposition ‡ux dependence of the nucleation and growth of adatom islandsis explained. Finally, the di¤usion processes which determine the shape of adatomislands are discussed.


Figure 1.1: Di¤usion mechanisms: adatom terrace di¤usion via hopping (a) andexchange (b) and adatom di¤usion to a lower layer via hopping (c) and exchange(d).

1.2.1 Adatom di¤usion

The terrace di¤usion of adatoms can either occur via a hopping mechanism or via anexchange mechanism. When adatoms di¤use across a terrace via a hopping mech-anism, the adatoms just hop from one local minimum to another on the potentialenergy surface. For metal (001) surfaces these minima are the fourfold hollow sites.The exchange mechanism for adatom di¤usion on the other hand, corresponds tothe mechanism where adatoms move by changing place with atoms in the outer-most surface layer. The exchange mechanism was …rst proposed by Basset andWebber for Pt/Pt(001) [1] and was predicted from …rst principle calculations byFeibelman to be energetically favorable in self-di¤usion on the Al(001) surface [2].Experimentally, this di¤usion mechanism was found on Pt(001) and Ir(001) surfaces[3, 4]. For both adatom di¤usion mechanisms, the di¤usion frequency is written asºd = º0 ¢ exp(¡Ed=kT ); where Ed is the activation energy for adatom di¤usion andº0 is the attempt frequency. The hopping mechanism and the exchange mechanismare illustrated in Fig. 1.1.

By analogy with the di¤usion of adatoms on a terrace, the adatom di¤usionacross a descending step edge may also occur via a hopping or an exchange mecha-nism. Exchange near steps occurs when a di¤using adatom approaches a descendingstep edge and drops into a lattice position in the underlaying layer before it reachesthe step. In this case, the underlaying layer of atoms pushes one atom outward toaccommodate the exchange event. The possibility of an exchange mechanism forstep-down di¤usion was discussed by Schwoebel and Shipsey [5] and later by Bassetand Webber [1]. That this process can occur was experimentally proven by FieldIon Microscopy (FIM) measurements on W/Ir(111) [6]. The activation energy foradatoms to cross a descending step edge can be higher than the activation energyfor adatom di¤usion on a ‡at terrace (typically about 200 meV for close-packed

1.2. HOMOEPITAXY 5

metal surfaces [7]). The additional activation barrier Es, often called the Ehrlich-Schwoebel [5, 8] or step-edge barrier, can therefore be regarded as a re‡ecting barrierat the step edge. The probability for an adatom to be re‡ected at a step, followingits attempt to descend, increases as 1 ¡ exp(¡Es=kT ). As a result, lowering thegrowth temperature decreases the adatom di¤usion across descending step edges.For metal (001) homoepitaxial systems, the step-edge barrier is much smaller thanthe activation barrier for terrace di¤usion (typically of the order of a few tens ofmeV’s [7]). In exceptional cases the activation energy may even be slightly negative.This may be the case when adatom di¤usion across a descending step edge proceedsvia an exchange mechanism.

Besides thermally activated motion of adatoms, atomic motion caused by thedynamics of the deposition process is possible as well. Thermal energy metal atoms,approaching the surface at typical energies of 0.1 to 0.25 eV, may use the heat of con-densation (typically 1 to 4 eV for metals) to move across the surface. This process,called transient mobility, was …rst proposed by Egelho¤ and Jacob [9]. From growthexperiments at 80 K, they estimated that about ten hops can occur for Cu/Cu(001).On the other hand, molecular dynamics calculations indicate that transient mobilityis negligible in metallic growth systems due to a fast thermalization of the depositedatoms [10, 11, 12, 13]. Furthermore, no evidence for transient mobility was found bya detailed analysis of the spatial distribution of deposited atoms in FIM experiments[14]. As a matter of fact it is now widely accepted that transient mobility e¤ectsare irrelevant for metal growth systems. Downward funneling is another possibleprocess of atomic motion caused by the deposition dynamics [15, 16]. Funneling isthe downward de‡ection of atoms deposited on step edges or small microfacets andleads to an enhanced atomic motion to lower surface layers. Funneling is alwayslimited to a small downward current for atoms incident very close to descendingsteps. It may well be considered as a solid-on-solid condition for an atom to cometo rest.

In this thesis, the di¤usion of adatoms on a ‡at terrace and across a step edgeis called intralayer mass transport and interlayer mass transport, respectively.

1.2.2 Growth modesDepending on the relative rate of intralayer mass transport and interlayer masstransport, three di¤erent growth modes can be distinguished. When intralayer masstransport is so e¢cient that adatoms predominantly attach to step edges (whichare always present on a real crystal surface), the …lm grows by step-‡ow, repeatingthe substrate morphology after the completion of each monolayer. This scenario isanticipated whenever the characteristic adatom di¤usion length on terraces, whichis controlled by substrate temperature and deposition ‡ux, is larger than the widthof the terraces. Step-‡ow growth does occur close to thermodynamic equilibrium(high substrate temperatures) and does not require any interlayer mass transport.However, far from thermodynamic equilibrium, i.e., under typical molecular beam


Figure 1.2: Illustration of step-‡ow growth (a), layer-by-layer growth (b) and mul-tilayer growth (c).

epitaxy (MBE)-conditions, the growth proceeds via nucleation and growth of adatomislands on the ‡at terraces of the substrate. In this case, interlayer mass transportdetermines the growth mode which may be layer-by-layer or multilayer growth. Forlayer-by-layer growth it is a necessary condition that atoms deposited on top ofadatom islands can descend from the island so that no stable nuclei are formed ontop of islands before they have coalesced to form a two-dimensional layer [7, 17].This is a realistic de…nition of layer-by-layer growth. Ideal layer-by-layer growth,i.e., initiation of growth in a new layer after completion of the previous one, cannever be reached in a real growth experiment. When nucleation of stable nucleion top of islands occurs before coalescence, the growth is called multilayer growth.In this case, the probability for an adatom to be re‡ected at a step, following itsattempt to descend, is large enough to establish a critical adatom density on top ofislands before coalescence. When all adatoms are re‡ected at the step edges, idealmultilayer growth is obtained. In this case, the distribution of exposed layers withthe layer height is a Poisson distribution [18, 19, 20, 21, 22].

In growth systems with a small step-edge barrier, e.g., metal (001) homoepitaxialsystems, all three growth modes can be obtained. At high substrate temperatureswhere the di¤usion of adatoms is large enough to reach pre-existing step edges, step-‡ow growth occurs. At intermediate substrate temperatures where growth proceedsvia nucleation and growth of adatom islands on terraces and where the adatomre‡ection probability at step edges is small, the growth is layer-by-layer. At lowsubstrate temperatures where the adatom re‡ection probability at step edges islarger, multilayer growth occurs. In general, growth far from equilibrium results inthe formation of mounds when a …nite step-edge barrier is present. These moundscoarsen slowly in time while the sides of the mounds turn into facets.

1.2.3 Nucleation

During the initial stage of growth, adatoms di¤use over the surface until they nucle-ate with others to form stable islands. The formation of stable adatom islands satu-

1.2. HOMOEPITAXY 7

rates when every deposited atom is able to di¤use to a stable island or a pre-existingstep edge. In homoepitaxial systems a saturation density of small adatom islandsis reached rapidly. After saturation the adatom islands grow two-dimensionallyuntil they coalesce. The nucleation process during the initial stage of growth deter-mines the intrinsic lateral length scale of a …lm, i.e., the average distance betweenadatom islands. Mean-…eld rate equations [23, 24, 25] and Monte Carlo simulations[26, 27, 28, 29] predict that the average island density, N, is given by:

N t ´(µ)µFº0

¶pexp

·p[Ed + (Ei=i)]

kT

¸: (1.1)

Here, p = i=(i + 1), with i the number of atoms above which islands are on theaverage stable against dissociation, Ed is the activation energy for adatom di¤usionon a terrace and º0 is the associated attempt frequency. Furthermore, Ei is thebinding energy of the critical island of size i+1, F is the deposition ‡ux and ´(µ) is aparameter which depends weakly on the …lm coverage µ. From Eq. 1.1 it is clear thatthe island density increases with decreasing substrate temperature and increasingdeposition ‡ux. The critical island size i can be determined from the dependenceof the island density on the deposition ‡ux, at …xed substrate temperature andcoverage [30]. At low substrate temperatures where the attachment of adatoms toislands is irreversible, (i = 1, p = 1=3, and E1 = 0), Ed can be extracted fromthe slope in a ln(N) versus 1=T plot. The extraction of the binding energy Eifrom the decrease of N with increasing substrate temperature is more problematic.First of all, i must be well de…ned, which is not always the case at elevated substratetemperatures. Second, it is possible that di¤erent di¤usion mechanisms are active indi¤erent temperature ranges [31]. Therefore, it is never su¢cient to draw conclusionssolely from the dependence of the island density on the growth temperature. Inaddition one should check its dependence (at …xed temperature) on the deposition‡ux F .

At very low substrate temperatures where the thermal di¤usion of adatoms isnegligible, the island density saturates, i.e., the average distance between islands isnot temperature dependent anymore. This is obviously not in accordance with Eq.1.1. The origin of a minimum island separation is not fully clear. The phenomenonmay be caused by an e¤ective di¤usion of adatoms along step edges and/or a tran-sient mobility of deposited atoms. For metal (001) surfaces it is well known thatthe activation energy for adatom di¤usion along step edges is in general smallerthan the activation energy for adatom di¤usion on a terrace. Step edge di¤usionis therefore still active at substrate temperatures where terrace di¤usion is alreadynegligible. Breeman et al. [32] have shown that step edge di¤usion at low substratetemperatures can indeed lead to a characteristic average distance of several latticeconstants between adatom islands.


Table 1.1: Experimental (e) and calculated (c) values of the activation energy for thedi¤usion of adatoms (Ed) and monovacancies (Ev) on a terrace and the di¤usion ofatoms along a step edge (Estep) for the Cu(001) surface. E and H indicate di¤usionvia hopping and exchange respectively. The listing of two values in some cases isthe result of two di¤erent calculation methods.

Ed (eV) Ed (eV) Ev (eV) Estep (eV)0.40 (e) [37] 0.66 (c) (H) [50] 0.47 (c) [57] 0.38 (c) [52]0.28 (e) [39] 0.415 (c) (H) [51] 0.42, 0.47 (c) [58] 0.27 (c) [53]0.36 (e) [44] 0.68 (c) (H) [52] 0.24 (c) [57]0.40 (e) [47] 0.45 (c) (H) [53]0.48 (e) [48] 0.51, 0.46 (c) (H) [54]0.39 (e) [49] 0.77, 0.18 (c) (E) [54]

0.43 (c) (H) [55]0.70 (c) (E) [55]0.50 (c) (H) [56]0.49 (c) (H) [57]0.70 (c) (E) [57]

0.52, 0.50 (c) (H) [58]

1.2.4 Island shape

The morphology of a growing …lm in the submonolayer regime is largely determinedby the shape of adatom islands. The adatom island shape depends on the abilityof atoms to di¤use along the edges of islands and around corners, i.e., on the ac-tivation energies for these di¤usion processes and the substrate temperature. Thedevelopment of near-equilibrium compact islands is favored when the atoms arrivingat the islands have enough mobility along the edge to …nd energetically favorablekink sites. In this situation, the adatom island shape re‡ects the symmetry of thesurface. On the other hand, rami…ed islands develop when the step edge di¤usionis limited (see e.g. Ref. [33, 34, 35] and references therein). This is typically thecase on fcc(111) surfaces. In the most extreme case, in which the atoms arriving atan island can neither migrate along the edge nor detach, growth produces islands offractal shapes with an universal fractal dimension of about 1.7 [34]. In Chap. 3 itis shown that the shape of adatom islands and three-dimensional adatom structuresnot only depends on thermally activated di¤usion processes: the deposition dynam-ics, or more speci…cally the deposition angle, considerably in‡uences the adatomstructure shape as well.

In this study on pattern formation and magnetic anisotropy in thin metal …lms,a Cu(001) crystal was used as a substrate. Experimental and calculated valuesfor the most important activation energies on Cu(001) are summarized in Table1.1. In this table the activation energy for the di¤usion of monovacancies is also

1.3. HETEROEPITAXY 9

listed while this is the dominant surface di¤usion process during ion sputtering(see Chap. 4). The scenario for homoepitaxial growth on Cu(001) is as follows[9, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]: step-‡ow growth, layer-by-layergrowth and multilayer growth can be obtained by tuning the substrate temperature(small step-edge barrier). The adatom islands in the submonolayer regime have anear-equilibrium almost square shape due to the fact that the mobility of step edgeatoms is much higher than that of adatoms on a terrace. In the temperature rangewhere growth proceeds via nucleation and growth of adatom islands on terraces,growth results in the formation of square mound structures.

1.3 Heteroepitaxy

For technological applications, heteroepitaxial growth systems (di¤erent substrateand …lm material) are of much greater interest than homoepitaxial systems. Due tothe di¤erence in substrate and …lm material, these systems may exhibit novel chem-ical, magnetic and mechanical properties. The phenomena observed in (ultra) thinheteroepitaxial …lms are linked to a reduced dimensionality and the unique proper-ties of the surface and interface regions which result from electronic modi…cationsand lattice strain. Speci…c functions can be realized on purpose by using di¤erentmaterials in the controlled growth of thin …lms or superlattices.

Heteroepitaxial growth close to thermodynamic equilibrium can be consideredas a wetting problem, governed by ¢° = °f + °i ¡ °s, where °f , °s and °i are thesurface free energy of the growing …lm and the substrate and the free energy of the…lm/substrate interface respectively [59]. If ¢° > 0, the overlayer will form three-dimensional adatom structures to minimize the total energy by exposing more ofthe substrate (multilayer or Volmer-Weber growth mode [60]). If on the other hand¢° < 0, the …lm starts growing by a complete monolayer. In the case of a stablemonolayer, further layer-by-layer or Frank van der Merwe growth [61] occurs if eachlayer wets the previous one. Although layer-by-layer growth is expected in homoepi-taxy close to thermodynamic equilibrium, it is extremely rare in heteroepitaxy. Tounderstand this it is noted that the present consideration neglects e¤ects due tolattice mis…t. In fact lattice strain has to be considered in each new layer: becauseof the inclusion of strain energies in the overlayer and interface free energy, theseenergies depend on the …lm thickness. As a result, three dimensional adatom struc-tures will form on one or a few ‡at layers in most heteroepitaxial growth systems(Stranski-Krastanov growth mode [62]). Sometimes, however, the growth systemmay respond by relaxing strain through the introduction of dislocations near theinterface still allowing the subsequent growth of smooth unstrained layers (see Sec.1.3.1).

In most applications, heteroepitaxial growth proceeds far from thermodynamicequilibrium. The …lm growth is then predominantly determined by kinetics (see pre-vious section) instead of thermodynamics. However, also far from thermodynamic


Figure 1.3: Schematic representation of strain relaxation by mis…t dislocations in aheteroepitaxial …lm.

equilibrium heteroepitaxy can be much more complicated than homoepitaxy. Forexample, the intra- and interlayer mass transport can di¤er considerably with layerheight. Furthermore, a di¤erence in the lattice constant of substrate and …lm ma-terial and a possible tendency of substrate and …lm material to alloy, can in‡uencethe evolution of the …lm morphology as well. In the following, the consequences oflattice mis…t and alloying are discussed.

1.3.1 Lattice mis…tAn important parameter in the evolution of the surface morphology during het-eroepitaxial growth is the lattice mis…t f , de…ned by:

f =b¡ aa; (1.2)

where a and b are the lattice constants of the substrate and …lm, respectively. Themis…t to the substrate can be accommodated in the growing …lm by elastic strain orby the formation of mis…t dislocations. In the …rst case, the lattice constant of the…lm parallel to the surface is …xed to the in-plane lattice constant of the substrate,while the …lm lattice is expanded or contracted perpendicular to the surface to keepthe atomic volume about constant (pseudomorphic …lm growth). In the secondcase, a dislocation network allows the …lm to grow with its own lattice constant(incoherent growth). The formation of mis…t dislocations during heteroepitaxialgrowth was …rst discussed by Frank van der Merwe [61] and reported by Matthews[63].

1.3. HETEROEPITAXY 11

The strain energy of a pseudomorphic monolayer is proportional to f 2, whereasthe energy of a dislocation network is proportional to f . Therefore, a critical mis…texist below which the …rst monolayer grows pseudomorphic. In general, this criticalmis…t is in the order of 10 %. For smaller mis…ts, the …lm grows pseudomorphicup to a critical thickness above which relaxation of the strain by mis…t dislocationsbecomes energetically favorable. An illustration of a heteroepitaxial …lm in which themis…t to the substrate is accommodated by elastic strain …rst and by the formationof mis…t dislocations thereafter, is shown in Fig. 1.3. The thickness over whichthe strain in the …lm is relaxed equals roughly the distance between dislocations, l.Geometric arguments show that l is connected with the in-plane lattice constant aof the substrate and b¤ of the growing …lm by:

l =ab¤

a¡ b¤ : (1.3)

In this expression, b¤ represents a value which can di¤er from the bulk lattice con-stant if a part of the mis…t is still accommodated by elastic strain after the formationof a dislocation network.

From aCu = 3:615 Å, bCo = 3:548 Å and bNi = 3:524 Å, it follows that the latticemis…t between Co and Cu and between Ni and Cu is -1.8 % and -2.5 %, respectively.If b¤ = b, an average dislocation separation of 200 Å for Co/Cu(001) and 140 Å forNi/Cu(001) can be expected. Note that a more detailed description at least involvesthe elastic constants of both the …lm and the substrate material.

1.3.2 AlloyingA severe problem in the preparation of an atomically ‡at interface can be alloyingof …lm and substrate material or even dissolution of the …lm material into the bulkof the substrate. In the ideal case, interdi¤usion of …lm and substrate is forbid-den by the phase diagram. An inspection of binary phase diagrams including Cu,Co and Ni [64], shows that complete insolubility is not found for Co on Cu andNi on Cu. The broad miscibility gaps greater than 90 %, however, predict thatnearly sharp interfaces can be obtained in these growth systems. Since the thermo-dynamic properties of the surface deviate from those of the bulk, surface con…nedalloying may be observed in systems which do not alloy in the bulk [65, 66, 67, 68].Since growth proceeds far from thermodynamic equilibrium in most heteroepitaxialsystems, interdi¤usion of …lm and substrate material does not occur very often.

Another possibility for the formation of an alloy is provided by the adatom dif-fusion mechanism. When adatom di¤usion across a terrace occurs via an exchangemechanism, adatoms are embedded into the outermost substrate layer, whereas ex-changed substrate atoms participate in the surface di¤usion processes. In this case,a surface alloy is, at least temporarily, formed in a limited number of layers closeto the initial …lm/substrate interface. Besides the formation of a relatively roughinterface, exchange between adatoms and substrate atoms can have a strong in‡u-ence on the nucleation process as well. If the embedded atoms act as additional


nucleation sites for adatom islands, conventional nucleation theory can not be ap-plied. While the creation of new nucleation sites continues as long as the exchangeprocess is active, a saturation density of small adatom islands is not reached rapidly,with a broad island size distribution as result. Furthermore, the temperature de-pendence of the adatom islands density can deviate from conventional nucleationtheory when the activation energy for adatom di¤usion via a hopping mechanismand an exchange mechanism di¤er from each other. The growth of Co on Cu(001)shows these deviations from conventional nucleation theory (see Chap. 5).

1.4 Ion sputteringIon sputtering is the erosion of a surface due to bombardment with energetic ions.The removal of surface atoms is caused by collisions between incident ions and atomsin the near surface layers of a substrate. Under most ion bombardment conditions,sputtering is caused by a linear collision cascade. An incident ion that penetrates intothe substrate, collides with several substrate atoms. During each of these collisions,energy is transferred to the substrate atoms. If more energy is transferred than thebinding energy at the lattice sites, primary recoil atoms are created. The primaryrecoil atoms collide with other substrate atoms distributing the energy via a collisioncascade. A surface atom is sputtered if the energy transferred to it has a componentnormal to the surface which is larger than the surface binding energy. A theorydeveloped by Sigmund describes surface sputtering from linear collision cascades[69, 70]. The collision cascade in this theory is linear in the sense that the collisionsbetween incident ions and substrate atoms as well as the collisions between twosubstrate atoms are assumed to be independent binary events taking place betweena moving ion/atom and an atom at rest.

The erosion during ion sputtering is measured by the sputtering yield Y , whichis de…ned as the mean number of atoms removed from the surface per incident ion.The linear collision cascade theory predicts that the sputtering yield from amorphousand polycrystalline substrates is given by:

Y =0:42U®¾n; (1.4)

where U is the binding energy of a surface atom and ® is a factor describing thee¢ciency of momentum transfer upon elastic collisions (depends mainly onM2=M1,whereM1 is the mass of the incident ion andM2 is the mass of the substrate atoms).In Eq. 1.4, ¾n is the nuclear stopping cross section for collisions between ions andatoms. Besides on M1 and M2, this nuclear stopping cross section depends on theion energy and the atomic number of the incident ion and the substrate atoms.The agreement of the measured sputtering yields with the theoretical prediction isfound to be fairly good over a wide range of incident ion energies and ion-substratecombinations. Below a threshold energy (Eth) of about 20 to 40 eV, no sputteringtakes place. Above this threshold, the yield …rst increases with increasing ion energy

1.4. ION SPUTTERING 13

and reaches a broad maximum in the energy range of 5 to 50 keV. The decrease ofthe sputtering yield at higher energies is related to the larger penetration of ionsinto the substrate and a lower energy deposition in the surface layers. In most casesthe sputtering yield is larger for higher mass ions, i.e., the sputtering yield from theCu(001) surface will be larger for Ar+-ions than for Ne+-ions with the same energy.

Besides the sputtering parameters included in the linear collision cascade theory,the angle of incidence of the ions also in‡uences the sputtering yield. For amor-phous and polycrystalline substrates, the sputtering yield increases monotonicallywith increasing angle of incidence up to a maximum between 60± and 80± (see forexample the results in Ref. [71] and the references therein for Ar+-ion sputteringof di¤erent metal crystals at Eion t 1 keV). The location of the maximum dependspredominantly on the ion energy, the ion mass, and the substrate temperature. Themonotonic increase of the sputtering yield is caused by an enhanced chance of cas-cade initiation close to the surface, while the decrease in the sputtering yield at verygrazing angles of incidence is due to an enhanced ion re‡ection probability.

For crystalline substrates, the sputtering yield is also in‡uenced by the latticestructure [72]. This is most pronounced for ion incidence along the close packedcrystal directions. In these directions, the sputtering yield is about a factor 2 to 5lower than for other directions of incidence. These minima are superimposed on thesteady increase of the sputtering yield with increasing angle of incidence. In general,the decrease of sputtering yield for ions incident along close-packed directions can beexplained by channeling [72]: as a consequence of a series of correlated collisions anion can be constrained to a trajectory between lattice rows or planes and thereforepenetrate more deeply into the substrate, with a lower sputtering yield as result.For crystalline substrates, the sputtering yield and the location of its maximumobviously also depend on the azimuthal direction of the incident ion beam.

For low energy (Eion . 10Eth) and/or low mass ion sputtering where the en-ergy transfer is either too small for higher generation recoils to be created or toocon…ned to the surface layers, the assumption of isotropic cascades implicit in Sig-mund’s theory no longer holds. In this sputtering regime, removal of surface atomspredominantly occurs by single knock-outs: direct recoil atoms formed during col-lisions with incident ions receive a su¢ciently high energy to leave the surface, butnot enough to generate a collision cascade. For sputtering under these conditions,anisotropy e¤ects due to the crystal structure and the incident ion angle are impor-tant. The energy dependence of the sputtering yield therefore deviates from the onepredicted by Sigmund’s theory. Matsunami et al. [73] showed that the sputteringyield in this anisotropic sputtering regime is fairly well described by including theterm [1 ¡ (Eth=Eion)0:5)] in Eq. 1.4.

As collisions between incident ions and substrate atoms do not exclusively cre-ate monovacancies, the evolution of the surface morphology during ion sputteringis more complicated than the evolution during homoepitaxial growth. In fact it hasbeen demonstrated that a number of adatoms (sputtering is an erosion process) canbe created on the surface during ion sputtering as well (see e.g. Ref. [74]). For


Figure 1.4: Illustration of monovacancy interlayer di¤usion via the detachment of astep edge atom (a) and exchange (b).

example, measurements by Girard et al. [75] show that adatom islands and vacancyislands grow simultaneous during 600 eV Ar+-ion sputtering of a Cu(001) surface.Besides the creation of monovacancies and adatoms, it is also possible that ion im-pact directly results in the formation of larger and thus more stable adatom andvacancy islands. The intrinsic lateral length scale of a sputtered surface is thereforedetermined by the di¤usion and nucleation of adatoms and vacancies, the recombi-nation of adatoms with vacancies and the e¤ectiveness with which stable islands arecreated during ion impact. As a consequence, conventional nucleation theory cannot be applied and the determination of activation energies from experimental datais problematic. As the di¤usion of adatoms and vacancies have a similar tempera-ture dependence it can, however, be expected that the average separation betweensurface structures increases with increasing substrate temperature for ion sputteringas well.

Just like the shape of adatom structures, the shape of vacancy structures dependson the ability of atoms to di¤use along the edges and corners of these structures.The development of near-equilibrium compact vacancy structures is favored whenatoms along the edge have enough mobility to …nd energetically favorable kink sites.Compact vacancy structures have been measured after ion sputtering on Cu(001)[75, 76], Ag(001) [77], Ni(001) [78], Pt(111) [79, 80, 81, 82], Au(111) [83], Cu(111)[84], and Si(001) [85]. The vacancy structures on these surfaces re‡ect the surfacesymmetry (they have a square and hexagonal shape on the (001) and (111) metalsurfaces and a rectangular shape on Si(001), respectively) and look like the inverseof adatom structures measured after homoepitaxial growth (pits instead of moundsare formed during ion sputtering).

The interlayer di¤usion of monovacancies is apparently di¤erent from that ofadatoms (see Fig. 1.4). The di¤usion of a monovacancy across an ascending stepmay proceed via the detachment of a step edge atom or exchange. The activa-tion energy for atom detachment from a step edge is quite large on metal (001)surfaces. Interlayer di¤usion of monovacancies is therefore only active at high sub-strate temperatures when this process is dominant. In other words a relatively large

1.5. THIN FILM MAGNETISM 15

step-edge barrier for vacancies should be expected. By analogy with growth, ef-…cient interlayer di¤usion is a prerequisite for layer-by-layer removal. When theactivation energy for exchange is considerably smaller than that for atom detach-ment, layer-by-layer removal may be obtained at lower substrate temperatures aswell. He scattering intensity oscillations, indicative of layer-by-layer removal, havebeen measured during ion sputtering of Pt(111) [86, 87].

1.5 Thin …lm magnetismA ferromagnetic material is characterized by a spontaneous magnetization belowthe Curie temperature TC . As the energy involved in the transition from the ferro-magnetic to the paramagnetic state is relatively large (in the order of 0.1 eV/atom),ferromagnetism is not a consequence of magnetic dipole interactions which wouldgive an orientation dependent energy di¤erence in the order of 10¡4 eV/atom. Thespontaneous magnetization is a consequence of the Pauli principle and the Coulombinteraction between electrons instead. Because Pauli’s principle excludes that twoelectrons with the same spin are at the same place, the Coulomb repulsion betweenelectrons with parallel spin is weaker compared to the repulsion between electronswith di¤erent spin. The resulting exchange hole favors a parallel alignment of spinsand is the origin of ferromagnetism for metals.

There are two main theoretical approaches to describe ferromagnetism: theHeisenberg model and the Stoner model. In the Heisenberg model localized sta-ble magnetic moments, resulting mainly from uncompensated electron spins, areconsidered. The interaction of these moments is dominated by an exchange interac-tion. The Heisenberg model is well suited to describe magnetism of mostly localizedelectrons which are found in materials such as 3d metal oxides and 4f metals andtheir compounds, but seems to be inappropriate for the description of itinerantferromagnets such as Fe, Co, and Ni. The Stoner model, on the other hand, isrestricted to the uncorrelated electron gas spread over the crystal in combinationwith an exchange interaction in a periodic potential. In this model it is assumedthat the Coulomb repulsion is mainly active between electrons with di¤erent spin.The Coulomb repulsion results in a di¤erent number of …lled states for spin-up andspin-down electrons and thus in ferromagnetic behavior when the energy gain indoing so exceeds the increase of kinetic energy. This limit is given by the Stonercriterion for ferromagnetism:

Jn0(EF) > 1; (1.5)

where J is the exchange constant and n0 is the density of states near the Fermilevel. The Stoner criterion states that metals, for which the product of the exchangeconstant and the density of states near the Fermi level is larger than one, should beferromagnetic. The Stoner model successfully describes the ferromagnetic behaviorof itinerant ferromagnets in the ground state.


In ultrathin …lms, both the ground-state magnetic moment and the temperaturedependence of magnetic order are di¤erent from those in bulk materials. The re-duced coordination number of atoms at a surface leads to a band narrowing andconsequently to an enhanced density of states near the Fermi level. As a conse-quence, the magnetic moments at the surface are larger than in the bulk. Epitaxialstrain in pseudomorphic magnetic …lms might increase n0 and thus the magneticmoment even further. As in bulk materials the spontaneous magnetization MS of aferromagnetic …lm decreases with increasing …lm temperature. Close to TC the …lmtemperature dependence of MS is given by:

MS =M0(1 ¡ TTC

)¯; (1.6)

where ¯ is a critical exponent which is characteristic for the quantum mechanicalproperties of the magnetic …lm. The Curie temperature of an ultrathin ferromagnetic…lm is in general lower than the Curie temperature of the bulk material. However,strongly increasing Curie temperatures have been measured with increasing …lmthickness in most heteroepitaxial growth systems, i.e., the bulk value is reachedrapidly.

1.5.1 Magnetic anisotropy

The magnetic anisotropy is de…ned by the magnetization direction dependent contri-bution to the free energy density f of a crystalline …lm. The anisotropy contributionsto the free energy density are in the order of a few ¹eV/atom and thus much smallerthan the total free energy density of a magnetic …lm. For the existence of long-rangemagnetic order and for the applications of ferromagnetic materials, however, mag-netic anisotropy is the decisive quantity. The magnetic anisotropy, for example,determines the direction of magnetization, coercive …elds and domain sizes. Ho-mogeneous magnetization in the direction in which f has a minimum is obtainedeasily (easy magnetization axis), while homogeneous magnetization in the directionin which f has a maximum requires a larger external …eld (hard magnetization axis).In the following, several anisotropy contributions are described, in which the polarangle µ with respect to the surface normal and the azimuthal angle Á with respectto some low symmetric axis in the surface plane are used.

(a) The magnetostatic anisotropy. The source of magnetostatic anisotropy isthe long-range dipolar interaction, which depends critically on the shape of a ferro-magnet. If the …lm thickness is small in comparison with the lateral …lm size, themagnetostatic anisotropy favors magnetization in the …lm plane. This can be ratio-nalized as follows: if MS has a component normal to the …lm plane, magnetic polesare generated which increase the magnetostatic energy. On the other hand, no polesare generated when the magnetization is completely in-plane. The in-plane magne-tization orientation is therefore energetically favorable. For thin ferromagnetic …lms

1.5. THIN FILM MAGNETISM 17

the magnetostatic anisotropy is given by:

fms = 2¼M2S cos

2 µ: (1.7)

(b) The magnetocrystalline anisotropy. The contribution of the magnetocrys-talline anisotropy to the free energy density can be expanded in successive powersof ®x, ®y and ®z, where ®i are the direction cosines of the magnetization directionwith respect to the crystal axes. For a cubic crystal, an expansion of the magne-tocrystalline anisotropy up to sixth order results in:

fmc =K0 +K4(®2x®2y + ®

2y®

2z + ®

2x®

2z) +K6®2x®

2y®

2z: (1.8)

The magnetocrystalline anisotropy is a consequence of the spin-orbit coupling, whichcouples the spin to the charge orbital density distribution in a crystal. The orbitalmotion of the magnetic electrons is in‡uenced by the lattice and this results ina free energy density di¤erence associated with the direction of MS. The easymagnetization axes of Co and Ni on Cu(001) are along the <110>-directions.

(c) The surface anisotropy. Any deviation from the crystalline isotropy may bethe source of additional anisotropy contributions. It was Néel who …rst noted thatthe dramatically reduced local symmetries in magnetic surfaces result in magneticsurface-type anisotropies. Surface anisotropies are a consequence of changes in thespin-orbit coupling which result from the broken symmetry in the surface electrondensity. In a quadratic approximation, the anisotropy is given by:

¾ =K2s cos2 µ +Ku sin2 µ cos2 Á: (1.9)

The …rst term describes the so called out-of-plane surface anisotropy, which is presentin all magnetic …lms. The second term is the in-plane surface anisotropy, which mustbe considered in stepped surfaces and surfaces with a lower symmetry (e.g. (110)surfaces).

(d) The magnetoelastic anisotropy. Another anisotropy contribution to the freeenergy density originates from strain in heteroepitaxial …lms. For a cubic crystal,an expansion of the magnetoelastic anisotropy up to second order has the form:

fme = B1("xx®2x + "yy®2y + "zz®

2z); (1.10)

where "ij is a strain tensor and B1 is the magnetoelastic coupling coe¢cient. ForCo, B1 is negative [88], whereas a positive magnetoelastic coupling coe¢cient hasbeen measured for Ni [89]. A lattice compression in a certain direction thus even-tually results in a hard and easy magnetization axis in that direction for Co and Nirespectively.

The di¤erent anisotropies (a)-(d) contribute to the total magnetic anisotropy ofa magnetic …lm:

ftot = fms + fmc + fme +¾s + ¾id; (1.11)


where ¾s and ¾i are the anisotropy contributions of the surface and interface respec-tively and d is the …lm thickness. Expression 1.11 only holds when the magneto-static and magnetoelastic anisotropies do not dependent on the …lm thickness. Inreal ferromagnetic …lms this is normally not the case. The magnetostatic anisotropydecreases with surface roughness, whereas a drastic decrease in the magnetoelasticanisotropy can be expected when …lm strain is relaxed by the formation of mis-…t dislocations. A spin reorientation transition may occur in thin magnetic …lmswhen the di¤erent anisotropy contributions do not have the same sign. Such a spinreorientation transition occurs when:

K2v +K2s +K2i

d= 2¼M2

S: (1.12)

In this expression, K2v is a second order magnetization anisotropy, which may con-sists of magnetocrystalline and magnetoelastic contributions. The anisotropy K2i

originates from the reduced local symmetry at the substrate/…lm interface (interfaceanisotropy). Expression 1.12 will be used in Chap. 7 to analyze the in‡uence of H2

and CO adsorption on the spin reorientation transition in Ni/Cu(001).

Chapter 2

Experimental

2.1 Introduction

Two di¤erent di¤raction techniques were used to study growth and sputtering,namely, thermal energy He atom scattering (TEAS) and spot pro…le analysis lowenergy electron di¤raction (SPA-LEED). With these techniques, quantities like theaverage island separation, the island shape, the surface defect density, the surfaceroughness and the facet angle can be determined with a high accuracy. Due to thesmall energy of He atoms, He atom scattering is sensitive to the outermost surfacelayer only. In addition, the physically and chemically non-destructive interactionbetween He atoms and surface atoms allows monitoring of the surface morphologyduring growth and ion sputtering. The information depth of electrons with anenergy between 20 - 300 eV is only 3 to 10 Å [90]. Therefore, SPA-LEED pro…lescontain information about a few surface layers. TEAS di¤raction pro…les are well de-scribed by the kinematic di¤raction approximation, whereas deviations are observedin the di¤raction pro…les obtained with SPA-LEED. These deviations are caused bythe …nite probing depth of electrons and multiple scattering e¤ects. The magneticproperties of thin …lms were studied by the magneto-optic Kerr e¤ect (MOKE).With a MOKE setup, hysteresis loops from thin magnetic …lms can be measuredeasily. From these hysteresis loops quantities like the magnetic anisotropy, the coer-cive …eld, the Curie temperature and the magnetic susceptibility can be determined.The information depth of MOKE is in the order of 100 - 200 Å. All experimentsdescribed in this thesis were performed in ultra-high vacuum chambers with a basepressure · 5 ¢ 10¡11 mbar.

This chapter is organized as follows: the kinematic di¤raction theory is discussedin the …rst section. In two subsequent sections, thermal energy He atom scatteringand SPA-LEED are explained. Subsequently, the magneto-optic Kerr e¤ect is dis-cussed and a conventional MOKE setup as well as a setup for Kerr microscopy aregiven. Finally, the procedure used to clean the Cu(001) sample is described in thelast section.

19

20 CHAPTER 2. EXPERIMENTAL

2.2 Di¤raction

2.2.1 Kinematic approximationA brief review of di¤raction theory within the kinematic approximation is now pre-sented. In the kinematic di¤raction approximation it is assumed that the surface isdivided into unit cells and only single scattering processes from surface atoms areconsidered. As the distance between source and surface and between surface anddetector is much larger than the atomic distances, the wavefunction of the scatteredparticles can be described by plane waves. The wavefunction can then be writtenas [91]:

ª(K;ki) =1N

X

n

Ãunitn (K; ki)eiK¢rn; (2.1)

where Ãunitn (K; ki) is the scattering amplitude or structure factor of the nth unitcell, K is the di¤erence between the …nal and initial wavevector (K = kf ¡ ki), rnis the position of the nth unit cell and N is a normalization constant related tothe number of scatterers. The measured di¤raction intensity is the square of thewavefunction ª(K; ki),

I(K; ki) = jª(K; ki)j2 : (2.2)

In the kinematic approximation the di¤raction intensity is split into the dynamicalform factor F (K;ki) and the lattice factor G(K),

I(K; ki) =¯̄Ãunitn (K;ki)

¯̄2 ¢ 1N 2

¯̄¯̄¯X

n

eiK¢rn¯̄¯̄¯

2

= F (K; ki) ¢G(K): (2.3)

The lattice factor G(K) depends only on the scattering vector K and the surfaceunit cell arrangement, which is described by the position vector rn. Since the dy-namical form factor F (K; ki) varies only slowly with the parallel scattering vectorK== [92, 93], the shape of the di¤raction pattern is predominantly determined bythe lattice factor G(K), i.e., the lattice factor contains information about the sur-face morphology. On the other hand, the dynamical form factor F (K; ki) stronglydepends on the incident particle energy. As a consequence, F (K; ki) in‡uences theabsolute intensity of di¤racted beams.

In the calculation of peak pro…les it can be more useful to use the correlationfunction C(u) [46, 94, 95, 96, 97],

C(u) =1N

X

r

f (r)f (r+ u); (2.4)

where f is the scattering factor of a surface scatterer, r is the position of a sur-face scatterer and u is a displacement vector. The correlation function C(u) gives

2.2. DIFFRACTION 21

the probability of …nding two surface scatterers separated by u. In the kinematicapproximation, the di¤raction intensity is given by the Fourier transform of C(u),

I(K) =1N

X

u

C(u)e¡iK¢u: (2.5)

2.2.2 Peak pro…lesThe di¤raction pattern of a completely ‡at, defect free surface consists of in…nitelysharp peaks when an ideal di¤raction instrument is used. However, peaks withoutany broadening can never be observed in a real experiment. First of all, di¤ractioninstruments are never ideal: a …nite intensity requires a …nite solid angle both for thesource and the detector. Second, surface defects are always present. Due to a spreadin the incident particle energy and a …nite divergence of the di¤raction beam, a realinstrument will always cause broadening of the di¤raction peaks. Mathematically,the instrumental e¤ect can be described by an instrument response function T (K).The measured di¤raction intensity J(K) is then given by the convolution of theideal di¤raction intensity I (K) with this instrument response function T (K),

J(K) =I(K)T (K): (2.6)

In real space, the convolution I (K)T (K) corresponds to a multiplication of thecorrelation function and the transfer function of the di¤raction instrument. Thefull width at half maximum (FWHM) of the transfer function, the so-called transferwidth, is a measure of the largest distance over which long-range correlations canbe resolved directly by a di¤raction experiment [98].

Surface defects can be classi…ed by their dimension. Zero-dimensional or pointdefects (e.g. vacancies, interstitials and impurities), produce a homogeneous back-ground at the expense of the Bragg peak intensities but do not cause a broadening ofpeaks. One-dimensional defects on the other hand, cause a splitting and/or broad-ening of di¤raction peaks. A schematic drawing of one-dimensional surface defectsand the intensity distribution at in-phase (Sz = dkz=2¼ = n, with d the interlayerdistance) and anti-phase (Sz = dkz=2¼ = (2n+1)=2) scattering conditions is shownin Fig. 2.1. If the distribution of defects is ordered to some degree, the defectedsurface can be thought of as a new superlattice, giving rise to higher order di¤rac-tion patterns. A regular step array, characterized by an up-and-down sequence intwo layers, is shown in Fig. 2.1(a). The waves scattered from the upper terraces ofthis array constructively interfere with the waves scattered from the lower terracesat in-phase scattering conditions. Therefore, the surface seems to be atomically ‡atand only Bragg peaks appear. At not exactly in-phase scattering conditions, theregular step array looks like a superlattice with period L. This ordered superlatticegives rise to a splitting of the di¤raction peaks, i.e., quasi-di¤use di¤raction peaksclose to the Bragg peaks appear. In particular, at anti-phase scattering conditions,the waves scattered from the upper terraces of the array destructively interfere com-pletely with the waves scattered from the lower terraces. As a consequence, Bragg


Figure 2.1: Illustration of one-dimensional surface defects and corresponding recip-rocal lattices and intensity distributions (after Ref. [99]): (a) regular up-and-downstep array in two layers, (b) irregular step array with average separation L, (c) com-pletely random distribution of steps in two layers, (d) random steps in many layers,(e) monotonic regular step array.

2.2. DIFFRACTION 23

di¤raction peaks are not observed. The splitting of the di¤raction peaks L¤, isrelated to the separation L via L¤ = 4¼=L.

Irregular step arrays in two layers are shown in Figs. 2.1(b) and (c). Com-pared to the array in (a), the step array in (b) is characterized by a broader sizeand separation distribution (average separation L). Again, only Bragg di¤ractionpeaks appear at in-phase scattering conditions. The broader separation distribution,however, causes a broadening of the quasi-di¤use di¤raction peaks at other scatter-ing conditions. Moreover, the broader size distribution gives rise to an incompletedestructive interference between the waves scattered from the upper and lower ter-races. Therefore, Bragg di¤raction peaks are also observed at anti-phase scatteringconditions. The splitting of the di¤raction peaks is still a good measure for the av-erage separation (L t 4¼=L¤) as long as well de…ned quasi-di¤use di¤raction peaksare measured. For more random separations, it is more accurate to use the FWHMof the quasi-di¤use intensity. No quasi-di¤use di¤raction peaks are observed whenthe geometric distribution of the step array is completely random (Fig. 2.1(c)).

The presence of irregular steps in many layers (Fig. 2.1(d)), cause a scatteringphase dependent broadening of di¤raction peaks. Facets can be de…ned when theseparation between steps is constant (Fig. 2.1(e)). These facets are inclined withrespect to the original surface and give rise to tilted rods in reciprocal space. Atin-phase scattering conditions, all terraces interfere constructively and Bragg di¤rac-tion peaks appear. At other scattering conditions, however, the position of the facetpeaks depends on the perpendicular scattering vector and thus on the incident par-ticle energy. Since the angle between tilted and normal rods is directly related tothe angle between facets and the original surface, the facet angle can be determinedfrom measurements of the facet peak position as a function of the incident particleenergy.

The one-dimensional examples in Fig. 2.1 are useful in the interpretation of two-dimensional di¤raction pro…les. Two examples: an isotropic distribution of islandson a surface results in peak splitting and thus in a di¤raction ring around the Braggpeaks. The diameter of this ring L¤ is related to the average island separation viaL¤ t 4¼=L. A distribution of mounds with facetted faces results in a di¤ractionpattern with facet peaks. These facet peaks follow the rods of the facet faces inreciprocal space.

Not all di¤raction features can be explained by the simple examples in Fig.2.1. For example, two-dimensional di¤raction pro…les contain information about theshape of adatom structures and about the azimuth dependent correlations betweensurface structures. The island shape contributes to a two-dimensional di¤ractionpro…le via the Fourier transform of the average auto correlation function of islands.For square islands, the Fourier transform is a two-dimensional sinc function withlobes in the direction perpendicular to the step edges. Such a pro…le looks like theoptical equivalent of Fraunhofer di¤raction from randomly distributed square aper-tures [100]. An isotropic distribution of square islands results in a di¤raction pro…leconsisting of two di¤erent contributions, one from the island separation distribution,


0 1 2 3 0 1 2 30 1 2 30.0

0.2

0.4

0.6

0.8

1.0

θ (ML) θ (ML)

c)b)a)

no

rmal

ized

inte

nsity

θ (ML)

Figure 2.2: Anti-phase deposition curves (peak height versus coverage) for an idealinstrument: (a) step ‡ow growth, (b) ideal layer-by-layer growth, (c) ideal multilayergrowth.

the other from the island size distribution. As outlined above, the contribution ofisland separations shows up as a homogeneous ring intensity at low parallel scatter-ing vectors. Since the length scale of island sizes is necessarily smaller than theirseparation, the fourfold symmetric island shape in‡uences the di¤raction pro…le atlarger scattering vectors. As the Fourier transform of the auto correlation func-tion of square islands is point symmetric in k== = 0, the island shape does note¤ect the di¤raction ring around Bragg peaks. However, for islands with a uniaxialshape anisotropy, e.g., rectangular islands, this no longer holds. Just like in thecase of square islands, the Fourier transform of the autocorrelation function is atwo-dimensional sinc function, but now the widths of the sinc function in the twohigh symmetry directions di¤er from each other. The intensity of the ring is there-fore reduced in the direction in which the sinc function has the smallest width, i.e.,parallel to the longest sides of the islands.

2.2.3 Bragg peak intensityThe intensity of the specular Bragg peak contains information about the verticalsurface roughness, i.e., the number of exposed layers. Characterization of the growthmode is therefore possible when the Bragg intensity (peak height) is measured duringgrowth. In the kinematic approximation the normalized specular Bragg intensity isgiven by:

II0

(Sz) =NX

n=0

NX

m=0

PnPm cos [2¼(n¡m)Sz] ; (2.7)

where Pn is the probability of …nding a surface atom in the nth layer and Sz is theperpendicular scattering phase (Sz = dkz=2¼). At anti-phase scattering conditions

2.2. DIFFRACTION 25

0.0 0.5 1.0 1.5 2.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

no

rmal

ized

inte

nsity

Sz

b)a)

Sz

Figure 2.3: Specular intensity as a function of the perpendicular scattering phase Szfor an ideal instrument: (a) ideal layer-by-layer growth, (b) ideal multilayer growth.The total coverage amounts to 0.5 ML (solid line), 1 ML (dashed line), 1.5 ML(dotted line) and 2 ML (dashed-dotted line).

(Sz = (2n+ 1)=2), Eq. 2.7 simpli…es to:

II0

anti

=

ÃNX

n=0

(¡1)nPn

!2

: (2.8)

During step-‡ow growth, preexisting steps move across the surface without increas-ing the surface roughness. Therefore, step-‡ow growth leads to a constant specularintensity (see Fig. 2.2(a)). Oscillations in the anti-phase scattering intensity will beobserved during ideal layer-by-layer growth. After deposition of (2n + 1)=2 mono-layer (ML) the surfaces of the two exposed layers are equal and the waves scatteredfrom these layers destructively interfere completely (I=I0 = 0). On the other hand,the initial condition is reestablished each time a layer is completely …lled (I=I0 = 1).The oscillatory behavior of the normalized specular Bragg intensity is illustrated inFig. 2.2(b). During ideal multilayer growth, the distribution of exposed layers withthe layer height becomes Poisson distributed [18, 19, 20, 21, 22]. In this case, thespecular intensity is given by [20]:

II0

anti

= e¡4µ; (2.9)

where µ is the total coverage (see Fig. 2.2(c)).The vertical …lm roughness after growth can be characterized by the perpen-

dicular scattering phase dependence of the specular Bragg intensity (a so-calledIV-curve). The total coverage µ and the deposited amount in the nth layer µn are


given by:

µ =NX

n=0

nPn; µn =NX

m=n

Pm : (2.10)

By using Eq. 2.7 and Eq. 2.10 it is possible to extract the layer distribution for athree level system when the total coverage is known. Figure 2.3 shows the calcu-lated normalized intensity for ideal layer-by-layer and multilayer growth at di¤erentcoverages. For ideal layer-by-layer growth, the specular intensity as a function ofSz repeats itself with a period corresponding to the growth of 1 ML, whereas theintensity gets more peaked around the in-phase scattering conditions with increasingcoverage for multilayer growth. The width of the intensity peak around in-phasescattering conditions is therefore a measure of the vertical surface roughness: ingeneral, the width of this peak decreases with increasing surface roughness.

2.3 Helium atom scatteringThermal energy He atom scattering was used to study the surface morphology duringgrowth and ion sputtering. Figure 2.4 shows a schematic drawing of the experimentalsetup. The He atom beam is created by the adiabatic expansion of high purity Hegas (99.9999%) through a nozzle with a diameter of 30 ¹m. During the expansion,the whole enthalpy of the He gas is transferred into a kinetic energy of EHe =5=2kTg, where Tg is the temperature of the stationary gas before expansion [20, 101].Since the nozzle setup does not allow cooling (Tg t 300 K), the He atom energyamounts to 67 meV (¸He = 0:56 Å). A skimmer with a diameter of 0.2 mm is usedto remove the outer regions of the He beam. After passing the skimmer, the Hebeam enters the main vacuum chamber through an aperture of 0.2 mm. The beamdivergence, which is determined by the aperture diameter and the distance betweenskimmer and aperture, amounts to 0.15±, whereas the beam diameter at the sampleposition is less than 1 mm. The re‡ected beam is detected by a quadrupole massspectrometer, which is di¤erentially pumped to reduce the He background pressure.Detector rotation in the plane of incidence enables experiments at di¤erent scatteringconditions. The angle of incidence of the He beam can be varied between 54± and71±. The pressure of the He gas before expansion is 3.5 bar, whereas the He pressurein the main chamber amounts to 6 ¢ 10¡9 mbar during He atom scattering.

Because of the low thermal energy of the He atoms and the strong repulsiveinteraction between the …lled electron shell of the He atoms and the outer valanceelectrons of the surface [102], the atoms are re‡ected at a distance of about 3-4 Åabove the surface [103, 104, 105]. He atom scattering is therefore sensitive to theoutermost surface layer only. Since the valence electrons are strongly delocalized atmetal surfaces, corrugations in the repulsive potential are very small at the re‡ectionpoint. Hence, the di¤raction pattern consists of an intense specular re‡ected peakand higher order di¤raction peaks which are a factor 103-104 less intense. Besides

2.3. HELIUM ATOM SCATTERING 27

Figure 2.4: Schematic drawing of the He atom scattering setup.

the surface sensitivity, the low energy of He atoms guarantees a non-destructiveinteraction between He atoms and the surface. He atom scattering is therefore anideal surface technique to study growth and ion sputtering in vivo.

Although He atom scattering is not very sensitive to the atomic structure of close-packed metal surfaces, it is extremely sensitive for surface defects. Surface defectssuch as vacancies, step edges and adsorbates, disturb the attractive potential overa rather large surface area, giving rise to di¤use scattering. Figure 2.5 shows aschematic drawing of the elastic scattering from a surface with an 1 ML high stepedge. He atoms which interact with the distorted surface potential close to thestep edge are di¤usively scattered. This di¤use scattering can be described by thewidth of the di¤use scattering stripe lst along the step edge. At in-phase scatteringconditions (Sz = n), the waves scattered from di¤erent layers constructively interferecompletely leaving di¤use scattering from step edges or other surface defects as theonly source for a reduction of the specular peak intensity. When only step edges areconsidered, the normalized specular peak intensity is given by [20]:

II0

in

= (1 ¡ lstsst)2 ; (2.11)

where sst is the density of steps on the surface. Eq. 2.11 shows that growth modescan be determined from in-phase He atom scattering measurements as well. Whengrowth proceeds by step-‡ow, the step density on the surface does not change andhence a constant in-phase scattering intensity will be observed. During layer-by-layer growth, the step density oscillates with a period corresponding to the growthof 1 ML, giving rise to an oscillation in the in-phase scattering intensity with thesame period. Finally, multilayer growth increases the step density monotonically


Figure 2.5: Helium atom scattering from a stepped surface.

and thus a monotonic decrease of the in-phase scattering intensity will result. OnCu(001) a di¤use scattering stripe of lst = 13 Å has been measured [106].

Although growth mode characterization is possible at in-phase scattering condi-tions, it is more general to use anti-phase scattering conditions. The equations inSec. 2.2.3 can be used to extract the surface layer distribution when di¤use scat-tering is neglected. Corrections for the limited transfer width of the He di¤ractioninstrument (t 450 Å) are necessary if the dimensions of surface structures becomecomparable with the transfer width. The minima of the intensity oscillations in-crease for large surface structures due to a decrease of the destructive interference.

2.4 SPA-LEEDSpot pro…le analysis low energy electron di¤raction (SPA-LEED) is the seconddi¤raction technique which was used to study growth and ion sputtering. A schematicdrawing of the SPA-LEED instrument is shown in Fig. 2.6. The Omicron SPA-LEED instrument consists of an electron gun with a LaB6 …lament, octopole de-‡ection plates and a channeltron. The di¤raction pattern is scanned over the smallentrance aperture of the channeltron by the octopole de‡ection plates (both theincident and re‡ected electron beam are de‡ected). The position of the electronbeam on the sample remains …xed during the measurement of a di¤raction pattern.On the other hand, the angle of incidence changes during a scan and is, moreover,electron energy dependent. Because of the high quality electron gun and the highsensitivity of the channeltron, a SPA-LEED instrument has a much higher transferwidth (t 1200 Å) than a conventional LEED instrument (t 150 Å), allowing highresolution measurements.

The kinematic di¤raction approximation is not fully applicable for LEED. Devi-ations from the kinematic approximation are apparent in the absolute intensity ofdi¤raction peaks. Nevertheless, the shape of di¤raction pro…les is still quite well de-

2.4. SPA-LEED 29

Figure 2.6: Schematic drawing of the SPA-LEED instrument.

4.0 4.5 5.0 5.5 6.0 6.5

0

2x105

4x105

6x105

8x105

1x106

i

nten

sity

(cp

s)

Sz

Figure 2.7: Intensity of the specular Bragg peak as a function of Sz after growth of0.5 ML Cu on Cu(001) at 250 K.


Figure 2.8: Magneto-optic Kerr e¤ect (a) and the coordinate system for the …lmmagnetization (b).

scribed by the kinematic di¤raction theory [93]. The interpretation of peak pro…lesis therefore straightforward in most cases. As an example of dynamical scatteringe¤ects, the perpendicular scattering phase dependence of the specular Bragg peakintensity (IV-curve) measured after growth of 0.5 ML Cu on Cu(001) is shown inFig. 2.7. The exposed areas of the two layers in this system are exactly the sameand therefore kinematic theory predicts I s cos(2¼Sz) (see Fig. 2.3(a)). Obviously,the cosine function is not fully measured. The deviations from the kinematic ap-proximation are caused by the …nite probing depth of electrons, multiple scatteringe¤ects and/or the energy dependence of the angle of incidence. This example il-lustrates that a quantitative determination of the vertical surface roughness fromSPA-LEED IV-curves is problematic when no full dynamical calculation is carriedout [107]. Qualitative information about the surface roughness, however, can stillbe extracted from these curves.

2.5 Magneto-optic Kerr e¤ect.The magneto-optic Kerr e¤ect (MOKE) involves a change of the polarization (po-lar and longitudinal e¤ect) or intensity (transverse e¤ect) of light re‡ected from amagnetic …lm. The Kerr e¤ect is produced by the combined e¤ect of spin-orbitcoupling and exchange interaction. Phenomenologically, these e¤ects are describedby a dielectric tensor with o¤-diagonal elements:

" = N 2

24

1 iQ cos' ¡iQ sin ° sin'¡iQ cos' 1 iQ cos ° sin'iQ sin ° sin' ¡iQcos ° sin ' 1

35 ; (2.12)

where N is the refractive index, Q is the complex magneto-optic constant (Voigtconstant) and ° and ' describe the direction of the …lm magnetization (see Fig.2.8(b)).Linearly polarized incident light can be viewed as a superposition of lefthand and right hand circular polarized plane waves. Due to the o¤-diagonal termsin the dielectric tensor of a magnetic …lm, the refractive indices for left hand and

2.5. MAGNETO-OPTIC KERR EFFECT. 31

Figure 2.9: Three Kerr con…gurations: polar geometry (a), longitudinal geometry(b), transverse geometry (c).

0 20 40 60 80-1.2

-0.9

-0.6

-0.3

0.0

0.3

0.6

0 20 40 60 80

-0.08

-0.04

0.00

0.04

0.08

0.12

0.16

0 100 200 300 400-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4c)b)a)

θi (°)

φ

,θ (

mra

d)

θi (°)

longitudinallongitudinalpolar

d (Å)

Figure 2.10: Calculated Kerr rotations (solid lines) and Kerr ellipticities (dashedlines) of p-polarized incident light for a Co …lm on a Cu substrate. d = 20 Å in (a)and (b), µi = 45± in (c).

right hand polarized light are di¤erent (nL;R = 1 § gQ=2, where g cos(k;M) is thecosine of the angle between the propagation vector k and the magnetization M).Asa consequence, the polarization of linearly polarized light rotates in a magnetic …lmdue to the di¤ering phase shifts of the two waves (real part of the refractive index)and the light acquires an ellipticity due to the di¤ering absorption rates of the twowaves (imaginary part of the refractive index).

The electrical …eld components of the re‡ected light parallel (p) and perpendic-ular (s) to the plane of incidence can be expressed in the electrical …elds of theincident light when Fresnel re‡ection coe¢cients r are used:

·ErpErs

¸=

·rpp rpsrsp rss

¸¢·E ipEis

¸: (2.13)

The Kerr rotation Á and Kerr ellipticity µ are related to the Fresnel re‡ection coef-…cients. For s and p-polarized incident light, Á and µ are expressed as:

Ás + iµs =rpsrss; ¡ Áp + iµp =

rsprpp: (2.14)


From the dielectric tensor " the Fresnel re‡ection coe¢cients and thus the Kerrrotation and Kerr ellipticity can be calculated [108, 109, 110, 111, 112, 113].

For the magneto-optic Kerr e¤ect three main con…gurations can be distinguished.In the polar geometry, the probed component of the magnetization is parallel tothe surface normal (° = 90±, ' = 0±). In the longitudinal geometry, the probedmagnetization is parallel to the surface and the plane of incidence (° = 90±, ' =90±). In these two geometries the magnetization has a component parallel to thepropagation direction of the light and therefore a polarization rotation and ellipticitycan be measured. In the transverse geometry the probed magnetization is parallelto the surface and perpendicular to the plane of incidence (° = 0±, ' = 90±). Inthis geometry no change of the light polarization but a change of the light intensityis measured. The three Kerr con…gurations are illustrated in Fig. 2.9.

When the refractive indices of the magnetic …lm and non-magnetic substrate andthe Voigt constant are known, it is possible to calculate the Kerr rotation and Kerrellipticity as a function of the magnetization direction, the angle of incidence and the…lm thickness. As an example, the Kerr rotation and Kerr ellipticity for a Co …lm ona Cu substrate was calculated. These calculations were carried out for HeNe laserlight, i.e., ¸ = 632:8 nm. For this wavelength the refractive indices and the Co Voigtconstant are NCu = 0:22 + i3:85, NCo = 2:25 + i4:10, and QCo = ¡0:0125 + i0:0157respectively [114]. The result is shown in Fig. 2.10. The calculations show amuch larger Kerr signal in the polar geometry than in the longitudinal geometry.Furthermore, the Kerr intensity is proportional to the …lm thickness d for d . 50 Å.This linearity has been con…rmed by experiments [115].

2.6 MOKE setupTwo di¤erent MOKE setups were used to study the magnetic properties of thinmetal …lms. Figure 2.11 shows a schematic drawing of the Kerr setup used in theexperiments described in Chap. 6. The setup consists of a HeNe laser (¸ = 632:8nm, 10 mW), two Glan-Thompson polarizers, a 1/4¸ plate, a Si-photodiode detectorand four current driven core-less coils (magnets). The four magnets are positionedoutside a small protrusion of the main vacuum chamber in such a way that magnetic…elds perpendicular (polar geometry) and parallel (longitudinal geometry) to thesurface plane can be applied. In both Kerr geometries, the maximum magnetic …eldamounts to 400 Oe. An illumination angle of 45± enables the e¤ective measurementof the magnetization perpendicular and parallel to the surface (see Fig. 2.10). Thepolarizers with a low extinction coe¢cient of ´ = 10¡4 are mounted on accuraterotation units. Finally, with the 1/4¸-plate the Kerr ellipticity instead of the Kerrrotation is measured. Insertion of a 1/4¸-plate has the advantage that ellipticitiescaused by the vacuum chamber windows can be eliminated.

Measurements of the Kerr ellipticity as a function of the external magnetic …eldstart with a minimization of the light intensity. A minimum light intensity or so-

2.6. MOKE SETUP 33

Figure 2.11: Schematic drawing of the MOKE setup: D: diaphragm, GT1 and GT2:Glan-Thompson polarizers.

Figure 2.12: Schematic view of the Kerr microscopy set-up: M: mirror, La: halogenlamp, L1: condensor, D: diaphragm, F1,F2 infrared and blue blocking …lters, L2:lens f = 100 mm, GT1,GT2: Glan-Thompson polarizers.


called dark intensity Id is reached when the two polarizer are crossed (one polarizeris oriented parallel to the plane of incidence, the other is oriented perpendicular tothis plane). Then, the polarizer in front of the photodiode is rotated by a smallangle ® and the background intensity Ib is measured. After this the light intensityI is recorded as a function of the magnetic …eld. For µ ¿ ® and µ ¿ ´, the Kerrellipticity is given by [116]:

µ =12®I ¡ IbIb ¡ Id

: (2.15)

In the experiments described in Chap. 7 a Kerr microscopy setup was used. Aschematic view of this setup is shown in Fig. 2.12. The microscope has two separatesections: an illumination part and a subsystem with a long distance microscopeobjective mounted to a CCD camera. The illumination section is attached to oneof the vacuum chamber windows and consists of a 50 W halogen lamp, collimatingoptics, blue and infrared blocking …lters, a focussing lens, and a Glan-Thompsonpolarizer. Another vacuum chamber port is used for the microscope objective andthe CCD camera. In front of the microscope objective a second polarizer is placedfor polarization analysis. The sample is illuminated with an incident angle of 20±with respect to the surface normal. The lateral resolution of the Kerr microscopeis about 10 ¹m [117]. This Kerr microscopy setup was used in the polar geometry,i.e., with the external magnetic …eld oriented perpendicular to the surface. Duringoperation, sequences of Kerr microscopy images with di¤erent magnetic …elds wererecorded at an acquisition time of about 10 s/image. From each sequence asymmetryimages, i.e., the di¤erence of two images divided by their sum, for the remanent andsaturation state were constructed. In the experiments described in Chap. 7 themicroscope was used to measure the changes in the critical thickness of the spinreorientation transition in Ni/Cu(001) during the adsorption of H2 and CO andthe growth of a Cu overlayer. Some measurements in Chap. 7 were performed usinga standard polar Kerr setup with a laser diode (¸ = 632:8 nm) as light source.

2.7 Sample preparationIn all experiments described in this thesis a Cu(001) sample was used as substrate.The sample was cut from a single crystal Cu rod, oriented with the aid of an X-raydi¤ractometer and mechanically and electrochemically polished, resulting in miscutangles · 0:1±. Before insertion into the UHV system the sample was heated inan Ar/H2 atmosphere at 900 K for about one day. This treatment is necessary todecrease the sulphur impurity level in the sample. In the middle of the UHV chamberthe Cu(001) sample was mounted to a manipulator. The sample was heated from therear by electron beam bombardment and is cooled by a cryostat, …lled with liquid N2.By changing the balance between heating and cooling the sample temperature wastuned between 100 and 1100 K. In the UHV system the sample was further prepared

2.7. SAMPLE PREPARATION 35

by cycles of sputtering with 800 eV Ar+-ions and prolonged heating at 800 K. Aftereach cycle the impurity level was measured with Auger electron spectroscopy (AES).When the surface impurity level was below the detection limit of AES (· 1%),the sample was simultaneously sputtered and annealed at 1100 K. This procedureresulted in a clean and well-ordered surface with an average terrace width ¸ 1000Å as was determined by AES and SPA-LEED. After each growth experiment, theinitial Cu(001) surface morphology was reproduced by sputtering at 300 K andsubsequent annealing at 800 K.

Chapter 3

Steering-enhanced roughening

3.1 IntroductionHomoepitaxial growth on single crystal surfaces far from thermodynamical equilib-rium usually proceeds via nucleation, growth, and coalescence of two dimensionalislands. Atoms originating from a particle beam arrive at the surface, get accommo-dated at the substrate, and begin thermally activated surface di¤usion. Since atomdi¤usion is the dominant dynamic process on the surface, much e¤ort has been madeto determine the rates of the di¤erent atom di¤usion processes. It is known for along time that two di¤usion processes play a key role in the evolution of the surfacemorphology during growth. The di¤usion of adatoms on a ‡at terrace determines theintrinsic lateral length scale of a …lm during the early stages of growth. On the otherhand, the growth mode is controlled by the di¤usion of adatoms across descendingstep edges. For layer-by-layer growth e¢cient interlayer di¤usion is a necessary con-dition. In the ideal case, one layer is almost completely …lled before nucleation andgrowth in the next layer is initiated. If, however, atom di¤usion across descendingstep edges is suppressed by an additional activation barrier (Ehrlich-Schwoebel orstep-edge barrier), growth in the next layer starts far before the previous one is …lledand mound structures develop (multilayer growth).

Compared to adatom di¤usion, the deposition of atoms on the surface has notbeen studied in detail. Up to now, growth studies have implicitly regarded the ‡uxof impinging atoms as being homogeneously distributed over the surface. This isremarkable since long-range attractive forces between incident atoms and substrateatoms lead to substantial acceleration towards the surface [11]. For atoms arrivingat grazing incidence this leads to substantial de‡ection or refraction e¤ects. Thelong-range attraction has no consequences for a ‡at surface: the refraction of theapproaching atoms is the same for all atoms and the incident atom ‡ux remainshomogeneously distributed. However, as soon as adatom islands grow, morphologydependent atom trajectories give rise to a redistribution of the incident atoms, i.e.,the incident atom ‡ux depends on the local surface morphology. In this chapter it isshown that refraction of atoms results in a preferential arrival on protruding terraces

37

38 CHAPTER 3. STEERING-ENHANCED ROUGHENING

such as islands. In fact, approaching atoms are focused onto the regions next to theleading edges of adatom islands. This phenomenon, which is most pronounced forgrazing incidence deposition and results in a signi…cantly increased roughness of thegrowing …lm, is named steering-enhanced roughening.

The growth of Cu/Cu(001) at normal incidence is characterized by the nucle-ation, growth and coalescence of two-dimensional square islands. The step edgesof the near-equilibrium shaped adatom islands are oriented along the closed-packed<110>-directions. The average separation between adatom islands is determined bythe nucleation process and depends critically on the activation energy for di¤usionof copper adatoms on (001)-terraces (0.36-0.40 eV), the substrate temperature, thedeposition rate and the number of atoms in the smallest stable island (the criticalisland size). The development of square islands is favored by the fact that the ac-tivation energy for di¤usion of atoms along step edges is much lower than that ofisolated adatoms on ‡at terraces (see Table 1.1). This enables adatom islands toassume their equilibrium shape already at high supersaturation, i.e., during MBE-growth. Upon further growth, mound structures develop [41, 42, 45, 46] which orderin a quite regular checkerboard-like pattern [46]. The slope of the mound sides de-pends on the growth temperature [41, 42, 46]. After normal incidence deposition,{113}-, {115}-, and {117}-facets have been obtained.

The Cu/Cu(001) growth experiments reported in this chapter were performed atdi¤erent deposition angles, di¤erent substrate temperatures, and along two di¤erenthigh symmetry azimuthal directions. The Cu was deposited by electron beam in-duced sublimation from a Cu disk at a deposition rate of about 0.25 ML/minute (ir-respective of the deposition angle). SPA-LEED was used to characterize the surfacemorphology in all homoepitaxial growth experiments. In order to suppress undesireddi¤usion after Cu deposition, the di¤raction pro…les were acquired at a low substratetemperature of about 100 K. The experimental results show that the evolution of thesurface morphology is drastically in‡uenced by the deposition geometry. Already inthe submonolayer regime distinct di¤erences in the surface morphology, developingat normal and grazing incidence deposition, are observed. During grazing incidencedeposition rectangular adatom islands instead of square ones develop. Upon fur-ther growth, symmetric mound structures, asymmetric mound structures, and wellordered ripple structures can be obtained, depending on the deposition geometry.Furthermore, the slope of the adatom structures becomes steeper with increasingdeposition angle.

This chapter is organized as follows: in Sec. 3.2 experimental results on thehomoepitaxial growth of Cu(001) at normal incidence and at a grazing angle of 80±are presented. The steering phenomenon is explained and illustrated with atomtrajectory calculations in Sec. 3.3. The last part of this section is focused on thedeposition angle and surface roughness dependence of steering. In the three subse-quent sections more experimental results on the growth of 40 ML Cu on Cu(001) arepresented. First, the selection of the mound slope as a function of the deposition an-gle is analyzed. Thereafter, the temperature dependence of the surface morphology

3.1. INTRODUCTION 39

-10 -5 0 5 10

-10

-5

0

5

10

-10-5

05

10 -10-5

05

10

-20 -10 0 10 20-20

-10

0

10

20

-20-10

010

20 -20-10

010

20

k[1-10]

(%BZ)

k

[11

0] (

%B

Z)

b)

a)

k[110]

(%BZ)k

[1-10] (%BZ)

k[1-10]

(%BZ)

k

[11

0] (

%B

Z)k

[1-10] (%BZ)

k[110]

(%BZ)

Figure 3.1: (a) SPA-LEED peak pro…le and contour plot of the specular beamacquired after normal incidence deposition of 40 ML Cu on Cu(001) at 250 K. Thepeak pro…le was obtained at E = 120 eV (perpendicular scattering phase in unitsof 2¼: Sz = 3:22). (b) The same after normal incidence deposition of 0.5 ML Cu at250 K: E = 133 eV (Sz = 3:40).


after normal and grazing incidence growth is described. Finally, the surface mor-phology after grazing incidence growth in the [110]- and [100]-azimuth is compared.The experimental results are discussed and qualitatively explained in Sec. 3.7. Thediscussion is mainly focused on the steering phenomenon and its consequences forsurface roughening and slope selection.

3.2 Normal versus grazing incidence depositionFigure 3.1(a) shows a SPA-LEED peak pro…le of the specular beam obtained afternormal incidence deposition of 40 ML Cu on Cu(001) at 250 K. The peak pro…leshows a well developed fourfold symmetry as should be expected for the Cu(001)surface. The observed di¤raction pattern can be interpreted straightforwardly asresulting from growth induced mound structures [41, 42, 45, 46]. The distance be-tween mounds after normal incidence deposition varies between about 25 Å and 250Å, depending on the temperature of the substrate during Cu deposition. The cou-ples of well developed parallel ridges along the <110>-directions in the peak pro…lereveal that the mounds are situated in a quite regular checkerboard pattern with thesmallest distance oriented along <100> [46]. The basis for this checkerboard pat-tern is laid already during growth of the very …rst monolayer, just after the onset ofcoalescence. It has been shown to be a natural consequence of the homogeneous Cuadatom di¤usion on Cu(001) combined with the growth of near-equilibrium shaped,thus square islands. The mound slopes are not very well de…ned and it takes severaltens of monolayers before slope selection starts. The slope of the mounds again de-pends on the growth temperature: the average slope decreases from corresponding{113}-facets below 180 K to {117}-facets between 280 and 320 K [41, 42, 46]. Thesmall facet peaks visible in Fig. 3.1(a) correspond to a {115}-slope orientation. Sidefaces formed by {111}-facets have not been observed at all after normal incidencegrowth of Cu/Cu(001).

Figure 3.1(b) shows a SPA-LEED peak pro…le of the specular beam obtainedafter normal incidence deposition of 0.5 ML Cu at 250 K. The observed di¤ractionring around the central (00) beam results from a quite narrow adatom island sep-aration distribution function. The homogeneous ring intensity re‡ects an isotropicradial distribution of adatom islands, caused by the homogeneous adatom di¤usionon Cu(001). The fourfold pattern at larger wavevector k== reveals the presence ofsquare adatom islands with edges in the close-packed <110>-directions on the sur-face. The fourfold pattern is comparable with the optical equivalent of Fraunhoferdi¤raction from randomly distributed square apertures. The development of squareadatom islands is favored by the fact that the mobility of ledge atoms is much higherthan that of isolated adatoms on the (001)-terraces (see Table 1.1). The diameterof the di¤raction ring re‡ects an average adatom island separation of 80 Å.

In contrast to normal deposition, molecular beam epitaxy (MBE) at grazing in-cidence destroys the fourfold symmetry of the …lm morphology. Instead, a twofold

3.2. NORMAL VERSUS GRAZING INCIDENCE DEPOSITION 41

-40

-20

0

20

40

-40-20

020

40

-40 -20 0 20 40-40

-20

0

20

40

-10-5

05

10

-10-5

05

10

-10 -5 0 5 10

-10

-5

0

5

10

k[110]

(%BZ)k

[1-10] (%BZ)

k[1 -10]

(%BZ)

k[1

10] (

%B

Z)

k[110]

(%BZ)k

[1-10] (%BZ)

b)

a)

k

[11

0] (

%B

Z)

k[1 -10]

(%BZ)

Figure 3.2: (a) SPA-LEED peak pro…le and contour plot of the specular beamacquired after deposition of 40 ML Cu at 80± with the Cu(001) substrate at 250K. The spot pro…le was obtained at E = 176 eV (Sz = 3:91). (b) The same afterdeposition of 0.5 ML Cu under identical conditions: E = 133 eV (Sz = 3:40). Thearrows in the contour plots indicate the deposition direction.


symmetric peak pro…le emerges with the plane of incidence acting as a mirror plane.Figure 3.2(a) shows a SPA-LEED peak pro…le of the specular beam obtained afterdeposition of 40 ML Cu on Cu(001) at a grazing angle of 80± with respect to thesurface normal. The Cu was deposited along the [110]-azimuth with the substrateat 250 K. The peak pro…le shows two well developed facet peaks in the plane ofincidence of the Cu atom beam. Perpendicular to the plane of incidence no distinctdi¤raction features are measured: the resulting pro…le is almost one-dimensional.The observed asymmetric di¤raction pro…le can be interpreted straightforwardly asresulting from growth induced parallel ripples at the Cu(001) surface. The orien-tation of these ripples is perpendicular to the plane of incidence of the Cu atombeam. The ripples are well de…ned and have an average length of about 500 Å,which can be concluded from the absence of out of plane di¤raction features andthe small out of plane width of the facet peaks. The slopes of the ripples on theilluminated and shadow sides correspond to (111)- and (113)-facets, respectively.Compared to normal incidence deposition ({115}-facet orientation) the slopes aresubstantially steeper and much better de…ned after grazing incidence deposition at80±. This clearly evidences a substantially enhancement of surface roughness af-ter grazing incidence deposition, compared to the situation after normal incidencedeposition.

The base for the morphology found after deposition of 40 ML Cu is again laidalready during the growth of the …rst monolayer. Figure 3.2(b) shows a SPA-LEEDpeak pro…le of the specular beam obtained after growth of 0.5 ML Cu at a grazingangle of 80± with the substrate at 250 K. The observed di¤raction ring around thecentral (00) beam is not rotationally symmetric but exhibits a clearly developedtwofold symmetry in this case. This remarkable beam pro…le with ring intensitymaxima in the deposition plane re‡ects an isotropic radial distribution of rectan-gular adatom islands in contrast to square adatom islands developing at normalincidence. The rectangular islands are distributed with their long sides perpendic-ular to the plane of incidence of the Cu atom beam and with their edges orientedalong the closed-packed <110>-directions. The equal di¤raction ring diameter inFig. 3.1(b) and Fig. 3.2(b) indicates that the average adatom island separation afternormal and grazing incidence deposition is the same within experimental error, i.e.,L = 80 Å.

To illustrate that an isotropic radial distribution of rectangular islands causesa twofold symmetry in the quasi-di¤use scattering ring, a peak pro…le of such anisland distribution was calculated. The result is shown in Fig. 3.3. In this two-dimensional calculation the isotropical distributed rectangular islands all have equalsizes and an aspect ratio of 3/2. The longest island side is about half the distancebetween the adatom islands. Just like in the case of square islands, the Fouriertransform of the auto correlation function is a two-dimensional sinc function, butnow the widths of the sinc function in the two high symmetry directions di¤er fromeach other. The intensity of the quasi-di¤use scattering ring is therefore reduced inthe direction in which the sinc function has the smallest width, i.e., the direction

3.2. NORMAL VERSUS GRAZING INCIDENCE DEPOSITION 43

Figure 3.3: Calculated quasi-di¤use peak pro…le of a surface with an isotropic radialdistribution of rectangular islands. The aspect ratio of the islands was 3/2 and theisland separation was twice the size of the longest side of the islands. The insetshows the orientation of the rectangular islands.

along which the adatom islands have their longest side. A comparison with thedi¤raction measurement in Fig. 3.2(b) reveals that the rectangular adatom islandshave their long sides oriented perpendicular to the plane of incidence of the Cu atombeam. Further estimates indicate that the rectangular islands, found after growthat a grazing angle of 80± with the substrate at 250 K, have an aspect ratio of about1.05. This ratio is consistent with global estimates on the basis of the observedisland distributions.

From Fig. 3.1 and Fig. 3.2 it can be concluded that, compared to normal in-cidence, grazing incidence deposition results in: - the development of rectangularadatom islands instead of square ones in the …rst monolayer, - enhanced surfaceroughness upon further growth, - the emergence of a ripple structure instead ofmounds. Furthermore, the mound slopes are substantially steeper after grazingincidence deposition than those obtained after normal incidence deposition at thesame temperature. Another remarkable di¤erence between normal and grazing inci-dence deposition is the degree of order of the distances between adatom structures.Figure 3.4 shows a line scan through the specular beam in the [110]-azimuth, i.e.,in the plane of incidence of the Cu atom beam, acquired after grazing incidencedeposition of 9 ML Cu on Cu(001) at 250 K. Besides the narrow central feature,


-20 -10 0 10 20

depositiondirection

inte

nsity

(ar

b. u

nits

)

k[110]

(%BZ)

Figure 3.4: SPA-LEED line scan through the specular beam in the plane of incidenceacquired after deposition of 9 ML Cu at 80± with the Cu(001) substrate at 250 K.The line scan was obtained at E = 116 eV (Sz = 3:18). The arrows indicate the …rstand higher order di¤raction peaks of the Fourier transform of the island separationfunction.

which represents the specular Bragg intensity, the di¤raction pro…le exhibits a lotof structure. The pro…le shows that the onset of asymmetry, which at prolongeddeposition results in well developed (111)- and (113)-facets on the illuminated andshadow sides of the ripples, is already present. The additional peaks re‡ect theaverage adatom structure separation. Up to fourth order di¤raction features can bedistinguished in Fig. 3.4, which is by far more than ever seen after normal incidencedeposition: after normal incidence deposition only …rst order peaks can be detected.This observation reveals that the surface ordering in the plane of incidence of the Cuatom beam is highly improved with respect to that obtained after normal incidencedeposition.

The enhanced lateral order at grazing incidence deposition can be rationalizedas follows: for layer-by-layer growth, which initially occurs at 250 K, the nucleationphase will lead to a rather narrow separation distribution function of the adatomislands. When growth at normal incidence proceeds, the separation distributionfunction related to the centres of gravity of the islands will even narrow quite con-siderably. This is due to the fact that islands grow fast in the directions in whichthey are surrounded by extended capture zones, i.e., the directions in which theydo not have other islands in their vicinity. On the other hand, island growth in thedirections in which islands have other islands in their vicinity is slow. This di¤erencein growth rate causes the centres of gravity of the islands to move in such a way that

3.3. STEERING 45

the average island separation distribution function narrows until coalescence sets in.Shortly before coalescence the separation distribution function will be most narrow.During grazing incidence growth the azimuthal asymmetry of the island growth ratewill also narrow the island separation distribution function. An important di¤erencewith normal deposition is the reduced atom impingement rate in the shadow zonesbehind the islands. This reduction hampers the coalescence of islands in the planeof incidence: the step edge advance rate of an illuminated step edge reduces stronglywhen it enters the shadow zone of a neighboring up-stream adatom island. Becauseof the hampered island coalescence in the plane of incidence, narrowing of the islandseparation distribution function will proceed longer in this direction if the di¤usionrate around island corners is low. The further developing three-dimensional struc-tures will therefore evolve on a base with a narrower separation distribution functionin the plane of incidence. Following this scenario, again the basis for the improvedorder is believed to be laid already in the …rst monolayer. At more advanced stagesof growth the situation is more complicated since the lateral variation in the amountof incident Cu atoms becomes strongly dependent on the local surface morphology(see next section). Still a quite well de…ned e¤ective shadow length will be active,which tends to favor enhanced lateral ordering in the plane of the incident Cu atombeam.

3.3 Steering

The di¤erences in the surface morphology after normal incidence and grazing inci-dence deposition can be explained by steering-enhanced roughening. Steering isthe focusing of incident atom ‡ux on protruding terraces. It is induced by long-rangeattractive forces between approaching atoms and substrate atoms. Thermal energymetal atoms, approaching the surface at typical energies of 0.1 to 0.25 eV, expe-rience long-range attractive forces before they come at rest in a several eV’s deepwell. This gives rise to substantial acceleration and in the case of grazing incidencedeposition substantial de‡ection towards the surface [11]. For a ‡at substrate thisphenomenon has initially no consequences: the incident atom ‡ux remains homoge-neously distributed. The atoms only arrive at an e¤ectively smaller polar angle ofincidence, which is determined by the energy of the incident atoms and the depth ofthe attractive well in front of the substrate. As soon as aggregates start to build uphowever, the redistribution of incident atom ‡ux becomes progressively more impor-tant. Surface roughness causes a distortion in the attractive potential, and thereforeatom trajectories are in‡uenced by the local surface morphology. The result is aredistribution of incident atom ‡ux in such away that atoms arrive preferentially onprotruding terraces.

Atom trajectory calculations were performed to substantiate the phenomenon ofsteering for di¤erent surface morphologies. In these calculations a Lennard-Jones


A B

0 25 50 75 100 125 150 175 200

0

4

8

12

16

20

lateral position (Å)

heig

ht (Å

)C

-0.10 eV

-0.03 eV

-0.01 eV

δA

δB

δC

Figure 3.5: Calculated equipotential energy contours and three atom trajectories fora surface with a monolayer high island on top of it (note the di¤erent length scaleon the two axes). The increase in the attractive potential is -0.1 eV for the solidcontour lines. The trajectory calculations for a deposition angle of 80± start at 20Å above the surface.

(12,6) pairwise potential was adopted. The potential is given by:

V (R) = D³a==R

´6·³a==R

´6¡ 2

¸; (3.1)

where a== is the in-plane lattice constant (2.55 Å for Cu) and D is a pairwise energywhich was …tted to the cohesive energy (D = 0.4093 eV for Cu). Normally such apairwise additive Lennard-Jones potential is believed to be inadequate to describethe attractive potential of metals in detail [118]. Sanders et al. [10], however, foundthat atom trajectory calculations with such a Lennard-Jones potential are satisfac-torily close to calculations with their most accurate many body density functionalbased potential energy surface. The Lennard-Jones pairwise potential was thereforeused to calculate the e¤ect of steering semi-quantitatively.

Figure 3.5 shows a cross-sectional view through the Cu(001) substrate along the[110]-azimuth. Please note that the vertical scale is extended by a factor of 8 withrespect to the horizontal one. On the substrate a monolayer high adatom islandis constructed. The …gure exhibits calculated equipotential energy contours (incre-ment -0.1 eV) as well as three calculated atom trajectories for atoms deposited at agrazing angle of 80±. The equipotential energy contours show substantial distortionin the attractive potential, which is related to the ascending and descending step

3.3. STEERING 47

edges. The lateral length of distortion is about 15 Å for the -0.01 eV contour. Calcu-lations show that 150 meV Cu atoms, deposited with a grazing angle of incidence of80±, actually hit the surface at an angle of 17±, when the trajectory passes throughan undistorted attractive potential (trajectory C in Fig. 3.5). When atoms passthrough a distorted attractive potential however, the trajectories can deviate sub-stantially (trajectory A and B in Fig. 3.5). The result of a surface roughness inducedvariation in atom trajectories is illustrated most clearly when the distance betweenthe impact point at which the atoms actually hit the surface and their target point(±A, ±B and ±C in Fig. 3.5) is considered. The target point is the intersection of theasymptotic long distance part of the trajectory with the surface. Atoms followingtrajectory A in Fig. 3.5 pass through a distorted attractive potential, which is re-lated to a descending step edge. They therefore suddenly experience the surface ata much larger distance and impact is further away. Consequently, the value of ±A isenhanced with respect to ±C. The value of ±A is further enhanced by strong lateralforces between the descending step edge and the approaching slow atom. These twoe¤ects give rise to a local reduction of the incident atom ‡ux just behind the adatomisland. On the other hand, atoms following trajectory B in Fig. 3.5 suddenly expe-rience the surface at a much smaller distance when they pass through the distortedattractive potential, which is now related to an ascending step edge. Therefore theactual position of impact is much closer to the target point and ±B is reduced withrespect to ±C . In addition, the lateral forces between the ascending step edge andthe approaching atom reduce ±B. The consequence is a local enhancement of theincident atom ‡ux just behind the leading edge of the adatom island. In fact allarriving atoms whose trajectories pass through areas of substantial distortion ofthe attractive potential related to ascending step edges contribute to enhanced ‡ux.They are focused on top of the adatom island, with the maximum atom ‡ux closeto the leading edge. This focusing of incident atom ‡ux on top of adatom structuresis called steering.

Numerous atom trajectories for di¤erent surface morphologies were calculated.From these calculations the inhomogeneous atom ‡ux at the surface normalized tothe homogeneous ‡ux far above the surface was derived. Three results are shownin Fig. 3.6. Figure 3.6(a) shows the calculated normalized atom ‡ux for a surfacewith a monolayer high adatom island on top of it and deposition at a grazing angleof 80±. The atom ‡ux enhancement factor amounts to about 1.6 at the front ofthe island and decreases to one going further downstream on an extended island.Behind the island the ‡ux of the incident atoms is reduced to about 0.7 close to thedescending step edge. Note that the atom ‡ux behind the islands never becomeszero as opposed to geometrical shadowing and that the range of reduced atom ‡ux(t 60 Å) is much larger compared to classical shadowing without steering (10 Å fordeposition at 80±). The reduction of incident atom ‡ux behind the adatom islandcompensates the ‡ux enhancement on top of the island as should be the case forparticle conservation reasons.

Figure 3.6(b) shows the calculated normalized atom ‡ux for the same surface


0.0

0.5

1.0

1.5

2.0

a)

norm

aliz

ed a

tom

flux

b)

-2

0

2

4

6

c)

Figure 3.6: Calculated incident atom ‡ux at the surface, normalized to a homoge-neous atom ‡ux far above the surface. (a) Surface with a 1 ML high island on topof it and a deposition angle of 80±. (b) Surface with a 1ML high island and normalincidence deposition. (c) Surface with a 3 ML high island and a deposition angle of80±.

but now for normal incidence deposition. Obviously the e¤ect of steering is muchsmaller for this deposition geometry. Only a small local enhancement of the incidentatom ‡ux is observed close to the step edges over a range of just one atom position.The inequality in atom ‡ux redistribution between normal incidence deposition anddeposition at a grazing angle of 80± is caused by the substantial di¤erence in atomvelocity parallel to the surface. The actual position of impact is very sensitiveto small distortions in the attractive potential when atoms have a relatively largevelocity component parallel to the surface. The result is a substantial redistributionof the incident atoms due to morphology dependent trajectories. On the otherhand, deviations in atom trajectories only change the position of impact slightlywhen atoms have a small velocity component parallel to the surface. The steeringe¤ect is therefore much weaker at normal incidence deposition. Similar argumentsapply for steering e¤ects around island edges parallel to the plane of incidence.

The in‡uence of surface roughness is illustrated in Fig. 3.6(c). This …gureshows the calculated normalized atom ‡ux for a surface with a 3 ML high adatomstructure on top of it and deposition at a grazing angle of 80±. Since the slopesof the adatom structure correspond to steep {111}-facets, the calculated atom ‡uxenhancement can be considered as an upper limit for 3 ML high structures. Theatom ‡ux enhancement on top of the adatom structure is obviously much largercompared to that for an 1 ML high adatom island (note the di¤erent vertical ‡uxscale in Fig. 3.6(a) and (c)). The di¤erence between Fig. 3.6(a) and Fig. 3.6(c) isexplained by an increased distortion in the attractive potential near the ascendingand descending step edges of the 3 ML high adatom structure. Flux variations upto an order of magnitude apply in Fig. 3.6(c).

The dependence of steering on the deposition angle and adatom structure height

3.3. STEERING 49

0 20 40 60 801.0

1.1

1.2

1.3

1.4

1.5

aver

age

norm

aliz

ed a

tom

flux

deposition angle (°)

Figure 3.7: Average normalized atom ‡ux on top of an adatom structure as a func-tion of the deposition angle. The length of the island top layer is 20 atoms and theisland height is 1 ML, 2 ML, 3 ML, 4 ML and 5 ML for the square-, circle-, uptriangle-, down triangle- and diamond symbols respectively.

is summarized in Fig. 3.7. This …gure shows the average normalized atom ‡uxon top of an adatom structure versus the deposition angle. The length of the toplayer of the adatom structure is 20 atoms. For smaller (larger) adatom structures theaverage ‡ux enhancement on top will be larger (smaller). Following the calculations,the focusing of incident atom ‡ux on top of adatom structures is small for depositionangles up to 50±, while steering increases considerably with increasing depositionangle above 50±. The average ‡ux on top of adatom structures also increases rapidlywith increasing structure height. However, the ‡ux enhancement per additionalmonolayer decreases. The average atom ‡ux on top of adatom structures saturatesfor structures of about 10 ML high.

The development of rectangular adatom islands instead of square ones duringgrazing incidence growth can be explained by steering. Steering, i.e., the focussingof incident atom ‡ux on top of adatom islands, is exactly compensated by an in-cident atom ‡ux reduction behind adatom islands. A direct consequence of theredistribution of incident atom ‡ux is a change of the adatom island growth rate.Since less atoms are deposited close to the shadow side of an adatom island, this sidegrows slower. The adatom island growth rate reduction in the deposition directionis only compensated when all “extra” deposited atoms on top of an adatom islandcontribute to the growth of the illuminated side. A part of the “extra” depositedatoms, however, leaks away to the perpendicular sides. Therefore, the adatom islandgrowth rate in the deposition direction is slightly smaller than the growth rate in


Figure 3.8: Illustration of the steering-induced elongation of growing adatom islands.The grayscale is a measure for the incident atom ‡ux on the surface during grazingincidence deposition. The solid and dashed arrows indicate the step edge growthrate during grazing and normal incidence deposition respectively.

the perpendicular direction. As a result, rectangular adatom islands evolve duringgrazing incidence growth with their longest side oriented perpendicular to the de-position direction. The consequence of steering for the growth of adatom islands isillustrated in Fig. 3.8.

The observed di¤erences in the surface morphology after normal incidence andgrazing incidence growth of 40 ML Cu on Cu(001) can be explained by steering aswell. Before discussing the e¤ects of steering for larger amounts of Cu deposits, moreexperimental results on grazing incidence growth will be presented. In Sec. 3.4 thedeposition angle dependence of slope selection at 250 K is described. Thereafter,the temperature dependence of the surface morphology after growth at a grazingangle of 80± is reported. Finally, the surface morphology after grazing incidencegrowth in the [110]- and [100]-azimuth is compared. The experimental results arediscussed extensively in Sec. 3.7. The discussion focuses primarily on the steeringphenomenon and its consequences for surface roughening and slope selection duringgrowth.

3.4 Slope selectionGrowth experiments at di¤erent grazing angles of incidence along the [110]-azimuthwere performed to characterize the in‡uence of the deposition angle on the surfacemorphology. This section describes the measured surface morphology after depo-

3.4. SLOPE SELECTION 51

-20

-10

0

10

20

-20-10

010

20

-20 -10 0 10 20-20

-10

0

10

20

-20 -10 0 10 20

k[110] (%BZ)

k[1-10]

(%BZ)

k[1-10] (%BZ)

k [110

] (%

BZ)

k// (%BZ)

Figure 3.9: SPA-LEED peak pro…le of the specular beam acquired after depositionof 40 ML Cu at 50± with the Cu(001) substrate at 250 K. The pro…le was obtainedat E = 173 eV (Sz = 3:87). The left inset shows line scans through the specularbeam in the [110]- (solid line) and [1-10]-direction (dashed line). The arrow in thecontour plot indicates the deposition direction.

sition of 40 ML Cu on Cu(001) at 250 K. Figure 3.9 shows a peak pro…le of thespecular beam obtained after deposition at a grazing angle of 50± with respect tothe surface normal. The left inset shows two line scans through the specular beam.The solid line is measured in the [110]-direction, i.e., in the plane of incidence of theCu atom beam, whereas the dashed line is measured perpendicular to this plane.Obviously, the two line scans are not identical, as is the case after normal incidencedeposition of 40 ML Cu. In the plane of incidence of the Cu atom beam the linescan is slightly asymmetric and shows two not very well developed facet peaks. Inthe perpendicular direction on the other hand, the line scan shows two facet peaks,which are much better developed compared to the facet peaks measured after normaldeposition. The observed di¤raction pattern can be interpreted as resulting fromgrowth induced mound structures. The four sides of the mounds still have a {115}-orientation, but now the slopes are better de…ned in the direction perpendicular tothe plane of incidence of the Cu atom beam. Furthermore, after growth at an angleof 50± no couples of well developed parallel ridges along the <110>-directions areobserved in the SPA-LEED peak pro…le. These ridges, which are observed after nor-


3.1

3.3

3.5

3.7

3.9

-40 -20 0 20 40

3.1

3.3

3.5

3.7

3.9

Sz

b)

a)

peak position (%BZ)

Figure 3.10: Position of the facet peaks as a function of the perpendicular scatteringphase for the illuminated side (…lled circles in (a)), the shadow side (open circles in(a)) and the perpendicular sides (…lled circles in (b)) of the mounds measured afterdeposition of 40 ML Cu at 70± with the Cu(001) substrate at 250 K.

-20 -10 0 10 20-30

-20

-10

0

10

20

30

k [110

] (%

BZ

)

k[1-10]

(%BZ)

-20 -10 0 10 20

b)a)

intensity (arb. units)

k// (%BZ)

Figure 3.11: (a) SPA-LEED contour plot of the specular beam acquired after de-position of 40 ML Cu at 85± with the Cu(001) substrate at 250 K. The contourplot was obtained at E = 178 eV (Sz = 3:93). The arrow indicates the depositiondirection. (b) Line scans through the specular beam in the [110]- (solid line) and[1-10]-direction (dashed line).

3.4. SLOPE SELECTION 53

20 30 40 50 60 70 80 9010

20

30

40

50

60

(115)

(113)

(111)sl

ope

angl

e (°

)


Figure 3.12: The measured slope angle after deposition of 40 ML Cu at 250 K as afunction of the deposition angle. The squares, circles and triangles give the slope ofthe illuminated, shadow and perpendicular adatom structure sides respectively.

mal incidence deposition (see Fig. 3.1(a)), indicate that the mounds are situated ina quite regular checkerboard pattern [46]. The base for this ordering phenomenon islaid already just after coalescence of growing adatom islands in the …rst monolayer.The absence of a checkerboard pattern after growth at 50± suggests that deviationsin the surface morphology are present already during the initial stages of growth.

Deposition at an angle between 55± and 70± leads to the formation of asymmetricmound structures. The sides of the mounds have a di¤erent slope orientation, whichcritically depends on the deposition angle. Although not very well de…ned, theaverage slope at the illuminated side of the mounds increases considerably from15± (corresponds to a (113)-facet) at a deposition angle of 50± to about 30± at adeposition angle of 65± with respect to the surface normal. Figure 3.10 shows theposition of facet peaks as a function of the perpendicular scattering phase Sz aftergrowth of 40 ML Cu at an angle of 70±. Deposition at a grazing angle of 70±results in mounds with an average slope angle of 42± at the illuminated side. Afterdeposition of 40 ML Cu at an angle between 55± and 70± the shadow side of themounds has a well de…ned slope which is smaller than the slope of the illuminatedside. The average slope increases gradually from 15± at a deposition angle of 50±to 23± at a deposition angle of 70±. In contrast to the illuminated and shadow sideof the mounds, the slope at the sides perpendicular to the incident Cu atom beamis almost constant. For deposition angles up to 70± the perpendicular sides have aslope which corresponds to a {115}-facet.


As described earlier, deposition at a grazing angle of 80± with the substrate at250 K leads to the formation of parallel ripples perpendicular to the incident Cuatom beam. The slope of the ripples on the illuminated and shadow side correspondto well de…ned (111)- and (113)-facets respectively. Perpendicular to the incident Cuatom beam only minor di¤raction features are measured. Remarkably, deposition ata grazing angle of 85± again leads to the formation of mound structures. Figure 3.11shows a peak pro…le of the specular beam obtained after deposition of 40 ML copperat 85±. This pro…le shows well developed facet peaks parallel as well as perpendicularto the plane of incidence of the Cu atom beam. The four sides of the moundshave a very well de…ned {111}-facet orientation. This slope orientation is neverobtained after normal incidence deposition (even not at lower growth temperatures)[41, 42, 46]. In the spot pro…le an additional facet peak originating from the shadowside of the mounds is observed. The position of this facet peak follows the rod ofthe (113)-surface in reciprocal space. The shadow side of the mounds thus consistsof (111)- and (113)-facetted areas.

Figure 3.12 summarizes the measured slope angle after growth of 40 ML Cu at250 K as a function of the deposition angle. The error bars in Fig. 3.12 are small forwell established facets, while somewhat larger error bars result for less well developedfacet peaks. In general, the slope angle increases with increasing deposition anglefor all mound sides. Figure 3.12 reveals that slopes corresponding to {115}-, {113}-,and {111}-facets can be obtained at a growth temperature of 250 K.

3.5 Temperature dependence

Figure 3.13 shows two SPA-LEED peak pro…les of the specular beam obtained aftergrowth of 40 ML Cu on Cu(001) at a grazing angle of 80± with the substrate at 200K ((a) and (b)) and 300 K ((c) and (d)) respectively. Both peak pro…les show welldeveloped facet peaks in the plane of incidence of the Cu atom beam as well as inthe perpendicular direction. The observed di¤raction pattern can be interpreted asresulting from growth induced mounds instead of ripples which are observed aftergrowth at 250 K (see Fig 3.2(a)). The di¤raction peak pro…le obtained after growthat 200 K (Fig. 3.13(a) and (b)) shows two facet peaks originating from the shadowside of the mounds. The positions of these facet peaks follow the rods of the (111)-and (113)-surfaces in reciprocal space. The average slope of the shadow side isthus steeper than the slope obtained after normal incidence growth at 200 K orgrazing incidence growth at 80± with the substrate at 250 K (in both cases the slopecorresponds to a (113)-facet). The facet peaks in the direction perpendicular tothe deposition direction correspond to well established {111}-facets. Remarkably,Fig. 3.13(a) and (b) does not show a well de…ned facet peak originating from theilluminated side of the mounds. In this case, only a faint di¤raction feature, whichfollows the rod of the (111)-surface in reciprocal space, is visible. The illuminatedside of the mounds therefore consists of less well de…ned (111)-facets.

3.5. TEMPERATURE DEPENDENCE 55

-10 -5 0 5 10

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-5

0

5

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-40

-20

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20

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-40 -20 0 20 40

d)b)

a)

k[1-10]

(%BZ)

k [110

] (%

BZ

)

k[1-10]

(%BZ)

k[110] (%

BZ

)

-40 -20 0 20 40

inte

nsity

(ar

b. u

nits

)

k// (%BZ)

-10 -5 0 5 10

c)

intensity (arb. units)

k// (%BZ)

Figure 3.13: SPA-LEED contour plots of the specular beam acquired after depositionof 40 ML Cu at 80± with the Cu(001) substrate at 200 K (a) and 300 K (c). Thearrows indicate the direction of deposition. In (b) and (d) line scans through thespecular beam in the [110]- (solid lines) and [1-10]-direction (dashed lines) are shown.The peak pro…les in (a) and (b) (T = 200 K) and (c) and (d) (T = 300 K) wereobtained at E = 275 eV (Sz = 4:88) and E = 278 eV (Sz = 4:91) respectively.


Table 3.1: Facet orientation of the sides of adatom structures measured after normalincidence deposition and deposition at 80o of 40 ML Cu with the Cu(001) substrateat 200 K, 250 K and 300 K.

normal deposition deposition at 80±

T (K) illuminated side shadow side perp. sides200 {113} (111) (111) and (113) {111}250 {115} (111) (113) {113}300 {117} (113) (113 and (115) {113}

The SPA-LEED peak pro…le obtained after growth at 300 K (Fig. 3.13(c) and(d)) shows a well developed facet peak originating from the illuminated side ofthe mounds. The position of this facet peak follows the rod of the (113)-surface inreciprocal space. The mound slope at the illuminated side is thus much steeper thanthe slope obtained after normal incidence growth at 300 K (slope corresponds to a(117)-facet) and less steep than the slope obtained after grazing incidence growthat 80± with the substrate at 250 K (slope corresponds to a (111)-facet). One broadfacet peak originating from the shadow side of the mounds is measured. Electronenergy dependent measurements show that the broad facet peak actually consists oftwo single peaks: one originating from (113)-facetted areas and the other originatingfrom (115)-facets. Therefore, the average mound slope at the shadow side is alsoless steep than the slope obtained after grazing incidence growth at 80± with thesubstrate at 250 K (only a well developed (113)-facet peak). Finally, Fig 3.13(c) and(d) show clear facet peaks in the direction perpendicular to the plane of incidenceof the incident Cu atom beam, which correspond to well established {113}-facets.

Table 3.1 summarizes the obtained mound slopes after deposition of 40 MLCu on Cu(001) at 200 K, 250 K and 300 K. In general, the slope decreases withincreasing growth temperature for both normal incidence deposition and depositionat a grazing angle of 80±. Furthermore, the slopes obtained after grazing incidencedeposition are steeper than those obtained after normal incidence growth.

3.6 Azimuthal dependenceIn the grazing incidence growth experiments described so far the Cu was depositedalong the [110]-azimuth, i.e., parallel to the direction in which steps of adatom islandsare oriented. To characterize the in‡uence of the azimuthal deposition direction,grazing incidence growth experiments along the [100]-azimuth were performed aswell. Figure 3.14 shows a SPA-LEED peak pro…le of the specular beam obtainedafter deposition of 40 ML Cu on Cu(001) at a grazing angle of 80± with the substrateat 250 K. The observed di¤raction pattern can be interpreted as resulting fromgrowth induced mound structures. The facet peaks in the <110>-directions re‡ect

3.7. DISCUSSION 57

-20-10

010

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-20 -10 0 10 20

-20

-10

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10

20

k

[1-10] (%BZ)

k[110]

(%BZ)

k

[110

] (%

BZ

)

k[1-10] (%BZ)

Figure 3.14: SPA-LEED peak pro…le of the specular beam acquired after depositionof 40 ML Cu at 80± with the Cu(001) substrate at 250 K. The deposition was alongthe [100]-azimuth, which is indicated by the arrow in the contour plot. The spotpro…le was obtained at E = 278 eV (Sz = 4:91).

that the step edges of the adatom structures are still preferentially oriented alongthe <110>-directions. From this it can be concluded that the azimuthal orientationof the mounds does not change with the azimuthal direction of deposition. The facetpeaks originating from the shadow sides of the mounds correspond to well established{113}-facets. The peak pro…le in Fig. 3.14 also shows less well developed {113}-facet peaks originating from the two illuminated mound sides. The observed averagemound slope is steeper than the slopes obtained after normal incidence growth at 250K (slope corresponds to {115}-facets). This reveals an enhanced surface roughnessafter grazing incidence deposition along the [100]-azimuth as well.

3.7 DiscussionIn this section the experimental results will be discussed in more detail. The …rstpart is devoted to the in‡uence of steering on the evolution of the surface roughnessduring growth, i.e., the in‡uence of steering on the …lm growth mode. Thereafter, thetemperature and deposition angle dependence of the mound slopes will be explainedqualitatively. Then, the discussion focuses on double facetted faces at the shadow


side of mounds. Finally, the observed changes of the surface pattern from moundsto ripples and back from ripples to mounds with increasing deposition angle will bediscussed.

The evolution of the surface morphology during homoepitaxial growth is gov-erned by two kinetic processes [7, 17, 23, 24, 119, 120, 121, 122, 123, 124]. The …rstprocess is nucleation during the early stages of monolayer growth. It determinesthe average separation between adatom islands L, which depends critically on theintralayer di¤usion of single adatoms, the deposition rate and the number of atomsin the smallest stable island (see Sec. 1.2.3). Under usual growth conditions, thedensity of adatom islands formed during a growth experiment increases with increas-ing supersaturation, i.e., with decreasing substrate temperature and with increasingdeposition rate. The second kinetic process that plays a key role in the evolution ofthe surface morphology is the interlayer di¤usion of adatoms. Interlayer di¤usion,or the descent of atoms from islands onto neighboring terraces, depends stronglyon the presence of a stable nucleus on top of the growing island. Once nucleationon top of growing islands is initiated, the interlayer di¤usion is reduced strongly.Nucleation on top of islands starts on the average when the island size surpasses acritical island radius Rc [17, 123]. The critical island radius depends on the growthtemperature and the height of the activation barrier for downward di¤usion at astep edge. The activation energy for adatoms to cross a descending step edge ishigher than the activation energy for adatom di¤usion on a ‡at terrace in mostgrowth systems. The additional step-edge barrier Es can therefore be regarded asa (partly) re‡ecting barrier at the step edge. The probability for an adatom to bere‡ected at a step, following its attempt to descend, increases as {1-exp(¡Es=kT )}.Lowering the growth temperature therefore increases the adatom density on top ofgrowing islands. For …nite values of Es this gives rise to enhanced nucleation, i.e.,the critical island size Rc at which nucleation on top of islands begins decreases.

When growth proceeds via homogeneous nucleation of adatom islands on ‡atterraces the growth can be characterized by two length scales: the average distancebetween adatom islands L and the critical island radius Rc. No stable nuclei areformed on top of adatom islands before coalescence if Rc is larger than half theseparation between adatom islands. In this case the growth mode is called layer-by-layer and the surface roughness after growth is small. On the other hand, ifRc is smaller than half the separation between adatom islands, nucleation on top ofislands occurs before coalescence. Now the growth is three-dimensional or multilayerand mound structures are formed. The purpose of the following discussion is notan exact determination of growth modes in Cu/Cu(001). Here, the critical islandradius Rc is used to illustrate the in‡uence of steering on the growth mode in aqualitative way. A decrease of Rc indicates a shift from layer-by-layer to multilayergrowth.

Homoepitaxial growth will proceed layer-by-layer in a broad temperature rangeif there is no step-edge barrier. The key point in understanding the growth behavioris that the ability of adatoms to descend from islands is independent of their ability

3.7. DISCUSSION 59

to reach the island edge. In fact, on the average, every deposited atom on topof an island has su¢cient time to reach the island edge before it is captured byother adatoms. This is guaranteed by the length scale (L) set during the nucleationprocess. Nucleation ceases when an atom deposited in between adatom islands hasa higher probability to reach the islands than to meet other adatoms to form a newnucleus. An adatom can at least freely travel a distance roughly equal to half thedistance between island centers. Since the average island radius before coalescenceis always smaller than the average distance between island centres, an adatom ontop of an island has the ability to reach the island edge before meeting other atomsdeposited on the same island. Therefore, if no signi…cant step-edge barrier is presentthe adatom density on top of an island will always be less than required for nucleationand no stable nuclei will be formed before coalescence, resulting in layer-by-layergrowth [7, 17].

The presence of a …nite step-edge barrier leads to multilayer growth at low sub-strate temperatures. Re‡ection of the adatoms at the island edges results in anenhanced atom density on top of islands and therefore in enhanced nucleation. Asa result the critical island radius Rc decreases. While Rc decreases more rapidlythan L with decreasing growth temperature [17] a transition from layer-by-layergrowth to multilayer growth occurs at a growth temperature for which Rc t 0:5L.It is thus the step-edge barrier which is primarily responsible for deviations fromlayer-by-layer growth.

The in‡uence of steering on the growth mode will now be discussed. Steeringgives rise to a heterogeneity of the incident atom ‡ux, i.e., a redistribution of theincident atoms due to their morphology dependent trajectories. Because of steering,atoms arrive preferentially on protruding terraces. It therefore always enhances theadatom density on top of growing islands. This leads in a very basic way to adecrease of the critical island radius Rc and thus to enhanced roughening of thegrowing surface, i.e., steering shifts the growth mode from layer-by-layer towardsmultilayer growth. The ultimate consequence of steering is that in principle layer-by-layer growth is never possible. Even for a vanishing step-edge barrier this will bethe case, as some steering e¤ect is always present (even for normal incidence). Thepoint that always Rc < 0:5L is explicitly emphasized since it is an important andgeneral aspect of this phenomenon in growth. This statement de…nitely holds in avery basic way, but is on the other hand of rather academic interest: the incidentatom ‡ux enhancement is by de…nition located near the descending step edges andmost of the excess adatom density will disappear easily by interlayer mass transportto the lower terrace.

Interlayer mass transport is less e¤ective in the presence of a step-edge barrier.This gives rise to a pronounced enhancement of the adatom density on top of grow-ing islands and therefore to a prominent decrease of the critical island radius Rc1. As a consequence, steering results in a signi…cantly increased roughness of the

1The number of adatoms per surface cell of area a2 on top of a slow growing island at a distancer from the center is given by [17]: ´(r) = F

4D a2(R2 +R2a® ¡r2), where F is the incident atom ‡ux,


growing …lm in the presence of a …nite step-edge barrier. From the experimentalresults and the discussion it follows that steering is autocatalytic: steering givesrise to an enhanced surface roughness, whereas a larger surface roughness resultsin an enhanced steering. In general, steering-enhanced roughening increases withdecreasing interlayer mass transport.

The temperature dependence of steering-enhanced roughening is partly con-trolled by the temperature dependence of interlayer mass transport. For a …xedstep-edge barrier height, the interlayer mass transport is reduced when the growthtemperature is lowered. The in‡uence of steering on surface roughening thereforeincreases with decreasing growth temperature. Besides this interlayer di¤usion re-lated temperature e¤ect, there is another temperature e¤ect which is related to thelateral length scale of the growing …lm. Intralayer di¤usion determines the densityof nuclei and therefore the separation between adatom islands. The island separa-tion and thus the average island size at a given coverage decreases exponentiallywith the growth temperature until a temperature is reached at which adatom dif-fusion is negligible (see Sec. 1.2.3). The average atom ‡ux enhancement on top ofislands is largest for small adatom islands. Steering-enhanced roughening thereforeincreases strongly with decreasing island sizes, i.e., with decreasing growth temper-ature. From this it is concluded that both the step-edge barrier related temperaturee¤ect as well as the island size related temperature e¤ect result in an enhanced in‡u-ence of steering on the surface morphology with decreasing temperature. Besides thegrowth temperature, the deposition rate in‡uences steering-enhanced roughening aswell. In general, the adatom island density on a surface and thus steering-enhancedroughening increases with increasing deposition rate.

Up to now, growth models have always regarded the ‡ux of impinging atoms asbeing homogeneously distributed over the surface. The experimental results and thediscussion above show that besides intralayer and interlayer di¤usion, steering mayhave an important in‡uence on the morphology of the growing …lm. Due to steeringthe incident atom ‡ux is not homogeneous anymore. The inhomogeneity in theincident atom ‡ux increases with increasing deposition angle, with increasing surfaceroughness and with decreasing growth temperature. In the following the in‡uence ofsteering on the selection of the slope angle will be discussed. Before steering e¤ectsare taken into account, slope selection without steering will be described.

In the presence of a …nite step-edge barrier mound structures are formed duringgrowth. These mounds coarsen slowly in time while the sides of the mounds turninto facets. Continuum models [125, 126] as well as Monte Carlo simulations [127,128, 129, 130] have been used to describe slope selection. An important parameterin slope selection is a net upward current in the presence of a step-edge barrier. Thestep-edge barrier causes preferential incorporation of di¤using adatoms at ascendingstep edges, de…ned as a net upward current. Step-adatom attraction found by

D is the di¤usion constant, R is the island radius and ® varies with temperature as exp(¡Es=kT ).Steering increases the incident atom ‡ux F and thus ´(r). From the equation it is clear thatsteering increases the adatom density on top of an island most when Es=kT is large.

3.7. DISCUSSION 61

Wang and Ehrlich [131] may also contribute to a net upward current. The netupward current alone however, does not lead to slope selection. Slope selectionrequires a counter-balancing downward current, which results from leakage throughthe step-edge barrier or ultimately may be due to downward funneling dynamics(see Sec. 1.2.1). Other processes such as transient mobility and knockout eventsat step edges, would have an even greater propensity for smoothening. MolecularDynamics studies, however, suggest that these events are not signi…cant [10, 11,12, 13]. The selected slope is determined by the balance between the upward- anddownward currents. Larger upward currents for instance caused by a signi…cantstep-edge barrier, lead to steeper slopes [125, 126, 127, 128, 129, 130]. On the otherhand, a small mound angle will develop when the upward current is signi…cantlycounteracted by a downward current.

Steering causes a redistribution of the incident atom ‡ux, which depends criti-cally on the local surface morphology. In general, the redistribution of incident ‡uxin favor of protruding terraces increases during growth (steering is autocatalytic).Due to steering the amount of atoms deposited on the higher terraces is larger thanthe amount of atoms deposited on the lower terraces. A part of the deposited atomsis incorporated at the ascending step edges. Steering, therefore drastically enhancesthe amount of incorporated atoms in the higher layers and thus leads to a largerslope angle. Figure 3.12 shows that this is indeed the case. The steering inducedhigher ‡uxes on more elevated terraces, although not …tting in the above de…nitionof upward currents, most literally contributes to upward currents. The slope angleof the mound/ripple structures increases monotonically with the deposition angle.In other words: the selected slope depends critically on the amount of steering.

Figure 3.12 shows that di¤erent slope orientations can be obtained at one andthe same growth temperature. This illustrates that slope selection is not determinedby a global thermodynamic equilibrium. Slope selection clearly has a kinetic origininstead. The slope angle is determined by kinetic processes on the surface andthe deposition geometry, in which steering plays an important role. The observedtemperature dependence of the slope angle for grazing incidence deposition (seetable 3.1) can be rationalized as follows: the average size of adatom structureson the surface and the interlayer mass transport decrease with decreasing growthtemperature. Therefore, the incident atom ‡ux on top of adatom structures increaseswith decreasing growth temperature, which results in steeper facets. For normalincidence deposition the observed temperature dependence of the slope angle ([41,42, 46] and table 3.1) may also be explained by steering. Though small, steeringstill causes a redistribution of atom ‡ux near step edges and thus steeper facets maybe obtained at lower growth temperatures. The exact in‡uence of steering on thetemperature dependence of slope selection, however, is not clear and is probablysmall under normal incidence growth conditions. Also without steering an increasein slope angle with decreasing temperature is expected. In the presence of a step-edge barrier, the preferential incorporation of di¤using adatoms at ascending stepedges increases with decreasing growth temperature, since the leakage through the


barrier is reduced. Therefore, the net upward current is enhanced and steeper slopeangles are obtained at lower growth temperatures. This is probably the dominantfactor for the evolution of steeper facets at lower temperatures.

In some growth experiments at grazing incidence two facet peaks originatingfrom the shadow side of the mounds are measured. For deposition at 80± twofacet peaks are found after growth at 200 K and 300 K, whereas deposition at 85±

results in a shadow side with two slope orientations at 250 K. The formation of twodi¤erent facets at the shadow side of the mounds may be rationalized as follows:initially the amount of steering is relatively small. Therefore, the enhancement ofincident atom ‡ux on top of adatom structures is sizeable only in the regions justbehind the leading edge. In this situation, the ‡ux enhancement close to the edgeson the shadow side is negligible. With increasing surface roughness however, theenhancement of the incident atom ‡ux on top of adatom structures increases (see…g. 3.6) and more atoms will be deposited on the back side of adatom structuresas well. This e¤ect is further enhanced because of a smaller lateral mound sizesin the higher layers. The “extra” deposited atoms will be incorporated mainly atstep edges in the higher layers resulting in a larger net upward current. Followingthis scenario, the facet angle will increase with increasing surface roughness, i.e.,increasing amount of deposited atoms. Double facetted shadow faces may thereforedevelop with the high facets being steeper than the facets at the base of the mounds.

As the experimental results show, di¤erent surface patterns can be obtained atone and the same growth temperature. Homoepitaxial growth of Cu on Cu(001) at250 K leads to the formation of symmetric mound structures at deposition anglesup to 50±, asymmetric mounds at deposition angles between 50± and 70±, well or-dered ripple structures at a deposition angle of 80±, and mounds with very steepfaces at a deposition angle of 85±. These remarkable changes from mounds to rip-ples and back from ripples to mounds can be explained by the existence of twolength scales: the average separation between adatom structures and the range ofreduced incident atom ‡ux behind adatom structures (shadow length). The separa-tion between adatom structures is determined by the activation energy for adatomdi¤usion on the (001)-terraces, the growth temperature, the deposition rate and thenumber of atoms in the smallest stable island and is by its nature quite well de…ned.The range of reduced incident atom ‡ux is obviously controlled by the depositionangle and the height of the adatom structures and consequently less well de…ned.When the range of reduced incident atom ‡ux is smaller than the separation be-tween adatom structures (small deposition angles), mound structures will develop.At larger shadow lengths, however, the coalescence of adatom structures in the de-position direction is suppressed, or better retarded. When the range of reducedincident ‡ux is smaller than the distance between adatom structures, coalescence isstill possible in the direction perpendicular to deposition. In this case ripples candevelop, which are oriented perpendicular to the plane of incidence of the Cu atombeam. A further increase of the shadow length seems to suppress the coalescence ofadatom islands in the direction perpendicular to the deposition direction as well. In

3.8. CONCLUSIONS 63

this situation, mounds instead of ripples are formed. This speculative scenario forpattern formation during grazing incidence deposition can be checked by taking alook at the experimental results at di¤erent growth temperatures. Deposition at agrazing angle of 80± results in mound structures at 200 K and 300 K, while ripplesare obtained at 250 K. Following the scenario, ripples can be expected at a smallerdeposition angle when growth proceeds at lower substrate temperatures. At lowgrowth temperatures, the average separation between adatom structures is smalland a relatively small shadow length, thus small deposition angle, is enough to sup-press coalescence in the deposition direction. For higher growth temperatures thisargumentation leads to an expected ripple structure at a larger deposition angle.Further experiments are necessary to check the scenario.

3.8 ConclusionsThe in‡uence of the deposition geometry on the evolution of the surface morphol-ogy during molecular beam epitaxy of Cu/Cu(001) was studied at substrate tem-peratures between 200 and 300 K. The growth fronts become progressively rougherupon rotation of the molecular beam from normal to more grazing incidence. Theremarkable kinetic roughening observed after growth at grazing incidence can berationalized in terms of steering. Steering is a direct consequence of long-range at-tractive forces between the incident atoms and the surface atoms and has so far beenoverlooked in growth studies. This generic phenomenon leads to a redistribution ofincident ‡ux: the incident particles are directed preferentially towards protrudingterraces, at the cost of ‡ux reduction on lower terraces. In general, steering shiftsthe growth mode from layer-by-layer towards multilayer growth. Calculations re-veal that steering increases with the angle of incidence (de…ned with respect to thenormal) and becomes sizable for MBE growth at angles larger than 50±. Steeringincreases with increasing adatom structure height, i.e., with proceeding deposition:kinetic roughening is auto-catalyzed.

Most of the experiments were performed with the (MBE-) plane of incidenceoriented along the [110]-azimuth. The deposition of 40 ML Cu leads to di¤erentsurface morphologies. At normal incidence fourfold symmetric mounds develop,arranged in a checkerboard-like pattern. When the angle of incidence is increased upto about 50± this pattern disappears, leaving symmetric mounds still intact. At moregrazing incidence asymmetric mounds evolve, with the exception of a limited angularwindow in which ripples develop, oriented perpendicular to the molecular beam. Thefacets of the grown adatom structures are steeper after deposition at more grazingangles of incidence. At 250 K slopes corresponding to {111}-, {113}- and {115}-facets can be obtained. This fact re‡ects the kinetic origin of slope selection. Theobserved facets are steeper for deposition at lower substrate temperatures. Theexperimental …ndings, including the temperature dependence, can be rationalizedin a relatively simple picture involving the action of steering combined with two


length scales set by nucleation on the ‡at surface and on top of adatom islands. Athird less well de…ned length scale is set by the shadow length. We conjecture thatripples oriented perpendicular to the plane of incidence develop when the lengthscales for nucleation and shadowing (depends on the deposition geometry) match.

Steering induced kinetic roughening is generic in growth experiments. Its conse-quences should be anticipated in hetero- as well as in homoepitaxy and are expectedto be more important in highly polarizable deposits and substrates. The evolv-ing morphology bears a de…nite signature of o¤-normal deposition already at polarangles of incidence of about 50±, a quite normal situation in experimental con…gu-rations. This feature should be taken into account whenever comparison betweenexperiments and/or experiment and theory is undertaken.

Chapter 4

Grazing incidence ion sputteringof Cu(001)

4.1 IntroductionThe mostly pursued way to pattern a surface by self-organization on a nanometerscale is via the control of growth processes. A large variety of surface structures canbe obtained by changing the growth parameters. In homoepitaxy it is well knownthat the substrate symmetry, the substrate temperature and the deposition ratedetermine the adatom structure shape, the arrangement of adatom structures, thelateral length scale, the surface roughness and the selection of facets. In additionto the growth temperature and the deposition rate, the experiments in Chap. 3show that the deposition angle drastically in‡uences the evolution of the surfacemorphology as well. This novel observation, which is explained by a phenomenonnamed steering, can also be a powerful tool to structure substrates on a nanometerscale. In heteroepitaxy even more possibilities to pattern a surface are available.The lattice mismatch between substrate and deposition material can for example beused to obtain well ordered nanostructures [67, 132, 133].

The morphology of a surface produced by ion sputtering has received far lessattention than that of a vapor-deposited …lm. Recent experimental studies show,however, that ion sputtering can be a powerful tool to tune the surface morphologyon a nanometer scale as well [134]. Surface structures similar to those obtained after…lm growth have been found after ion sputtering. For example, it has been shownthat sputtering produces square pits on Cu(001) [75, 76], Ag(001) [77] and Ni(001)[78], hexagonal ones on Pt(111) [79, 80, 81, 82], Au(111) [83] and Cu(111) [84], andelongated ones on Si(001) [85]. Thus, the surface structures found after ion sput-tering re‡ect the surface symmetry and look like the inverse of mound structures,which are obtained after homoepitaxial growth. Experimental studies on amorphousmaterials [135], semiconductors [136, 137, 138, 139], and metals [140, 141] show thato¤-normal ion sputtering generates a ripple structure on the surface. Dependingon the angle of incidence µ, the ripples can be oriented either perpendicular (µ

65

66 CHAPTER 4. GRAZING INCIDENCE ION SPUTTERING OF CU(001)

close to the surface normal) or parallel (µ close to grazing incidence) to the planeof incidence. The ripples have a characteristic wave length which is de…ned by thesputtering conditions such as ion energy, ion ‡ux, and substrate temperature and bythe material properties. Both the rotation of the ripple structure as a function of theangle of incidence and the ripple wave length have been theoretically explained interms of a linear instability caused by surface curvature dependent sputtering, whichcompetes with and dominates surface smoothing due to thermal di¤usion [142]. Thecurvature dependent roughening, …rst proposed by Bradley and Harper, results fromthe fact that the energy deposition which causes sputtering is maximized below thesurface. As a result, ions incident on a protrusion are likely to sputter atoms fromthe neighboring slopes, while ions incident on a through are likely to sputter atomsnear the through. Consequently, the erosion is greater in a depression than on anelevation. Under o¤-normal ion sputtering conditions the instability is anisotropic,giving rise to characteristic ripple patterns. Qualitatively, the continuum model de-veloped by Bradley and Harper (BH-model) is appealing. In order to get a betterquantitative agreement between experiment and theory additional terms, includingalso non-linear terms, have been proposed. For example, Mayer et al. [135] used astochastic roughening term together with the roughening instability to account forthe roughening behavior of SiO2 in the low ‡uence regime. Cuerno and Barabási[143, 144] introduced a non-linear term in order to explain the experimentally ob-served scaling laws. Their model is characterized by an initial stage in which ripplesare formed and a subsequent stage in which non-linearities gain importance with acrossover to a rough surface as result. The stabilization of a linear instability by anon-linear term has also been studied by Rost and Krug [145]. As a last exampleof a BH-model modi…cation, Bales et al. [146] discussed the in‡uence of shadowing.Shadowing is described by a non-linear term and gains importance with increas-ing surface roughness. Besides continuum models, thin …lm growth has also beenextensively studied by kinetic Monte Carlo simulations. Comparable simulationsfor the evolution of the surface morphology during ion sputtering are rare. A realkinetic Monte Carlo simulation of the evolution of the surface morphology duringo¤-normal ion sputtering has been performed for the …rst time by Koponen et al.[147]. Their simulations take the local surface topography, shadowing e¤ects andlocal sputtering yield variations due to surface curvature into account, while thesurface di¤usion is described by a simpli…ed model. The result for a 5 keV Ar+-ion sputtered amorphous carbon surface yields a well de…ned ripple structure whichis oriented perpendicular and parallel to the ion beam for µ = 30± and µ = 60±,respectively.

The formation of a ripple structure during ion sputtering of metal surfaces hasbeen extensively studied by the research group of Valbusa [77, 140, 141, 148, 149].Normal incidence sputtering of Cu(110) with 250 K · T · 270 K produces a wellde…ned ripple structure in the [001]-direction, while a second ripple structure in the[110]-direction appears when 350 K · T · 360 K [140]. A similar ripple structurein the [110]-direction is obtained after normal incidence sputtering of Ag(110) at

4.1. INTRODUCTION 67

270 K · T · 320 K [148]. In the case of ion sputtering at normal incidence,the ion beam does not break the surface symmetry and the corresponding rippleinstability does not grow. The twofold symmetric surface morphology observed atnormal incidence can therefore be assigned unambiguously to the e¤ect of surfacedi¤usion. For rectangular lattices like Cu(110) and Ag(110), the intra- and interlayerdi¤usion rates of adatoms and vacancies is di¤erent along the two inequivalent [001]and [110]-directions. The anisotropic surface di¤usion results in a well de…ned ripplestructure, whose orientation depends on the e¤ectiveness of the di¤erent di¤usionprocesses in the [001] and [110]-direction, i.e., on the activation energies and thesubstrate temperature.

For sputtering at o¤-normal angles of incidence, the ion-beam direction in-troduces a symmetry breaking and thus a preferential erosion direction is estab-lished. The resulting ripple structure on Cu(110) is predominantly determined bythe anisotropy in the surface di¤usion processes when µ is smaller than a criticalangle (µc t 60±), while the ripple instability is most important for µ larger than thecritical angle [140, 141]. Therefore, the orientation of the ripple structure is indepen-dent of the azimuthal direction of ion sputtering when µ < µc (the ripples are alwaysin the [001]-direction at 180 K). This is completely di¤erent from that reported onamorphous materials and amorphized semiconductors for which o¤-normal ion sput-tering with µ < µc produces ripples which are always oriented perpendicular to theion beam [142, 143]. For Cu(110), the ripples are elongated in the ion-beam direc-tion when preferential erosion is e¤ective (µ > µc), i.e., the azimuthal direction ofion sputtering determines the orientation of the ripple structure. An ion sputteringinduced ripple structure is not only observed on surfaces with an uniaxial symme-try such as Cu(110) and Ag(110). Ion sputtering of a fourfold symmetric Ag(001)surface at µ = 70± and a relatively low substrate temperature results in a ripplestructure as well [149]. For ion sputtering of Ag(001) at smaller ion beam angles(µ < µc), the preferential erosion is less e¤ective with the formation of square pitsas result [77, 149]. The ion sputtering results on Cu(110) have been explained bya modi…cation of the di¤usive term in the Cuerno and Barabási continuum model[140, 143]. The proposed di¤usion term takes di¤erent activation energies for in-tralayer and interlayer di¤usion in the two inequivalent [001]- and [110]-directionsinto account.

In this chapter, the evolution of the surface morphology of a Cu(001) substrateduring grazing incidence ion sputtering (µ = 80±) will be discussed. During grazingincidence ion sputtering, an extremely well ordered one-dimensional line structureforms in a large temperature range. For all azimuthal sputtering angles, the linesare oriented parallel to the plane of incidence. Remarkably, at elevated substratetemperatures the average separation between lines not only depends on the sputter-ing temperature but on the azimuthal direction of ion sputtering as well. Moreover,at low temperatures where thermal di¤usion of adatoms and vacancies is negligible,the line separation clearly depends on the ion energy.

This chapter is organized as follows: in Sec. 4.2 experimental results on graz-


ing incidence ion sputtering in the [110]-direction are presented. The line structureis analyzed by SPA-LEED and its dependence on the sputtering temperature isdiscussed. In Sec. 4.3 a scenario for the formation of lines is proposed. In thesubsequent section experimental results on grazing incidence ion sputtering in the[100]-direction are presented. The discussion in this section is focused on the sim-ilarities (the formation of parallel lines) and apparent di¤erences (the average lineseparation) between sputtering experiments with ions incident along the [110]- and[100]-direction. Finally, the in‡uence of the ion energy on the evolution of the surfacemorphology at low substrate temperatures is analyzed in Sec. 4.5.

4.2 Ion sputtering in the [110]-direction

From STM measurements it is known that ion sputtering of the Cu(001) surfaceat 300 K generates square vacancy islands with rounded corners for ion beam an-gles between µ = 0± [75] and µ = 45± [76]. The step edges of these equilibriumshaped vacancy islands are oriented along the close-packed <110>-directions, whilethe corners are rounded due to …nite temperature entropic e¤ects. The developmentof square islands is favored by the fact that the mobility of step edge atoms is muchhigher than that of isolated vacancies and adatoms on the (001)-terraces (see Table1.1). The measurements by Ritter et al. [76] show that the isotropic surface dif-fusion on Cu(001) at T = 300 K is large enough to compensate for the ion beaminduced symmetry breaking at µ = 45±, i.e., the surface structures still re‡ect thesquare symmetry of the (001)-surface. While the evolution of the Cu(001) surfacemorphology during o¤-normal ion sputtering is a result of the interplay betweenanisotropic roughening and isotropic surface di¤usion, it can be expected that thein‡uence of the ion beam angle increases with decreasing sputtering temperature.Figure 4.1(a) shows a SPA-LEED contour plot of the specular beam obtained after800 eV Ar+-ion sputtering at µ = 30± with the Cu(001) substrate at 250 K. The ion‡ux © and the sputtering time t were © = 2:7£ 1013 ions cm¡2s¡1 (measured with aFaraday cup) and t = 60 min respectively, while the azimuthal ion beam orientationwas in the [110]-direction, i.e., in the preferred step edge direction. The rotationalsymmetric beam pro…le in Fig. 4.1(a) re‡ects an isotropic radial distribution ofsquare surface structures (comparable to the ones observed with STM [75, 76]).Therefore, the ion sputtering conditions used in this experiment do not break thesurface symmetry. Furthermore, from the broadening of the central (00) beam (nodi¤raction ring) it can be concluded that the separation between the surface struc-tures is less well de…ned compared to the situation after homoepitaxial growth (seeFig. 3.1(b)). The di¤erence between ion sputtering and growth is caused by thecomplex nature of the sputtering process. As described in Sec. 1.4, collisions be-tween incident ions and substrate atoms do not exclusively create monovacanciesbut adatoms and larger vacancy islands as well. The creation of di¤erent surfacedefects results in a broadening of the surface structure separation distribution. Fig-

4.2. ION SPUTTERING IN THE [110]-DIRECTION 69

-10 -5 0 5 10-15

-10

-5

0

5

10

15

-10 -5 0 5 10-15

-10

-5

0

5

10

15a)

k[1-10] (%BZ)

k [110

] (%

BZ

)b)

k[1-10] (%BZ)

k[110] (%

BZ

)

Figure 4.1: SPA-LEED contour plots of the specular beam acquired after 800 eVAr+-ion sputtering of the Cu(001) surface at 30± (a) and 60± (b) with the substrateat 250 K. In both experiments the bombardment time was 60 minutes, while an ion‡ux of 2:7 £ 1013 ions cm¡2s¡1 and 1:6 £ 1013 ions cm¡2s¡1 was used in (a) and(b) respectively. The peak pro…les were obtained at E = 275 eV (Sz = 4:89). Thearrows indicate the ion sputtering direction.

ure 4.1(b) shows a SPA-LEED contour plot of the specular beam obtained afterion sputtering at µ = 60±. Except for the ion beam angle and the ion ‡ux (© =1:6 £ 1013 ions cm¡2s¡1 in this case), the ion sputtering parameters are equal tothose used in the experiment displayed in Fig. 4.1(a). In contrast to ion sputteringat µ = 30±, ion sputtering at µ = 60± destroys the fourfold symmetry of the …lmmorphology. Instead, a twofold symmetric beam pro…le emerges with the plane ofincidence acting as a mirror plane. Although surface symmetry breaking is obviousunder these ion sputtering conditions, the further interpretation of the beam pro…leis less straightforward. The beam pro…le re‡ects a distribution of asymmetric pitswhose illuminated and shadow sides have slightly di¤erent orientations. Further-more, the enhanced intensity in the direction perpendicular to the ion beam seemsto indicate that the ordering of the surface structures is better in this direction thanin the direction parallel to the plane of incidence.

The asymmetry in the surface morphology increases considerably when the Cu(001)surface is sputtered at even more grazing angles of incidence. Figure 4.2 shows aSPA-LEED peak pro…le of the specular beam obtained after 800 eV Ar+-ion sput-tering at µ = 80± with the Cu(001) substrate at 250 K. The ion ‡ux © and thesputtering time t were © = 5£1012 ions cm¡2s¡1 and t = 60 min respectively, whilethe ion beam orientation was in the [110]-direction. The peak pro…le shows twowell developed peaks perpendicular to the plane of incidence of the Ar+-ion beam.Parallel to this plane no distinct di¤raction features are measured. The measured


105

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-5

0

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10

-8 -4 0 4 84.7

4.8

4.9

5.0

k[1-10]

(%BZ)k

[110] (%BZ)

k [110

] (%

BZ)

k[1-10]

(%BZ)

k[1-10]

(%BZ)

S

z

Figure 4.2: SPA-LEED peak pro…le and contour plot of the specular beam acquiredafter 800 eV Ar+-ion sputtering at 80± in the [110]-direction with the Cu(001) sub-strate at 250 K. © = 5 £ 1012 ions cm¡2s¡1 and t = 60 min. The peak pro…le wasobtained at E = 273 eV (Sz = 4:88) and the arrow in the contour plot indicates theion sputtering direction. The left inset shows the position of the …rst (…lled circles)and second order (open circles) separation correlation peaks as a function of Sz.

position of the di¤raction peaks as a function of the perpendicular scattering phaseSz is shown in the left inset. Obviously, the peaks follow vertical rods in reciprocalspace, which are parallel to the rod of the central (00) beam. Therefore, the di¤rac-tion peaks re‡ect ordering in the surface plane and well de…ned facet faces are notpresent on the Cu(001) surface after grazing incidence ion sputtering: the measuredpeaks are …rst order separation correlation instead of facet peaks.

The almost one-dimensional di¤raction pattern must be interpreted as resultingfrom ion sputtering induced parallel lines on the Cu(001) surface. The orientation ofthese lines is parallel to the plane of incidence. The degree of order of the distancesbetween the lines is high, i.e., the line separation distribution function is narrow.This follows from the fact that in addition to the very clear …rst order correlationpeaks, second order di¤raction features are measured as well. These second orderdi¤raction features appear as shoulders in the spot pro…le at twice the distancebetween the …rst order peaks and the central (00) beam (see open circles in the leftinset). The average length of the lines is about 220 Å, which can be concluded from


3.5 4.0 4.5 5.0 5.5 6.0

0

2x105

4x105

6x105

8x105

1x106

4.8 5.0 5.2

inte

nsity

(cps

)

Sz

Sz

I (ar

b. u

nits

)

Figure 4.3: Intensity of the specular Bragg peak as a function of Sz after 800 eVAr+-ion sputtering at 80± with the Cu(001) substrate at 250 K. The inset shows thesame measurement (solid line) together with the specular Bragg intensity measuredafter growth of 0.5 ML Cu at 250 K (dashed line).

the small width of the ordering peaks in the direction of the incident ion beam.The roughness of the Cu(001) surface after ion sputtering at µ = 80± is rela-

tively small. This can be concluded from Bragg peak intensity measurements as afunction of the perpendicular scattering phase Sz. When the kinematic di¤ractionapproximation is applicable, it is possible to calculate the exact surface roughnessfrom the perpendicular scattering phase dependence of the specular Bragg peak in-tensity (see Sec. 2.2.3). In general, the intensity gets more strongly peaked aroundthe in-phase scattering conditions (Sz = n, with n an integer) with increasing sur-face roughness. This is illustrated by the calculations in Fig. 2.3(b). Although thekinematic approximation is not fully applicable when SPA-LEED is used (see Sec.2.4), several experimental studies have shown that it is possible to extract surfaceroughness information from SPA-LEED measurements reasonably well [150, 151].Figure 4.3 shows the measured intensity of the specular Bragg peak as a functionof the perpendicular scattering phase Sz after ion sputtering at µ = 80± with theCu(001) substrate at 250 K. The relatively small width of the peaks around thein-phase scattering conditions is partly due to the …nite probing depth of electronsand multiple scattering e¤ects, i.e., deviations from the kinematic approximation.To get an idea of the actual surface roughness the peak around Sz = 5 is comparedto the same peak measured after growth of 0.5 ML Cu on the Cu(001) substrateat 250 K (see inset). In the latter case the surface morphology consists of two ex-


-5 0 5 -5 0 5 -5 0 5

175 K 200 K

225 K 250 K 300 K

150 K

Inte

nsity

(ar

b. u

nits

)

L*

k

// (%BZ)

Figure 4.4: SPA-LEED line scans through the specular beam acquired after 800 eVAr+-ion sputtering at 80± in the [110]-direction and di¤erent substrate temperatures.© = 5 £ 1012 ions cm¡2s¡1 and t = 60 min. The dashed and solid line scans weremeasured in the plane of incidence and the perpendicular direction respectively, andobtained at E = 280 eV (Sz = 4:94).

posed layers (substrate and …rst monolayer) with exactly equal surface areas. Fromkinematic di¤raction theory it follows that such a layer distribution results in anintensity I s cos(2¼Sz). The measured deviation from this behavior (dashed line inthe inset) shows that multiple scattering e¤ects are important indeed. Compared tothe peak measured after growth of 0.5 ML Cu, the width of the peak around Sz = 5is smaller after ion sputtering at µ = 80±. Therefore, the surface roughness is larger,i.e., more than two layers are exposed. However, the di¤erences in the two mea-surements are small and thus the number of exposed layers is limited after grazingincidence ion sputtering as well. The creation of adatom islands during ion sput-tering, resulting in the exposure of at least three layers, is probably responsible forthe slightly larger surface roughness. The absence of facet peaks in the SPA-LEEDpeak pro…les obtained after ion sputtering also indicates a small surface roughness.Normally, facets form on the Cu(001) substrate during surface roughening and theygive rise to di¤raction peaks which follow a tilted rod in reciprocal space. After ionsputtering no such di¤raction features are measured. From this and the width ofthe peak around Sz = 5 we suppose that the line structures obtained after grazingincidence ion sputtering are only one layer deep, while the (compared to growth)enhanced roughness is attributed to adatom islands, created by sputtering.

A well ordered line structure evolves in a wide temperature range when an ionbeam angle of µ = 80± is used. This is illustrated by the SPA-LEED measurements


0.003 0.004 0.005 0.006 0.007

100

143

T (K)

166333 200250

50

60

80

200L

(Å)

1/T (1/K)

Figure 4.5: Average line separation as a function of the sputtering temperature forAr+-ion sputtering in the [110]-direction. µ = 80±, © = 5 £ 1012 ions cm¡2 s¡1 andt = 60 min.

in Fig. 4.4. The dashed and solid line scans through the specular beam are mea-sured in the plane of incidence and the perpendicular direction respectively and theintensity is normalized to the intensity of the in-phase Bragg peak at Sz = 5. Forsubstrate temperatures between 175 K and 300 K, the spot pro…les show well de-veloped peaks perpendicular to the plane of incidence of the Ar+-ion beam, whileno distinct di¤raction features are measured parallel to this plane. As outlined ear-lier these spot pro…les must be interpreted as resulting from ion sputtering inducedline structures with the lines oriented parallel to the plane of incidence. From theSPA-LEED measurements in Fig. 4.4 and many others, the average line separationas a function of the sputtering temperature was determined. The average line sep-aration L is related to the distance between the …rst order correlation peaks L¤ viaL = (200¢a==)=L¤(%BZ). The temperature dependence ofL is shown in Fig. 4.5. Atsubstrate temperatures above 200 K, the average separation between lines increaseswith increasing temperature due to an enhanced surface di¤usion of mainly monova-cancies. Because of this enhanced di¤usion, nucleation of monovacancies results in alower density of stable vacancy islands. The separation between the lines, which areformed in a later stage of ion sputtering, is related to (but not necessarily the sameas) the distance between the vacancy islands after nucleation. As a consequence,the line separation also increases with increasing sputtering temperature.

In the case of homoepitaxial growth, the slope in the L versus 1=T plot can be


used to determine the activation energy for adatom di¤usion on ‡at terraces. Forseveral reasons it is too ambiguous to extract the activation energy for monovacancydi¤usion from the slope in Fig. 4.5. First of all, not only monovacancies but alsoadatoms and larger vacancy islands are created during ion sputtering. The adatomswill di¤use over the surface until they meet others to form a stable adatom island orthey recombine with vacancies. In both cases, adatoms in‡uence the lateral lengthscale of the growing …lm. The direct creation of larger vacancy islands increases thedensity of stable vacancy islands. As a consequence, the energy tentatively obtainedfrom the slope in Fig. 4.5 deviates considerably from the activation energy formonovacancy di¤usion on ‡at terraces when direct creation of larger vacancy islandsis e¢cient. Another uncertainty is the exact relation between the line separationmeasured after prolonged ion sputtering and the distance between stable vacancyislands immediately after nucleation. Because of the anisotropic growth of vacancyislands (see Sec. 4.3), the coalescence of islands may change the lateral length scaleset during the initial stage of surface erosion. An indication for this is the measureddi¤erence in the average line separation after grazing incidence ion sputtering in the[110]- and [100]-direction (see Sec. 4.4).

At substrate temperatures below 200 K, the average separation between lines isnot temperature dependent anymore (see Fig. 4.5). The constant line separationat these low sputtering temperatures is caused by a negligible thermal di¤usion ofvacancies on the surface. The minimum line separation is about 54 Å (21 atomic dis-tances), which is considerably larger than the minimum separation between adatomislands measured after homoepitaxial growth (t 26 Å [47]). In the case of ho-moepitaxial growth, the minimum separation between adatom islands is not fullyexplained. The low activation energy for atom di¤usion along step edges (t 0:5 Ed)indicates that this di¤usion process may be important for the occurrence of a char-acteristic separation between the islands. It has been shown that the rearrangementof clusters by step edge di¤usion at low temperatures already leads to a characteris-tic distance between islands of a few atomic distances [32]. The separation betweenlines measured after ion sputtering at low temperatures must have a completelydi¤erent origin. It is probably caused by an energy transfer from incident ions tothe Cu(001) surface. This energy transfer results in a locally enhanced “surfacetemperature” exactly around the position of ion impact and enables vacancies todi¤use until the transferred energy is relieved again. The ion impact induced dif-fusion of vacancies dominates the thermal di¤usion of vacancies at low sputteringtemperatures. Therefore, the average line separation must be expected to be ionenergy dependent and substrate temperature independent below about 200 K. Thesputtering experiments described in Sec. 4.5 reveal that this is the case indeed.

The degree of order of the distances between the lines is high for substratetemperatures between 175 K and 300 K (see Fig. 4.4). The fact that a well orderedline structure evolves at a relatively high substrate temperature of 300 K, shows thatfast isotropic di¤usion of vacancies and adatoms together with an e¤ective di¤usionof atoms along step edges is not enough to compensate for the ion beam induced


-10 -5 0 5 10

-10

-5

0

5

10

k[1-10]

(%BZ)

k

[110

] (%

BZ)

Figure 4.6: SPA-LEED contour plot of the specular beam acquired after 800 eVAr+-ion sputtering at 80± in the [110]-direction with the Cu(001) substrate at 100K. © = 5 £ 1012 ions cm¡2 s¡1 and t = 60 min. The contour plot was obtained atE = 275 eV (Sz = 4:89) and the arrow indicates the sputtering direction.

symmetry breaking, i.e., the erosion of the Cu(001) substrate is highly anisotropic.From ion sputtering experiments at µ = 70± and a substrate temperature of 250 Kit follows that preferential sputtering is clearly more e¤ective at an angle of µ = 80±:ion sputtering at µ = 70± and T = 250 K does not result in a well developed linestructure, i.e., the ion beam induced symmetry breaking is largely compensatedby the surface di¤usion processes. The same conclusion about the e¤ectiveness ofpreferential sputtering follows from a comparison with ion sputtering experimentson Ag(001) by Rusponi et al. [149] (the activation energies for the di¤erent di¤usionprocesses on Ag(001) are similar to those on Cu(001) [77]). In their experiments,ion sputtering of the Ag(001) surface at µ = 70± only resulted in parallel rippleswhen T · 250 K.

Below a substrate temperature of 175 K the degree of order of the distancesbetween the lines decreases considerably. This is illustrated by the SPA-LEED linescans measured after ion sputtering at 150 K (see Fig. 4.4). After ion sputtering atthis temperature, less well developed correlation peaks are measured perpendicularto the plane of incidence. At an even lower sputtering temperature of 100 K, nocorrelation peaks but a one-dimensional broadening of the specular beam is mea-sured (see Fig. 4.6). The reduction of lateral order at low sputtering temperaturescan be attributed to an enhanced step edge roughness. On the Cu(001) surfacestraight step edges are obtained in the <110>-directions when atom di¤usion along


step edges is e¤ective: a high mobility of step edge atoms reduces the step edgeroughness caused by the attachment of vacancies and adatoms. On the other hand,rough step edges are obtained during growth or ion sputtering when step edge di¤u-sion is small (low substrate temperatures). The activation energy for atom di¤usionalong step edges in the <110>-directions on the Cu(001) surface is about 0.5 Ed(see Table. 1.1). From this activation energy it follows that the step edge di¤usiondecreases considerably when the substrate temperature is lowered from 175 K to100 K, with an enhanced step edge roughness as result. As the step edges in theion beam direction roughen, both the line width distribution function and the lineseparation distribution function broaden. From di¤raction theory it follows that abroadening of the size and separation distribution functions lead to a broadeningand decrease of the separation correlation peaks in the di¤raction pattern (150 K). Ifthe step edge roughness is even larger (negligible step edge di¤usion), the separationcorrelation between steps is completely lost. In that case, uncorrelated rough stepedges in the direction parallel to the incident ion beam broaden the specular beamin the perpendicular direction. This is observed in the spot pro…le measured afterion sputtering at 100 K (Fig. 4.6).

4.3 Scenario

As outlined in Sec. 1.4, the total interaction of an ion with the surface can beconsidered as a sequence of linear collisions. For very large angles of incidence,the ions interact with a large number of surface atoms. These interactions lead tosmall ion de‡ections and …nally to total ion re‡ection. When the incident ion angleis reduced systematically, a critical angle will be reached at which ion penetrationtrough the uppermost surface layer sets in. For ion beam angles smaller than thiscritical sputtering angle, ion penetration induces a linear cascade of collisions amongthe substrate atoms. Atoms located at the surface may be a¤ected by these collisionsand acquire enough energy to leave to surface. For grazing angles of incidence thesputtering from a linear collision cascade may be dominated by single knock-outsputtering, i.e., the direct removal of a near surface atom. This feature is namedrecoil process. In general, the erosion of the surface is most e¤ective for ion beamangles which are a little smaller than the critical sputtering angle. Assuming arigid lattice the value of the critical sputtering angle depends on several parameterssuch as the ion energy and the mass of the ions and the substrate atoms. Otherimportant parameters are the distance between the surface atoms and thus theazimuthal direction of sputtering. The separation between Cu(001) surface atomsis smallest in the [110]-direction and is a factor

p2 larger in the [100]-direction. As

a consequence, the critical sputtering angle is larger for ion sputtering in the [100]-than in the [110]-direction. For an ideal rigid Cu(001) lattice the critical angle iswell de…ned and smaller than 80± for incident particles with masses and energiesconsidered here. Therefore, ion sputtering at µ = 80± would not erode the surface,

4.3. SCENARIO 77

i.e., the surface would totally re‡ect the incident ions (we neglect the disturbancecaused by pre-existing steps, which is justi…ed by the low concentration). Theexperiments, however, show that the Cu(001) surface is eroded during ion sputteringat µ = 80±. This erosion is made possible by thermal vibrations of surface atoms.These thermal vibrations increase the chance that a surface atom is sputtered. Thecritical sputtering angle for a real vibrating lattice is thus larger than the one fora rigid lattice as well as temperature dependent. In spite of the fact that thermalvibrations enhance the sputtering probability, the erosion of the Cu(001) surface issmall when an ion beam angle of 80± is used.

The evolution of a well ordered line structure during ion sputtering at µ = 80±depends on a number of parameters such as the critical angle, the mobility of va-cancies and step edge atoms (which are determined by the activation energies andthe substrate temperature) and the ion energy. Although adatoms are created onthe surface during ion sputtering, they are disregarded in the following scenario.This simpli…cation seems reasonable because adatoms on the Cu(001) surface aree¤ectively removed by grazing incident ions. As outlined above, sputtering of theCu(001) surface at µ = 80± is dominated by collisions between vibrating surfaceatoms and incident ions. The sputtering yield is small under the sputtering condi-tions used in the erosion experiments. This is indicated by the low sputtering yieldmeasured for normal incidence ion sputtering of Cu(001) and the very grazing angleof incidence. For © = 3:1£1013 ions cm¡2s¡1 and µ = 0±, small He intensity oscilla-tions with a period of 50 seconds were measured at elevated substrate temperatures(800 eV Ar+-ions). The sputtering yield which results from these measurements isabout one atom per incident ion. This agrees reasonably well with sputtering yieldsreported in literature. From the measurements by Girard et al. [75], a sputteringyield of one ion per incident atom can be extracted for 600 eV Ar+-ions, while asputtering yield of about 2 atoms per ion is measured by Snouse et al. [152] andSouthern et al. [153] for ion energies between 500 eV and 1000 eV. As outlined inSec. 1.4, the sputtering yield increases with an increasing ion beam angle up toa maximum between 60± and 80±. Beyond this maximum the sputtering yield de-creases rapidly. Although the exact dependence of the sputtering yield on the angleof incidence is unknown, the quite small sputtering yield at normal incidence andthe very grazing angle of incidence (80±) indicate that the sputtering yield from theCu(001) surface will be very small. Note that the reduction of the sputtering yieldis caused by an enhanced probability for ion re‡ection at grazing angles of incidenceand not necessarily by a reduction of the number of sputtered surface atoms perpenetrating ion. Grazing incidence ion sputtering will mainly create monovacanciesat a relatively low rate. These monovacancies di¤use isotropically over the surfaceuntil they nucleate with other vacancies to form a stable vacancy island. The dif-fusion of vacancies is thermally activated at elevated substrate temperatures andinduced by an energy transfer from incident ions to the surface at low substratetemperatures.

The sputtering probability changes drastically in the neighborhood of a vacancy


islands. As vacancy islands grow, the screening of the illuminated step edge bythe shadow step edge decreases, with an strongly enhanced sputtering probabilityfor the illuminated step edge atoms as result (preferential sputtering). In otherwords, a larger distance between surface atoms increases the e¤ective critical angleand therefore the probability of ion penetration into the substrate. The preferentialsputtering of the illuminated step edge leads to elongation of the vacancy islands inthe direction of the incident ion beam, i.e., rectangular vacancy islands are formed.The di¤erence in sputtering rate between atoms in a terrace and atoms in an illu-minated step edge is even more pronounced because of the di¤erence in incident ion‡ux. The ion ‡ux on an illuminated step edge is larger by almost a factor 6 whenan ion beam angle of 80± is used (purely geometrical factor). Moreover, it is wellknown that the thermal vibrations of step edge atoms are larger than the vibrationsof atoms in a terrace [32]. This also slightly enhances the preferential sputtering ofstep edge atoms.

Because of the grazing angle of incidence, the growth of isotropically distributedvacancy islands is much faster in the direction of the incident ion beam than in theperpendicular direction. This growth anisotropy results in a preferential coalescenceof vacancy islands parallel to the plane of incidence. After coalescence the evolutionof the surface morphology is more complicated. It is however clear that two processescontribute to the smoothing and ordering of the step edges and thus to the formationof a line structure. First of all, the e¤ective di¤usion of atoms along the step edgesin the <110>-directions reduces the step edge roughness. This process and its e¤ecton the degree of order is already discussed in the previous section. A second processthat smooths the step edges in the plane of incidence is preferential sputteringof illuminated kink site atoms. Illuminated kink site atoms are sputtered mucheasier than other step edge atoms because of the smaller e¤ective critical angle andthe locally higher incident ion ‡ux. As a result, the step edge roughness which isintroduced by the attachment of vacancies and adatoms is reduced. The smoothingof the step edges in the direction parallel to the plane of incidence results in theformation of well ordered lines after preferential coalescence in the same direction.Upon further ion sputtering, the number of exposed layers increases slightly (at mosta few layers are eroded simultaneously), while the line structure does not changedramatically. This is comparable to the evolution of the surface morphology duringhomoepitaxial growth (so-called memory e¤ect). At the same time, the di¤usionprocesses on the surface enhance the order of the distances between the lines.

The scenario for the formation of a well ordered line structure on the Cu(001)is illustrated in Fig. 4.7. First vacancies are created at a relatively low rate. Thesevacancies di¤use isotropically until they nucleate to form stable vacancy islands (a).Due to preferential sputtering of the illuminated step edges, the vacancy islandsgrow much faster in the ion beam direction than in the perpendicular direction,i.e., elongated islands are formed (b). Finally, the vacancy islands coalesce in thedirection parallel to the plane of incidence. The roughness of the step edges in theion beam direction is reduced by an e¤ective step edge di¤usion and preferential


Figure 4.7: Illustration of the scenario for the formation of a parallel line structureduring grazing incidence ion sputtering. (a) nucleation of vacancies, (b) elongationof vacancy islands due to preferential sputtering, (c) coalescence of vacancy islandsin the plane of incidence.

sputtering of illuminated kink site atoms. This results in a well ordered line struc-ture parallel to the plane of incidence of the ion beam (c).

4.4 Ion sputtering in the [100]-directionIn Sec. 4.2 the evolution of the Cu(001) surface morphology during ion sputteringat µ = 80± in the [110]-direction was discussed. In this section grazing incidence ionsputtering results in the [100]-direction will be presented. Figure 4.8 shows a SPA-LEED peak pro…le of the specular beam obtained after 800 eV Ar+-ion sputtering inthe [100]-direction. Except for the azimuthal direction, the ion sputtering parame-ters are exactly the same as those used in Fig. 4.2. Again an almost one-dimensionaldi¤raction pattern is measured with clear separation correlation peaks perpendicu-lar to the plane of incidence of the Ar+-ion beam and no distinct di¤raction featuresparallel to this plane. The spot pro…le must be interpreted straightforwardly asresulting from ion sputtering induced lines parallel to the plane of incidence, i.e.,the lines are parallel to the [100]-direction. As a consequence, the step edges of thelines are oriented in an energetically unfavorable direction. From this it follows thatpreferential sputtering in the ion beam direction is much more e¤ective than surfacedi¤usion processes which tend to form equilibrium shaped surface structures withstep edges in the <110>-directions. In other words, the elongation of the vacancyislands in the ion beam direction is not compensated su¢ciently by atom di¤usionalong the step edges. The result that preferential erosion is the dominant processfor µ = 80± is in accordance with measurements by the research group of Valbusa[140, 141]. On Cu(110) they measured a critical angle µc of about 60±. For µ < µcsurface di¤usion processes determine the evolution of the surface morphology, whilefor µ > µc preferential sputtering is the dominant process.


105

0-5

-10105

0-5

-10

-10 -5 0 5 10

-10

-5

0

5

10

k[010] (%BZ)

k[100]

(%BZ)

k

[100

] (%

BZ

)

k[010] (%BZ)

Figure 4.8: SPA-LEED peak pro…le and contour plot of the specular beam acquiredafter 800 eV Ar+-ion sputtering at 80± in the [100]-direction. T = 250 K, © = 5£1012ions cm¡2s¡1 and t = 60 min. The spot pro…le was obtained at E = 275 eV(Sz = 4:89) and the arrow in the contour plot indicates the sputtering direction.

Although a high degree of order of the distances between lines is obtained afterion sputtering in the [100]-direction, a comparison between the spot pro…les in Fig.4.2 and Fig. 4.8 indicates that the degree of order is a little less compared to thesituation after sputtering in the [110]-direction. In Fig. 4.2 clear second order cor-relation features are visible, whereas only faint shoulders around twice the distancebetween the …rst order correlation peaks and the central (00) beam are visible inFig. 4.8. This di¤erence in the degree of order can be attributed to the step edgeroughness. In the case of ion sputtering in the [100]-direction, the step edges arealong the energetically unfavorable [100]-direction. The steps in the [100]-directioncan be considered as [110]-steps with a lot of kinks (on the average one kink per stepedge atom). Due to this large number of kink sites, the incorporation of di¤usingatoms along the step is much easier. Therefore, the atom di¤usion length alongthe step edge is much smaller for steps in the [100]- than in the energetically fa-vorable [110]-direction. Since step edge di¤usion reduces the roughness introducedby the attachment of vacancies and adatoms, a larger step edge roughness is ex-pected for steps in the [100]-direction. As outlined earlier, an enhanced step edgeroughness broadens the line width distribution function as well as the line separation


distribution function. The broadening of both distribution functions leads to lesspronounced separation correlation peaks in the di¤raction pattern.

The temperature dependence of the line separation after ion sputtering in the[100]-direction was also measured. The result is shown in Fig. 4.9 (open circles).For comparison, the earlier presented line separation after ion sputtering in the[110]-direction is shown in this …gure as well (…lled circles). As is the case forion sputtering in the [110]-direction, a well ordered line structure develops duringsputtering in the [100]-direction at sputtering temperatures between 175 K and300 K. For sputtering temperatures below 200 K the line separation is constantand equal for both ion sputtering directions (t 54 Å or 21 atomic distances). Atthese low substrate temperatures the thermal di¤usion of vacancies is negligible andthe average distance between the lines is predominantly determined by the energytransfer from incident ions to the surface. Remarkably, the line separation for thetwo sputtering directions is clearly di¤erent at substrate temperatures above 200K. In this temperature range, the distance between the lines is largest after ionsputtering in the [100]-direction. Moreover, the line separation ratio, L[100]=L[110],increases with increasing substrate temperature. This ratio as a function of thesputtering temperature is shown in Fig. 4.10.

The apparent di¤erence in line separation and its increase with substrate tem-perature is not fully understood. Below a plausible scenario for the evolution ofthe surface morphology during grazing incidence ion sputtering along the [110]-and [100]-direction is presented. First, it is most probable that the origin of thisphenomenon does not lay in the creation nor the di¤usion of vacancies, i.e., thedi¤erence in length scale does not evolve during the initial stages of surface erosion.There are two arguments for this statement. First of all, a di¤erent critical anglefor ion sputtering in the [110]- and [100]-direction does not cause the di¤erence inline separation. This was checked by an ion sputtering experiment at µ = 83± in the[100]-direction. With respect to the critical angle, the result of this experiment canbe compared to grazing incidence ion sputtering at µ = 80± in the [110]-direction:due to the di¤erent incident ion angles the di¤erence in the critical angle, causedby the di¤erent distances between atoms in the two high symmetry directions, iscompensated. The resulting line separation after ion sputtering at µ = 83± in the[100]-direction is still larger (by the same factor) than the line separation after ionsputtering at µ = 80± in the [110]-direction. From this it follows that the possibledi¤erence in sputtering yield does not cause the measured line separation di¤erencein the two high symmetry directions. Moreover, one should have expected the op-posite behavior: a suspected higher sputtering rate for sputtering along [100] shouldlead to smaller distances. A second argument for the statement above is that thedi¤usion of vacancies (and adatoms) on the Cu(001) surface is isotropic. As a con-sequence, the distribution of stable vacancy islands immediately after nucleation isisotropic as well, i.e., there is no di¤erence in the distance between the islands inthe [110]- and [100]-direction. A more probable origin of the di¤erence in line sepa-ration is the elongation and the subsequent coalescence of vacancy islands. This is


0.003 0.004 0.005 0.006 0.007

100

143

T (K)

166333 200250

50

60

80

300L

(Å)

1/T (1/K)

Figure 4.9: Average line separation as a function of the sputtering temperaturefor 800 eV Ar+-ion sputtering in the [100]- (open circles) and [110]-direction (…lledcircles). µ = 80±, © = 5 £ 1012 ions cm¡2 s¡1 and t = 60 min.

150 175 200 225 250 275 3000.9

1.0

1.1

1.2

1.3

1.4

1.5

L [1

00]/L

[110

]

T (K)

Figure 4.10: Line separation ratio L[100]=L[110] as a function of the sputtering tem-perature.


Figure 4.11: Illustration of the lateral length scale during grazing incidence ionsputtering at a low substrate temperature. (a) distance between stable vacancyislands directly after nucleation. (b) distance between elongated vacancy islandsshortly before coalescence.

a complicated process in which several surface di¤usion processes play an importantrole. In the following, probable di¤erences in the coalescence process for the two ionsputtering directions and their in‡uence on the line separation will be discussed.

An isotropic distribution of stable vacancy islands on the Cu(001) surface is takenas starting point. From the arguments outlined above it follows that an isotropicdistribution of vacancy islands with an equal lateral separation is expected to evolveduring ion sputtering in both the [110]- and [100]-direction. Such a surface morphol-ogy is found after the …rst phase in the formation of parallel lines (see Fig. 4.7(a)).In the subsequent phase, preferential sputtering of the illuminated step edges re-sults in an elongation of vacancy islands parallel to the plane of incidence (see Fig.4.7(b)). It is most probable that the di¤erences between ion sputtering in the [110]-and [100]-direction are re‡ected in the evolution of the surface morphology duringthis sputtering phase. At low substrate temperatures (T . 200 K), the anisotropicerosion in the ion beam direction clearly dominates the surface di¤usion processes.Therefore, the elongation of vacancy islands is hardly suppressed, with a large islandaspect ratio as result: after the removal of several tens of a monolayer, the averagewidth of the vacancy islands is still very small for ion sputtering in both the [110]-and [100]-direction. Upon further ion sputtering the islands coalesce in the directionof the incident ion beam and a line structure evolves on the surface. Since the islandaspect ratio is large at the onset of coalescence, lines are formed in between initialnucleation sites as well. This inevitably leads to an average distance between lineswhich is smaller than the distance between vacancy islands directly after nucleation.The change in the lateral length scale during this stage of ion sputtering is illustratedin Fig. 4.11. At low substrate temperatures, the island aspect ratio is expected tobe large for ion sputtering in the [110]- and [100]-direction. As a consequence, the


average line separation is the same after grazing incidence ion sputtering in thesetwo high symmetry directions.

The situation for grazing incidence ion sputtering at elevated temperatures (T &300 K) is di¤erent. In this case, the anisotropic erosion in the ion beam direction doesnot dominate the surface di¤usion processes: the e¤ective di¤usion of atoms alongstep edges opposes the elongation of vacancy islands. Now, the growth of vacancyislands is di¤erent for ion sputtering in the [110]- and [100]-direction. Preferentialsputtering during grazing incidence ion sputtering in the [110]-direction favors thecreation of step edges in this direction. Since the [110]-direction is the energeticallyfavorable step edge direction, the e¤ective step edge di¤usion only tends to mini-mize the total step edge length. This obviously results in only slightly less elongatedvacancy islands on the Cu(001) surface. Preferential sputtering during grazing in-cidence ion sputtering in the [100]-direction on the other hand, creates step edgesin the energetically unfavorable [100]-direction. The e¤ective step edge di¤usionopposes this creation and tends to transform the [100]-step edges into [110]-stepedges. At elevated substrate temperatures this process is likely to be quite e¤ec-tive. Therefore, the growing vacancy islands have a diamond-like shape which isonly slightly elongated in the ion beam direction. In other words, the driving forcebehind island aspect ratio reduction is step edge length minimization and step edgetransformation (locally the [100]-steps transform into [110]-steps) for ion sputteringin the [100]-direction. As a result, the average width of vacancy islands after re-moval of several tens of a monolayer is larger for ion sputtering in the [100]-direction(diamond-like shape) than in the [110]-direction (rectangular shape).

Since the island aspect ratio is still considerably large during ion sputtering in the[110]-direction at elevated substrate temperatures, lines are formed in between initialnucleation sites. The average separation between lines is thus reduced compared tothe separation between vacancy islands directly after nucleation. On the other hand,ion sputtering in the [100]-direction at elevated substrate temperatures results invacancy islands with a smaller aspect ratio. Now, line formation in between initialnucleation sites is strongly reduced and consequently a larger average line separationis expected. The measured increase in the line separation ratio L[100]=L[110] (see Fig.4.10) can be rationalized by a gradual change from the low- to the high sputteringtemperature scenario.

An indication for the above scenario is provided by the SPA-LEED measurementsdisplayed in Fig. 4.2 and Fig. 4.8. The two peak pro…les in these …gures wereacquired after grazing incidence ion sputtering in the [110]- and [100]-direction ata substrate temperature of 250 K, i.e., a temperature at which L[100]=L[110] t 1:3(see Fig. 4.10). Following the above scenario it is expected that the average linelength is larger after grazing incidence ion sputtering in the [110]-direction. Linescans through the ordering peaks in the direction of the incident ion beam revealthat a di¤erent line length is observed indeed. Figure 4.12 shows two line scansthrough the ordering peaks parallel to the plane of incidence and normalized to themaximum ordering peak intensity acquired after ion sputtering in the [110]- (solid


-8 -6 -4 -2 0 2 4 6 80.0

0.2

0.4

0.6

0.8

1.0

n

orm

aliz

ed in

tens

ity

k// (%BZ)

Figure 4.12: SPA-LEED line scans through a …rst order correlation peak in thedirection of the incident ion beam acquired after 800 eV Ar+-ion sputtering at 80± inthe [110]- (solid line) and [100]- direction (dashed line). T = 250 K, © = 5£1012 ionscm¡2s¡1 and t = 60 min. The line scans were obtained at E = 275 eV (Sz = 4:89).

line) and [100]-direction (dashed line). The FWHM of the ordering peaks, which isa measure for the average line length, is clearly smaller after ion sputtering in the[110]-direction, i.e., the average line length is larger. From the ordering peak widthin the ion beam direction the average line length is estimated to be 220 Å and 130 Åafter grazing incidence ion sputtering in the [110]- and [100]-direction respectively.

The scenario seems to be con…rmed by normal incidence ion sputtering exper-iments as well. Figure 4.13 shows line scans through the specular beam acquiredafter normal and grazing incidence sputtering with 800 eV Ar+-ions at 300 K. Theion ‡ux © and the sputtering time t were © = 5£ 1012 ions cm¡2s¡1 and t = 60 minrespectively in all three experiments. Full three-dimensional peak pro…les obtainedafter normal incidence deposition show a homogeneous di¤raction ring around thecentral (00) beam and a fourfold symmetry at larger k==. As outlined in Sec. 2.2.2,such peak pro…les can be interpreted straightforwardly as resulting from an isotropicdistribution of square vacancy islands. The position of the di¤raction ring equalsthe position of the ordering peaks acquired after grazing incidence ion sputtering inthe [100]-direction. The average vacancy island separation after normal incidenceion sputtering is thus comparable with the average line separation after grazing in-cidence ion sputtering in the [100]-direction and clearly larger than the average lineseparation after grazing incidence ion sputtering in the [110]-direction. We notethat the sputtering yield for normal incident ions must be larger than that of graz-ing incident ions, resulting in a larger removal rate. Normally, the lateral length


-6 -4 -2 0 2 4 6

[110]

[100]

inte

nsity

(ar

b. u

nits

)

normal

k// (%BZ)

Figure 4.13: SPA-LEED line scans through the specular beam acquired after 800 eVAr+-ion sputtering at 80± in the [110]- and [100]-direction and after normal incidenceion sputtering. T = 300 K, © = 5 £ 1012 ions cm¡2s¡1 and t = 60 min. The …rsttwo line scans were measured perpendicular to the plane of incidence. All line scanswere obtained at E = 280 eV (Sz = 4:94).

scale on a surface decreases with increasing removal rate. Since the vacancy islandseparation after normal incidence ion sputtering is still considerably larger thanthe average separation between lines after grazing incidence ion sputtering in the[110]-direction, the measurements in Fig. 4.13 seem to indicate a reduction of thelateral length scale during ion sputtering in the [110]-direction, i.e., the separationbetween lines is smaller than the separation between vacancy islands directly afternucleation.

Besides grazing incidence ion sputtering experiments in the [110]- and [100]-direction, some experiments were performed with the ion beam oriented along the[210]-direction, i.e., in between [110] and [100]. Figure 4.14 shows SPA-LEED linescans through the specular beam obtained after 800 eV Ar+-ion sputtering at 80±with the Cu(001) substrate at 250 K. A line structure parallel to the plane of inci-dence evolves during grazing incidence ion sputtering in the [210]-direction as well.


-6 -4 -2 0 2 4 6

[110]

[100]

inte

nsity

(ar

b. u

nits

)

[210]

k// (%BZ)

Figure 4.14: SPA-LEED line scans through the specular beam acquired after 800eV Ar+-ion sputtering at 80± in the [110]-, [100]- and [210]-direction. T = 250K, © = 5 £ 1012 ions cm¡2s¡1 and t = 60 min. The line scans were measuredperpendicular to the plane of incidence and obtained at E = 280 eV (Sz = 4:94).

Figure 4.14 reveals that the average line separation is the same after ion sputteringin the [100]- and [210]-direction. Obviously, the arguments used to explain the lineseparation after ion sputtering in the [100]-direction also hold for the [210]-direction:the creation of energetically unfavorable step edges in the [210]-direction is opposedby an e¢cient step edge di¤usion, leading to slightly elongated vacancy island witha diamond-like shape in the ion beam direction. Because of the small aspect ratio,no lines are formed in between initial nucleation sites and therefore the evolvingline separation is larger than the line separation observed after ion sputtering in the[110]-direction.

For even higher sputtering temperatures it is expected that the acting surfacedi¤usion processes compensate the anisotropy generated by erosion completely. Inthis case, square vacancy islands grow and the coalescence of these islands is not one-dimensional anymore. As a consequence, a fourfold symmetric surface morphologyinstead of a line structure forms.


4.5 Ion impact induced surface di¤usion

From irradiation-assisted thin …lm growth it is well known that simultaneous ionbombardment and …lm growth enhances the surface di¤usion. This phenomenon isused to lower the deposition temperature and to improve the properties of semicon-ductors [155, 156], oxides [157, 158], nitrides [159, 160], and carbides [161]. Althoughion-assisted growth is applied frequently, detailed studies on ion impact induced sur-face di¤usion are sparse. Early papers by Caville et al. [162] and Drechsler et al.[163] indicate that the impact of hydrogen and helium ions on tungsten crystalsenhances the surface di¤usion. More quantitative results on the ion impact inducedexchange of adatoms (Ni, Fe, Co) with substrate atoms (Ir) [164] and the ion im-pact induced surface di¤usion of germanium adatoms on Si(111) [165] have beenpublished more recently.

In this section, the in‡uence of the ion energy on the evolution of the surfacemorphology, i.e., the ion impact induced surface di¤usion during grazing incidenceion sputtering, is discussed. All experiments were performed at µ = 80± with theion beam along the [110]-direction and the substrate at 150 K. The low sputteringtemperature was chosen while the in‡uence of the ion energy is most pronouncedfor temperatures at which thermal surface di¤usion is limited. The measured lineseparation after sputtering with Ar (open circles) and Ne ions (…lled circles) as afunction of the incident ion energy is shown in Fig. 4.15. Obviously, the averageline separation increases with increasing incident ion energy. In principle, the lineseparation enhancement may originate from three ion energy dependent parameters:the ion ‡ux, the sputtering yield and the ion impact induced surface di¤usion.

The experimental results in Fig. 4.15 were obtained with di¤erent incident ion‡uxes (the ion ‡ux increases monotonically with ion energy). At elevated substratetemperatures, a change in the incident ion ‡ux a¤ects the density of stable vacancyislands directly after nucleation and thus the average line separation after prolongedion sputtering. A decrease of the incident ion ‡ux leads to a larger line separationin this case. On the other hand, no ion ‡ux dependence is expected when thermalsurface di¤usion is negligible (low substrate temperature). Now, time dependentprocesses, such as surface di¤usion, are frozen and consequently the surface mor-phology evolves irrespective of the incident ion ‡ux. This conjecture was checkedby 800 eV Ar+-ion sputtering experiments with di¤erent incident ion ‡uxes. Theseexperiments, performed with a constant ion ‡uence and a substrate temperature of150 K, did not show any variation in the average line separation at all when theincident ion ‡ux was changed by more than a factor 30 (from © = 5 £ 1012 ionscm¡2s¡1 to © = 1:5£1011 ions cm¡2s¡1). Moreover, one should expect a decreasinglength scale with increasing ion energy when the ‡ux plays an important role. Sincethe ion ‡ux increases with increasing ion energy, the observed trend in Fig. 4.15 isopposite to that.

The sputtering yield increases with increasing ion energy as well. This results inan enhanced density of di¤using monovacancies and/or the creation of more stable

4.5. ION IMPACT INDUCED SURFACE DIFFUSION 89

0 400 800 1200 1600 2000 240020

40

60

80

100

120

L

(Å

)

Eion

(eV)

Figure 4.15: Ion energy dependence of the line separation for Ar+- (open circles)and Ne+- (…lled circles) ion sputtering in the [110]-direction. µ = 80±, T = 150 Kand t = 60 min.

vacancy islands. As the experiments with di¤erent ion ‡uxes showed, an enhanceddensity of monovacancies does not change the lateral length scale at low substratetemperatures. Moreover, here again the creation of more stable vacancy islands athigher ion energies would decrease the average line separation, which is obviouslynot measured. Therefore, the ion energy dependence of the line separation can notbe explained by a change in the sputtering yield. While the ion energy dependenceof the ion ‡ux and the sputtering yield do not explain the ion energy dependence ofthe average line separation, this dependence is attributed to an ion impact inducedsurface di¤usion.

The ion impact induced surface di¤usion is rationalized as follows: grazing inci-dent ions penetrate into the substrate at the position where a vacancy is created viaknock-out sputtering. In the substrate the ions collide with several surface and/ornear surface atoms. During each of these collisions, energy is transferred to substrateatoms. If more energy is transferred than the binding energy at the lattice sites,primary recoil atoms are created. These recoil atoms can either leave the surface ordistribute the transferred energy via a linear collision cascade. The latter process re-sults in a locally enhanced surface temperature exactly located around the positionof ion impact, i.e., just in the neighborhood of a generated vacancy. As a result, thesurface di¤usion is locally enhanced until the transferred energy is relieved again.During grazing incidence ion sputtering, the surface di¤usion is dominated by thedi¤usion of vacancies. An enhanced vacancy di¤usion results in a smaller density of


stable vacancy islands and thus in a larger line separation. The ion energy depen-dence of the average line separation is in‡uenced by several parameters: the totalamount of transferred energy during collisions between ions and substrate atoms,the lateral size of the region in which the surface temperature is enhanced after ionimpact and the time the surface needs to relieve the transferred energy, i.e., to cooldown again. In the following these three parameters are discussed.

The energy transfer to the surface depends critically on the energy and massof incident ions and the angle of incidence. The average transferred energy andthus the amount of ion impact induced surface di¤usion increases with increasingion energy. Hence, a larger average line separation is obtained after ion sputteringwith high energy ions. The lateral size of the region in which the surface tempera-ture is enhanced after ion impact is quite large. A typical cascade has a radius ofabout 100 Å and computer simulations by Harrison et al. [154] of normal incidentsputtering on Cu(001) by 600 eV Ar+-ions have shown that sputter ejection rarelyoccurs due to collision sequences initiated more than about 5 monolayers below thesurface. The collision cascade will even be more con…ned to the surface for graz-ing incident ion angles. The transferred energy from incident ions to the surfaceis relieved through surface phonons. The cool down time after ion impact dependson the transferred energy. Calculations by Sanders et al. [10] have shown that thetransferred energy by particles of only several eV’s is completely relieved by phononsin a few picoseconds. The transferred energy by noble gas ions of about 1 keV isconsiderably larger. As a consequence, the surface needs a longer time to cool down.During this time, surface di¤usion is possible in the region around the position ofion impact. Although the surface energy is relieved su¢ciently slow to allow forconsiderable surface di¤usion, it is relieved fast enough to prevent that overlappingregions are excited. For example, a ‡ux of © = 5 £ 1012 ions cm¡2s¡1 results in anaverage time of 0.2 seconds between ion impact in the same region of 100 nm2 (aboutthe size of an excited region). The time between vacancy creation and thus energytransfer in the same region will even be longer due to the re‡ection of incident ions.

The exact ion energy and ion mass dependence of the parameters discussed aboveis unknown. Therefore, a complete description of the measured line separationin terms of these parameters is not possible. An additional complication in sucha description is the indistinct relation between line separation and ion sputteringinduced surface di¤usion. The local temperature enhancement of the surface afterion impact does not only activate monovacancy di¤usion. It may for example alsolead to the decay of stable vacancy islands and/or the di¤usion of larger vacancyislands. Each of these surface di¤usion processes in‡uences the density of stablevacancy islands and thus the average line separation after prolonged ion sputtering.In spite of this all, the experiments clearly show that an enhanced energy transfer tothe surface causes the average line separation to increase with increasing ion energy.Moreover, the measurements indicate that the line separation depends linearly onthe incident ion energy within the experimental uncertainty. A linear …t to thedata points obtained after Ne+-ion sputtering is shown in Fig. 4.15 (solid line).

4.5. ION IMPACT INDUCED SURFACE DIFFUSION 91

Interestingly, extrapolation to zero ion energy yields a line separation of about 26Å (10 atomic distances). This separation equals the average separation betweenadatom islands measured after homoepitaxial growth at low substrate temperatures.During MBE of Cu, the kinetic energy of incident atoms is about 0.15 eV. Therefore,the energy transfer from these atoms to the surface is limited, i.e., transient mobilityof deposited atoms can be neglected [10]. The resemblance suggests that the minimalseparation between surface structures is intrinsically the same after ion sputteringand homoepitaxial growth. This minimum is most probably determined by stepedge di¤usion. However, the actual lateral length scale after ion sputtering is largerdue to the energy transfer from incident ions to the Cu(001) surface.

Figure 4.15 reveals no distinct di¤erence in the average line separation aftersputtering with Ar+-ions and Ne+-ions of the same energy (only sputtering withan ion energy of 400 eV results in a slightly di¤erent line separation). The almostequal line separation suggests that the amount of transferred energy scales withthe energy and not with the mass of the incident ions. This can be rationalized asfollows: the incident ions penetrate into the substrate exactly at the position wherethey create a vacancy by a direct knock-out process. In the substrate the ions willloose their energy via collisions with surface or near surface atoms till they come torest (the probability of ion implantation is rather high). As a consequence, Ar+-ionsand Ne+-ions will on the average transfer a similar amount of energy to the Cu(001)substrate. Di¤erences in the line separation are therefore only expected to resultfrom the di¤erence in the lateral size of the collision cascade (the cross-section forNe+-ions is smaller than that of Ar+-ions, resulting in a larger penetration length).

One of the observed di¤erences between sputtering with Ar+-ions and Ne+-ionsis the ion energy above which no well ordered line structure forms at 150 K. ForAr and Ne this energy is about 1000 eV and 2200 eV, respectively. The increaseof the sputtering yield with increasing ion energy and the di¤erence in sputteringyield for Ar+-ions and Ne+-ions might explain this feature. Since more and largervacancy and adatom islands are created with increasing sputtering yield, the amountof surface di¤usion, which is limited in time and space at 150 K (di¤usion is onlypossible for a short time around the position of ion impact), is most probably toosmall to order these surface defects above a certain ion energy and ion mass.

The in‡uence of ion impact induced surface di¤usion is most pronounced at lowsputtering temperatures where thermal di¤usion of vacancies is negligible. In thistemperature range (T . 200 K for 800 eV Ar+-ion sputtering of Cu(001)), the aver-age line separation is ion energy dependent and substrate temperature independent.At somewhat higher sputtering temperatures, both ion impact induced and thermalsurface di¤usion determine the lateral length scale on the Cu(001) surface. Now, theaverage line separation depends on the ion energy and the substrate temperature.When the sputtering temperature is further enhanced, thermal surface di¤usionstarts to dominate ion impact induced surface di¤usion. In this temperature range,the in‡uence of the ion energy on the average line separation is less pronounced andeventually vanishes practically spoken.


4.6 ConclusionsIn this chapter it was shown that grazing incidence ion sputtering is a powerful toolto create one-dimensional structures on a nanometer scale. Ion sputtering of theCu(001) surface at 80± results in parallel lines of only a few layers deep. The orien-tation of these lines is always parallel to the plane of incidence. The degree of orderof the distances between the lines is very high in an extended temperature range.Furthermore, the sputtering temperature can be used to tune the line separationbetween 5 nm and 20 nm. The formation of a well ordered line structure is ratio-nalized by preferential sputtering of illuminated step edge atoms. This preferentialsputtering leads to the elongation and subsequent coalescence of vacancy islandsparallel to the plane of incidence. After the uniaxial coalescence of vacancy islands,the step edge roughness is e¤ectively reduced by step edge di¤usion and preferentialsputtering of illuminated kink site atoms. Besides the sputtering temperature, theaverage line separation depends on the azimuthal direction of the incident ion beamand the incident ion energy. The in‡uence of the azimuthal sputtering directionincreases with increasing substrate temperature. The ion energy dependence of theline separation is most probably caused by an ion impact induced surface di¤usionand it is most visible at low temperatures where thermal surface di¤usion is neg-ligible. Grazing incidence ion sputtering may well be used to structure substrates,which may subsequently act as well ordered templates for controlled preparation ofheteroepitaxial structures.

Chapter 5

Co and Co/Cu multilayer growthon Cu(001)

5.1 IntroductionBecause of its importance for both studying magnetic properties and their poten-tial for magnetic sensor and storage devices, Co/Cu multilayers have been studiedintensively since the discovery of giant magnetoresistance (GMR) [166, 167] andoscillatory magnetic coupling [168, 169, 170] in multilayers. GMR e¤ects can oc-cur when the magnetization in alternating layers is antiparallel, that is when theexchange coupling between the magnetic layers is antiferromagnetic. Under theseconditions the electrical conductivity is less than that of ferromagnetically coupledlayers. For a given ferromagnetic layer thickness antiferromagnetic coupling occursat certain spacer layer thicknesses. Some of the largest GMR e¤ects have been foundin antiferromagnetically coupled Co/Cu multilayers with a Cu spacer layer thicknessof about 9 Å (t 5 ML) [171]. The high GMR in Co/Cu multilayers is mainly dueto a strong spin dependent scattering at the interfaces. As a consequence, the mag-netic properties of these multilayers are very sensitive to growth conditions. A poorde…nition of the Co/Cu interfaces, as a result of interface alloying or insu¢cientlayer-by-layer growth may in‡uence the spin dependent scattering at the interfacesdrastically. Furthermore, interfacial roughness may deteriorate the antiferromag-netic coupling between Co layers and thus reduce the GMR e¤ect. The controlledgrowth of Co and Cu …lms, their properties and perfection are therefore crucial todevice technology based on Co/Cu multilayers.

Smooth multilayers can not be created when growth proceeds close to thermo-dynamic equilibrium. Following the discussion in Sec. 1.3, material A will growsmoothly on substrate B provided the surface free energy of B is larger than thesum of the free energies of the surface A and that of the interface A/B. Accord-ingly, it is impossible to grow smooth …lms of B on A, when A initially wets B. Thesurface free energy of Cu and Co as well as the interface free energy are ¾Cu = 1:9Jm¡2, ¾Co = 2:7 Jm¡2 and ¾CoCu = 0:2 Jm¡2 [172, 173], respectively. Therefore,

93

94 CHAPTER 5. CO AND CO/CU MULTILAYER GROWTH ON CU(001)

multilayer growth of Co on Cu (Volmer-Weber) and layer-by-layer growth of Cuon Co (Frank van der Merwe) is expected from a thermodynamic point of view.Since heteroepitaxial growth proceeds far from thermodynamic equilibrium in mostapplications, the growth mode is predominantly determined by kinetics and quitesmooth multilayers can be obtained.

The growth of Co on Cu(001) is pseudomorphic up to a …lm thickness of atleast 12 ML [174, 175]. In comparison with bulk face-centered cubic (fcc) Co, thetetragonally distorted (fct) lattice is expanded by 1.9 % in the …lm plane and com-pressed by 2.5 % along the surface normal [176]. The strain in the Co …lm, which isinduced by the tetragonal distortion, increases with increasing …lm thickness. Thiscontinues up to a critical thickness (¸ 12 ML), where the onset of the formationof mis…t dislocations reduces the tetragonal distortion. Since the layer thicknessin Co/Cu multilayers is typically 5-7 ML, mis…t dislocations do not deteriorate theantiferromagnetic coupling in these systems.

In this chapter the initial growth of Co and Co/Cu multilayers on Cu(001) isdiscussed. Special emphasize is laid on the temperature dependence of interface andsurface roughness caused by a limited interlayer mass transport and/or surface alloy-ing. The surface morphology was characterized by He atom scattering experimentsduring- and SPA-LEED measurements after growth. The SPA-LEED measurementswere performed at a low substrate temperature of 100 K in order to suppress unde-sired surface di¤usion after deposition. In Sec. 5.2 the temperature and depositionrate dependence of Co/Cu(001) growth is discussed. The nucleation process duringthe initial stages of growth is described in Sec. 5.3. For Co/Cu(001), the temper-ature dependence of the adatom islands density clearly deviates from conventionalnucleation theory. This deviation is explained and a scenario for the evolution of thesurface morphology during growth at elevated substrate temperatures is given. InSec. 5.4 the annealing of thin Co …lms on Cu(001) is discussed. The chemical com-position of the outermost surface layer during annealing was studied by CO-titrationexperiments. Finally, the temperature dependence of Co/Cu multilayer growth onCu(001) is described in Sec. 5.5. A remarkable symmetry in the growth of Co onCu and of Cu on Co is discussed there.

5.2 Growth modes in Co/Cu(001)He atom scattering was used to monitor Co growth modes on Cu(001). The normal-ized specularly re‡ected He intensity, I=I0, under anti-phase di¤raction conditions(Sz = 2:5) was recorded for di¤erent substrate temperatures as a function of depo-sition time. The Co was deposited by electron beam induced sublimation from aCo wire at a deposition rate of about 0.33 ML/minute. The results for T ¸ 270K are shown in Fig. 5.1. Except for the …rst layer, persistent oscillations are ob-served, indicative of well developed layer-by-layer growth. After the deposition of2 ML of Co, the growth proceeds via nucleation and growth of two-dimensional

5.2. GROWTH MODES IN CO/CU(001) 95

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Figure 5.1: Temperature dependence of the normalized specular anti-phase He scat-tering intensity, I=I0, measured during deposition of Co on Cu(001) at T ¸ 270K.

adatom islands. Co atoms deposited on top of these islands can descend from theisland so that no stable nuclei are formed on top of the islands before they havecoalesced to form an almost completely …lled two-dimensional layer. To get a morequantitative idea of the surface roughness, the height distribution of the depositedlayers was calculated from the He intensity maxima. Assuming an ideal instrumentand a three-level system these calculations yield that the growing layer is …lled toa fraction (3 +

pI=I0)=4, e.g., at an intensity maximum of I=I0 = 0:7 the growing

layer is …lled to 96%.The average height of the specular He peak during one period increases from the

…rst to the fourth Co layer. The course of the He intensity during deposition is notonly an indication for the vertical roughness of the growing …lm but for the laterallength scale as well. Since di¤use scattering from step edges reduces the He intensity,small adatom islands reduce the intensity more than larger ones. Furthermore, theanti-phase He intensity is enhanced for surfaces with a large lateral length scale


due to the limited transfer width of the instrument (t 450 Å). Consequently, theincrease of the average height of the specular He peak provides indirect evidencefor an enhanced lateral length scale of the growing …lm, i.e., the average separationbetween adatom structures increases with the number of Co layers. This can berationalized by an enhanced mobility of Co atoms on Co layers compared to themobility of Co atoms on the Cu(001) surface. The monotonic increase of the averageheight of the specular He peak up to the fourth layer does not necessarily imply thatthe mobility of Co atoms increases monotonically with the layer height as well. Adi¤erent adatom mobility in the …rst and subsequent layers is enough to explain theobserved behavior. The gradual increase of the average adatom island separationis then caused by the a so-called memory e¤ect, i.e., the lateral length scale inthe growing layer is in‡uenced by that of the previous one. Direct evidence for anenhanced mobility of Co atoms on Co layers compared to the mobility of Co atomson the Cu(001) surface is provided by SPA-LEED measurements described later (seeFig. 5.3).

The implication of an enhanced mobility of Co atoms on Co layers will be dis-cussed now. As the step-edge barrier is …nite, a Co atom on top of an island willeventually succeed in descending from the island if it hits the island boundary oftenenough before it is captured by new Co atoms landing on top of the island. Since theCo atom mobility on top of Co islands is enhanced compared to the mobility duringthe initial stages of growth, the visiting frequency at the island edge is larger than inhomoepitaxial growth. As a consequence, the enhanced mobility of Co atoms on Colayers contributes to improved layer-by-layer growth. Several growth experimentshave shown that improved layer-by-layer growth can be achieved by a reductionof the adatom mobility during nucleation (low growth temperature), followed byan enhancement of the adatom mobility during further monolayer growth (elevatedgrowth temperature) [124, 177, 178, 179, 180, 181]. This growth manipulation pro-cedure is known as “the concept of two mobilities”. The measurements in Fig. 5.1reveal that the two mobility concept is an intrinsic feature of Co growth on Cu(001).Besides the adatom mobility e¤ect, a change of the step-edge barrier height with the…lm thickness might in‡uence the interlayer mass transport as well. A decreasingstep-edge barrier would obviously give rise to improved layer-by-layer growth. Thein‡uence of the step-edge barrier height is discussed later.

An exception to well developed layer-by-layer growth is observed during thedeposition of the …rst monolayer. The amplitude of the …rst intensity oscillation issmaller than the amplitudes of subsequent oscillations. After deposition of 1 ML Coat 273 K, no maximum in the He intensity is measured at all. The small intensity oreven complete absence of the …rst maximum indicates an ine¢cient interlayer masstransport from the second to the …rst layer. As a result, nucleation of Co atoms ontop of adatom islands sets in early, i.e., far before coalescence. This initial growthmode in Co/Cu(001), often called bilayer growth, has been measured by di¤erentdi¤raction techniques [182, 183, 184, 185] and scanning tunneling microscopy (STM)[186, 187, 188]. An example: a second layer fractional coverage of about 10 % was


measured with STM after deposition of 1 ML Co at 330 K [187, 188] (note thatbilayer growth indicates early nucleation in the second layer instead of growth oftwo monolayer high adatom islands). The He atom scattering experiments in Fig.5.1 compare well with these STM measurements. From the …rst intensity maximumat 323 K, a second layer fractional coverage of 12 % is estimated.

Since the measurements in Fig. 5.1 reveal an enhanced mobility of Co atoms onCo layers, the initial deviation from layer-by-layer growth is most probably causedby a substantial step-edge barrier, i.e., Co atoms deposited on top of a monolayerhigh adatom island can easily reach the island edge but their probability to descendfrom the island is small due to a re‡ecting step-edge barrier. With increasing growthtemperature there is a transition from bilayer to layer-by-layer growth of the …rstmonolayer. The absence of a …rst maximum at 273 K indicates bilayer growth,whereas the high …rst monolayer maximum at 370 K reveals clear layer-by-layergrowth (the maximum second layer fractional coverage is estimated to be 6 % afterdeposition of 1 ML in this case).

At substrate temperatures below 250 K, the Co/Cu(001) growth mode starts todeviate from layer-by-layer growth. The measured specularly re‡ected He intensityat three di¤erent growth temperatures as a function of deposition time are shownin Fig. 5.2. Although less intense, He intensity oscillations are still observed at 249K. The reduced amplitude of the oscillations reveals a less well developed layer-by-layer growth. As is the case for growth at 273 K, no …rst monolayer oscillation isobserved, i.e., the …rst monolayer of Co grows in a bilayer fashion at 249 K as well.

The Co uptake curve measured at a substrate temperature of 207 K is completelydi¤erent. The average He intensity increases monotonically with the Co …lm thick-ness up to at least 11 ML. Besides the average He intensity, the amplitude of thegrowth oscillations increases with the amount of deposited Co as well. The courseof the di¤raction intensity indicates once more that the mobility of Co atoms on Colayers is enhanced compared to the mobility of Co atoms on the Cu(001) surface.In addition, the He intensity measurement reveals a transition from multilayer tolayer-by-layer growth with increasing …lm thickness. To further characterize thegrowth of Co on Cu(001) at 207 K, SPA-LEED peak pro…les were analyzed after de-position. Characteristic cuts through specular peak pro…les, measured on Co …lmswith di¤erent thicknesses, are shown in Fig. 5.3(a). Full three-dimensional peakpro…les show a homogeneous di¤raction ring around the specular Bragg peak and afourfold symmetry at larger k==. As outlined in Sec. 2.2.2, such peak pro…les canbe interpreted straightforwardly as resulting from an isotropic distribution of squareadatom islands. From the diameter of the di¤raction ring, i.e., the distance betweenthe side peaks in Fig. 5.3(a), the average island separation was determined usingL = (200 ¢ a==)=L¤(%BZ). The result is shown in Fig. 5.3(b).

The average island separation amounts to 26 Å (10 atoms) after deposition of0.5 ML Co. Since the thermal di¤usion of Co atoms on the Cu(001) surface isnegligible at 207 K (see next section), this island separation is a minimum. In otherwords, lowering the growth temperature does not decrease the distance between


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Figure 5.2: Temperature dependence of the specular anti-phase He scattering inten-sity measured during deposition of Co on Cu(001) at T · 250 K.


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Figure 5.3: (a) SPA-LEED line scans through the specular beam acquired afterCo/Cu(001) growth at 207 K. The line scans were obtained at E = 180 eV (Sz =3:74). (b) The average adatom island separation at 207 K as a function of Cocoverage.

islands any further. The minimum island separation in the …rst Co layer equals theminimum island separation in Cu/Cu(001) under the same deposition conditions.In the homoepitaxial case, the minimum island separation is most probably dueto an e¤ective di¤usion of atoms along island edges [32]. The equal Cu and Coadatom island separation after growth at low substrate temperatures suggests thatthe activation energy for Co step edge di¤usion is lower than the activation energyfor the di¤usion of Co adatoms on a Cu(001) terrace. The measurements in Fig.5.3 directly reveal an increasing average island separation with increasing Co …lmthickness. The thermal di¤usion of Co atoms on Co layers is thus not negligibleat 207 K. The average island separation after deposition of 6.5 ML Co at 207 K isabout twice the island separation measured after growth of 0.5 ML Co. From thecourse of the specular He intensity in Fig. 5.2 and the island separation in Fig.5.3(b) it is expected that the average island separation at 207 K increases even moreupon further growth.

An exponentially decaying specularly re‡ected He intensity without any oscilla-tions is measured during Co growth at 120 K, indicative for multilayer growth. Atthis low substrate temperature, the probability for a Co adatom to be re‡ected at astep edge, following its attempt to descend, is large. This results in the nucleationof Co atoms on top of islands far before coalescence. The low He intensity aftergrowth of about 1 ML (I=I0 t 0) indicates that thermal di¤usion of Co atoms onCo layers is also negligible at 120 K.


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Figure 5.4: Deposition rate dependence of the specular anti-phase He scatteringintensity measured during deposition of Co on Cu(001) at T = 298 K.

The deposition rate dependence of initial Co growth on Cu(001) was investigatedat a growth temperature of 298 K. Figure 5.4 exhibits three Co uptake curves mea-sured during deposition at di¤erent rates as a function of Co coverage. Evidently,the …rst monolayer intensity maximum increases with decreasing deposition rate,indicating improved layer-by-layer growth. Growth of Co at a deposition rate of0.33 ML/minute results in a very faint …rst oscillation, whereas a pronounced …rstintensity maximum is measured during growth at 0.025 ML/minute. The observedtransition from bilayer to improved layer-by-layer growth of the …rst monolayer is inaccordance with theoretical considerations [7, 17, 123]. Nucleation theory predictsthat the critical coverage, de…ned as the coverage at which nucleation on top ofislands sets in, increases with increasing temperature and decreasing deposition rate[7]. Hence, a shift towards better de…ned layer-by-layer growth can be expectedwhen the deposition rate is lowered at a …xed substrate temperature.

Remarkably, the height of the second intensity maxima does not depend on thedeposition rate. This intriguing observation reveals a second layer …lling of about 94% after deposition of 2 ML Co for all three deposition rates. Obviously, this is not inaccordance with theoretical considerations. The observed growth behavior is mostprobably due to a mechanism not included in theory: thermally activated exchangeof Co adatoms and Cu substrate atoms. This atomic exchange process in‡uencesthe chemical composition of the …rst layer. Since an enhanced number of Co atomswill exchange sites with Cu substrate atoms when the deposition rate is lowered,the amount of Cu in the …rst layer increases with decreasing deposition rate. Thedeposition rate dependent chemical composition of the …rst layer may explain the

5.3. SURFACE ALLOYING DURING CO/CU(001) GROWTH 101

remarkable growth behavior of the second layer. The atomic exchange process isdiscussed in the next section. Since the deposition rate dependence of the secondintensity maxima is not in accordance with theoretical consideration, the qualitativeagreement between the …rst intensity maximum and theory might be fortuitous.

The uptake curves in Fig. 5.4 exhibit another peculiarity. The initial slope atµ = 0 ML is about the same for all three measurements. Normally, the initial slopeis predominantly determined by di¤use scattering from adatoms and small adatomislands. From nucleation theory it follows that the average adatom island size at agiven coverage increases with decreasing deposition rate. Since the step density onthe surface and thus the di¤use scattering from these steps decreases with increasingisland sizes, the initial slope is expected to be less steep when the deposition rate islowered. The deviation from this behavior in Fig. 5.4 is attributed to site exchangeof Co adatoms and Cu substrate atoms. The atomic exchange process leads toembedding of Co atoms in the substrate, resulting in enhanced di¤use scattering.As has been shown amply, the He-re‡ectivity is extremely sensitive to structuraldisorder (see Ref. [20] and references therein).

5.3 Surface alloying during Co/Cu(001) growth

The temperature dependence of the surface morphology at sub-monolayer Co de-posits is discussed in this section. The measured average island separation afterdeposition of 0.5 ML Co on Cu(001) as a function of the substrate temperaturewas determined from SPA-LEED peak pro…les obtained after growth. The result isplotted in Fig. 5.5. Up to about 220 K, the average island separation is constant. Inthis temperature range the thermal di¤usion of Co adatoms on the Cu(001) surfaceis negligible. As discussed earlier, the minimum island separation is probably dueto active step edge di¤usion at these low substrate temperatures. In between 220K and 320 K, the separation between islands increases with increasing substratetemperature as expected from conventional nucleation theory (see Sec. 1.2.3). Athigher temperatures, however, a sudden drop from 80 Å at 323 K to 40 Å at 365 K ismeasured. This anomaly is accompanied by a broadening of the side peaks in SPA-LEED peak pro…les, resulting in the relatively large error bars in Fig. 5.5 at highertemperatures. The strong decrease of the average island separation around 330 Kis attributed to a thermally activated exchange of Co adatoms and Cu substrateatoms. At elevated temperatures, deposited Co atoms have a non-zero probabilityof exchanging sites with Cu substrate atoms. As a consequence, embedding of Coatoms in the outermost surface layer takes place and a surface alloy is formed. Theembedded Co atoms act as additional nucleation sites and/or reduce the adatommobility, giving rise to an enhanced island density on the surface. While the cre-ation of new nucleation sites continues as long as the exchange process is active, asaturation density of small adatom islands is not reached rapidly above 330 K. Thecreation of nucleation sites by atomic exchange was treated theoretically by mean-


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Figure 5.5: Average adatom island separation after deposition of 0.5 ML Co onCu(001) as a function of growth temperature.

…eld rate equations and Monte-Carlo simulations [189, 190, 191]. Simulations byMeyer et al. [190] indeed show that the island density as a function of the substratetemperature has a minimum at a temperature which can be related to the onset ofsigni…cant atomic exchange. A decreasing island separation with increasing growthtemperature was also observed in Ni/Ag(111) [190].

The exchange of Co adatoms with atoms of the Cu(001) surface during ini-tial growth was observed in several STM investigations [187, 188, 192]. The STMmeasurements reveal that site exchange results in a broadening of the island sizedistribution. During the deposition of sub-monolayer amounts of Co at elevatedsubstrate temperatures (T ¸ 330 K), small and large islands with di¤erent chemicalcomposition grow simultaneously. The large number of small islands consist of aCo/Cu mixture, whereas the small number of large islands consist of Cu with someCo around the edges. The broad island size distribution and size-dependent com-positional heterogeneity of adatom islands can be explained as follows. Initially, Coatoms on Cu(001) only explore the Cu terrace sites. At su¢ciently high probabilitiesfor site exchange, Co atoms inevitably are embedded into the terrace releasing Cuatoms onto the terrace. Thus during the …rst stages of growth the di¤using adatomsare predominantly Cu atoms. Because of a relatively low activation energy for di¤u-sion of Cu atoms on Cu(001) (t 0:40 eV see Table 1.1), a low density of fast growingadatom islands emerges. At more advanced stages of growth the situation becomesmore complicated. First the embedded Co atoms cause an enhanced heterogeneity,

5.4. ANNEALING OF THIN CO FILMS 103

which hampers the di¤usion of Cu adatoms and gives rise to prolonged nucleation.This results in an enhanced probability for deposited Co atoms to either encounterdi¤using Cu atoms to form a nucleus or explore the edges of the large Cu islands be-fore …nding suitable terrace sites to get embedded. Having met suitable in-plane Cubinding partners, there probably is no need for further embedding. Consequently,this train of events leads to small, mixed Co/Cu adatom islands and larger adatomislands with a quite homogeneous Cu centre and Co-rich edges.

The turnover from initial bilayer growth of Co on Cu(001) at low temperatures tolayer-by-layer growth at higher temperatures (see Fig. 5.1) as well as the combineddecrease of the average island separation and the change of the island size distribu-tion occurs around 330 K. The reason for layer-by-layer growth of the …rst monolayermay therefore be related to a thermally activated exchange of Co adatoms and Cusubstrate atoms. The possible causality between layer-by-layer growth and site ex-change can be rationalized by a compositional dependent step-edge barrier height.At low growth temperatures where atomic exchange is negligible, adatom islandsconsist mainly of Co. The complete absence of a …rst monolayer intensity oscillationbelow 273 K indicates that downward di¤usion of Co atoms from monolayer highCo adatom islands is hindered by a substantial step-edge barrier, resulting in bilayergrowth. At elevated growth temperatures on the other hand, small islands and partsof the edges of large islands consist of mixed Co/Cu areas. A possible explanationfor the strong increase of the …rst monolayer intensity oscillation with increasinggrowth temperature, i.e., the transition from bilayer to layer-by-layer growth, is en-hanced interlayer mass transport due to a smaller step-edge barrier for intermixedstep edges compared to that for monolayer high Co step edges on Cu(001).

5.4 Annealing of thin Co …lms

The di¤erence in surface free energy for Co and Cu causes thin Co …lms to bethermodynamically instable on Cu(001). Annealing a Co …lm will therefore changethe surface morphology into a lower free energy con…guration. In principle thereare two possible con…gurations. First, annealing may result in three-dimensionalclustering of the Co …lm. Second, free energy reduction is possible by segregation ofCu to the surface of the Co …lm. Several STM investigations suggest that the latterprocess actually occurs during annealing above 450 K [188, 193, 194, 195]. At thesehigh substrate temperatures, Cu segregates through …lm defects leaving behind deepsquare pits in the substrate. After annealing the outermost surface layer consists ofCu areas and intermixed Co/Cu areas with a c(2x2) periodicity [188, 195].

In this section results on the evolution of the surface morphology during an-nealing are reported. He atom scattering was used to monitor the morphologicalchanges as a function of substrate temperature. Additional information concern-ing the chemical composition of the outermost surface layer was obtained by COtitration experiments. Here, the lack of direct information on the chemical compo-


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Figure 5.6: CO titration curve of a 2 ML thick Co …lm on Cu(001) at 298 K. The…lm was grown at 298 K and subsequently exposed to a CO partial pressure of1:2 ¢ 10¡8 mbar.

sition of the exposed layer is compensated by making use of the di¤erent a¢nityof CO to Co and Cu, respectively. Thermal desorption spectra for CO adsorbedon Co/Cu(001) show a main peak at about 400 K, whereas on Cu(001) CO is onlystable at temperatures below 170 K [196]. The large di¤erence in desorption tem-perature together with the He atom scattering sensitivity for adsorbates enables achemical characterization of the outermost surface layer.

Figure 5.6 shows a CO titration curve for a 2 ML thick Co …lm, normalized tothe specularly re‡ected He intensity after deposition. Cobalt was deposited at 298K and immediately after growth the surface was exposed to a CO partial pressureof 1:2 ¢ 10¡8 mbar at the same temperature. On the freshly deposited Co …lma CO saturation coverage is established rapidly, resulting in an extremely low Here‡ectivity. Since it is well known that a complete monolayer of CO acts as an almostperfect di¤use scatterer [20], the saturation of the titration curve is interpreted asthe formation of a complete CO layer on the Co …lm, i.e., the exposed layer containsno measurable amount of Cu. The measured saturation exposure of about 1.5 Lcompares well with CO adsorption experiments reported in literature [196].

The thermal behavior of a 2 ML thick Co …lm on Cu(001) was studied in twoways. First, the specularly re‡ected He intensity from the clean Co …lm was recordedduring annealing up to 523 K. Such a measurement reveals changes of the surfacemorphology as a function of annealing temperature. After annealing at 523 K for 15minutes the substrate was cooled slowly to 137 K. Second, the same annealing exper-iment was performed in a CO background pressure of 1:2 ¢ 10¡8 mbar. CO titration

5.4. ANNEALING OF THIN CO FILMS 105

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Figure 5.7: Temperature dependence of the specular anti-phase He scattering in-tensity measured during annealing of a 2 ML thick Co …lm on Cu(001). The openand …lled circles were measured in UHV (p · 10¡10 mbar) and in a CO backgroundpressure of 1:2 ¢10¡8 mbar, respectively. The heating/cooling rate was 0.33 K/s andthe annealing time at 523 K was 15 minutes.

curves which are obtained in this way contain information about the temperaturedependence of the morphology and the chemical composition of the outermost sur-face layer. The results for a heating/cooling rate of 0.33 K/s are shown in Fig.5.7. Both curves are normalized to the specularly re‡ected He intensity after Codeposition at room temperature.

Initially, the re‡ected He intensity from the clean Co …lm (open circles) decreaseswith increasing substrate temperature due to Debye-Waller e¤ects. At about 370K, the intensity suddenly increases slightly, forming a small local maximum. Thesmall intensity increase is attributed to the desorption of a small amount of COfrom the Co surface. We note that an CO coverage of only 0.3% would su¢ce tobe consistent with this explanation. Immediately after the small intensity increase,the He intensity decreases dramatically around 400 K, indicating severe rougheningof the surface morphology. This surface roughening is caused by segregation of Cuatoms to the Co surface. The segregation process, which is driven by the di¤erencein surface free energy of Cu and Co, results in a surface morphology with deep squarepits [188, 193]. The He intensity saturates after annealing at 523 for 15 minutes,indicating no further changes of the surface morphology. During subsequent coolingthe He intensity increases monotonically due to Debye-Waller e¤ects.

The CO titration experiment starts with a CO saturation coverage on a 2 MLthick Co …lm. The initial intensity in the CO titration curve (…lled circles) is there-


fore almost zero. Upon heating, desorption of CO around 370 K is almost instanta-neously followed by the morphological changes referred to above. After complete COdesorption the CO titration curve merges into the curve for the clean Co …lm withinexperimental error. The course of the CO titration curve during cooling containsinformation about the chemical composition of the outermost surface layer after an-nealing at 523 for 15 minutes. Above 400 K, CO neither adsorbs on Cu nor on Coand therefore the He intensity increases monotonically (Debye-Waller e¤ects). Inbetween 170 K and 400 K, however, CO adsorbs on Co only. As a consequence, thedi¤erent course of the two intensity curves below 400 K can be attributed completelyto the presence of a small amount of Co in the exposed surface layer. The slightintensity decrease in between 230 K and 400 K indicates that Co surface atoms arenot nucleated in large Co clusters. A cluster size dependent CO adsorption temper-ature may explain the monotonic decrease of the specularly re‡ected He intensity,i.e., CO adsorption becomes possible on an increasing number of small Co clustersduring cooling. At about 230 K, the He intensity decreases more dramatically. Asthe temperature is still to high for the adsorption of CO on Cu, the sudden intensitydecrease is most probably due to CO adsorption on intermixed Co/Cu areas witha c(2x2) periodicity [188, 195]. Finally, around 170 K the He intensity decreases toits extremely low initial value. This can be attributed to the adsorption of CO onCu areas, resulting in the formation of a two-dimensional layer of carbon monoxideon the annealed …lm.

The experiments in Fig. 5.7 suggest that Cu starts to segregate to the Co surfaceat a temperature of 400 K. A similar annealing experiment on a 4 ML thick Co …lmreveals a segregation temperature of 450 K. Hence, interdi¤usion depends on the Co…lm thickness for small thicknesses. The measured segregation temperature for a 2ML thick Co …lm is about 70 K higher than the onset temperature for signi…cantexchange of Co adatoms and Cu substrate atoms during growth.

5.5 Co/Cu multilayer growth on Cu(001)

To characterize the temperature dependence of the interface morphology in Co/Cumultilayers, the specularly re‡ected He intensity was measured during multilayergrowth at various substrate temperatures. In these multilayer growth experimentsCo and Cu were deposited at a deposition rate of about 0.25 ML/minute. Figure5.8 exhibits three uptake curves measured during intermittent deposition of 4 MLof Co and 4 ML of Cu. The arrows indicate interruption of the deposition of Co andinitiation of that of Cu and vice versa. The appearance of persistent oscillations inthe uptake curves reveals well developed layer-by-layer growth resulting in smoothmultilayers. The most striking feature, however, is the reduced …rst intensity os-cillation for growth of Cu on fct Co(001), i.e., the …rst amplitude after initiatinggrowth of another material is smaller for Co on Cu and for Cu on Co. The courseof the He intensity shows that a deep …rst minimum and a slightly less deep second

5.5. CO/CU MULTILAYER GROWTH ON CU(001) 107

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Figure 5.8: Temperature dependence of the normalized specular anti-phase He scat-tering intensity measured during deposition of Co/Cu multilayers on Cu(001).


minimum for the initial growth of Co on Cu is followed by a sequence of a shallow…rst minimum and a deeper second minimum for the initial growth of Cu on Co.This feature is repeated during the deposition of the next periods of the Co/Cumultilayer. Furthermore, the temperature dependence of the …rst monolayer inten-sity oscillations is comparable: the …rst intensity oscillation is negligible at 270 Kand considerable at 370 K. The symmetry of growth fronts in Co/Cu multilayers onCu(001), which was observed independent of the Co and/or Cu layer thickness, isremarkable. From a thermodynamic point of view one should expect that it is im-possible to grow smooth …lms of Cu on Co, when Co initially wets Cu. The growthsymmetry must therefore be rationalized in terms of kinetic growth considerations.

The physics behind the observed growth symmetry is not clear cut and belowonly a few possible ingredients for an explanation are given. After initiation of Cugrowth, a relatively high …rst minimum is observed, indicative for a larger adatommobility of Cu on Co compared to that of Co on Cu. The mobility of Cu adatoms onCo layers is, however, smaller than the mobility of Cu adatoms on Cu layers. Thiscan be concluded from the increase of the average height of the specular He peak upto a …lm thickness of 3 ML. As a result, Cu atoms deposited on top of monolayerhigh adatom islands can easily reach the island edge. The reduced …rst intensitymaximum is therefore most probably caused by a substantial step-edge barrier formonolayer high Cu steps on Co …lms.

The specularly re‡ected He intensity after growth of a 16 ML thick Co/Cu mul-tilayer is larger than the intensity measured after growth of 16 ML Cu or Co onCu(001) at the same temperature. This di¤erence is most pronounced at rela-tively low substrate temperatures. Well developed layer-by-layer growth, resultingin smooth multilayers, can be explained by a varying mobility of adatoms with thelayer height. The mobility of atoms in the second and subsequent layers of a newmaterial is considerably larger than in the …rst layer. The low adatom mobility inthe …rst layer leads to a high density of small adatom islands. Atoms landing ontop of these islands are much more mobile and will therefore visit the island edgefrequently. As a consequence, the probability for atoms to descend from the islandsis high, giving rise to well developed layer-by-layer growth.

The measurements in Fig. 5.8 reveal smooth Co/Cu multilayer growth in a largetemperature range, i.e., the interface roughness caused by reduced interlayer masstransport is limited. On the other hand, Co/Cu interfaces and possibly Cu/Cointerfaces roughen considerably due to signi…cant surface alloying above 330 K. Theinterfaces, which are crucial for antiferromagnetic coupling between Co layers andGMR e¤ects, are therefore de…ned best for growth temperatures below 330 K.

5.6 ConclusionsThe evolution of the surface morphology during growth of Co on Cu(001) dependscritically on surface alloying. Thermally activated exchange of Co adatoms and Cu

5.6. CONCLUSIONS 109

substrate atoms becomes signi…cant around 330 K. The exchange process in‡uencesthe growth of the …rst monolayer considerably. Since embedded Co atoms act asadditional nucleation sites and/or reduce the adatom mobility, a sudden increase ofthe adatom island density is observed around 330 K. Furthermore, exchange of Coadatoms and Cu substrate atoms leads to a broad island size distribution. Except forthe …rst monolayer, well de…ned layer-by-layer growth is observed for Co on Cu(001)and Cu on fct Co(001). The initial bilayer growth at low temperatures is attributedto a substantial step-edge barrier for Co atoms on monolayer high Co islands andCu atoms on monolayer high Cu islands. The improved layer-by-layer growth of the…rst monolayer of Co above 330 K suggests a lower step-edge barrier for intermixedstep edges. Segregation of Cu atoms to the Co …lm surface occurs during annealingof thin Co …lms above 400 K. The onset temperature for Cu segregation through a2 ML thick Co …lm is about 70 K higher than the onset temperature for signi…cantatomic exchange during growth. After prolonged annealing at 523 K, the outermostsurface layer consists of small Co clusters, intermixed Co/Cu areas, and pure Cuareas.

Chapter 6

Magnetic anisotropy inCo/Cu(001)

6.1 IntroductionMagnetic anisotropies in ultrathin …lms are inherently related to the structureand morphology of the …lms. In thin …lms of fourfold symmetry, such as Coon Cu(001), the cubic in-plane magnetic anisotropy is a natural consequence ofthe crystal symmetry. Additional uniaxial in-plane magnetic anisotropies havebeen measured in …lms grown on stepped surfaces [197, 198, 199]. The micromag-netic origin of this uniaxial anisotropy is currently believed to arise from missingbonds (Néel-type anisotropy) [199, 200, 201, 202] and/or strain (magnetoelasticanisotropy) [200, 203, 204] at surface steps. Since a long time it is known thatgrazing incidence deposition also induces an uniaxial in-plane magnetic anisotropy[205, 206, 207]. This magnetic anisotropy is connected to an uniaxial surface mor-phology which develops during grazing incidence growth. Growth induced uniaxialmagnetic anisotropy in Co …lms (150 Å - 1000 Å) has been studied as a function ofthe deposition angle recently [208]. Furthermore, an uniaxial easy axis perpendic-ular to the deposition direction has been measured in ultrathin magnetic …lms (20Å) [209].

In Chap. 3 it was shown that the evolution of surface morphology during molec-ular beam epitaxy (MBE) of Cu/Cu(001) is drastically in‡uenced by the depositiongeometry. Already in the submonolayer regime distinct di¤erences in the surfacemorphology, developing at normal and grazing incidence deposition, were observed.During grazing incidence deposition rectangular adatom islands instead of squareones develop. Upon further growth, fourfold symmetric mound structures form atnormal incidence deposition, whereas asymmetric mounds or ripples evolve at graz-ing incidence deposition. In other words, grazing incidence deposition destroys thefourfold symmetry of the Cu(001) surface. Instead, a twofold symmetric surfacemorphology develops with the plane of incidence acting as a mirror plane. Sim-ilar symmetry breaking e¤ects should be expected for grazing incidence MBE of

111

112 CHAPTER 6. MAGNETIC ANISOTROPY IN CO/CU(001)

Co/Cu(001). As the magnetic anisotropies in ultrathin …lms are inherently relatedto the …lm morphology, the magnetic anisotropy in thin Co …lms on Cu(001) willbe in‡uenced by the deposition geometry as well.

This chapter is devoted to a systematic study of the in‡uence of the depositionangle on the magnetic anisotropy in ultrathin magnetic …lms grown by molecularbeam epitaxy (MBE). Particularly, the investigations were focused on a few MLthick Co …lms on Cu(001) grown with incident angles up to 80± with respect tothe surface normal. Grazing incidence deposition of Co in‡uences the magneticanisotropy indeed: an additional in-plane uniaxial magnetic anisotropy, with theeasy axis oriented perpendicular to the plane of incidence, was measured. Theuniaxial anisotropy in ultrathin Co …lms is directly related to the formation ofelongated adatom structures during growth. The evolution of an uniaxial surfacemorphology can be rationalized by steering (see Chap. 3), i.e., the focussing ofincident atom ‡ux onto the top of growing adatom structures. Steering and as aresult the uniaxial magnetic anisotropy increase with increasing deposition angle.

During most Co growth experiments, the temperature of the Cu(001) substratewas kept at 250 K, which is far below the onset temperature for signi…cant atomicexchange during growth (see Chap. 5). Cobalt was deposited by electron beaminduced sublimation from a Co-wire at a rate of about 0.1 ML/minute. The deposi-tion rate was calibrated by He atom scattering before growth and checked by Augerelectron spectroscopy after …lm analysis. The azimuthal direction of deposition wasalong the closed packed [110]-direction, which is a preferential step edge directionand an easy magnetization direction in Co/Cu(001). Immediately after depositionthe temperature of the Cu substrate was quenched rapidly in order to suppress un-desired surface di¤usion. The Co …lms were analyzed by MOKE and SPA-LEED.The MOKE measurements were performed with the setup described in Sec. 2.6 (seeFig. 2.11). The azimuthal rotation of the sample made it possible to apply magnetic…elds at angles varying from -45± to 35± with respect to the Co deposition direction.

6.2 Deposition angle dependence

As a …rst result it is demonstrated that Co …lms grown with a grazing angle of in-cidence exhibit a large in-plane uniaxial magnetic anisotropy. Magnetization loopswere measured at 175 K with the external magnetic …eld applied along di¤erentazimuthal directions. Figure 6.1 shows the result for a 4 ML thick Co …lm, grownwith a deposition angle of 80± with respect to the surface normal. Parallel to thedeposition direction a hard axis magnetization curve with two loops at large ex-ternal …eld is measured (Fig. 6.1(a)). At the …elds where the loops appear themagnetization switches from the uniaxial easy direction (perpendicular to the de-position direction) into the uniaxial hard direction (parallel to the deposition direc-tion) or vice versa. Around zero …eld a linear behavior is found indicating coherentmagnetization rotation away from the uniaxial easy direction. Comparable hard

6.2. DEPOSITION ANGLE DEPENDENCE 113

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-50

0

50

100

c)

b)

a)

Hs

Hs2

Hs1

K

err

ellip

ticity

(µra

d)

H (Oe)

Figure 6.1: In-plane hysteresis curves for a 4 ML thick Co …lm on Cu(001), grownat 250 K with a grazing angle of 80± with respect to the surface normal. Themagnetization curves were obtained at 175 K. The applied magnetic …eld is 0±, 20±and 45± away from [110], i.e., away from the deposition direction, in (a), (b) and(c), respectively.


Figure 6.2: The deposition, anisotropy and applied …eld geometry used in the ex-periments. Grazing incidence deposition in the [110]-direction results in an uniaxialmagnetic anisotropy with the easy axis perpendicular to the plane of incidence.Longitudinal MOKE measurements are possible with the applied …eld at an anglebetween 45± and 125± with respect to the [110]-direction (shaded region).

axis hysteresis curves have been obtained for Co …lms grown on stepped Cu(001)[201, 202, 203, 210, 211, 212, 213]. When the external …eld is applied at an angle of45± with respect to the deposition direction, i.e., along a cubic hard magnetizationaxis and in between the uniaxial hard and easy magnetization axes, the hysteresisloop exhibits a high squareness with an extremely sharp switching behavior (Fig.6.1(c)). The measured curve is, however, not saturated indicating magnetizationreversal along the uniaxial easy axis. The small slope beyond the switching …eldsshows that a large magnetic anisotropy hinders magnetization rotation in the di-rection parallel to the applied …eld. This magnetic anisotropy consists mainly of acomponent with fourfold symmetry, i.e., the cubic magnetic anisotropy in grazingincidence deposited Co …lms is still larger than the uniaxial magnetic anisotropy(see below).

Hysteresis loops with three irreversible transitions were measured on grazing in-cidence deposited Co …lms when the external …eld was applied at an angle between10± and 30± from the deposition direction (see Fig. 6.1(b)). The remarkable hystere-sis loop reveals that the magnetization reversal process is mediated by the nucleationand propagation of domain walls and not by coherent rotation. In systems with acubic anisotropy and an uniaxial anisotropy that is aligned along one of the cubic


easy axes, one and two jump hysteresis curves can be measured when magnetizationreversal proceeds via coherent rotation. The observed switching behavior in thesesystems depends on the direction of the applied …eld and the ratio of the uniaxial tocubic anisotropy constants. When magnetic switching proceeds via the nucleationand propagation of domain walls, one, two and three jump hysteresis curves can beobtained [214]. Three jump switching between four stable domain con…gurations,each aligned close to one of the cubic easy axis, involves one jump of 180±. In caseof domain wall propagation this jump can be made when the total energy gain iscomparable to the energy cost in propagating domain walls. Magnetic domain struc-tures, several hundred microns large, have been measured in ultrathin Co …lms onCu(001) [215, 216].

A phenomenological energy model will be used to explain the results in moredetail and to determine the anisotropy constants for Co …lms grown with di¤erentgrazing angles of incidence. In this model it is assumed that magnetic switchingproceeds via the nucleation and propagation of domain walls, such that switchingoccurs at applied …elds smaller than the anisotropy …eld. Furthermore it is assumedthat domain wall propagation as opposed to domain wall nucleation is the limitingfactor in the magnetic switching process.

Figure 6.2 illustrates the deposition, anisotropy and applied …eld geometry usedin the model. In the growth experiments, the azimuthal direction of depositionwas along the closed packed [110]-direction. The MOKE measurements in Fig. 6.1show that in addition to a cubic anisotropy (K4) an uniaxial anisotropy (Ku) hasto be considered. The orientation of the uniaxial easy axis is perpendicular to thedeposition direction. Hence, the free energy density E(Á) for grazing incidencedeposited Co …lms on Cu(001) can be written as:

E(Á) = Ku sin2(Á) +K4

4cos2(2Á) ¡MH cos(Á¡ µ); (6.1)

where Á is the angle of magnetization with respect to the [110]-direction and µ isthe angle between the applied …eld and the [110]-direction. The cubic anisotropyK4 has been found to be negative for Co …lms on Cu(001) [215, 216, 217, 218], i.e.,the cubic easy directions are parallel and perpendicular to the deposition direction.

First, the magnetic switching behavior with the applied …eld parallel to thedeposition direction is discussed. Fig. 6.1(a) shows that a transition from a singledomain state in the [110]-direction to a state in the direction perpendicular to thedeposition direction occurs at a large negative …eld. The exact domain structureafter switching can not be extracted from the measured hysteresis curve. It ispossible that a small deviation in the applied …eld direction causes a single domainstructure with the magnetization aligned along the [110]-direction when µ is a littleless than 90± or with the magnetization aligned along the [110]-direction when µ isa little more than 90±. However, the error in the applied …eld direction is small (§3±). It is therefore more probably that both magnetization orientations are presentafter the …rst magnetic switching. Such coexistence of two domain orientations


perpendicular to the applied …eld has been observed in iron …lms on Ag(001) [219].After switching an almost linear increase of the Kerr ellipticity is observed. Theexternal …eld which rotates the magnetization in the domains slightly towards the[110]-direction causes this behavior. The magnetization rotation can be describedby the equation of motion, dE(Á)=dÁ = 0. For small rotation angles the slope ofthe hysteresis curve depends linearly on 1/(Ku ¡K4) [220, 221]:

IkH

=MsIs

2(Ku ¡K4); (6.2)

where Ik=H is the slope of the hysteresis curve around zero …eld,Ms is the saturationmagnetization and Is is the saturation Kerr ellipticity. In the case of larger rotationangles a slight deviation from the linear behavior can be observed. This makes aseparation of Ku and K4 possible when (Ku ¡ K4) is small [221]. In the grazingincidence deposited Co …lms separation was not possible and only the quantity(Ku ¡K4) could be determined from the slope around zero …eld.

As outlined earlier, switching of the magnetization between the four cubic easydirections is mediated by domain wall propagation. Therefore the equation of mo-tion can not be used to describe the observed irreversible transitions. Domainpropagation makes reorientation of the magnetization in Co …lms possible whenthe energy gain is comparable to the energy density cost for propagating domainwalls. The magnetic switching behavior in thin …lms with an in-plane cubic anduniaxial magnetic anisotropy can be described by a simple phenomenological model[213, 214, 219]. In this model the activation energy involved in establishing a do-main wall is ignored and only the energy needed to move a domain wall is considered.This energy, interpreted as the maximum height of the defect energy barriers whichthe domain walls encounter when they propagate, is indicated by ²90± and ²180± for90± and 180± domain walls, respectively. The free energy density for single domainstates with the magnetization oriented along one of the four easy cubic axis can befound by substituting the relevant values of Á into Eq. 6.1:

E[110] =Ku +K4

4+HM sin(µ) (6.3)

E[110] =K4

4+HM cos(µ) (6.4)

E[110] =K4

4¡HM cos(µ) (6.5)

E[110] =Ku +K4

4¡HM sin(µ) (6.6)

Based on the MOKE measurements shown in Fig. 6.1, in which only small rotationsaway from the cubic easy axes are observed, the good approximation is made thatthe irreversible transitions observed in the hysteresis curves are caused by magneticswitching between the <110>-directions. Such a transition occurs when the energydensity advantage ¢E in doing so is equal to the energy density cost in propagating


a domain wall of the relevant type. For an applied …eld in the deposition direction([110]-direction) two irreversible jumps are measured. First, a transition from [110]to [110] or [110] occurs when ¢E = Ku +HMs = ²90±. Therefore, the switching…eld Hs1 is given by: Hs1 = (¡Ku + ²90±)=Ms. In the same way it can be derivedthat a second transition from [110] or [110] to [110] occurs at a switching …eldHs2 = (Ku + ²90±)=Ms. Measuring the two coercive …elds makes it possible todetermine the uniaxial anisotropy: Ku = (Hs2 ¡Hs1)Ms=2 = HsMs. Note that theshift …eld Hs does not equal the uniaxial anisotropy …eldHu, which is usually de…nedas Hu = 2Ku=Ms. The uniaxial anisotropy …eld is given by: Hu = 2Hs instead. Therelation for Ku together with the earlier derived relation for (Ku ¡K4) will be usedto determine the anisotropy constants for Co …lms grown with a di¤erent grazingangle of incidence. The shift …eld has been used to analyze the magnetic anisotropyin di¤erent uniaxial growth systems [201, 202, 210, 211, 222, 223, 224, 225, 226].

With the help of the phenomenological energy model outlined above, the threejump switching behavior can be explained. For the 4 ML thick Co …lm depositedat a grazing angle of 80±, three irreversible transitions were observed for applied…elds with 60± < µ < 80± and 100± < µ < 120±. For applied …elds with 60± < µ <80±, the …rst transition from [110] to [110] is followed by a transition from [110] to[110]. This second transition is mediated by the propagation of 180± domain walls.Finally, a third transition occurs from [110] to [110]. From a comparison of theenergy densities in the four cubic easy directions it can be derived that a three jumpswitching route is energetically favored when [214]:

45± < µ < tan¡1(Ku=²90±); (6.7)180± ¡ tan¡1(Ku=²90±) < µ < 135±: (6.8)

In this derivation it was assumed that ²180± = 2²90±, which is normally observed incubic systems. From the model it follows that three jump switching can only beobserved when Ku > ²90± (follows from Eq. 6.7). Furthermore, the range of applied…eld angles at which three jump switching is observed increases with increasinguniaxial anisotropy.

The single jump hysteresis curve measured with the applied …eld 45± away fromthe deposition direction (Fig. 6.1(c)), i.e., with the applied …eld along a cubic hardaxis, reveals switching of the magnetization from [110] to [110] and vice versa. Ro-tation of the magnetization towards the direction of the applied …eld after switchingis hindered by a large magnetic anisotropy, i.e., 300 Oe is not enough to saturate themagnetization. Theoretically, the remanent Kerr ellipticity should be smaller thanthe saturation Kerr ellipticity by a factor 1/

p2. From the saturation Kerr intensity

measured in Fig. 6.1(a) and the remanent Kerr intensity measured in Fig. 6.1(c) itfollows that this is indeed the case within experimental error.

Figure 6.3 shows four MOKE measurements on a 5 ML thick Co …lm, grownwith a deposition angle of 50± with respect to the surface normal. Again, a hardmagnetization curve with two irreversible transitions is measured when the external…eld is applied parallel to the deposition direction (Fig. 6.3(a)). Though smaller


-300 -150 0 150 300

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-50

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50

100

H (Oe)

K

err

ellip

ticity

(µr

ad)

b)

c) d)

a)

Figure 6.3: In-plane hysteresis curves for a 5 ML thick Co …lm on Cu(001), grownat 250 K with a grazing angle of 50± with respect to the surface normal. Themagnetization curves were obtained at 175 K. The applied magnetic …eld is 0±, 20±,30± and 45± away from [110], i.e., away from the deposition direction, in (a), (b), (c)and (d), respectively.

than in Fig. 6.1, the shift …eld and thus the uniaxial anisotropy is still substantial.Besides this di¤erence in shift …eld, a di¤erence in remanent Kerr ellipticity is alsomeasured. For the Co …lm grown with a deposition angle of 50± the remanentKerr intensity is non-zero. The measured remanent intensity may be caused byan error in the applied …eld direction: when the external …eld is applied slightlyaway from the deposition direction ([110]-direction) a small remanent Kerr intensitywould be measured. While zero remanence was not observed in any of the numerousKerr measurements (…elds have been applied at di¤erent angles close to the [110]-direction), it is more probable that the non-zero remanent Kerr ellipticity is causedby a multidomain pattern. In this case, the orientation of the magnetization atzero applied …eld is along the [110] and/or the [110]-direction in most domains.Some domains at zero applied …eld are, however, oriented along [110] and [110] for


increasing and decreasing magnetic …eld strength respectively. This obviously givesrise to a non–zero remanent Kerr intensity.

For applied …elds between 10± and 30± away from the deposition direction, threeirreversible transitions are measured (see Fig. 6.3(b) and (c)). From the longitudinalKerr measurements with the applied …eld in di¤erent azimuthal directions it is clearthat the remanent Kerr ellipticity increases with an increasing angle between theapplied …eld and the deposition direction. Furthermore, the applied …elds at whichthe …rst and the third magnetic switching occur increases with increasing anglebetween the applied …eld and the deposition direction. These two e¤ects as well asthe decreasing coercive …eld of the inner hysteresis loop are easily explained by theexperimental geometry and the phenomenological model described earlier. Again, asquare hysteresis loop is obtained when the …eld is applied at an angle of 45± withrespect to the deposition direction (Fig. 6.3(d)).

The deposition angle dependence of the in-plane magnetic anisotropy in Co …lmson Cu(001) was studied for incident atom beam angles between 0± and 80±. Figure6.4 shows an overview of MOKE results on 5 ML thick Co …lms grown at 250 K. Themeasurements are performed at 175 K with the applied magnetic …eld parallel to thedeposition direction. After normal incidence deposition only a small deviation froma square hysteresis loop is measured. The observed deviation is caused by a smalluniaxial anisotropy, which probably originates from residual steps on the Cu(001)surface. As mentioned earlier, a magnetic step anisotropy has been measured forthin magnetic layers on stepped surfaces [197, 198, 199] and has been consideredfrom a theoretical point of view as well [199, 200, 227].

Deposition at an angle of 10± with respect to the surface normal results alreadyin a non-normal growth induced uniaxial magnetic anisotropy. In this case, twoirreversible transitions are measured: …rst a transition from the uniaxial hard to theuniaxial easy and than from the uniaxial easy to the uniaxial hard magnetizationaxis occurs. The uniaxial anisotropy of this Co …lm is too small to align all spinsin the direction perpendicular to the deposition direction. The measured remanentKerr intensity is therefore non-zero. As one can see in Fig. 6.4 the shift …eld and thusthe uniaxial anisotropy increases monotonically with increasing deposition angle upto 80±.

Following the phenomenological model the uniaxial anisotropy is given by: Ku =HsMs, whereMs is the saturation magnetization of the Co …lm. Neutron di¤ractionexperiments have shown that the magnetic moment of Co in Co/Cu(001) is the sameas in bulk Co [228]. Therefore, the fcc-Co bulk saturation magnetization (Ms = 1422Oe) is used here. From the hysteresis curves in Fig. 6.4 and from many others, theuniaxial magnetic anisotropy was determined as a function of the deposition angle(see Fig. 6.5). Each data point in Fig. 6.5 is the result of an averaging over at leastthree independently measured hysteresis curves. Obviously, the uniaxial magneticanisotropy increases with increasing deposition angle. For a 5 ML thick Co …lm theuniaxial anisotropy is the largest when the Co atoms are deposited at an angle of80± with respect to the surface normal.


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80°

40° 50°

60° 70°

10° 20°

30°

0°

K

err e

llipt

icity

(µra

d)

H (Oe)

Figure 6.4: In-plane hysteresis curves for 5 ML thick Co …lms on Cu(001), grown at250 K with di¤erent deposition angles. The magnetization curves were obtained at175 K with the applied magnetic …eld parallel to the deposition direction.

Figure 6.6 shows the quantity (Ku ¡K4) as a function of the deposition angle.Qualitatively, the angular dependence of (Ku ¡ K4) is equal to that of Ku: themagnetic anisotropy (Ku¡K4) increases up to 80±. Even though we averaged over atleast three hysteresis curves, the small slope around zero …eld still results in relativelylarge error bars. Below a deposition angle of 40± an accurate determination of(Ku¡K4) was not possible. At these deposition angles the remanent Kerr ellipticityis relatively large. This indicates that domains parallel and perpendicular to thedeposition direction are both present after the …rst magnetic switching. The slopeof the hysteresis curve around zero …eld can therefore be the result of two e¤ects:coherent magnetization rotation and a change of the population of domains by thepropagation of the domain walls.

In the inset of Fig. 6.6 the cubic magnetic anisotropy K4 is plotted. Despite


0 20 40 60 800

1

2

3

4

5

K

u (10

5 erg

/cm

3 )


Figure 6.5: Uniaxial magnetic anisotropy Ku in 5 ML thick Co …lms on Cu(001) asa function of deposition angle.

0 20 40 60 80

8

10

12

14

0 20 40 60 80-14

-12

-10

-8

-6

(K

u-K4)

(105 e

rg/c

m3 )


dep. angle (°)

K4

(105 e

rg/c

m3 )

Figure 6.6: Total magnetic anisotropy Ku ¡K4 in 5 ML thick Co …lms on Cu(001)as a function of deposition angle. The inset shows the cubic anisotropy constant K4.


relatively large error bars the conclusion can be drawn that the absolute value ofthe cubic anisotropy increases slightly with increasing deposition angle as well. Ex-trapolation leads to a cubic anisotropy constant of -7.0§1.5£105 erg/cm3 for a 5ML thick Co …lm grown at normal incidence. This anisotropy constant is close tothe values for 4 ML and 10 ML thick Co …lms on Cu(001) found by Heinrich et. al.[218] (-7.2£105 erg/cm3 and -9.2£105 erg/cm3, respectively). The result is, however,inconsistent with the total cubic anisotropy constant for 5 ML Co/Cu(001) reportedin Ref. [217] (-2.1£105 erg/cm3). Since magnetic anisotropy in Co/Cu(001) changesrapidly around a …lm thickness of 4 ML [221], the discrepancy with the latter exper-imental result might be due to small di¤erences in the thickness calibration. To getan idea of the strength of the uniaxial anisotropy in grazing incidence deposited Co…lms the values of Ku are compared with the uniaxial anisotropy constant found inCo/Cu(1 1 13) [204]. In a Brillouin Light Scattering study the total uniaxial mag-netic anisotropy constant for a 5 ML thick Co …lm on Cu(1 1 13) was determinedto be 4.0£105 erg/cm3 (interpolation of Fig. 3 in Ref. [204]). A comparable uni-axial magnetic anisotropy constant in 5 ML thick Co …lms on Cu(001), depositedat 80± and with the substrate at 250 K, was measured (see Fig. 6.5). After lessgrazing incidence deposition the growth induced uniaxial anisotropy in Co/Cu(001)is smaller.

6.3 Surface morphology

The measured uniaxial anisotropy in Co …lms can be explained by the formation ofan uniaxial surface morphology during grazing incidence growth. SPA-LEED peakpro…les measured after Co growth and magnetic characterization reveal distinctdi¤erences between normal and grazing incidence deposited Co …lms. Figure 6.7shows a pro…le of the specular beam obtained after normal incidence deposition of 5ML Co on Cu(001) at 250 K. With increasing wavevector k== parallel to the surface,two di¤erent patterns evolve. Close to the central (00) beam a circular ring isobserved, whereas at larger k== the pattern clearly shows a fourfold symmetry. Thechange from circular to fourfold symmetry indicates that the di¤raction patternconsists of two di¤erent contributions, one from a quite narrow structure separationdistribution, the other from the structure size distribution. The adatom structureseparation contribution shows up as a circular …rst order di¤raction ring at low k==.The homogeneous ring intensity measured after normal incidence Co growth re‡ectsan isotropic radial distribution of square adatom structures. From the position ofthe ring in reciprocal space, the average adatom structure separation L is estimatedto be L t 80 Å. Since adatom structure sizes are necessarily smaller than theirseparation, the island size contribution to the di¤raction pattern shows up at largerk==. Consequently, the fourfold symmetry at larger wavevector in Fig. 6.7 is dueto Fraunhofer di¤raction and re‡ects the square shape of adatom structures whichare distributed with their edges oriented along the close-packed <110>-directions.

6.3. SURFACE MORPHOLOGY 123

105

0-5

-10

-10-5

05

10

-10 -5 0 5 10

-10

-5

0

5

10

-10 -5 0 5 10

k[1-10]

(%BZ)k

[110] (%BZ)

k[1-10]

(%BZ)

k [110

] (%

BZ)

k// (%BZ)

inte

nsity

(arb

. uni

ts)

Figure 6.7: SPA-LEED peak pro…le of the specular beam acquired after normalincidence growth of 5 ML Co on Cu(001) at 250 K. The peak pro…le was obtainedat E = 290 eV (Sz = 4:75). The left inset shows two line scans through the specularbeam in the [110]- (solid line) and [1-10]-direction (dashed line).

The development of square adatom structures during normal incidence Co growthon Cu(001) is in accordance with scanning tunneling measurements [186, 188]. Thenear-equilibrium structure shape is due to a su¢ciently large atom mobility alongstep edges.

In contrast to normal incidence deposition, molecular beam epitaxy at grazingincidence destroys the fourfold symmetry of the …lm morphology. Instead, a twofoldsymmetry emerges with the plane of incidence acting as a mirror plane. Figure6.8 shows a pro…le of the specular beam obtained after deposition of 5 ML Co onCu(001) at a grazing angle of 80± with the substrate at 250 K. In this case, thering around the central (00) beam is not homogeneous but exhibits a well developedtwofold symmetry. As outlined in Chap. 3, such a di¤raction ring with maximain the deposition direction can be interpreted as resulting from an isotropic radialdistribution of elongated adatom structures in contrast to square ones growingat normal incidence deposition. The elongated adatom structures are oriented withtheir longest side perpendicular to the plane of incidence of the Co atom beam. Thedi¤raction intensity of the two maxima in the di¤raction ring clearly di¤er fromeach other in Fig. 6.8. This asymmetry was not observed after deposition of 0.5


105

0-5

-10

-10-5

05

10

-10 -5 0 5 10

-10

-5

0

5

10

-10 -5 0 5 10

k[1-10]

(%BZ)

k[110]

(%BZ)

k[1-10] (%BZ)

k

[110

] (%

BZ

)

k// (%BZ)

inte

nsity

(arb

. uni

ts)

Figure 6.8: SPA-LEED peak pro…le of the specular beam acquired after depositionof 5 ML Co at 80± with the Cu(001) substrate at 250 K. The peak pro…le wasobtained at E = 290 eV (Sz = 4:75). The left inset shows two line scans throughthe specular beam in the [110]- (solid line) and [1-10]-direction (dashed line). Thearrow in the contour plot indicates the direction of deposition.

ML Cu on Cu(001) at a grazing angle of 80± (see Fig. 3.2(b)). The asymmetryin the plane of incidence reveals the evolution of di¤erent slopes at the illuminatedand shadow side of adatom structures. Upon further growth asymmetric mound orripple structures may be formed (as is the case for Cu/Cu(001), see Chap. 3).

The development of elongated adatom structures during grazing incidence growthcan be explained by a phenomenon introduced in Chap. 3: steering-enhancedroughening. Steering originates from long-range attractive forces between inci-dent atoms and substrate atoms and leads to preferential arrival of atoms on topof adatom structures. Thermal Co atoms, approaching the surface at energies ofabout 0.15-0.20 eV, experience a long-range attractive well several eV’s deep. Thisgives rise to substantial de‡ection of non-normal deposited atoms towards the sur-face. Initially, this has no consequences: the de‡ection is the same for all atomsand thus the incident atom ‡ux remains homogeneously distributed. However, assoon as adatom structures start to form, the redistribution of material becomes pro-gressively more important. Surface roughness causes a distortion in the attractivepotential, and therefore atom trajectories are in‡uenced by the local surface mor-

6.3. SURFACE MORPHOLOGY 125

phology. The result is a redistribution of the incident atom ‡ux, such that atomsarrive preferentially on top of adatom structures. This steering phenomenon wassubstantiated by atom trajectory calculations in Sec. 3.3.

For the experimental results reported in this chapter, the most important con-sequence of steering is a radial asymmetry in the growth rate of adatom structures.At grazing incidence deposition less atoms are deposited behind adatom structures.As a result, the growth rate of the shadow side of adatom structures is reduced. Thereduction of incident atom ‡ux is exactly compensated by an incident atom ‡ux en-hancement on top of adatom structures. Since a part of the “extra” deposited atomson top of adatom structures leaks to the perpendicular sides, the in-plane structuregrowth rate is smaller in the deposition direction than in the perpendicular direc-tion. As a consequence, elongated adatom structures evolve with their longest sideperpendicular to the plane of incidence of the Co atom beam.

The calculations in Sec. 3.3 show that the amount of steering depends criti-cally on two parameters: the surface roughness and the deposition angle. Withincreasing surface roughness the distortions in the attractive potential become morepronounced. Therefore, the atom trajectories di¤er more from each other with amore inhomogeneous incident atom ‡ux as result: steering enhanced roughening isauto-catalyzed. For normal incidence deposition only a small local enhancement ofthe incident atom ‡ux close to step edges was calculated. However, as the deposi-tion angle increases the lateral range as well as the amount of incident atom ‡uxon top of adatom structures increase, with a larger aspect ratio as result. This is inagreement with SPA-LEED measurements. The monotonic increase of the in-planeuniaxial magnetic anisotropy (see Fig. 6.5) can therefore be fully attributed to asteering-induced elongation of adatom structures in the direction perpendicular tothe plane of incidence.

An in-plane uniaxial magnetic anisotropy has been observed after grazing in-cidence deposition of Co on Cu(001) before [222]. Remarkably, though rectangu-lar adatom structures were suggested as a possible explanation for the uniaxialanisotropy, the formation of these elongated structures and thus the uniaxial mag-netic anisotropy was not ascribed to grazing incidence growth. In that study, thesmall miscut of the Cu crystal (only 0.1±) was used to explain the possible formationof rectangular adatom structures. Obviously, this is not in agreement with the graz-ing incidence growth experiments and calculations of the steering phenomenon inthis thesis: rectangular adatom structures develop because of considerable steeringe¤ects at grazing incidence deposition.

For relatively thick grazing incidence deposited Co …lms on glass substrates (15nm - 100 nm) a critical deposition angle at which the easy axis of magnetizationrotates by 90± has been found [208]: below and above this critical angle the easyaxis of magnetization is perpendicular and parallel to the deposition direction re-spectively. Such a rotation of the easy axis is not observed in ultrathin Co …lmson Cu(001). In 5 ML thick Co …lms (t 1 nm) the easy axis of magnetization isalways oriented perpendicular to the deposition direction (see Fig. 6.5). This dif-


ference in magnetic behavior can most probably be attributed to an increase of theshadow length with increasing surface roughness. As outlined in Chap. 3, ripplesperpendicular to the plane of incidence develop when the length scale for nucleationand shadowing match. Following the discussion in Sec. 3.7 we conjecture that amaximum structure aspect ratio (ripple structure), and thus a maximum uniaxialanisotropy, is obtained at a deposition angle which decreases with increasing surfaceroughness (…lm thickness).

The micromagnetic origin of the uniaxial anisotropy may arise from missingbonds at step edges (Néel-type anisotropy), uniaxial strain (magnetoelastic anisotro-py), and shape e¤ects (shape or magnetostatic anisotropy). For elongated adatomstructures the number of step edge atoms and thus missing bonds is di¤erent inthe two high symmetry directions. The uniaxial magnetic anisotropy may thereforeoriginate from this symmetry breaking. This is more plausible since recent Co growthexperiments on stepped Cu(001) showed that the step-induced uniaxial anisotropyin this system arrises from the missing bonds at step edges [201, 202]. In elongatedadatom structures the strain, which originates from a 1.9 % lattice mismatch, may berelaxed anisotropically. Magnetoelastic contributions may therefore also contributeto the uniaxial magnetic anisotropy. The magnetostatic contribution to the totalanisotropy will align the easy axis of magnetization parallel to the long sides of theelongated adatom structures, i.e., perpendicular to the deposition direction.

6.4 Annealing and Cu adsorption

The MOKE and SPA-LEED measurements reveal that the growth induced uniax-ial magnetic anisotropy is directly related to the formation of elongated adatomstructures during grazing incidence deposition. A decreasing uniaxial magneticanisotropy can therefore be expected when the fourfold symmetry of the surfaceis restored. To check this conjecture, annealing experiments on grazing incidencedeposited Co …lms were performed. Annealing activates adatom di¤usion processeswhich not only tend to smooth the Co …lm but reshape the adatom structures totheir energetically favorable square form as well. The di¤usion of step edge atomsaround the corners of adatom structures and detachment/attachment processes canfor example reduce the aspect ratio of elongated adatom structures. Fig. 6.9 showsa selection of Kerr hysteresis curves measured during annealing of a 4 ML thick Co…lm which was deposited at a grazing angle of 80± with respect to the surface normal(same …lm as in Fig. 6.1). The heating rate was about 0.08 K/s in this experiment.Up to a …lm temperature of 300 K the measured shift …eld Hs and thus the in-planeuniaxial magnetic anisotropy is nearly constant. Increasing the temperature further,however, results in a monotonic decrease of the shift …eld. At these temperaturesthe adatom di¤usion processes responsible for surface smoothing and adatom struc-ture reshaping become active on the experimental timescale. The onset temperaturefor surface smoothing derived from this experiment is considerably lower than that

6.4. ANNEALING AND CU ADSORPTION 127

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-100

0

100

-300 0 300-125

0

125

175 K

400 K 425 K

450 K 475 K

300 K 350 K

375 K

175 K

Ker

r el

liptic

ity (µ

rad)

H (Oe)

Figure 6.9: In-plane hard axis hysteresis curves for a 4 ML thick Co …lm on Cu(001),grown at a grazing angle of 80± with respect to the surface normal. The magnetiza-tion curves were obtained during annealing (heating rate: of 0.08 K/s).

derived from the annealing experiments in Sec. 5.4. The lower onset temperaturecan be explained by a larger roughness of the “as grown” …lm. The di¤erence in…lm roughness is due to a lower growth temperature (250 K instead of 298 K) andsteering-enhanced roughening (deposition at 80± instead of 0±). The square hystere-sis curve measured at a …lm temperature of 450 K indicates that annealing the Co…lm to this temperature results in a negligible in-plane uniaxial magnetic anisotropy.A square hysteresis curve is measured also when the sample is cooled from 475 Kback to 175 K. The transition is therefore irreversible: annealing a grazing incidencedeposited Co …lm destroys the growth induced twofold surface morphology. As aconsequence, the in-plane uniaxial magnetic anisotropy, which is directly connectedwith the surface morphology, disappears. This is also illustrated in Fig. 6.10, whichshows uniaxial anisotropy constant Ku as a function of …lm temperature.


150 200 250 300 350 400 4500.0

0.5

1.0

1.5

2.0

K

u (1

05 erg

/cm

3 )

T (K)

Figure 6.10: Uniaxial magnetic anisotropy Ku in a 4 ML thick Co …lm, grown at80± with the Cu (001) substrate at 250 K, as a function of annealing temperature.

Besides surface smoothing and reshaping of adatom structures, interdi¤usion alsooccurs during annealing of Co …lms on Cu(001) (see Sec. 5.4 and Refs. [184, 188, 193,194, 195]). At elevated temperatures Cu segregates toward the …lm surface leavingbehind deep square pits in the substrate. The driving force for the segregationof Cu substrate atoms is the lower surface free energy of Cu compared to thatof Co (¾Cu = 1:9 J/m2 and ¾Co = 2:7 J/m2 [172, 173]). For Co …lms on Cu(001)interdi¤usion was found at annealing temperatures above 400 K and 450 K for 2 MLand 4 ML thick …lms, respectively (see Sec. 5.4). As a consequence, interdi¤usioncan not be excluded in the annealing experiment shown in Fig. 6.9 and Fig. 6.10.This is con…rmed by annealing experiments on Co …lms grown on stepped Cu(001)substrates [212]: although surface steps remain, a strong reduction ofKu is observedabove 350 K for 2.5 ML thick Co …lms. The reduction ofKu is most probably due toa decrease of the number of missing bonds at Co step edges caused by the segregationand subsequent attachment of Cu atoms in these experiments.

From the annealing experiments it can be expected that the uniaxial magneticanisotropy will be smaller after grazing incidence Co growth at elevated tempera-tures. Furthermore, it can be expected that a Cu cap layer a¤ects the magneticbehavior of grazing incidence deposited Co …lms. A number of growth experimentswere performed to check these conjectures. The …rst conclusion that can be drawnfrom these experiments is that the growth induced uniaxial magnetic anisotropy de-creases with increasing growth temperature indeed. Figure 6.11 shows a hysteresiscurve acquired after grazing incidence deposition of 5 ML Co at 70± with the sub-strate at 300 K. The shift …eld in this hard axis magnetization curve is considerably

6.4. ANNEALING AND CU ADSORPTION 129

-300 -150 0 150 300

-100

-50

0

50

100

K

err

ellip

ticity

(µra

d)

H (Oe)

Figure 6.11: In-plane hard axis hysteresis curve for a 5 ML thick Co …lm on Cu(001),grown at 300 K with a grazing angle of 70± with respect to the surface normal. Themagnetization curve was obtained at 175 K.

smaller than that measured after grazing incidence growth with the same deposi-tion angle but with the substrate at 250 K (see Fig. 6.4). The uniaxial anisotropyconstant Ku is 2.5£105 erg/cm3 and 0.3£105 erg/cm3 after growth at 250 K and300 K respectively, i.e., Ku decreases by about a factor 8. Two e¤ects account forthis. First of all, the adatom structure size increases exponentially with increasinggrowth temperature. For large adatom structures the average enhancement of theincident atom ‡ux on top of structures (‡ux enhancement per surface area) is smallcompared to that on top of smaller structures. The adatom structure growth ratein the deposition- and perpendicular direction will therefore di¤er less at elevatedgrowth temperatures with a smaller aspect ratio (less elongated shape) as result.Second, due to an enhanced surface di¤usion at higher growth temperatures theadatom structure shape deviates less from the energetically favorable square shape.In other words, surface di¤usion reduces the consequences of steering.

From experiments on stepped surfaces it is well known that the adsorption ofCu atoms onto stepped Co …lms leads to a strong reduction of the step-inducedanisotropy strength [201, 202, 210, 211]. Such a strong reduction of the uniaxialmagnetic anisotropy was measured after Cu adsorption on grazing incidence de-posited Co …lms as well. Figure 6.12 shows hysteresis curves acquired before andafter growth of 0.5 ML Cu on a 5 ML thick grazing incidence deposited Co …lm.The Co …lm was grown at 70± with the Cu(001) substrate at 250 K, whereas theCu was deposited at normal incidence and the same temperature. Obviously, Cuadsorption leads to a reduction of the uniaxial magnetic anisotropy. From the shift


-300 -150 0 150 300

-100

-50

0

50

100 a)

K

err

ellip

ticity

(µr

ad)

H (Oe)

-300 -150 0 150 300

-100

-50

0

50

100 b)

H (Oe)

Figure 6.12: (a) In-plane hard axis hysteresis curve for a 5 ML thick Co …lm onCu(001), grown at 250 K with a grazing angle of 70± with respect to the surfacenormal. (b) In-plane hard axis hysteresis curve for the same Co …lm acquired afternormal incidence growth of 0.5 ML Cu at 250 K. Both magnetization curves wereobtained at 175 K.

…eld the anisotropy constant is determined to be Ku = 1.0£105 erg/cm3 after Cuadsorption, which is about a factor 2.5 smaller than the anisotropy constant for theuncovered Co …lm. No further decrease of the in-plane uniaxial magnetic anisotropywas measured for larger amounts of Cu deposits. The measurements in Fig. 6.12seem to indicate that the micromagnetic origin of the uniaxial anisotropy in grazingincidence deposited Co …lms arises mainly from missing bonds at Co step edges.During Cu growth the number of missing bonds is reduced by the attachment of Cuatoms to Co step edges. When all the step edges are fully decorated by Cu atoms,no further decrease of Ku can be expected. This is obviously the case after normalincidence growth of 0.5 ML Cu.

6.5 Conclusions

The in‡uence of the deposition angle on the magnetic and structural anisotropy inultrathin Co …lms on Cu(001) was studied for angles between 0± and 80±. Graz-ing incidence molecular beam epitaxy along the [110]-azimuth results in an in-planeuniaxial magnetic anisotropy. For deposition angles ¸ 10± the easy axis of mag-netization is oriented perpendicular to the plane of incidence. The strength of theuniaxial magnetic anisotropy increases monotonically upon rotation of the incidentmolecular beam from normal to more grazing incidence. SPA-LEED measurementsreveal that the observed magnetic behavior in Co/Cu(001) is directly related tothe formation of an uniaxial surface morphology during grazing incidence growth:


elongated instead of square adatom structures evolve. The long sides of the elon-gated adatom structures are oriented perpendicular to the plane of incidence andthe island aspect ratio increases with increasing deposition angle. The in‡uence ofthe deposition angle on the evolution of the surface morphology is rationalized interms of steering. Steering is a direct consequence of long-range attractive forcesbetween incident atoms and substrate atoms and leads to a redistribution of incidentatom ‡ux: the incident atoms arrive preferentially on top of adatom structures atthe cost of ‡ux reduction behind structures. Due to this redistribution of incidentatom ‡ux the adatom structure growth rate is larger in the direction perpendicularto the plane of incidence, with the result that elongated structures evolve. Whilesteering increases with the deposition angle, the measured increase of the aspectratio is explained naturally by this phenomenon as well. The surface morphologyand thus the magnetic behavior of an ultrathin Co …lm are the result of an inter-play between steering and surface di¤usion processes. Therefore, growth at elevatedtemperatures or post annealing reduces the adatom structure aspect ratio and theuniaxial magnetic anisotropy drastically. The micromagnetic origin of the uniaxialmagnetic anisotropy in grazing incidence deposited Co …lms arises mainly from themissing bonds at Co step edges (Néel-type anisotropy). Steering-induced uniaxialmagnetic anisotropy should always be anticipated in grazing incidence MBE growthof magnetic …lms.

Chapter 7

Spin reorientation transition inNi/Cu(001)

7.1 IntroductionUltrathin ferromagnetic layers often show a di¤erent magnetic behavior to the bulk.Reduced symmetry and a modi…ed lattice constant due to pseudomorphic growthmay change the magnetic moment and in‡uence the direction of the magnetizationaxis. The direction of the magnetization in the remanent state is determined –within the phenomenological model – by the interplay of a thickness dependent part(surface/interface anisotropy) and a thickness independent part (volume anisotropy)of the anisotropy energy density and the magnetostatic anisotropy energy density.A spin reorientation transition may occur when these three anisotropies do nothave the same sign. Reorientation from out-of-plane to in-plane magnetization hasbeen observed for a number of ultrathin magnetic …lms, typically in the 2 to 6ML thickness range [229, 230, 231]. Contrary to this, a transition from in-planemagnetization to out-of-plane magnetization at 7–10 ML has been measured for Ni…lms on Cu(001) [232, 233, 234, 235, 236].

The anomalous spin reorientation transition in Ni …lms on Cu(001), which hasbeen investigated intensively during the last years [89, 232, 233, 234, 235, 236, 237,238, 239, 240, 241, 242, 243, 244, 245, 246, 247], can be described by the e¤ectivesecond order magnetization anisotropy energy K2 and the magnetostatic anisotropyenergy 2¼M2

s (see Sec. 1.5). It has been shown that for small …lm thickness K2

can be written as the sum of a thickness independent volume anisotropy (K2v)and a thickness dependent surface (K2s) and interface anisotropy (K2i): K2 =K2v+(K2s+K2i)=d, with d the …lm thickness. The direction of the magnetization isperpendicular to the …lm plane whenK2 > 2¼M2

s . Normally,K2v describes the mag-netocrystalline bulk anisotropy. However, the growth of Ni on Cu(001) is pseudo-morphic up to a …lm thickness of at least 11 ML [239, 248]. In comparison with bulkfcc Ni (a== = 2:49 Å ) the tetragonally distorted (fct) lattice is expanded by 2.5% inthe …lm plane and compressed by 3.2% along the surface normal [248]. The tetrago-

133

134 CHAPTER 7. SPIN REORIENTATION TRANSITION IN NI/CU(001)

nal distortion leads to a strain induced anisotropy contributionKme = ¡3=2¸¾, with¸ the bulk magnetostriction constant and ¾ the stress, which in bulk Ni would leadto a 2.5% in-plane lattice expansion [232, 238]. Since the strain induced anisotropycontribution (30 ¹eV/atom [232]) is about two orders of magnitude larger than themagnetocrystalline anisotropy of bulk Ni (¡0:39 ¹eV/atom), the latter can be ig-nored completely. Therefore, K2v t Kme for thin Ni …lms on Cu(001). The surfaceand interface anisotropies K2s and K2i are either thought to be of entirely “Néel-type” origin [232, 238] or contain a magnetoelastic anisotropy contribution as well[89, 249].

For thin Ni …lms on Cu(001) the positive volume anisotropy is compensated bylarge negative surface and interface anisotropies. Therefore, contrary to most mag-netic systems, the magnetization of thin Ni …lms is in-plane up to a critical thicknessdc, where K2 equals the shape anisotropy 2¼M2

s and the magnetization switches toout-of-plane. Critical thickness values ranging from 7 ML [232, 233, 234], 8 ML [235]up to 10 ML [236] have been reported in literature. The stress in the Ni …lm, whichis induced by the tetragonal distortion, increases with increasing …lm thickness.This continues up to a critical thickness (¸ 11 ML), where the onset of strain re-laxation reduces the tetragonal distortion. From there on, the volume anisotropyK2v becomes thickness dependent and decreases with reduced lattice distortion, i.e.,with increasing …lm thickness. Consequently, a second spin reorientation occurs ata thickness dc2; where the e¤ective second order anisotropy energy K2 equals theshape anisotropy 2¼M2

s again. This spin reorientation transition is less sharp thanthe …rst one, occurring at a thickness of 37 ML [238] to 50 ML [239]. Nowadays, it iswell accepted that the strain induced anisotropy contribution to K2v is responsiblefor the perpendicular magnetization in Ni/Cu(001).

As described above, the in-plane magnetization is caused by large negative sur-face and interface anisotropies. Therefore, a change of the surface or interfaceanisotropy will shift the spin reorientation transition to a di¤erent Ni …lm thickness.Possible ways to in‡uence the surface anisotropy are growth of a metallic overlayer,variation of the surface roughness or adsorption of a gas. For Ni on Cu(001) thee¤ect of overlayers [89, 237, 238, 239, 240] and surface roughness [241] have beenstudied recently, while less attention has been paid to the in‡uence of gaseous ad-sorbates. This is remarkable since changes in the magnetic moment of the …rst layerhave been found after H2 adsorption on Ni(111) [250] and Ni(001) [251, 252, 253]in the past. It is therefore expected that gaseous adsorbates will in‡uence the spinreorientation transition in thin Ni …lms on Cu(001) as well. In this chapter, experi-mental results on the e¤ect of H2 and CO adsorption on Ni/Cu(001) are presented.Furthermore, the adsorption results are compared to the measured in‡uence of a Cucap layer and the surface roughness.

In the past, in depth studies have been made on the adsorption/desorption kinet-ics and corresponding structure of H2 and CO on Ni(001). Here, a brief summary ofthe relevant results is given. H2 adsorbs dissociatively on Ni(001) in fourfold hollowsites [254, 255]. No ordered surface structure forms at a substrate temperature of

7.2. H2/NI/CU(001) 135

300 K [256, 257]. At 200 K a quasi-ordered p(2£2) overlayer structure developsafter adsorption of 0.5 L H2 (which corresponds to a coverage of about 0.5 ML of Hatoms) [254]. For low and medium H2 exposures (up to 5 L at 100 K) the thermaldesorption spectra consist of only one peak, labeled ¯2, at 350 K for a heating rateof about 15 K/s [257, 258, 259]. Upon further exposure (exposure > 10 L H2) ashoulder develops (¯1), whose population is much less than that of the main des-orption state. The isosteric heat of adsorption in the ¯2 state is about 1.0 eV/H2

molecule [257, 260].The adsorption/desorption behavior and structure of CO on Ni(001) is more

complex than that of H2. The CO molecules adsorb on top of Ni surface atomsfor coverages up to 0.5 ML [261, 262, 263, 264, 265, 266]. The orientation of theCO molecule at such a terminal adsorption site is perpendicular to the surfacewith the carbon bonded to a Ni surface atom [267, 268]. Low energy electrondi¤raction measurements always show a clear c(2£2) superstructure for coveragesup to 0.5 ML [267, 268, 269, 270]. For temperatures below 160 K a complete c(2£2)structure develops at an exposure of about 2 ML [261, 270]. For a coverage between0.25 and 0.5 ML a partial occupation of bridge sites has been reported by someauthors [262, 266], whereas others found only top site adsorption up to 0.5 MLCO coverage [265]. Upon further CO exposure two new patterns develop. First atransition to a c(5

p2 £

p2)R45± superstructure with a coverage of 0.6 ML occurs

which is followed by a transition to a p(3p2£

p2)R45± structure with a coverage of

0.68 ML (saturation coverage for T < 250 K) [265, 271]. Thermal desorption spectrafor CO adsorbed in the c(2£2) structure on Ni(001) show a peak labeled ¯2 at 440K for heating rates of about 10 – 15 K/s [258, 259, 262, 266]. The isosteric heatof adsorption in this state is about 1.25 eV/CO molecule [258, 270]. For coveragesbetween 0.25 and 0.5 ML a shoulder at 350 K (labeled ¯1) develops. The thermaldesorption spectra for CO adsorbed in the more dense p(3

p2 £

p2)R45± structure

show an additional peak at 280 K.

7.2 H2/Ni/Cu(001)

All adsorption experiments were conducted in ultra-high vacuum (base pressure< 4 £ 10¡11 mbar) using the Kerr microscope described in Sec. 2.6. Wedge-likeNi …lms were grown with electron-beam evaporation on a Cu(001) surface at atemperature of 298 K. The growth rate, calibrated with MEED before growth ofthe wedge and checked by AES after Kerr microscopy measurements, was about0.5 ML/min. During growth the pressure in the vacuum chamber never exceeded 2£ 10¡10 mbar. In the adsorption experiments the wedge-like Ni …lm was exposed tothe adsorbate at T = 143 K and a pressure of 1 £ 10¡9 mbar. In order to excludesurface roughness induced changes in the spin reorientation transition, the Ni …lmwas annealed to 453 K prior to adsorbate adsorption. This results in a smooth Nisurface without any signi…cant substrate interdi¤usion [246, 272]. The annealing


6

7

8

9

10

11

12

N

i th

ick

ness

(M

L)

Ke

rr

asy

mm

etr

y

0 . 12 - 0 . 01

0 0 .4

H2 e x po s u r e (L )

0 .7 1 .1 1 .4

Figure 7.1: Polar Kerr asymmetry images of the same section of a Ni wedge onCu(001) for …ve H2 exposures at T = 143 K. The Ni thickness increases from thebottom to the top of the image as indicated by the scale on the left hand side. Thebright area indicates the presence of perpendicular magnetization, the dark areain-plane magnetization.

behavior of Ni/Cu(001) is thus di¤erent from that of Co/Cu(001) (see Sec. 5.4).The spin reorientation transition during H2 exposure was measured by Kerr

imaging a Ni wedge. The Kerr images were taken with the repeated sequence of -300, 0, +300, 0 Oe external …eld. In Fig. 7.1 the asymmetry image, i.e., the di¤erenceof the image for -300 and +300 Oe divided by their sum, is displayed for …ve H2

exposures of the same selected stripe of 0.6 mm £ 5 mm at T = 143 K. At thelow end of the stripe, corresponding to 5.5 ML Ni thickness, the asymmetry is zeroindicating that there is no polar Kerr asymmetry and therefore no perpendicularcomponent of the magnetization. In the experimental geometry (see Fig. 2.12), themagnetization component parallel to the …lm does not signi…cantly contribute tothe measured Kerr asymmetry. Using bulk optical constants the longitudinal Kerre¤ect is estimated to be smaller by a factor 12. Experimentally, an even smallerlongitudinal Kerr e¤ect was found.

For the clean Ni …lm (…rst stripe), no Kerr asymmetry is measured up to a …lmthickness of about 11 ML, i.e., the magnetization is in-plane. However, at 11 MLa very fast increase of the polar Kerr asymmetry is observed, followed by a linearincrease of the asymmetry with …lm thickness. The spin reorientation transition inthe clean Ni wedge takes place within a thickness range of only 1 ML. The thicknessdc at which the spin reorientation from in-plane magnetization to perpendicular

7.2. H2/NI/CU(001) 137

0 10 20 30 40 500

20

40

60

80

100

120

140

H

c (O

e)

Ni thickness (ML)

Figure 7.2: Coercive …eld as a function of Ni …lm thickness, measured at 273 K.

magnetization occurs, is not related to the thickness at which a dislocation networkstarts to develop to reduce the …lm strain. O’Brien et al. [239] found a strongincrease of the coercive …eld at a thickness of 13 ML, which can be interpreted asthe onset of dislocation formation. This is in agreement with the Kerr measurementdisplayed in Fig. 7.2. This measurement shows a strong increase of the coercive …eldat a Ni …lm thickness of about 16 ML. Furthermore, Müller et al. [248] found nosigni…cant reduction of the tetragonal distortion up to a …lm thickness of at least11 ML. Consequently, the spin reorientation transition in the clean Ni …lm occursbelow the onset of mis…t dislocations.

Exposure to H2 immediately shifts the border of the spin reorientation transitionto a smaller Ni …lm thickness. The displayed exposure in Fig. 7.1, which is measuredwith an ion gauge, is not corrected for the H2 ionization probability and the positionof the gas inlet and the ion gauge with respect to the Cu(001) substrate. The actualH2 exposure is therefore larger, approximately by a factor of 3-4. A H2 exposureof 1.7 L at 143 K reduces the critical thickness by about 4 ML. Exposing more H2

to the Ni surface does not shift the border of the spin reorientation transition alot more. Compared to H2 adsorption measurements in literature [254, 257], theactual H2 coverage at which the shift of the critical thickness saturates is close to1 ML of H atom coverage. The critical thickness, de…ned as the thickness at whichthe Kerr asymmetry measured with an applied …eld of 300 Oe dropped to 1/2 ofthe extrapolated full polar signal, was determined from Kerr images taken duringH2 exposure at 143 K. The results for two di¤erent Ni wedges as a function of H2

exposure are shown in Fig. 7.3. Christmann et al. [257] showed that H2 adsorption


0.0 0.5 1.0 1.56

7

8

9

10

11

12

d

c (M

L)

H2 exposure (L)

Figure 7.3: Critical thickness of the spin reorientation transition in a Ni …lm onCu(001) as a function of H2 exposure at 143 K. The circular and triangular datapoints were measured on two di¤erent Ni wedges. An exponentially decaying …tfunction to the data points is shown as a solid line.

on Ni(001) obeys a …rst order adsorption process. In such an adsorption process,the sticking coe¢cient decreases linearly with increasing coverage. This results ina time dependence of the H2 coverage µ(t) proportional to 1 ¡ exp(¡ct), with cbeing a constant and t the exposure time, when H2 desorption is neglected. In theexperiments, in which H2 is adsorbed at 143 K, the desorption of H2 is negligible.From Fig. 7.3 it follows that the measured critical thickness decays exponentiallywith H2 exposure as well. An exponentially decaying …t function to the data pointsis shown as a solid line. This leads to the conclusion that the H2 coverage and thecritical thickness have the same H2 exposure dependence, suggesting that the criticalthickness decreases linearly with H2 coverage.

Figure 7.4 shows the critical thickness dc as a function of substrate temperaturefor the clean (squares) and H2 covered Ni …lm (circles). The thickness at whichthe remanent Kerr asymmetry dropped to 80% (10%) of the extrapolated polarKerr asymmetry of the same thickness is indicated as …lled (open) symbols (seeinset). The average measured time per data point for both the clean and the H2

covered surface was about 5 minutes, which corresponds to a heating/cooling rateof 0.03 K/s. The datapoints for the uncovered Ni wedge were taken for decreasingtemperature. Because of unavoidable H2 adsorption (of the order of 0.05 L), dcmight be reduced already at low temperatures. From several uptake curves, dcas a function of H2 exposure, it is estimated that H2 adsorption would lead to a

7.2. H2/NI/CU(001) 139

150 200 250 300 350 400 450

6

7

8

9

10

11

12

H2 covered

clean

10% 80%

d

c (M

L)

T (K)

4 6 8 10 120

2

4

6

8

10

K

err

asym

met

ry (%

)

d (ML)

remanence H

ext = 300 Oe

10%

80%

Figure 7.4: Critical thickness of the spin reorientation transition in a Ni …lm onCu(001) as a function of substrate temperature for the clean surface (squares) andfor the surface exposed to 1.7 L H2 at 143 K (circles). Open (…lled) symbols representthe thickness at which the remanent Kerr asymmetry dropped to 10% (80%) of theextrapolated polar Kerr asymmetry of the same thickness. The inset shows themeasured Kerr asymmetry as a function of Ni thickness at 233 K for the H2 covered…lm. The small arrow at the open squares at 143 K indicates an estimate of thereduction of the critical thickness by possibly adsorbed small traces of H2 at lowtemperature.

decrease of dc of less than 0.4 ML for the clean …lm at 143 K (this is indicated byan arrow in Fig. 7.4). About 1.7 L of H2 was adsorbed at 143 K for the H2 coveredNi …lm. Thereafter, Kerr images were taken for increasing substrate temperatureand dc was determined in the same way as for the clean Ni …lm. The border of thespin reorientation transition hardly changes upon heating up to about 270 K. At thissubstrate temperature however, a shift to larger …lm thickness is observed. This shiftcan be attributed completely to the onset of H2 desorption. The critical thicknessincreases strongly at a substrate temperature of 300 K. As mentioned above, TPDmeasurements show a H2 desorption peak at 350 K [258, 259] (¯2 desorption peak)for a heating rate of about 15 K/s. Because of the much lower heating rate used inthe measurements displayed in Fig. 7.4 (only 0.03 K/s), H2 desorption occurs at alower temperature. Assuming …rst order desorption kinetics, the 50 K shift of thedesorption peak is consistent with a desorption energy of 1:0 eV/H2 molecule if apre-exponential factor of about 1015 is assumed. At a substrate temperature of 330 Kthe critical thickness merges into the curves for the clean Ni …lm within experimentalerror. The close similarity of the behavior of (the derivative of) the critical thickness


dc and the TPD spectra is an additional indication for the linear dependence of dcon the H2 coverage. Consequently, the change of the critical thickness dc can beattributed entirely to a change of the surface anisotropy energy K2s.

From the change ofK2s upon H2 exposure, not only a shift of the …rst spin reori-entation transition is expected but a shift of the second spin reorientation transitionis expected as well. A thick Ni wedge, ranging from 0 to 90 ML, was grown at 298 Kto investigate the in‡uence of H2 adsorption on the second critical thickness dc2. Thepolar Kerr asymmetry as a function of Ni …lm thickness at T = 273 K was derivedfrom Kerr images of the steep Ni wedge. The result for the clean and the H2 coveredNi wedge are shown in Fig. 7.5. The solid lines represent the Kerr asymmetry withan applied external …eld of 300 Oe and the dashed lines represent the remanentKerr asymmetry. Because of the limited external magnetic …eld, saturation of the…lm magnetization could be achieved only for Ni …lms below a thickness of about50 ML (see Fig. 7.6). The Kerr asymmetry for larger Ni …lm thickness representsthe corresponding quantities from a minor hysteresis loop with a …eld amplitude of300 Oe. Therefore, a reduction of the Kerr asymmetry does not necessarily mean areduction of the Kerr asymmetry in the magnetically saturated state. Nevertheless,a nonvanishing polar Kerr asymmetry is measured in the whole thickness range forboth the remanent state as well as the state with an applied external …eld of 300Oe. This clearly indicates that the second spin reorientation occurs over a broadthickness range. The observed magnetic behavior is in qualitative agreement withmeasurements in Ref. [239], which show a gradual transition to in-plane magnetiza-tion over a thickness range of about 15 ML. The onset of an in-plane signal and theonset of the reduction of the remanent polar XMCD-signal occurs at about 40 MLin those measurements. Furthermore, Bochi et al. [249] and Jungblut et al. [238]found an already entirely in-plane magnetization for Ni …lms thicker than 60 ML.The measurements in Fig. 7.5 seem to indicate that the range of the second spinreorientation transition is somewhat broader. The discrepancy between the experi-mental results might be due to a di¤erence in the preparation of Ni …lms, a¤ectingthe strain relaxation. Both the clean and the H2 covered …lm show a perpendic-ular magnetization up to about 50 ML in Fig. 7.5. The measurements with anapplied …eld of 300 Oe cannot be used for thicker Ni …lms, because a change of theKerr asymmetry may simply be caused by a change of the coercivity and thereforedi¢cult to interpret.

While for H2 covered Ni …lms the remanent Kerr asymmetry and the Kerr asym-metry at saturation coincide, indicating rectangular hysteresis loops, the remanentKerr asymmetry starts to deviate from the saturation value at about 45 ML for theclean Ni …lm. At this …lm thickness the external …eld of 300 Oe is still su¢cient tosaturate the …lm magnetization as can be seen in Fig. 7.6. The di¤erence betweenthe clean and the H2 covered …lm is therefore caused by a spontaneous creation ofdomains in the clean Ni …lm. This obviously does not happen for the H2 covered…lm. The energy / (AKeff )1=2, withKef f the e¤ective anisotropy energy and A theexchange energy, to form a domain wall must thus be larger for the H2 covered Ni

7.2. H2/NI/CU(001) 141

0 20 40 60 80

0

10

20

30

40

50

300 Oe remanence

from minorhysteresis loop

from saturated hysteresis loop

clean

H2 covered

Ni thickness (ML)

K

err

asym

met

ry (%

)

Figure 7.5: Polar Kerr asymmetry as a function of Ni …lm thickness in the remanentstate (dashed lines) and in the magnetization state with an applied …eld of 300 Oe(solid lines) for a clean and H2 covered Ni …lm at 273 K.

6 ML

14 ML

24 ML

34 ML

-200 0 200

Ker

r el

liptic

ity (

arb.

uni

ts)

44 ML

-200 0 200

H (Oe)

54 ML

-200 0 200

64 ML

-200 0 200

74 ML

Figure 7.6: Polar Kerr ellipticity hysteresis loops for di¤erent Ni …lm thickness,measured at 273 K. Note, an external applied …eld of 300 Oe is not enough tosaturate the …lm magnetization of Ni …lms thicker than 50 ML.


6

7

8

9

10

11

12

N

i th

ick

ness

(M

L)

0 0 . 4

C O e x po s u re ( L )

0 .6 0 .9

0 .12 -0 . 01

Ke

rr

asy

mm

etr

y

1 .1

Figure 7.7: Polar remanent Kerr asymmetry images of the same section of a Niwedge on Cu(001) for …ve CO exposures at 143 K.

…lm. Assuming that it is Keff which is mostly a¤ected by the adsorption of H2, itcan be concluded that the anisotropy is enhanced by H2 exposure, so that the secondspin reorientation transition is expected at a larger Ni …lm thickness. However, avalue for the critical thickness dc2 cannot be derived from the data in Fig. 7.5.

7.3 CO/Ni/Cu(001)On the Cu(001) surface a Ni wedge, ranging from 3.9 ML to 12.5 ML, was grownto study the consequences of CO adsorption. The changes in the spin reorientationtransition during CO adsorption, as monitored by Kerr microscopy imaging, is dis-played in Fig. 7.7. This …gure shows selected stripes of remanent state asymmetryimages for …ve CO exposures at T = 143 K. The imaged surface area is the samefor each stripe and corresponds to 0.6 mm £ 5 mm. Obviously, exposure to COalso shifts the border of the spin reorientation transition to smaller …lm thickness.The displayed exposure is determined from the pressure as read from the ion gaugewithout any further corrections. Due to the position of the ion gauge with respectto substrate and gas inlet, the actual CO exposure is somewhat larger (by a factor 2maximum). Figure 7.7 reveals that the critical thickness decreases to 8 ML duringCO exposure of only 1.1 L. No further shift of the spin reorientation transition tosmaller …lm thickness is measured upon further CO exposure. Compared to COadsorption measurements in literature [261, 270], the actual CO coverage at whichthe shift of the critical thickness saturates is close to 0.5 ML, with the CO molecules

7.3. CO/NI/CU(001) 143

150 200 250 300 350 400 450

6

7

8

9

10

11

12

CO covered

clean

10% 80%

d

c (M

L)

T (K)

4 6 8 10 120

2

4

6

8

10 remanence H

e xt = 300 Oe

K

err a

sym

met

ry (

%)

d (ML)

10%

80%

Figure 7.8: Critical thickness of the spin reorientation transition in a Ni …lm asa function of substrate temperature for the clean surface (squares), for the surfaceexposed to 1.2 L CO at 143 K (circles) and for the CO covered surface after annealingat 453 K (triangles). Open (…lled) symbols represent the thickness at which theremanent Kerr asymmetry dropped to 10% (80%) of the extrapolated polar Kerrasymmetry of the same thickness. The inset shows the measured Kerr asymmetryas a function of the Ni thickness at 233 K for the CO covered …lm.

adsorbed in a c(2£2) overlayer structure.

Figure 7.8 shows the critical thickness dc as a function of substrate temperaturefor the clean (squares) and CO covered Ni …lm (circles and triangles for increas-ing and decreasing temperature respectively). Open (…lled) symbols indicate thethickness at which the remanent Kerr asymmetry dropped to 10% (80%) of theextrapolated polar Kerr asymmetry of the same thickness. The inset shows the re-manent Kerr asymmetry as a function of …lm thickness for the CO covered surfaceat T = 233 K. At this temperature the reorientation from in-plane to perpendicularremanent magnetization occurs in a small thickness range of less than 0.2 ML. Themeasured critical thickness for the CO Ni …lm (increasing substrate temperature)decreases linearly to 7.4 ML at T = 300 K. At about 320 K the border of the spin re-orientation transition starts to increase. This increase can be attributed completelyto the onset of CO desorption from the Ni surface (¯2 desorption peak). Analo-gous to the case of H2 desorption discussed above, CO desorption occurs at a lowertemperature than in the usual TPD spectra because of the much lower heating rate(about 0.03 K/s in Fig. 7.8 compared to 10-15 K/s in Refs. [258, 259, 262, 266]).The strong increase of the critical thickness at about 380 K is in complete agreement


with TPD measurements indicating a desorption energy of about 1.25 eV (…rst orderdesorption kinetics and a pre-exponential factor of 2£1014 is assumed). The temper-ature interval in which CO desorption occurs is broader than that for H2 desorption(compare Fig. 7.4 and Fig. 7.8). This is in agreement with the less pronounced ¯1TPD peak in the case of H2 desorption. The weak increase of dc at temperaturesjust below 380 K might be due to CO desorption from the slightly weaker bound¯1 adsorption site. At a substrate temperature of 453 K, the critical thickness ofthe CO covered Ni …lm is almost equal to the one measured for the clean Ni …lm.Annealing at this temperature for several minutes results in a critical thickness (10.4ML (10% datapoints)), which is equal to the clean Ni …lm. From this it is concludedthat 453 K is su¢cient to clean the surface. Auger electron spectroscopy measure-ments con…rm this: only a small fraction of CO (close to the detection limit of theCMA Auger spectrometer) remained on the Ni surface, which does not change thecritical thickness of the spin reorientation transition signi…cantly. This is illustratedalso by the datapoints for decreasing substrate temperature. The critical thicknessfor the CO covered and annealed Ni …lm (triangles) and the clean Ni …lm (squares)is the same within experimental error.

7.4 Cu/Ni/Cu(001)

Separate determination of the surface (K2s) and interface anisotropy (K2i) is not pos-sible in the experiments described above. Both anisotropies have the same thicknessdependence and therefore only the sum of K2s and K2i can be calculated. How-ever, separation can be achieved when the critical thickness observed for clean, H2

covered and CO covered Ni …lms is compared to the critical thickness of a thin Ni…lm capped with Cu. In the latter case, the spin reorientation is in‡uenced by 2K2i

instead of K2s + K2i. To determine the surface and interface anisotropy separately,a Cu wedge was grown perpendicular on a Ni wedge. Both wedges were grown at 298K and the Ni wedge was not annealed prior to Cu deposition. The critical thicknessof the spin reorientation transition as a function of the Cu layer thickness and thesubstrate temperature was determined using Kerr microscopy.

Figure 7.9 shows the critical thickness dc as a function of substrate temperaturefor the clean (squares) and the Cu covered (circles and triangles) Ni …lm. In this…gure, dc was determined as the thickness at which the remanent Kerr asymmetrydropped to 10% of the extrapolated value. The growth of Cu on Ni/Cu(001) shiftsthe border of the spin reorientation transition to smaller …lm thickness as well. Ata Cu coverage of 2 ML the critical thickness is reduced by 3 ML with respect tothe clean Ni surface. Further growth of Cu does not change the critical thickness ofthe spin reorientation transition any further. A shift to thinner Ni …lms upon Cucoverage was also observed by O’Brien et al. [239]. However, in their measurementsthe transition from in-plane to perpendicular magnetization shifted only by 1 MLfrom 7 to 6 ML. The critical thickness of 6 ML in their Cu covered Ni …lm is close

7.4. CU/NI/CU(001) 145

150 200 250 300 350 400 450

6

7

8

9

10

11

12

always ||para-

magnetic

⊥ for Cu/Ni/Cu

always ⊥

d

c (M

L)

T (K)

Figure 7.9: Critical thickness of the spin reorientation transition in a Ni …lm as afunction of substrate temperature for the clean Ni surface (squares) and for the Nisurface capped with 2 ML Cu (triangles) and 5 ML Cu (circles). The solid line is apower law TC(d)=TC(1) = 1 ¡ (d=d0)¡¸ with TC(1) the bulk Curie temperature,d0 = 3:6 ML and ¸ = 1:2.

4 5 6 7 8 9 10 11 12

0

2

4

6

8

10

before annealing after annealing

K

err a

sym

met

ry (

%)

Ni thickness (ML)

Figure 7.10: Polar Kerr asymmetry as a function of Ni thickness at 233 K for aNi wedge covered with 5 ML Cu. The solid and dashed line represent the Kerrasymmetry before and after annealing the …lm at 453 K respectively.


to the values in Fig. 7.9 when the 0.8 ML uncertainty in the thickness calibrationis considered. The smaller shift is attributed to a partial H2 pre-coverage of the Ni…lm in Ref. [239]. The result in Fig. 7.9, is inconsistent with the magnetoelasticmodel described by Bochi et al. [249], which predicts a shift of the spin reorientationtransition towards larger …lm thickness.

The measurement of the critical thickness at di¤erent substrate temperatures iscompletely reversible. Annealing the sandwich structure to 453 K for about 10 min-utes does not in‡uence the spin reorientation transition in the Ni …lm. This is illus-trated in Fig. 7.10. This …gure shows the Kerr asymmetry at 233 K, measured before(solid line) and after (dashed line) annealing to 453 K. Since the small di¤erence inthe magnitude of the Kerr asymmetry is within the experimental error, no changein the onset of the polar Kerr asymmetry is observed. The shift of the data pointstowards larger values above 350 K (Fig. 7.9) is not due to an increase of the thicknessat which the magnetization switches from in-plane to out-plane but is due to thetransition from the ferromagnetic to the paramagnetic phase. In other words, thedisplayed data points above 350 K do not indicate the …lm thickness at which thereorientation from perpendicular magnetization to in-plane magnetization occurs.They mark the boundary where the out-of-plane remanent magnetization disap-pears instead. The solid line in Fig. 7.9 is a power law TC(d)=TC(1) = 1¡ (d=d0)¡¸with TC(1) the bulk Curie temperature, d0 = 3:6 ML and ¸ = 1:2. Such a value of¸ is commonly measured for many systems [273]. The measured value of TC(d) for agiven …lm thickness is lower by up to 60 K compared to that reported for uncoveredNi …lms on Cu(001) [233, 243]. Small di¤erences in the thickness calibration mightaccount for this partially. On the other hand, covering a Ni …lm with a Cu cap layerreduces TC as well. In the experiments described in Ref. [240], a Cu coverage of2.8 ML lowered TC by more than 30 K.

7.5 Surface anisotropy energy

The interface and surface anisotropy of the uncovered, H2-, CO- and Cu coveredNi …lms were calculated from the measured critical thicknesses. In the calculationsthe value 30 ¹eV/atom for the strain induced volume anisotropy K2v [232] and2¼M2

s = 7:5 ¹eV/atom for the magnetostatic anisotropy was used. In principle theremight be di¤erences in the properties of the Cu/Ni and Ni/Cu interface. However,the experimental observation that the spin reorientation transition is independent ofthe Cu thickness above 2 ML and thermally stable upon annealing at 453 K indicatesthat the two interfaces can be considered as equal. The interface anisotropy energyK2i in Cu/Ni/Cu(001) is then given by the expression 2K2i = (2¼M2

s ¡K2v)dc. At300 K a critical thickness of dc = 7:4 ML for the Ni …lm capped with Cu is measured.This results in a value of K2i = ¡83 ¹eV/atom for a single Cu/Ni interface.

The surface anisotropy K2s for the clean Ni …lm at 300 K yields ¡153 ¹eV/atom,which follows from the measured critical thickness of 10.5 ML for the uncovered Ni

7.5. SURFACE ANISOTROPY ENERGY 147

…lm. The anisotropy energy K2s = ¡153 ¹eV/atom at the Ni/vacuum interfaceis much larger than the anisotropy energy K2i = ¡83 ¹eV/atom at the Ni/Cuinterface. This is in agreement with a recent ab initio calculation by Uiberackeret al. [274] and with experiments by O’Brien et al. [239]. The calculation showsthat the band energy di¤erence, and therefore the magnetic anisotropy energy, ismuch larger at the surface than at the interface. For a comparison with theoreticalcalculations, the values for K2s, K2i, K2v, and 2¼M2

s have to be extrapolated toT = 0 K. The temperature dependence of dc(T ) for the uncovered and the Cucovered Ni …lm is not very large as can be seen from Fig. 7.9. This is due to a similartemperature dependence ofK2i andK2s on the one hand andK2v on the other hand:while K2i and K2s are negative and K2v is positive, the temperature dependence ofdc(T ) is largely canceled. The temperature dependence of K2v has been measuredby Farle et al. [247]. When the extrapolated value K2v = 72 ¹eV/atom at T = 0 Kfrom Ref. [247] and the extrapolated critical thickness dc(0 K) = 11:6 ML for theclean Ni …lm are used, K2s +K2i ¼ ¡700 ¹eV/atom results. This value is muchlarger than the result of two theoretical calculations which yield a value of about¡100 ¹eV/atom [274, 275]. However, in Ref. [274] the de…nitions of K2s and K2i

are di¤erent from those used to analyze the experimental data. In the theoreticalwork, K2s and K2i are essentially the magnetic anisotropy energy of the surfaceNi layer and the interface Ni layer, respectively, while in the experimental workK2s and K2i are determined from the extrapolation down to zero …lm thickness.These two de…nitions lead to the same result only in the case that the magneticanisotropy energy does not change with thickness in the interior of the …lm, whichis, according to the calculation in Ref. [274], not ful…lled. A recent theoreticalwork by Henk et al. [276] indeed shows, that for a Ni …lm thickness up to at least10 ML the superposition of the interface and surface part strongly deviates fromtrue thin …lm geometry calculations. This indicates that quantized thin …lm statessigni…cantly contribute to the anisotropy energy.

From the measurements of dc on the adsorbate covered Ni …lms, the change ofK2s upon H2 and CO adsorption can be estimated. Extrapolation of the measuredcritical thickness to 300 K results in dc = 6:8 ML and K2s = ¡70 ¹eV/atom forthe H2 covered Ni …lm. Hence, the absolute value of the surface anisotropy energydecreases dramatically upon H2 adsorption. It seems that H2 and Cu adsorptionreestablishes a more bulk like behavior of the Ni surface. A drastic decrease of thecritical thickness is observed upon CO adsorption as well. If the measured criticalthickness dc = 7:3 ML for the CO covered Ni surface at 300 K is taken, a surfaceanisotropy energy K2s = ¡81 ¹eV/atom is obtained. The measured critical thick-ness at 300 K as well as the calculated surface anisotropy energies are summarizedin Table 7.1. From the experimental results in this chapter it can be concludedthat covering a Ni …lm with H2, CO or Cu reduces the surface anisotropy energyapproximately by 50%. The reduction of the surface anisotropy energy shifts theborder of the spin reorientation transition to smaller Ni …lm thickness. The criticalthickness is reduced by 4 ML and 3 ML upon H2 and CO/Cu coverage, respectively.


Table 7.1: Measured critical thickness dc of the spin reorientation transition at T= 300 K and derived surface anisotropy energies K2s. The surface anisotropy isderived using K2v = 30 ¹eV=atom, and 2¼M2

s = 7:5 ¹eV=atom from Ref. [232].

dc (ML) K2s (¹eV/atom)Ni/Cu(001) 10.5 -153

H2/Ni/Cu(001) 6.8 -70CO/Ni/Cu(001) 7.3 -81Cu/Ni/Cu(001) 7.4 -83

The in‡uence of H2 adsorption on the second spin reorientation transition willnow be discussed. The negative surface anisotropy energy causes in-plane magne-tization. The adsorption of H2 reduces this anisotropy, with a broader thicknessrange in which the direction of the magnetization is perpendicular to the …lm planeas result, i.e., the border of the …rst and second spin reorientation transition shiftto a smaller and larger Ni …lm thickness, respectively. The measurements shown inFig. 7.5 indicate a shift of the second spin reorientation transition to larger Ni …lmthickness indeed.

The in‡uence of CO and especially H2 adsorption on the magnetic propertiesof thin magnetic layers should even be considered in experimental setups with agood base pressure and without intentional gas exposure. For example, a H2 partialpressure of 3 £ 10¡11 mbar at 300 K will result in an equilibrium coverage of about0.1 ML [257]. A decrease of temperature by 20 K or an increase of the H2 pressureby a factor of 10 will increase this coverage by more than a factor of 3 and this equi-librium coverage is already reached after 30 minutes. In the experiments describedin Sec. 7.2 (base pressure < 4 £ 10¡11 mbar), the possible e¤ect of H2 adsorptionis indicated by a small arrow in Fig. 7.4. In this measurement the amount of H2

adsorption was minimized by fast data acquisition during decreasing substrate tem-perature. Therefore, in general the e¤ect of H2 adsorption on the spin reorientationtransition can be more pronounced. Due to a higher desorption temperature, e¤ectsof CO adsorption on the magnetic properties are expected even at elevated substratetemperatures. However, because of the usually much smaller partial pressure of COcompared to H2 unintentional CO adsorption can be avoided much easier than H2

adsorption.

7.6 Surface roughnessIn the experiments described in Sec. 7.2 and Sec. 7.3 the Ni …lms were annealed at453 K for several minutes before adsorption of H2 or CO. This resulted in smooth…lms [246] but did not change the magnetic properties besides a small reductionof the coercive …eld [272]. It has been shown that surface roughness may a¤ect dc

7.6. SURFACE ROUGHNESS 149

150 200 250 300 350 400 4509

10

11

12

"as grown"

annealed to 453 K

d

c (M

L)

T (K)

Figure 7.11: Critical thickness of the spin reorientation transition in a Ni …lm as afunction of substrate temperature for a Ni wedge grown at 298 K (triangles) andthe same wedge after annealing at 453 K (circles). The …lled symbols indicate thethickness at which the Kerr asymmetry with 300 Oe external …eld dropped to 50%of the extrapolated asymmetry. The open symbols indicate the thickness at whichthe remanent Kerr asymmetry dropped to 80% of the extrapolated asymmetry.

as well [227, 241]. To characterize the in‡uence of surface roughness on the spinreorientation transition, the critical thickness measured on “as grown” and annealedNi …lms will be compared in this section. Figure 7.11 shows the temperature de-pendence of the critical thickness for an “as grown” (triangles) and annealed Ni …lm(circles). The open symbols represent the critical thickness determined from thevanishing of the remanent polar Kerr asymmetry (drop to 80% of the extrapolatedKerr asymmetry as illustrated in the inset of Fig. 7.4), while the …lled symbols rep-resent the critical thickness determined from the Kerr asymmetry with an appliedmagnetic …eld of 300 Oe (drop to 50% of the Kerr asymmetry). The data for the “asgrown” Ni …lm were …rst collected by lowering the substrate temperature, startingfrom 298 K (the deposition temperature) directly after growth. As discussed above,the critical thickness at the lowest temperature might be slightly reduced alreadydue to H2 adsorption. The data above room temperature were taken afterwardswith increasing temperature. Above 320 K the H2, adsorbed during growth of theNi …lm and during the time the sample was below room temperature, is completelydesorbed. Therefore, the open triangles above 320 K indicate the vanishing of theremanent polar magnetization of the clean …lm with the “as grown” surface mor-phology. At high temperatures close to the Curie temperature the remanent polar


Kerr asymmetry disappears below a thickness of 10 ML. This might be caused by theformation of domains [277] with domain sizes below the resolution of our Kerr mi-croscope [117]. The in‡uence of domain formation is absent in the critical thicknessderived from the Kerr asymmetry with an applied …eld of 300 Oe (…lled symbols).In both cases, a reduced critical thickness of up to about 0.4 ML is found for the“as grown” (rougher) Ni wedge compared to the annealed …lm. At elevated temper-atures smoothing of the “as grown” …lm becomes signi…cant and the datapoints ofthe “as grown” …lm merge into those of the annealed …lm.

The reduction of the critical thickness can be explained by a roughness-induceddecrease of the e¤ective surface anisotropy K2s [227, 278]. Two separate contribu-tions to the decrease of K2s can be distinguished. First, step edge atoms con-tribute only half of the surface anisotropy of atoms in the terrace. Therefore,¢K2s = R step/terrace £ K2s=2, with Rstep/terrace the ratio between the number ofstep edge atoms and the number of atoms in the terrace. Second, the magnetostaticanisotropy decreases with surface roughness. Following Ref. [278], this contribu-tion can be calculated from the average terrace width » and height 2¾. From STMmeasurements by Shen et al. [272] a rms roughness of 1.5 Å and an average islandseparation of about 60 Å for a 10 ML thick Ni …lm can be derived. From these pa-rameters and the theory in Ref. [227] it follows that the change of the magnetostaticanisotropy is less than 1 ¹eV/atom: This change is very small and can therefore beignored. The total contribution of the roughness to the surface anisotropy K2s iscalculated to +15 ¹eV/atom. As is evident from Fig. 9 of Ref. [272], annealing of a10.2 ML Ni …lm results in strong reduction of the surface roughness. The adatomstructure height is reduced by approximately a factor 2, whereas the average islandseparation is enhanced by a factor 2. The remaining contribution of the surfaceroughness to the surface anisotropy of the annealed Ni …lm is only +4 ¹eV/atom.From these parameters a di¤erence of 0.5 ML in critical thickness can be calculated(the critical thickness is smaller for the “as grown” Ni …lm), close to the experimen-tally observed di¤erence of less than 0.4 ML. The shift of the critical thickness issmall compared to the observed shift after H2, CO or Cu adsorption. Consequently,changes in the surface morphology have only a minor e¤ect on dc.

7.7 Conclusions

The adsorption of H2, CO or Cu reduces the critical thickness of the spin reorien-tation transition in Ni/Cu(001) drastically. The reduction of the critical thicknessafter H2 and CO adsorption is about 4 ML and 3 ML, respectively. The shift of thespin reorientation transition to smaller Ni …lm thickness is attributed to a decreaseof the negative surface anisotropy energy. The calculation of the surface anisotropyenergy for H2, CO, and Cu covered Ni …lms on Cu(001) yield values about 50%smaller than that for uncovered Ni …lms. Compared to H2, CO and Cu adsorp-tion, the in‡uence of surface roughness is negligible. A shift of less than 0.4 ML is


observed after annealing a room temperature grown Ni …lm at T = 453 K. The ob-served in‡uence of H2 and CO adsorption on the magnetic properties of Ni/Cu(001)may well be representative for the in‡uence of adsorbates on thin magnetic …lms ingeneral.

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[3] G.L. Kellogg and P.J. Feibelman, Phys. Rev. Lett. 64, 3143 (1990).

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[5] R.L. Schwoebel and E.J. Shipsey, J. Appl. Phys. 37, 3682 (1966).

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Summary

In this thesis several mechanisms controlling the surface morphology and magneticanisotropy of thin metal …lms are described. In the di¤erent chapters the focus is laidon the in‡uence of the deposition and ion sputtering geometry (polar and azimuthalangle of incidence), the in‡uence of the substrate temperature, and the in‡uence ofadsorbates. The surface morphology was investigated with thermal energy heliumatom scattering (TEAS) and spot pro…le analysis low energy electron di¤raction(SPA-LEED), whereas the magneto-optic Kerr e¤ect (MOKE) was used to studythe magnetic properties of thin …lms.

In Chap. 3 the in‡uence of the deposition geometry on the evolution of the sur-face morphology during molecular beam epitaxy (MBE) of Cu/Cu(001) is described.The growth fronts become progressively rougher upon rotation of the molecularbeam from normal to more grazing incidence. This remarkable kinetic rougheningis explained by steering. Steering refers to preferential arrival of incident atoms ontop of adatom structures, at the cost of incident ‡ux reduction on lower terraces.Steering originates from long-range attractive forces between incident atoms andsubstrate atoms and it shifts the growth mode from layer-by-layer toward multi-layer growth. Steering has remained undetected in more than a century of growthstudies, which was facilitated by a rather marginal ‡ux heterogeneity occurring dur-ing deposition of material at normal incidence. However, when an o¤-normal growthgeometry is selected, ‡ux heterogeneity easily becomes substantial giving rise to en-hanced surface roughness. Calculations reveal that the redistribution of incident‡ux increases with the angle of incidence and becomes sizeable for MBE growth atangles larger than 50±: Calculations also show that steering becomes increasinglyimportant with increasing height of the adatom structures, i.e., steering leads toauto-catalyzed kinetic roughening.

The experiments in Chap. 3 reveal that the deposition geometry in‡uencesthe shape and slope of growing adatom structures. At normal incidence fourfoldsymmetric mounds develop, arranged in a checkerboard-like pattern. In contrastto this, asymmetric mounds or ripples evolve during growth at angles larger than50±. The well-ordered ripples, which are obtained after growth at 80± with theCu(001) substrate at 250 K, are oriented perpendicular to the plane of incidence.The facets of the grown adatom structures are steeper after deposition at moregrazing incidence. Slopes corresponding to {111}, {113} and {115} facets can beobtained at a growth temperature of 250 K. The fact that di¤erent facets are formed

167

168 SUMMARY

at one and the same temperature directly re‡ects the kinetic origin of slope selection.The experimental …ndings in Chap. 3 are explained by a combination of steering,shadowing, and surface di¤usion processes. The measurements reveal that steeringalready in‡uences the surface morphology during the growth of the …rst monolayer.At grazing incidence rectangular adatom islands evolve in contrast to square onesgrowing at normal incidence. The long sides of the adatom islands are orientedperpendicular to the plane of incidence.

The so far unanticipated steering phenomenon should be taken into accountwhenever comparison between experiment and/or experiment and theory is under-taken. Its consequences may vary from insigni…cant for monolayer high adatomislands and normal incidence deposition to substantial for grazing incidence depo-sition. Steering is expected to be stronger for metals than for semiconductors orisolators.

Grazing incidence ion sputtering of the Cu(001) surface is described in Chap. 4.Ion sputtering at an angle of 80± results in a well-ordered line structure of only afew monolayers deep. The orientation of the lines is, irrespective of the azimuthaldirection of ion sputtering, parallel to the plane of incidence. The separation be-tween the lines increases exponentially with the sputtering temperature above 200K. This opens the way to the creation of well-ordered one-dimensional structureswith a tunable lateral distance between 5 nm and 20 nm. The formation of linesis explained by preferential sputtering of illuminated step edge atoms. After theformation of an isotropic distribution of small vacancy islands, preferential sput-tering of the illuminated steps leads to elongation and subsequent coalescence ofvacancy islands parallel to the plane of incidence. After coalescence, the step edgeroughness is e¤ectively reduced by step edge di¤usion and preferential sputtering ofilluminated kink site atoms. The experiments in Chap. 4 reveal two other parame-ters that in‡uence the surface morphology during grazing incidence ion sputtering.First, the azimuthal direction of ion sputtering in‡uences the separation betweenlines at elevated substrate temperatures. The dependence on the azimuthal direc-tion of incidence is most probably caused by a di¤erence in the elongation of vacancyislands during the initial stages of surface erosion. Second, the energy of incidentions in‡uences the separation between lines at low substrate temperatures. The ionenergy dependence is attributed to an ion impact induced surface di¤usion. Col-lisions between incident ions and substrate atoms result in an energy transfer tothe surface. This energy transfer leads to a locally enhanced surface temperatureexactly around the position of ion impact and enables vacancies to di¤use until thetransferred energy is relieved again.

In Chap. 5 the growth of Co and Co/Cu multilayers on Cu(001) is described.SPA-LEED measurements suggest signi…cant exchange of Co adatoms and Cu sub-strate atoms above 330 K. The exchange process in‡uences the surface morphologyduring the growth of the …rst and subsequent monolayers. The embedded Co atomsin the outermost surface layer act as additional nucleation sites. As a result, a sud-den increase of the adatom island density is measured around 330 K. Furthermore,

169

exchange of Co adatoms and Cu substrate atoms leads to a broadening of the islandsize distribution. Except for the …rst monolayer, the growth of Co on Cu(001) andCu on fct Co(001) proceeds layer-by-layer. The remarkable growth behavior of thissystem leads to Co/Cu multilayers with smooth interfaces as long as surface alloy-ing is limited (T < 330 K). Segregation of Cu to the Co …lm surface occurs duringannealing. The onset temperature for Cu segregation through a 2 ML and 4 MLthick Co …lm is 400 K and 450 K, respectively. After prolonged annealing at 523 K,the outermost surface layer consists of small Co clusters, intermixed Co/Cu areas,and pure Cu areas.

The deposition angle dependence of the in-plane magnetic anisotropy in ultrathinCo …lms on Cu(001) is described in Chap. 6. Grazing incidence MBE of Co along the[110]-azimuth results in an in-plane uniaxial magnetic anisotropy, whose strengthincreases with increasing deposition angle. For deposition angles larger than 10±the magnetic easy axis is oriented perpendicular to the plane of incidence. Theuniaxial magnetic anisotropy is directly related to the formation of elongated adatomstructures during o¤-normal growth. The long sides of the elongated structures areoriented perpendicular to the plane of incidence, i.e., parallel to the magnetic easyaxis. The formation of elongated instead of square adatom structures is explained bysteering, which is described in Chap. 3. Attractive forces between incident atomsand substrate atoms give rise to preferential arrival of incident atoms on top ofadatom structures, resulting in an anisotropy in the adatom structure growth rate.The micromagnetic origin of the uniaxial magnetic anisotropy in grazing incidencedeposited Co …lms arises mainly from missing bonds at Co step edges. This followsfrom the observed decrease of the anisotropy upon covering a Co …lm with Cu.

In Chap. 7 the in‡uence of H2, CO and Cu adsorption on the magnetic anisotropyin thin Ni …lms on Cu(001) is described. Due to the interplay of di¤erent magneticanisotropy contributions, a rotation of the magnetization from in-plane to out-of-plane occurs at a …lm thickness of about 11 ML. The adsorption of H2, CO or Cureduces the critical thickness of the spin reorientation transition drastically. Thisreduction is about 4 ML and 3 ML after H2 and CO or Cu adsorption, respectively.The shift of the spin reorientation transition to lower …lm thickness is attributed toa decrease of the surface anisotropy energy. The experiments reveal that the surfaceanisotropy energy for covered Ni …lms is about 50% smaller than for uncovered(clean) Ni …lms. Due to the adsorption sensitivity, the in‡uence of CO and especiallyH2 adsorption on the magnetic properties of thin magnetic layers should even beconsidered in experimental setups with a good base pressure and without intentionalgas exposure. The in‡uence of the surface roughness on the spin reorientationtransition is small. Annealing a room temperature grown Ni …lm results in a shiftof only 0.4 ML.

170 SUMMARY

Samenvatting

Dit proefschrift beschrijft verschillende mechanismen die bepalend zijn voor de op-pervlaktemorfologie en magnetische anisotropie van dunne metaal…lms. In de ver-schillende hoofdstukken ligt de nadruk op de invloed van de depositie- en sputter-geometrie (zowel de polaire als de azimutale hoek van inval), de invloed van desubstraattemperatuur en de invloed van adsorptie. De oppervlaktemorfologie isbestudeerd met helium verstrooiing en hoge resolutie elektronen di¤ractie, terwijlhet magneto-optische Kerr e¤ect gebruikt is om de magnetische eigenschappen vandunne metaal…lms te bestuderen.

In hoofdstuk 3 wordt de invloed van de depositiegeometrie op de evolutie van deoppervlaktemorfologie tijdens de groei van Cu/Cu(001) beschreven. Uit de experi-menten volgt dat de ruwheid van het oppervlak toeneemt als de groei in plaats vanloodrecht op het oppervlak meer scherend plaatsvindt. De opmerkelijke kinetischeverruwing tijdens scherende groei kan worden verklaard met een fenomeen dat wijsteering noemen. Steering verwijst naar het bij voorkeur aankomen van invallendeatomen op de hoge terrassen van het oppervlak ten koste van een ‡uxverlaging opde lage terrassen. Het steeringe¤ect is een gevolg van attractieve krachten tussen in-vallende atomen en substraatatomen en leidt tot een verschuiving van laag voor laaggroei (resulterend in een glad oppervlak) naar driedimensionale groei (resulterend ineen ruw oppervlak). Steering is gedurende een eeuw van groeistudies over het hoofdgezien. Dit komt o.a. doordat groei bij loodrechte inval slechts een kleine ‡uxhetero-geniteit tot gevolg heeft. Bij scherende inval is de herverdeling van invallende ‡ux endaarmee de verruwing van het oppervlak echter veel groter. Berekeningen geven aandat de herverdeling van invallende ‡ux belangrijk wordt voor invalshoeken groterdan 50± (ten opzichte van de oppervlaktenormaal). De berekening laten tevens ziendat het steeringe¤ect toeneemt met een toenemende hoogte van de oppervlaktestruc-turen. Steering leidt daarom tot een autokatalytische verruwing van het oppervlak.

De experimenten in hoofdstuk 3 laten zien dat de depositiegeometrie zowel devorm als de helling van driedimensionale oppervlaktestructuren beïnvloedt. Bij eenloodrechte inval van Cu atomen ontstaat een schaakbordpatroon van viervoudigsymmetrische piramidestructuren. De oppervlaktemorfologie verandert sterk alseen invalshoek groter dan 50± wordt ingesteld. In dat geval kunnen asymmetrischepiramide- of ribbelstructuren ontstaan. De goed geordende ribbelstructuren, diebij een invalshoek van 80± en een substraattemperatuur van 250 K ontstaan, zijnloodrecht op het vlak van inval georiënteerd. De zijvlakken van de driedimensionale

171

172 SAMENVATTING

structuren zijn steiler na groei bij meer scherende inval. Zijvlakken die correspon-deren met {111}, {113} en {115} facetten kunnen bij een groeitemperatuur van250 K worden verkregen. Het feit dat verschillende facetten bij een vaste groeit-emperatuur kunnen ontstaan, toont direct aan dat de selectie van de zijvlakhellingeen kinetische in plaats van een thermodynamische oorsprong heeft. De experi-mentele resultaten in hoofdstuk 3 kunnen worden verklaard door een combinatievan steering, schaduwwerking en di¤usieprocessen op het oppervlak. De metingenlaten tevens zien dat steering de oppervlaktemorfologie al tijdens de groei van deeerste atoomlaag beïnvloedt: bij scherende inval ontstaan rechthoekige in plaats vanvierkante eilanden. De lange zijden van de rechthoekige eilanden zijn loodrecht ophet invalsvlak georiënteerd.

Als een groeiexperiment met een ander groeiexperiment dan wel met groeitheoriewordt vergeleken, zal men rekening moeten houden met het tot nu toe onopgemerktesteeringe¤ect. De invloed van steering is klein voor lage oppervlaktestructuren enloodrechte inval en groot voor scherende inval. Het is te verwachten dat het steering-e¤ect groter is voor metalen dan voor halfgeleiders en isolatoren.

De structurering van het Cu(001) oppervlak tijdens ionenbombardement wordtgedetailleerd beschreven in hoofdstuk 4. Ionenbombardement met een invalshoekvan 80± (ten opzichte van de oppervlaktenormaal) resulteert in een goed geordendelijnstructuur van slechts enkele atoomlagen diep. De lijnen zijn, onafhankelijk van deazimutale invalsrichting, parallel aan het invalsvlak georiënteerd. De afstand tussende lijnen neemt boven 200 K exponentieel toe met de substraattemperatuur. Ionen-bombardement met een grote invalshoek kan daarom gebruikt worden om ééndimen-sionale structuren met een onderlinge afstand van 5 nm tot 20 nm te maken. Hetontstaan van een lijnstructuur kan met preferentiële erosie van beschenen stapran-den worden verklaard. Na het ontstaan van een isotrope verdeling van kleine va-catureeilanden, leidt preferentiële erosie van de beschenen stapranden tot een bijnaééndimensionale groei van deze eilanden. Dit heeft tot gevolg dat de coalescentievan vacatureeilanden parallel aan het vlak van inval plaatsvindt. Na coalescentiewordt de ruwheid van stapranden e¤ectief verkleind door de di¤usie van atomenlangs stapranden en door preferentiële erosie van beschenen kinkatomen. De exper-imenten in hoofdstuk 4 laten zien dat er nog twee andere parameters zijn die deoppervlaktemorfologie tijdens ionenbombardement beïnvloeden: de azimutale inval-srichting en de ionenenergie. Bij relatief hoge substraattemperaturen is de afstandtussen de lijnen afhankelijk van de azimutale invalsrichting. Deze afhankelijkheidis hoogst waarschijnlijk te verklaren door een verschil in vacaturelengte tijdens hetbegin van het erosieproces. Bij lage substraattemperaturen is de afstand tussen delijnen afhankelijk van de ionenenergie. Deze energieafhankelijkheid kan verklaardworden door ion-geïnduceerde oppervlaktedi¤usie. Bij botsingen tussen invallendeionen en substraatatomen wordt energie overgedragen aan het oppervlak. Deze en-ergieoverdracht resulteert in een lokale verhoging van de oppervlaktetemperatuur.Door de lokale verhoging van de oppervlaktetemperatuur is vacaturedi¤usie tijdelijkmogelijk.

173

In hoofdstuk 5 wordt de groei van Co en Co/Cu multilagen op Cu(001) beschreven.Di¤ractie metingen na de groei van een halve atoomlaag Co op Cu(001) suggererendat een e¢ciënte uitwisseling van gedeponeerde Co atomen en Cu substraatatomenboven een substraattemperatuur van 330 K plaatsvindt. Dit uitwisselingsprocesbeïnvloedt de oppervlaktemorfologie tijdens de groei van de eerste en de daaropvolgende atoomlagen. De Co atomen in de buitenste laag van het oppervlak func-tioneren als extra plaatsen voor eilandnucleatie. Dit heeft tot gevolg dat de ei-landdichtheid rond een temperatuur van 330 K plotseling toeneemt. Naast dezetoename van de eilanddichtheid heeft uitwisseling van gedeponeerde Co atomen enCu substraatatomen ook een grote variatie in de eilandgrootte tot gevolg.

Met uitzondering van de eerste atoomlaag groeit Co op Cu(001) en Cu op fctCo(001) laag voor laag. Het opmerkelijke groeigedrag van dit systeem leidt totCo/Cu multilagen met gladde scheidvlakken als de uitwisseling van Co atomen enCu atomen gering is (T < 330 K). Tijdens het verwarmen van een gegroeide Co…lm di¤underen Cu substraatatomen naar het …lmoppervlak. Deze di¤usie van Cuatomen begint bij 400 K en 450 K voor een Co …lm van respectievelijk 2 atoomlagenen 4 atoomlagen dik. Het verwarmen van een Co …lm tot 523 K resulteert in eenbuitenste oppervlaktelaag bestaande uit kleine Co clusters, gemixte Co/Cu clustersen gedeelten met alleen Cu.

De depositiehoek afhankelijkheid van de magnetische anisotropie in dunne Co…lms op Cu(001) wordt beschreven in hoofdstuk 6. Scherende groei van Co langs de[110]-richting heeft een in het …lmvlak liggende uniaxiale magnetische anisotropietot gevolg. De anisotropiesterkte neemt toe met toenemende invalshoek en de mag-netisch gemakkelijke as is loodrecht op het invalsvlak georiënteerd. De uniaxialemagnetische anisotropie is direct gerelateerd aan het ontstaan van langgerekte op-pervlaktestructuren tijdens scherende groei. De lange zijden van deze structurenzijn loodrecht op het invalsvlak, dus parallel aan de magnetisch gemakkelijke as,georiënteerd. Het ontstaan van langgerekte structuren kan met het in hoofdstuk 3beschreven steeringe¤ect worden verklaard. Attractieve krachten tussen invallendeatomen en substraatatomen hebben tot gevolg dat invallende atomen bij voorkeur opde hoogste terrassen van het oppervlak aankomen. Deze herverdeling van invallende‡ux leidt tot een anisotrope groei van oppervlaktestructuren. Uit micromagnetischoogpunt kan de uniaxiale magnetische anisotropie voornamelijk worden verklaarddoor de vrije bindingen aan Co stapranden. Dit kan worden geconcludeerd uit degrote afname van de uniaxiale magnetische anisotropie tijdens de groei van een Culaag op een Co …lm.

In hoofdstuk 7 wordt de invloed van H2, CO en Cu adsorptie op de magnetischeanisotropie in dunne Ni …lms op Cu(001) beschreven. De verschillende anisotropiebi-jdragen in Ni/Cu(001) hebben een magnetisatierotatie van parallel aan- tot lood-recht op het …lmvlak bij een …lmdikte van ongeveer 11 atoomlagen tot gevolg. Doorde adsorptie van H2, CO en Cu neemt de kritische dikte van de spin reoriëntatieovergang drastisch af. Deze afname is ongeveer 4 en 3 atoomlagen na de adsorptievan respectievelijk H2 en CO/Cu. De verschuiving van de spin reoriëntatie over-

174 SAMENVATTING

gang naar een kleinere …lmdikte is te verklaren door een afname van de magnetischeanisotropie aan het oppervlak. De experimenten laten zien dat de magnetischeanisotropie aan het oppervlak voor bedekte Ni …lms ongeveer 50% kleiner is dan datvoor onbedekte (schone) Ni …lms. De gevoeligheid voor adsorptie heeft tot gevolgdat men altijd rekening moet houden met de e¤ecten van CO en met name H2 (zelfsbij experimenten met een goede basisdruk en zonder het doelbewust inlaten van gas).In tegenstelling tot adsorptie heeft oppervlakteruwheid slechts een beperkte invloedop de spin reoriëntatie overgang. Het verwarmen van een bij kamertemperatuurgegroeide Ni …lm resulteert in een verschuiving van slechts 0.4 atoomlagen.

Dankwoord

Aan het einde van vier jaar onderzoek in de leerstoel Vastesto¤ysica kan ik metplezier terugkijken op deze periode. Ik wil van deze gelegenheid gebruik maken omeen aantal mensen te bedanken voor de prettige samenwerking en hun bijdrage tothet welslagen van mijn proefschrift.

Allereerst wil ik mijn promotor Bene Poelsema bedanken voor de mogelijkheiddie hij mij heeft geboden om te promoveren. Zijn enthousiasme in discussies enstimulerende ideeën heb ik altijd erg gewaardeerd.

Louis Jorritsma wil ik bedanken voor de goede samenwerking in het begin vanmijn promotie. Door hem leerde ik de verschillende meettechnieken en het vac-uumsysteem goed kennen. Zonder deze goede introductie was de start van mijnpromotieonderzoek niet zo voorspoedig verlopen.

Een grote bijdrage aan het experimentele onderzoek is verder geleverd door Ton,Dennis en Giovanni. Ton heeft zich tijdens zijn afstuderen bezig gehouden met degroei van kobalt op koper. De resultaten van dit onderzoek zijn in hoofdstuk 5verwerkt. Ik wil Ton tevens bedanken voor de gezellige tijd op de tennisbaan enin de stad. Dennis heeft onderzoek gedaan naar het sputteren van een koperopper-vlak. Veel metingen in hoofdstuk 4 zullen hem bekend voorkomen. Ik wil Dennisook bedanken voor de leuke discussies over de meetresultaten, waarin hij altijd eenduidelijk eigen mening had. Giovanni, thanks a lot for your enthusiasm and the nicetime we had during your stay in Enschede. I wish you all the best with the last partof your study.

Mein besonderer Dank gilt Herrn Prof. Dr. J. Kirschner für die Möglichkeit dreiMonate am Max-Planck Institut für Mikrostrukturphysik in Halle zu verbringen.Bei Rudiger Vollmer möchte ich mich gerne bedanken für die gute Zusammenarbeit,aus des Kapitel 7 hervorgegangen ist. Außerdem will ich mich bei allen anderenKollegen aus Halle bedanken, mit denen ich innerhalb und außerhalb des Institutseine schöne Zeit verlebt habe.

Zonder technische ondersteuning is onderzoek niet mogelijk : Herman Oerbekke,Gerard Kip en Geert Mentink bedankt voor het werk dat jullie in de afgelopen vierjaar hebben verricht.

Alle mensen die tijdens mijn promotie in de leerstoel Vastesto¤ysica aanwezigwaren wil ik bedanken voor de gezellige werksfeer en de hulp bij mijn promotie. Inhet bijzonder wil ik Marcus bedanken voor de leuke tijd op vloer vijf, in de staden in het sportcentrum. Herbert, Harold, Ben, Georg, Wulf, Paul, Petra, Chera,

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176 DANKWOORD

Cristina en Rianne bedankt voor jullie bijdrage en de leuke tijd. Ik wens Erwin,Esther, Frank, Marcus, Oguzhan en Ronny veel succes bij hun promotieonderzoek.

Tenslotte wil ik graag van de gelegenheid gebruik maken om mijn ouders tebedanken voor hun ondersteuning tijdens mijn studie en mijn promotieonderzoek.

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