Annual Report 1999 - uni-konstanz.de

SOLID STATE andCLUSTER PHYSICS

Annual Report 1999

Universität KonstanzFachbereich Physik

UniversitätKonstanz

350 500 650

GaN:Pt, 4 K

Pt1

15 meV

17 d

FWHM ~ 6 meV

YL

PL

inte

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.u

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s)

wavelength (nm)

3.5 3.0 2.5 2.0

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x 40

1.47 1.43

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Fie

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Depth z (nm)

Universität KonstanzFachbereich Physik

Annual Report

1999

Solid State and Cluster Physics

Universität Konstanz, Fachbereich Physik D-78457 Konstanz, Universitätsstraße 10

Tel. (07531) 88-2415; Telefax (07531) 88-3888

E-mail: [email protected] http://www.uni-konstanz.de/FuF/Physik/

mailto:[email protected]

http://www.uni-konstanz.de/FuF/Physik/

Cover pictures (from top):

�� LPE layer for solar cell application grown on a polycrystalline substrate (article 1.12) �� Monte Carlo-configuration of a pure CO-monolayer on graphite (article 1.31) �� Field profile inside a YBCO film in the Meissner state (article 1.1) �� Structures produced by colloid monolayer lithography (article 1.15) �� Photoluminescence spectra of 191Pt doped GaN (article 1.6) �� Al70 cluster on graphite (article 2.3)

Editing: M. Deicher, Ch. Niedermayer, T. Blasius, A. Maier Printing: Fabian, Konstanz

© 2000 Universität Konstanz, Fachbereich Physik

This report can be downloaded in Adobe® Portable Document Format (PDF) from http://www.ub.uni-konstanz.de/serials/phyfest.htm

http://www.ub.uni-konstanz.de/serials/phyfest.htm

http://www.ub.uni-konstanz.de/serials/phyfest.htm

I. Preface

By this annual report we present a comprehensive survey of our department’s activities in solid state physics and cluster physics in 1999. This report was possible by the large amount of interesting contribu-tions from our colleagues. We thank all co-workers from the secretaries’ offices, central services, laborato-ries and workshops of the university contributing to the results of the previous year.

It is a great pleasure to report the recognition given to the Konstanz research in form of awards in 1999, namely the ‘Ecology Design Award’ (sunways company) for Dr. Fath (LS Bucher) and the ‘Dornier Special Award’ (Dornier company) for colloid masks and nano-structuring (LS Leiderer).

We gratefully acknowledge the generous support given by several research institutions, institutes and companies, in particular the ‘German Research Society’ (DFG), the ‘European Union’ (scientific projects: ACE, ASCEMUS, HIT, Fast-IQ, SIMU), the ‘State of Baden-Württemberg’, the ‘German Ministry of Education, Science, Research and Technology’ (BMBF), the ‘East European Office of the BMBF’, the ‘Ger-man-Israeli-Foundation’ (GIF, Jerusalem), the ‘Paul-Scherrer-Institute’ (Villingen/Switzerland), the ISOLDE/CERN (Geneva/Switzerland), and the companies ASE, Bayer, centrotherm, Ersol, EKRA, Merck, Solon, sunways, Winter, Zeiss and BP Solarex (USA/GB), DISCO HiTec (J), Elkem (N), Evergreen Solar(USA), Eurosolare (I), GT Solar (USA), Helios (I), Photowatt (F), Shell Solar (NL).

Konstanz, July 2000

Peter Nielaba

iv Universität Konstanz - Solid State and Cluster Physics

Contents

I. Preface iii

II. Research Reports 1

1. Solid State Physics 1

1.1 Direct measurements of the penetration of a magnetcic field into a superconductor in the Meissner state .....................................................................................1

1.2 Temperature dependence of the magnetic penetration depth in an YBa2Cu3O7-� film ..................................................................................................................2

1.3 Low temperature vortex structures of the mixed state in underdoped Bi2Sr2CaCu2O8+� (Bi-2212) single crystals...........................................................................3

1.4 Ultrafast magneto-optical studies...........................................................................................5

1.5 Electrical characterization of 111Ag doped GaN ....................................................................7

1.6 Near-infrared-photoluminescence in GaN doped with radioactive platinum.........................9

1.7 Observation of free H after annealing of GaN implanted with 117Cd(117In)........................11

1.8 Behavior of doping atoms in CdCr2Se4 ...............................................................................13

1.9 Crystalline silicon solar cells – new materials .....................................................................15

1.10 Compound semiconductors for photovoltaics / materials for thermoelectric applications ..................................................................................................17

1.11 Industrial solar cell development .........................................................................................20

1.12 Thin film silicon solar cells on low-cost metallurgical silicon substrates............................23

1.13 Novel solar cells ...................................................................................................................24

1.14 Solar cell characterization ....................................................................................................29

1.15 Colloidal mask lithography..................................................................................................31

1.16 Surface structuring with ultrashort laser pulses ...................................................................32

1.17 Metallic nanostructures on metaldichalcogenides................................................................33

1.18 Self-organized growth of epitaxial CoPt3 nanostructures on WSe2 .....................................34

1.19 Co islands on WSe2..............................................................................................................35

1.20 A low energy muon study of the dipolar fields produced by an assembly of iron nanoclusters in silver ....................................................................................................36

1.21 Dimensional cross-over in AuFe spin-glass studied by low energy muons .........................37

1.22 Magnetic anisotropy and chemical long-range order in epitaxial ferrimagnetic CrPt3 films .....................................................................................................38

1.23 Structure of Pt/Mn superlattices grown by molecular beam epitaxy ...................................40

1.24 Modified growth of Co on Cu(111) using In as an interlayer ..............................................42

1.25 Laser cleaning of silicon surfaces ........................................................................................44

1.26 Range of low energy muons in Cu films..............................................................................46

1.27 Response of the electric field gradient on an external electric field.....................................47

1.28 Diffusion of muons in metallic multilayers..........................................................................49

1.29 Energy dependence of muonium formation in solid Ar, N2, Xe, and SiO2..........................50

Annual Report 1999 v

1.30 Progress on the low energy �+ apparatus .............................................................................51

1.31 Phase transitions in two dimensional (adsorbed) layers at low temperatures ......................52

1.32 Phase transitions in alloys with elastic interactions .............................................................54

1.33 Enrichment of surfaces in contact with stable binary mixtures ...........................................56

1.34 Elastic constants from microscopic strain fluctuations and melting of hard disks in two dimensions ...............................................................................................58

1.35 Low temperature properties of molecular solids..................................................................60

1.36 Structures, phases, and phase transitions in solids in reduced geometry .............................62

1.37 Correlations and dynamic ordering processes near solid surfaces .......................................64

1.38 Transport processes in glasses..............................................................................................68

2. Cluster Physics 70

2.1 The structure of medium sized silicon cluster anions ..........................................................70

2.2 Time resolved dynamics of electronic excitations in C-3 ......................................................72

2.3 Deposition of mass selected aluminum clusters...................................................................74

2.4 A new experimental setup for the in situ investigation of the electronic, vibrational and chemical properties of monodisperse supported clusters ..............................................76

2.5 Sputtering with cluster ions..................................................................................................78

III. Publications and Talks 80

1. Publications ..........................................................................................................................80

2. Conference contributions .....................................................................................................85

3. Lectures ................................................................................................................................91

4. Theses...................................................................................................................................93

IV. Staff and Guests 96

Annual Report 1999 1

II. Research Reports

1. Solid State Physics

1.1 Direct measurements of the penetration of a magnetcic field into a superconductor in the Meissner state

E.M. Forgan, T.J. Jackson and T.M. Riseman (University of Birmingham, Birmingham B15 2TT, United Kingdom) in collaboration with H.Glückler, E. Morenzoni and T. Prokscha (Paul-Scherrer-Institut,CH-5232 Villigen, Schweiz) Ch. Niedermayer, M. Pleines and G. Schatz M. Birke, J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig)

Low energy muons extend the utility of �SR to thin films and multilayers, and to studies of near surface properties distinct from bulk behavior 1). In this report we describe the use of low energy muons to measure di-rectly the in plane penetration depth �ab of an YBa2Cu3O7-� (YBCO) superconducting film in the Meissner state. The depth of muon implantation was controlled between 20 and 150 nm by tuning the in-coming muon energy from 3 to 30 keV.

The YBCO film was a 700 nm thick film grown epi-taxially on a 50 mm diameter LaAlO2 substrate by H. Kinder's group at TU München. The magnetic field B0 of approximately 10 mT was applied using a permanent magnet assembly as shown in 2).

Fig. 1: Field profile inside the YBCO film in the Meiss-ner state at different temperatures. Inverse triangles: 20 K, triangles: 50 K, diamonds: 70 K, and squares: 80 K.

The field was applied perpendicular to the YBCO c-axis after zero field cooling the sample through the su-perconducting transition, so that the field was screened by supercurrents flowing within the ab-planes. Twinning within the ab planes precluded experiments with the field applied along a unique in-plane axis. The depth de-pendent field profile B(z) within such a semi-infinite su-perconducting slab follows from the well-known Lon-don exponential decay law, and is described by

� ��

� �0

cosh( )

coshab

ab

d zB z B

d

�

�

�

�

where d is the half thickness of the film 3). The results of our measurements are shown in Fig. 1, in which the solid lines represent fits of equation 1 to the experimen-tal data, shown by the points. The muon implantation profile was determined from simulations 4) and the field at the most probable depth determined from Maximum Entropy analysis 5) of the decay histograms.

Equation 1 describes the data well, yielding a value of �ab at 20 K of 146(3) nm, with which other less direct determinations agree 6). This method offers unique pos-sibilities for measurements of the field penetration in other geometries and materials where the London law is not expected to apply.

(1) E. Morenzoni et al., Physica B in press (2) H. Glückler et al., Progress on the low energy �+ appa-

ratus, PSI Scientific Report, Vol. 1 (1999) (3) D. Schoenberg, Superconductivity, (Cambridge Univer-

sity Press, Cambridge,1952) (4) H. Glückler et al., Physica B in press (5) T.M. Riseman and E.M. Forgan, Physica B in press (6) Ch. Niedermayer et al., Physical Review Letters 83

(1999) 3932 0 20 40 60 80 100 120 140 160

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T(K) � (nm)20 146(3)50 169(4)70 223(4)80 348(6)

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Depth z (nm)

2 Universität Konstanz - Solid State and Cluster Physics

1.2 Temperature dependence of the magnetic penetration depth in an YBa2Cu3O7-�� film

M. Pleines, Ch. Niedermayer and G. Schatz in collaboration with H.Glückler, E. Morenzoni and T. Prokscha (Paul-Scherrer-Institut,CH-5232 Villigen, Schweiz) M. Birke, J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig) E.M. Forgan, T.J. Jackson and T.M. Riseman (University of Birmingham, Birmingham B15 2TT, United Kingdom)

In many of the potential applications of high tem-perature superconductors thin films will play an impor-tant role. A proper characterization of the supercon-ducting parameters of these films is therefore of great interest. One of the fundamental parameters is the mag-netic penetration depth �ab. We have used the low en-ergy muon source 1) to study the temperature depend-ence of �ab of an YBa2Cu3O7-� (YBCO) film.

The measurements were performed on a 700 nm thick, c-axis orientated YBCO film (Tc = 87.5 K), grown epitaxially by thermal coevaporation on a LaAlO3 substrate. The film was characterized by a spa-tially resolved Jc - measurement using an inductive technique 2). The Jc(77 K) map of the investigated film, displayed in Fig.1, shows that the critical current density is very homogeneous over the whole sample area of the 2 inch wafer.

Fig. 1: Map of the critical current density Jc. In the area of the film (2 inches diameter) the critical current den-sity varies between 2.5×106 A/cm2 and 3×106 A/cm2.

An external field of 10.4 mT was applied parallel to the c-axis of the film. The sample was then field-cooled into the superconducting state. The energy of the in-coming muon beam was fixed at 29 keV.

YBCO is an extreme type II superconductor. When a magnetic field Hext > Hc1 is applied, a vortex lattice of the magnetic flux is formed. The field variation B(r) within the vortex lattice produces an asymmetric field distribution p(B) with a cusp which corresponds to the most probable field Bsad.

The measured field distribution was obtained from the time evolution of the muon spin polarization P(t) via

Maximum Entropy Technique. As it shown earlier 3) there is a good agreement between measured and theo-retical field distribution.

The penetration depth can be derived from the shift between the mean field Bext and the cusp field Bsad:

0

2( )ext sad

ab

B B c H�

��

Figure 2 shows the temperature dependence of the magnetic penetration depth �ab. The solid curve repre-sents a fit to a power law of the form:

� �� 1 2( ) (0) 1 nab ab cT T T� �

�

� �

with �ab = 137(10) nm and n = 1.7(3)

Fig. 2: Temperature dependence of the magnetic pene-tration depth �ab of a 700 nm thick YBCO film. For comparison the dashed lines with n = 2 and n = 4 are shown, where n = 4 is obtained from the two fluid model and observed for classical superconductors.

Our value of the penetration depth �ab(0) is in good agreement with results from conventional �SR meas-urements 4) on bulk samples. The inset shows �ab(T)/�ab(0) below 55 K in more detail together with data points from conventional �SR measurements on YBa2Cu3O6.95 single crystals 4). There is a very good agreement between both sets of data. The observed lin-ear temperature dependence was taken as evidence for an unconventional symmetry (d-wave) of the supercon-ducting order parameter.

(1) E. Morenzoni et al., Appl. Magn. Reson. 13 (1997) 219 (2) H. Kinder et al., Physica C 107 (1997) 282 (3) Ch. Niedermayer et al., Phys. Rev. Lett. 83 (1999) 3932 (4) J.E. Sonier et al., to be published

-24-24

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1.3 Low temperature vortex structures of the mixed state in underdoped Bi2Sr2CaCu2O8+�� (Bi-2212) single crystals

T. Blasius and Ch. Niedermayer in collaboration with J.L. Tallon and D.M. Pooke (New Zealand Institute for Industrial Research, Lower Hutt, New Zealand) A. Golnik, C.T. Lin, and C. Bernhard (Max Planck Institut für Festkörperforschung, Stuttgart, Germany)

One of the striking features of the high - Tc supercon-ductors (HTSC) is the influence of their electronic and magnetic anisotropy on the nature of the mixed state. The vortex lines in these systems reveal, contrary to conventional superconductors, a discreteness due to the layered structure of the HTSC. With the magnetic field applied along the c-axis direction (perpendicular to the CuO2 planes) the vortex lines can be viewed as stacks of pancake vortices. These quasi-two-dimensional vortex currents reside within the superconducting planes and are connected across the insulating spacer layers via electromagnetic interaction and Josephson coupling. Depending on the anisotropy �s = �c / �ab, where �c and �ab are the out-of-plane and in-plane penetration depths, the CuO2 layer spacing s and �ab, a wide variety of coupling scenarios from dominating electromagnetic coupling, (�ab < �s s), to dominating Josephson coupling (�ab > �s s) have been reported 1,2).

Here we present transverse-field muon spin rotation (TF-�SR) data on underdoped Bi-2212 single crystals, which were grown by a floating-zone technique as de-scribed elsewhere 3). In TF-�SR experiments, spin-po-larized muons are implanted into the bulk of the crystal. An external magnetic field Hext is applied perpendicular to the initial polarization of the muon spin and parallel to the c-axis of the crystals. The muons come to rest at interstitial locations, r, which are randomly distributed on the length scale of the magnetic penetration depth �ab. Their spins start to precess in the local magnetic field with the Larmor frequency �

� = �

� B(r), where �

�

is the gyromagnetic ratio of the muon with �� / 2� = 135.54 MHz / T. The time evolution of the

muon spin polarization P(t) is measured by monitoring the decay positrons, which are preferentially emitted along the muon spin direction at the instant of decay. The probability distribution of the local magnetic field n(B

� ) is extracted from P(t) via Fast Fourier Transform or Maximum entropy techniques and contains detailed information on the vortex structure.

For a static flux line lattice, n(B� ) is asymmetric 4)

with a pronounced tail towards high fields due to muons that stop near the vortex cores, a cusp that corresponds to the field at the saddle point between adjacent vortices and a cutoff on the low field side corresponding to the field minimum at the point that is most remote from the vortex cores.

A typical example for such a field distribution is shown in Figure 1, which has been measured at 5 K after field cooling in an external field of 8 mT. The additional feature at the external field value is due to a small frac-

tion of muons (~ 5%) not stopping in the sample which is included in the data analysis by a Gaussian distribu-tion. The solid line is a fit to the data as described in 3). Imperfections in the vortex lattice and instrumental resolution have been accounted for by a Gaussian con-volution with a smearing of ~8% in n(B

� ). The best result has been realized with �ab = 2000 (50) Å. The asymmetry of n(B

� ) can be characterized by the dimen-sionless parameter � � < �B3 >1/3 / < �B2 >1/2, where < �Bn > are the nth central moments of n(B

� ) [4]. A value of � ~ 1.2 is typical for a static well ordered flux line lattice, whereas 1 > � > 0 either indicates a disor-dered static vortex structure or else vortex dynamics in excess of the typical �SR time scale of � � 10-6 s 4,5).

Fig. 1: Magnetic field distribution (open squares) at T = 5 K determined in a field-cooled TF-�SR experiment on underdoped Bi-2212 single crystals (Tc = 77 K) in an applied field of �oHext = 8 mT. The solid line represents a fit to the data as described in [1].

Figure 2 shows observed field distributions at 5 K after field cooling in 8 mT and 10.3 mT. Figure 3 sum-marizes the results for the parameters � and Bsh of the field distribution n(B� ) for the measured field depend-ence at 5K after field cooling. The sudden reduction of � and Bsh at B* � 8.5 mT indicates a strong change in the vortex structure. The pinning properties of the different vortex states have been tested by reducing the applied field after the field-cooling process. For a rigidly pinned vortex state n(B

� ) will not follow the change of the applied field, whereas for a depinned vortex array n(B

� ) will follow the changes of Hext. The finding that on the time scale of hours n(B

� ) at T = 5 K is unaffected by the reduction of the external field by several mT indicates that the observed changes in n(B

� ) are of static rather than dynamic nature.

-4 -2 0 2 4 6

�oHext = 8.0 mT, T = 5 K

Bi2212underdoped, T

c = 77 K

n (

B�� )

[ ar

b. u

nits

]

B�� - ��o

Hext

[ mT ]


Fig. 2: Magnetic field distributions from field-cooled TF-�SR experiments at T = 5 K on underdoped Bi-2212 single crystals (Tc = 77 K).

As shown by E.H. Brandt 4) for the case of a static vortex state, the above described behavior can be ac-counted for only by disorder in the vortex lines along the c-axis direction on a length scale of �ab. For anisotropic systems with �ab < �s s, as for example underdoped Bi-2212, such a behavior has been related to a 'dimensional crossover' at Bcr � �o / (�ab )

2 [5]. To attribute the sudden change in the vortex structure at B* � 8.5 mT to Bcr � �o / (�ab )

2, �ab ~ 5000 Å is required in strong disagreement with the measured value of �ab ~ 2000 Å. However, as proposed by A.E. Koshelev, L.I. Glazman and A.I. Larkin 2), A.E. Koshelev and V. Vinokur 2) and E.H. Brandt 4), the observed changes in the internal field distribution are due to random displacements of the pancake vortices within the individual vortex lines induced by the pinning potential. The corresponding transition with increasing field is then a disorder-induced destruction of the vortex lattice, which is more pronounced in systems with large anisotropy due to the softening of the vortex lines.

Interestingly, we observe an increase of � and Bsh for fields �oHext � 350 mT = Bcp (Figure 3). Such a partial restoration of the coupling between the pancakes across the insulating spacer layers has been observed up to now only for increasing temperatures [6]. For the static case, this behavior may be related to the change in the pinning properties from single vortex pinning to bundle pinning [1] as the vortex density and thus the interaction be-tween the vortices increases. Additional experiments probing in detail the pinning properties have to be done to check for this possibility.

In summary, we find by TF-�SR experiments on un-derdoped Bi-2212 single crystals (Tc = 77 K) that the strong changes in the low-temperature vortex state at B*= 8.5 mT are consistent with a disorder-induced destruction of the vortex lattice. In addition, we obtained for the first time evidence for a low temperature resto-ration of the coupling in the c-axis direction for �oHext � 350 mT.

Fig. 3: Field dependence of � and Bsh of n(B� ) at

T = 5 K determined from field-cooled TF-�SR experi-ments on the underdoped Bi-2212 sample (Tc = 77 K).

(1) G. Blatter, V. Feigel'man, V.B. Geshkenbein, A.I. Larkin and V. Vinokur, Rev. Mod. Phys. 66 (1994) 1125

(2) A.E. Koshelev, L.I. Glazman and A.I. Larkin, Phys. Rev. B 53 (1996) 2786, A.E. Koshelev and V. Vinokur, Phys. Rev. B 57 (1998) 8026

(3) T. Blasius, PhD-thesis, Universität Konstanz 2000, http://www.ub.uni-konstanz.de/kops/volltexte/2000/405/ and references therein

(4) E.H. Brandt, J. Low Temp. Phys. 73 (1988) 355, ibid Phys. Rev. Lett. 63 (1989) 1106 and 66 (1991) 3213

(5) S.L. Lee, P. Zimmermann, H. Keller, R. Schauwecker, M. Warden, M. Savic, D. Zech, R. Cubitt, E.M. Forgan, P.H. Kes, T.W. Li, A.A. Menovsky, and Z. Tarnawski, Phys. Rev. Lett. 71 (1993) 3862, C.M. Aegerter, S.L. Lee, H. Keller, E.M. Forgan, and S.H. Lloyd, Phys. Rev. B 54 (1996) R15661

(6) T. Blasius, Ch. Niedermayer, J.L. Tallon, D.M. Pooke, A. Golnik and C. Bernhard, Phys. Rev. Lett. 82 (1999) 4926

-4 -2 0 2 4 6

� ~ 0.2

� ~ 1

�oH

ext = 8.0 mT

�oHext = 10.3 mT

Bi-2212underdoped, Tc = 77 K

n (

B�� )

[ ar

b. u

nits

]

B�� - ��o

Hext

0.2

0.4

0.6

0.8

1.0

��

( �

oHex

t = 5

.8 m

T )

�� (

�oH

ext )

10 100 1000

0.2

0.4

0.6

0.8

1.0

Bcp

B*

Bsh

( �

oHex

t = 5

.8 m

T )

��oHext [ mT ]

Bsh

( �

oH e

xt )

http://www.ub.uni-konstanz.de/kops/volltexte/2000/405/


1.4 Ultrafast magneto-optical studies

B.-U. Runge, U. Bolz, B. Böck, C. Häfner and P. Leiderer

1. Investigations of flux avalanches in high-Tc superconductors

An ultra fast magneto-optic pump-probe technique has been used to trigger and image a flux instability in high-temperature superconducting thin films. Snapshots of the dendritic flux avalanche spreading into the film could be obtained with a time resolution in the picosec-ond range.

The dynamics of magnetic flux avalanches in high-temperature superconductors (HTSC) is of great interest not only from a fundamental point of view, but also with respect to the application of these materials e.g. as cur-rent limiters in the field of electrical power distribution. Previous studies 1) have shown that much of the flux dy-namics in YBa2Cu3O7-� takes place well below the nanosecond range. Therefore it is necessary to improve the time resolution into the picosecond regime to get more detailed information about the processes involved.

All samples studied were 330 nm thick epitaxially grown c-axis oriented YBa2Cu3O7-� films deposited by thermal evaporation onto SrTiO3 2). The experiments were carried out in a small continuous flow cryostat, which had two optical windows with a diameter of 25 mm. For detecting the magnetic field penetrating the superconductor we used a doped ferrimagnetic iron gar-net layer grown onto gadolinium-gallium-garnet sub-strate by liquid phase epitaxy with an additional alumi-num layer 3). This magneto-optical layer was placed just above the YBCO film. By using a home-built polariza-tion microscope the local Faraday rotation of the linearly polarized light caused by the local magnetic field Hz in the magneto-optical layer was made visible with nearly crossed polarizer and analyzer as an intensity contrast and imaged with a 12 bit slow-scan CCD camera.

The YBCO film was zero field cooled down to 10 K. After reaching a stable temperature an external magnetic field Bext perpendicular to the sample surface was ap-plied. Magnetic flux penetrated into the superconducting film first from the edges until a local equilibrium of the flux distribution due to the pinning force and the mag-netic force was reached. This induces a current distribu-tion in the superconducting film. That current distribu-tion can be disturbed to initiate a magnetic instability. For this purpose we used a single pulse of a Ti:sapphire laser (� = 800 nm, half width � = 150 fs) which was fo-cused onto the film from the substrate side to a spot di-ameter of about 50 µm. The sample temperature in the focus could not be measured directly, but from the pulse energy we estimate that the temperature rises well above the critical temperature.

If the perturbation is sufficiently strong, this triggers a magnetic instability, in which a magnetic flux ava-lanche penetrates into the film. In order to record snap-shots of the flux moving into the sample a beam splitter

is used to separate part of the trigger pulse and send it through a delay line for illumination of the sample at a well defined time after the trigger event. This time can be varied from below zero (illumination before trigger) to several 100 ns with an accuracy in the picosecond range.

Fig. 1: Snapshots of the flux penetration at delay times of 3.2 ns, 13.5 ns and 41.2 ns after the trigger event. Sample temperature T = 10 K, external magnetic flux density Bext = 19 mT. The size of the images shown is 1.8�1.8 mm2.

Fig. 1 shows typical snapshots at delay times of 3.2 ns, 13.5 ns and 41.2 ns for a sample temperature of T = 10 K and an external magnetic flux density of Bext = 19 mT. In order to have reproducible starting conditions, for each image the sample was heated above the critical temperature and zero field cooled again to 10 K. The form of the dendritic structure is found to be similar from image to image and for all delay times used, although the individual dendrites are not identical for subsequent laser pulses. The width of the dendrites and their mutual distance remains about constant during the process. A “typical spreading velocity” of the den-drites was calculated measuring the distance between the starting point of the avalanche (i.e. the laser focus) and the tip of a typical dendrite in the center of the ava-lanche. The average of this velocity over the first 41.2 ns is found to be 3.2(2)×104 m/s which is far above the velocity of sound in YBCO. In Fig. 2 we show the time dependence of the length of a typical dendrite.

In conclusion we have improved the time resolution for the magneto-optical observation of magnetic flux avalanches in high-Tc superconductor thin films from nanoseconds to picoseconds by using laser pulses with a half width of less than one picosecond. This allows a much more precise determination of the spreading ve-locity of the dendrites. We find 3.2(2)×104 m/s. This value is slightly lower than the value of 5(2)×104 m/s reported in an earlier study 1) which is probably due to differences in the sample preparation. The increased time resolution will allow us to study the very beginning of the flux avalanche and other phenomena caused by perturbation of superconducting films.

The authors would like to thank H. Kinder and K. Numssen for providing the YBCO films as well as H.


0 10 20 30 40 50

660

680

700

720

740

760

780

800

820

time [s]

de

tec

torsi

gna

l[m

V]

Dötsch and E. Il'yashenko for providing iron garnet layers.

Fig. 2: Length of a typical dendrite close to the center of the dendritic flux structure plotted as a function of time after the trigger event. The dotted line is a guide to the eye.

2. Pulsed magneto-optic Kerr measurements of thin magnetic cobalt films

The magnetic behavior of cobalt and its alloys is of special interest, as magnetic ordering can be observed in sufficiently supercooled melts 4). Up to now these stud-ies have been carried out using an electromagnetic levi-tation technique. This limits the cooling rate to about 100 K/s. Much higher cooling rates (and therefore lower temperatures of the supercooled melt) can be achieved using laser annealing on the nanosecond time scale. As an important first step towards the observation of the magnetic behavior of thin cobalt films during laser an-nealing and melting we performed magneto-optic Kerr (MOKE) measurements using single pulses of a Nd:YAG laser system. As the Co film is molten by the pulse and the melting time depends strongly on the pulse energy, it would be desirable to have absolutely repro-ducible pulse energies. But typically the energy varies by 5-10% from pulse to pulse not allowing averaging of the signal over subsequent pulses. It is therefore neces-sary to record the magneto-optic signal as well as the pulse power for each individual pulse with a time reso-lution of about 1 ns. Fig. 3 shows first results of such a measurement. In this case the sample was not really molten to create a change in the magnetic properties but

rather a sinusoidally slowly varying external magnetic field was applied in the plane of a Co film of 30 nm thickness. The resulting magneto-optic signal was de-tected and normalized to the pulse energy for each indi-vidual pulse (half width �10 ns) at a repetition rate of 10 Hz. The magnetic response of the film looks rather square than sinusoidal, indicating that the magnetic field was strong enough to drive the film into saturation. Our result shows the feasibility of single pulse Kerr meas-urements with our setup. Currently measurements are under way in which we melt the sample by each pulse and simultaneously record the thermal radiation in order to relate the magnetic properties to the temperature of the sample.

Fig 3: Pulsed MOKE measurement of 30 nm thick Co film. The strength of the external magnetic field was varied sinusoidally with a frequency of about 0.07 Hz and an amplitude of 10 mT. The film is driven into satu-ration, as can be seen from the rather square form of the detector signal.

(1) P. Leiderer, J. Boneberg, P. Brüll, V. Bujok and S. Herminghaus, “, Phys. Rev. Lett. 71 (1993) 2646

(2) P. Berberich, W. Assmann, W. Prusseit, B. Utz, and H. Kinder, J. of Alloys & Compounds 195 (1993) 271

(3) M. Wallenhorst, Herstellung und Charakterisierung magnetooptischer Eisengranatfilme für nichtreziproke Wellenleiter und magnetooptische Sensoren, PhD thesis, Universität Osnabrück (1998)

(4) C. Bührer, Der Flüssige Ferromagnet - Kritisches Ver-halten am magnetischen Phasenübergang der flüssigen Phase von Co80Pd20, PhD thesis, Universität Bonn (1998)

0 10 20 30 400

500

1000

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length

[µm

]

delay time [ns]


1.5 Electrical characterization of 111Ag doped GaN

A. Stötzler, M. Dietrich and M. Deicher in collaboration with ISOLDE Collaboration (CERN, Geneva)

The great interest on GaN is mainly based on the po-tential applications in optoelectronics and high tem-perature electronics. Most of the work during the last years have been focused on the optical properties and due to the difficulties in interpreting the gathered data there are only limited reports on the electrical properties of GaN 1,2). In spite of the fast development of new growing techniques, GaN is still a highly defective ma-terial. Especially after ion implantation and annealing it is extremely hard to distinguish between the intrinsic de-fects present in the GaN layer, defects caused by an-nealing or the levels introduced intentionally or uninten-tionally by implantation. Another problem is, that due to the small thickness of the epitaxial layer the measured values are strongly distorted by degenerate layers at the GaN/sapphire interface. The usual way of determining activation energies by temperature dependent Hall measurements often fails since low temperatures are re-quired and the lower the temperatures the greater the in-fluence of this distortion effect 3).

Defects are getting distinguishable if one uses radio-active dopands. The concentration of a defect containing a radioactive atom is changing with the element specific half-life of the decay while the concentrations of all other defects remain unchanged. Therefore, the fraction of activated ions after annealing, the carrier type or the influence on resistivity and mobility can be determined directly from exponential fits to the data.

Photoluminescence (PL) experiments on 111Ag-doped GaN have shown that Ag and Cd are introducing strong PL signatures in the PL spectra of GaN 4). In order to in-vestigate the electronic properties of Ag and Cd in GaN Hall measurements on 111Ag-doped GaN were performed.

For the Hall measurements a 1.5 µm epitaxial GaN layer grown on an AlN/c-sapphire substrate with a size of 5 �� 5 mm2 was used. The nominally undoped layer was n-type with a free carrier concentration of 5 � 1016

cm-3 prior to the annealing. The sample was doped by ion implantation with the radioactive isotope 111Ag at the on-line mass separator facility ISOLDE at CERN. This isotope decays within a half-life of 7.45 d into sta-ble 111Cd. The implantation energy was 260 keV and a maximum dose of 1 � 1013 cm-2 was used. During im-plantation the sample was covered with an aperture of 5 mm diameter in order to achieve a symmetric and ho-mogeneous implantation area. The Gaussian shaped im-plantation profile is centered at 56 nm depth with a width of 13 nm. The peak concentration is about 4 � 1018 ions/cm2. To reduce the implantation induced damage the sample was annealed 600 s in an evacuated quartz ampoule together with a piece of elementary Si at 1573 K 5). During annealing a SiNx layer develops at the

GaN surface which prevents the epitaxial layer from de-composition usually observed at such high annealing temperatures. After annealing the SiNx layer was re-moved by etching in a solution of 2 HF: 5 HNO3 : 2 C2H4O2. The electrical characterization was performed by van der Pauw Hall measurements using alloyed (473 K, 60 s) Indium contacts at the corners of the sample.

Fig. 1: Resistivity (upper graph) and carrier- concen-tration n of 111Ag-doped GaN (1013 cm-2, 260 keV) plotted as a function of temperature. The solid square spectra were recorded 3 h after annealing and the open square spectra were recorded 25 d after annealing.

Fig. 1 shows the net carrier-concentration n = (ND-NA) and the resistivity of the 111Ag-doped sample 3 h (solid squares) and 25 d (open squares) after implanta-tion and annealing as a function of temperature. For clarity only two of the 15 measurements are shown. One can clearly observe, that during the 25 d the carrier-con-centration n decreases and that the resistance in-creases. GaN is a highly n- type material and the higher the temperatures the greater the influence of the native donors on the resistivity and carrier concentration. At lower temperatures the effect of the native donors and activated intrinsic carriers can be minimized and there-fore the changes in the carrier-concentration and espe-cially the resistivity are more pronounced.

3 4 5 6 7 8 9 10 110.8

1.0

1.2

1.4

1.6

1.8

2.0

3 h 25 d

n (1

017/c

m3 )

1000/TM (K-1)

0.4

0.6

0.8

1.0

1.2

3 h after annealing 25 d

� (�

cm)

300 200 150 100

Temperature (K)


In Fig. 2 the resistivity and carrier-concentration re-corded at 130 K are shown as a function of time after annealing. The solid lines correspond to exponential least square fits using the following equations:

1/ 2

1/ 2

(ln 2) /0

(ln 2) /0

( )

( )

t tn

t t

n t n A e

t A e��

�

�

� �

� �

The fits on the carrier concentrations yield an average half-life of t1/2 = (5.78 0.72) d in rough agreement with the nuclear half-life of the isotope while the fits on the resistivities yield the correct average half-life of t1/2 = (7.39 0.34) d. In contrast to the resistivity meas-urements the carrier concentration strongly depends on the positioning of the sample in the magnetic field and therefore the deviation of the half-life determined from the carrier concentrations is reasonable.

Fig. 2: Carrier-concentration (circles) and resistivity (squares) of 111Ag-doped GaN (1013 cm-2, 260 keV) re-corded at 130 K as a function of time after annealing.

Ag is a group Ib element and from valence arguments should act as a double acceptor. Cd, being a group IIb element should form a single acceptor. Therefore during the transmutation of Ag (two holes) to Cd (one hole) the number of additional holes should decrease and the con-centration of the majority carriers (electrons, n-type material) should increase in contrast to the observed be-havior. From our results we conclude that Ag does not form a double acceptor level in GaN, or that this accep-tor levels are not ionisized up to 300 K.

The fits on the carrier-concentrations yields an aver-age amplitude of An = 1.04 � 1016 cm-3 carriers. This means, that at annealing temperatures of 1573 K only 18.6 % of all implanted ions are activated during the an-

nealing procedure, since the concentration of implanted ions in the sample volume was 5.6 �� 1016 cm-3. Addi-tionally, those results are an explanation of the low frac-tion of Cd-H-pairs in GaN found with PAC measurements 6).

Fig. 3: Hall mobility of 111Ag-doped GaN plotted as a function of temperature. The spectra were recorded 3 h and 25 d after implantation and annealing.

In Fig. 3 the hall-mobility is shown as a function of temperature. The spectra were taken 3 h and 25 d after implantation and annealing. An increasing mobility can be observed only at temperatures above 150 K presum-able due to a decrease in phonon scattering. If one as-sumes an increasing concentration of ionized impurities (Ag0 �� Cd-) the mobility should decrease in contrast to the results.

Our results show that Cd acts as an acceptor in con-trast to Ag. However, annealing temperatures above 1573 K are required to activate all of the implanted dopands and achieve p-type GaN.

(1) S.J. Pearton, C.R. Abernathy, C.B. Vartuli, J.C. Zolper,

C. Yuan and R.A. Stall, Appl. Phys. Lett. 67 (1995) 1435 (2) J.C. Zolper, H.H. Tan, J.S. Williams, J. Zou,

D.J.H. Cockayne, S.J. Pearton, M. Hagerott Crawford and R.F. Karlicek, Appl. Phys. Lett. 70 (1997) 2729

(3) D.C. Look and R.J. Molnar, Appl. Phys. Lett. 70 (1997) 3377

(4) A. Stötzler, R. Weissenborn, M. Deicher and the ISOLDE Collaboration, Physica B 273-274 (1999) 144

(5) A. Burchard, E.E. Haller, A. Stötzler, R. Weissenborn, M. Deicher and the ISOLDE Collaboration, Physica B 273-274 (1999) 96

(6) A. Burchard, M. Deicher, D. Forkel-Wirth, E.E. Haller, R. Magerle, A. Prospero and A. Stötzler, in: Defects in Semiconductors 19, eds. G. Davies and M.H. Nazare, Materials Science Forum Vol. 259-263 (Trans Tech Pub-lications 1997) p. 1099

0 5 10 15 20 25 30

0.94

0.96

0.98

1.00

1.02

1.04

n (1

017/c

m3 )

Time (d)

0.76

0.78

0.80

0.82

0.84

0.86

0.88

TM=130 KFit: <t1/2> = (7.39 ± 0.34)d

TM= 130 KFit: <t1/2> = (5.78 ± 0.72) d

� (�

cm)

100 150 200 250 300

60.0

70.0

80.0

90.0

100.0

3 h 25 dM

obilit

y (c

m2 /V

s)

Temperature (K)


1.6 Near-infrared-photoluminescence in GaN doped with radioactive platinum

A. Stötzler and M. Deicher in collaboration with ISOLDE Collaboration (CERN, Geneva)

Since the development of blue diodes, GaN has attracted great attention. Most of the investigations on the optical properties of GaN have focused on shallow levels and only little information about deep levels in GaN was gathered. Since the last years the interest on deep levels in GaN is increasing not only due to the po-tential applications of Er-doped 1) GaN for optical fiber communications or the discovery of near-infrared (NIR) luminescence in V-doped 2) GaN. It also has been shown 3,4), that the entire visible spectrum can be cov-ered by doping GaN with the rare-earth elements Tm, Pr or Er. Additionally, the transition metals Cr and Fe were found to introduce luminescence in the near infrared re-gion 5). Another interesting property of transition metals in semiconductors is that their energy levels are ap-proximately equidistant to the vacuum levels for differ-ent materials 6). This can be used to estimate the band discontinuities of a heterojunction, as shown for AlN/GaN 7).

Platinum, being a transition metal as well, is known to create luminescence centers in Si 8), where Pt is often used to control the carrier lifetimes. In GaN no Pt-re-lated luminescence has been reported up to now. The aim of this experiment was to investigate the optical properties of GaN doped with Pt. In contrast to the re-sults described above, the chemical assignment of the optical transitions was not performed by a comparison with the corresponding energy level schemes consider-ing crystal field splitting but by the use of radioactive isotopes. If an optical transition is due to a recombina-tion center in which the parent or daughter isotope is in-volved, the concentration of that defect will change with the element specific half-life of the radioactive decay. The changing defect concentration then shows up in the changing PL intensity of the corresponding transition.

The GaN sample used was a 1.5 µm epitaxial layer grown on AlN/c-sapphire by metal organic vapor phase epitaxy (MOVPE) purchased from Cree Research. The sample was doped by ion implantation with the radioac-tive isotope 191Pt at the on-line mass separator ISOLDE at CERN. The implantation energy was 60 keV and a maximum dose of 3 � 1012 ions/cm2 was used. To serve as a reference, a small part of the sample was not im-planted. The implantation induced damage was reduced by annealing the sample at 1300 K for 20 min in sealed quartz ampoules filled with nitrogen gas at a pressure of 1 bar at room temperature. The isotope 191Pt transmutes with a half-life of t½ = 2.9 d 9) into stable 191Ir. This chemical transmutation was monitored by photolumi-nescence spectroscopy (PL).

The PL experiments were carried out at 4 K using a He flow cryostat. The luminescence was excited with the 325 nm line of a HeCd-laser, dispersed with a 0.75 m

monochromator and detected either with a cooled GaAs-photomultiplier in the visible and UV range or a liquid-N2 cooled Ge detector in the infrared region.

The UV-VIS part of the luminescence recorded after ion implantation and annealing is shown in Fig. 1.

Fig. 1:Photoluminescence spectra of 191Pt-doped GaN recorded with a PMT at 4 K. The spectra were recorded within 17 d after implantation and annealing at 1300 K. All spectra are normalized to the PL intensity at 2.2 eV.

All spectra are normalized to the same PL intensity at 2.2 eV. The spectrum recorded 16 h after ion implanta-tion and annealing shows a peak at 3.468 eV (Fig. 1). The intensity of this donor bound exciton emission (D0X) 10) drops by a factor of about 30 in intensity com-pared to the reference part, showing that some implan-tation damage still remains after the annealing procedure and this decrease is not caused by the annealing proce-dure itself. However, the full width at half maximum (FWHM) of about 6 meV of the DX transition indicates still an overall good material quality. A longitudinal phonon replica 11) of the (D0X) transition at 3.376 eV and the yellow luminescence 12) band (YL) at 2.2 eV were also observed. At 1.461(3) eV a new transition la-beled Pt1 can be observed accompanied by a second line centered at 1.446(3) eV. As shown in Fig. 1 the PL in-tensity of these transitions decreases and finally vanishes within 17 days after annealing. The apparent strong drop in intensity below 1.43 eV is caused by the decreasing sensitivity of the photomultiplier tube.

Since nothing else is changing but the decreasing Pt concentration due to the radioactive decay this clearly shows that these transitions must be caused by a recom-bination center involving Pt.

Fig. 2 shows 8 of the 15 recorded PL spectra covering the infrared range of 191Pt-doped GaN taken within

350 500 650

GaN:Pt, 4 K

Pt1

15 meV

17 d

FWHM ~ 6 meV

YLPL

inte

nsity

(arb

. uni

ts)

wavelength (nm)

3.5 3.0 2.5 2.0

4 d16 hDoX-LO

DoX

energy (eV)

840 870

x 40

1.47 1.43


27 days after annealing. All spectra were normalized to the PL intensity at 1.3 eV. The first PL spectrum re-corded 16 h after annealing shows new intense NIR lu-minescence labeled with Pt2. Six single transitions, each separated by (15 1) meV, are detectable starting with the first transition centered at 1.273(1) eV. Within the following 27 d the PL intensity of all six transitions de-creases continuously. Finally, after 27 d no NIR lumi-nescence can be detected any longer. Therefore we con-clude that these transitions have to be Pt-related as well.

Fig. 2:Photoluminescence spectra of 191Pt-doped GaN recorded with a Ge detector at 4 K within 27 d after im-plantation and annealing at 1300 K. All spectra are normalized to the PL intensity at 1.3 eV. The lowest spectrum (reference) corresponds to the unimplanted part of the sample.

In Fig. 3, the PL intensities of both Pt related PL-bands are plotted as a function of time after implantation and annealing. The solid lines correspond to exponential fits to the data using the following equation:

1/ 2(ln 2) /0( )Pt Pt t tI t I e�

�

The open squares correspond to the integral PL inten-sity of the Pt1 transitions. The fit yields a half-life of (2.6 0.6) d. The solid circles show the integral PL in-tensity of the Pt2 transitions. In this case the exponential fit to the data yields a half-life of (3.1 0.3) d. Both values are in good agreement with the nuclear half-life of 191Pt (t½ = 2.9 d). These results clearly show, that the corresponding recombination center contains exactly one Pt atom. The involvement of more than one Pt atom in this defect would show up in a smaller time constant. As shown in Fig. 2, the unimplanted reference part of the sample does not show any of these transitions after annealing and therefore annealing effects causing these transitions can be excluded. Furthermore, we do not ob-serve any other changes in the whole spectral region between 0.9 eV up to 3.5 eV, in particular no new lines coming up, so we conclude that iridium does not intro-duce any optically active recombination centers in GaN.

Fig. 3: Normalized integral PL intensities of the Pt-re-lated transitions Pt1 and Pt2 in GaN as a function of time after annealing. The solid lines correspond to ex-ponential fits to the data using equation 1.

Using the radioactive isotope 191Pt, we have shown for the first time that Pt introduces near-infrared photo-luminescence consisting of two single transitions (Pt1) at 1.461 eV and 1.446 eV followed by a set of seven addi-tional transitions (Pt2) starting at 1.273 eV each sepa-rated by 15 meV in energy. The time dependence of the Pt-related PL intensities clearly shows, that the corre-sponding recombination center involves exactly one Pt atom, but the exact recombination mechanism responsi-ble for the several transitions is not clear yet, and addi-tional investigations are needed to clarify this.

(1) J.D. MacKenzie, C.R. Abernathy, S.J. Pearton,

U. Hömmerich, J.T. Seo, R.G. Wilson and J.M. Zavada, Appl. Phys. Lett. 72 (1998) 2710

(2) B. Kaufmann, A. Dörnen, V. Härle, H. Bolay, F. Scholz and G. Pensl, Appl. Phys. Lett. 68 (1996) 203

(3) A.J. Steckl, M. Garter, D.S. Lee, J. Heikenfeld and R. Birkhahn, Appl. Phys. Lett. 75 (1999) 2184

(4) R. Birkhahn, M. Garter, and A.J. Steckl, Appl. Phys. Lett. 74 (1999) 2161

(5) R. Heitz, P. Thurian, I. Loa, L. Eckey, A. Hoffmann, I. Broser, K. Pressel, B.K. Meyer and E.N. Mokhov, Appl. Phys. Lett. 67 (1995) 2822

(6) J.M. Langer and H. Heinrich, Phys. Rev. Lett. 55 (1985) 1414

(7) J. Baur, M. Kunzer, K. Maier, U. Kaufmann and J. Schneider, Appl. Phys. Lett. 65 (1994) 2211

(8) G. Armelles, J. Barrau and J.P. Noguier, Phys. Rev. B 33 (1986) 1243

(9) Table of Isotopes, CD ROM Edition, Version 1.0 ed. V.S. Shirley, S.Y. Frank Chu (John Wiley, New York, 1996)

(10) A.K. Viswanath, J.I. Lee, S. Yu, D. Kim, Y. Choi and C. Hong, J. Appl. Phys. 84 (1998) 3848

(11) R.L. Bergman, D. Alexson, P.L. Murphy, R.J. Nemanich, M. Dutta, M.A. Stroscio, C. Balkas, H. Shin and R.F. Davis, Phys. Rev. B 59 (1999) 12977

(12) H.M. Chen, Y.F. Chen, M.C. Lee and M.S. Feng, Phys. Rev. B 56 (1997) 6942

940 960 980 1000 1020 1040 1060

GaN:Pt, 4 K

15 m

eV

reference

27 d

16 h

PL in

tens

ity (a

rb. u

nits

)

wavelength (nm)

1.31 1.29 1.27 1.25 1.23 1.21 1.19 1.17

Pt2

energy (eV)0 5 10 15 20 25 30

Pt1: t1/2 = (2.6 ± 0.6) dPt2: t1/2 = (3.1 ± 0.3) d

PL

inte

nsity

(arb

. uni

ts)

time (d)


1.7 Observation of hydrogen in GaN doped with 117Cd(117In)

M. Dietrich, A. Stötzler, R. Weissenborn and M. Deicher in collaboration with ISOLDE-Collaboration (CERN, Geneva, Switzerland)

The current research on GaN is driven by its promis-ing applications as a material for LEDs and laser diodes in the blue and UV region 1). One aspect to be investigated is the behavior of H in GaN. During different steps of device processing, like crystal growth or chemical etching, H can be introduced into the material unintentionally. It may change the electrical properties by saturating dangling bonds, passivating shallow and deep level dopants and impurities or causing new, H-related levels in the band gap. Therefore the understanding of the behavior of H in GaN is essential for optimization of different processing steps. We have recently reported on studies of Cd-H pairs in GaN with perturbed �-�-angular correlation spectroscopy (PAC) 2). Implanted 111mCd substitutes the Ga-site and can act as an acceptor after annealing of the implantation damage. H is implanted with low energy and trapped by Cd. The orientation of two different Cd-H pairs as well as their dissociation energy have been determined 2).

The same Cd-H pairs should form using the isotope 117Cd. H will be released after the nuclear disintegration 117Cd � 117In because In is isoelectronic to the host element Ga and the probe does not act as an acceptor anymore. The initially captured H may then leave the probe and start to diffuse. This onset of diffusion is investigated with PAC. Similar studies in InP and GaAs have been carried out successfully in the past 3).

A prerequisite of these studies is the activation of the dopants implanted. Due to the high melting point of GaN and its tendency to loose N from the surface at temperatures above 1200 K, only a partial removal of implantation defects by annealing is possible. This an-nealing of the sample after implantation of 111mCd has been studied in detail. After treatment of the crystal at 1323 K under N2-atmosphere, 60 % of the probes sub-stitute an undisturbed lattice site 4). At higher tempera-tures GaN starts to degrade. The possibility to reach temperatures up to 1573 K by adding a small amount of Al to the sample has been observed recently 5).

We report on experiments that use this new technique to study the annealing of GaN after implantation of 117Cd(117In). GaN grown on sapphire has been im-planted with 117Ag that decays to 117Cd with a half-live of 73 s at the on-line mass separator ISOLDE at CERN. The implantation was carried out with an energy of 60 keV and a dose of 1.2×1012 cm-2. Most PAC-meas-urements have been carried out at ambient temperature with the c-axis of the crystal pointing between two de-tectors at 45°.

Fig. 1 shows the fraction of 117Cd(117In) probe atoms at identical lattice sites in GaN (top), the quadrupole

coupling constant Q (center) and the width of its distri-bution � Q in dependence on the annealing temperature (bottom). After thermal treatment at 773 K, 51(1) % of the probes are exposed to a unique electric field gradient (EFG). The fraction increases with increasing annealing temperature to 81(1) % at 1073 K and remains mainly constant to the final temperature of 1558 K. Thus, about 80 % of the probes are at sites with no defects present in the nearest neighborhood. Nevertheless, there are de-fects further away that are not directly correlated with the probe atoms. These are responsible for the distribu-tion of EFG represented by � Q. The remaining 20 % of probes experience correlated defects in their nearest neighborhood creating strong non-unique EFG.

Fig. 1: Fraction of 117Cd(117In) atoms at identical lat-tice sites in GaN (top), quadrupole coupling constant �Q (center) and width of its distribution ��Q (bottom) in dependence on the annealing temperature. The samples were annealed in evacuated quartz ampoules with ad-ditional Al.

The quadrupole coupling constant after annealing at 1073 K has a value of Q = 20.9(1) MHz. From this value one can calculate the EFG that a Ga-atom would experience at the same position with help of the Stern-heimer correction. This gives the largest component of

0

20

40

60

80

100fr

actio

n (%

)

20.0

20.5

21.0

21.5

�Q (

MH

z)

600 800 1000 1200 1400 16000

1

2

��

Q (

MH

z)

annealing temperature (K)


the EFG-tensor as Vzz = 1.0×1021 V/m2. The result is in good agreement with the EFG at an undisturbed Ga-site in GaN as Vzz = 0.7×1021 V/m2 determined by NMR 6). This comparison proves once more the substitution of the Ga-site by Cd.

The quadrupole coupling constant Q does not change significantly at annealing temperatures above 900 K. The width of the distribution � Q decreases sharply between 773 K and 973 K. At higher temperatures one observes a distribution of the values. Nevertheless, the width of the distribution exhibits the tendency to become smaller until the final temperature of 1573 K.

Summarizing the slope of the fraction of probes and that of the distribution of the quadrupole coupling con-stant, we get the following result: Annealing at tem-peratures above 1073 K does not brake the bonds be-tween probes and the remaining correlated defects in their nearest neighborhood. On the other hand, the den-sity of uncorrelated defects can be decreased by anneal-ing at higher temperatures. The annealing of GaN under N2-atmosphere after implantation of 111mCd shows similar behavior. The saturation of the fraction of 60 % is already reached after annealing at 900 K 4).

We have implanted H into annealed samples. Fig 2. shows the PAC-spectrum of 117Cd(117In) in GaN after annealing at 1523 K and low energy implantation of H (300 eV, 1×1015 cm-2, 423 K). The spectrum was re-corded with the sample held at a temperature of 10 K.

Fig. 2: PAC spectrum of 117Cd(117In) in GaN after ad-ditional implantation of H. The measurement has been carried out at 10 K. Besides the slow modulation caused by the lattice EFG, a high frequency is visible which represents 6(2) % of the probe atoms.

Besides the dominating interaction of the probe atoms in undisturbed environments, a fraction of 6(2) % is ex-posed to a different EFG characterized by a quadrupole coupling constant of Q = 344(8) MHz. This interaction is caused by free H atoms that are close to the 117Cd(117In) probes after the nuclear disintegration. With the probe 111mCd, two different configurations of Cd-H pairs represented by different EFG have been dis-tinguished 2). Since the observed fraction of probes be-ing influenced by H is hardly above the detection limit, we cannot speculate about a second configuration.

There are two possible explanations for the small fraction. The more unlikely is that hydrogen diffuses

extremely fast. The decay scheme of 117Cd is rather complex and the time between elemental transmutation and emission of the �-quantum that is used as a start trig-ger for the PAC measurement is 5 ns. One could imag-ine that a large fraction of 117Cd probes traps H. This will move away to a large extent during the 5 ns before the measurement starts and only a small fraction is visi-ble for the 117In probes in the end.

We have discussed the incomplete annealing in detail in this report. Both the correlated and uncorrelated de-fects that influence the PAC spectrum can be electroni-cally active. They may provide a high density of traps for H with higher trapping probability than our dopant 117Cd. Furthermore these defects may cause an incom-plete electrical activation of the probe atoms and the ob-served H-related fraction reflects the electrically active dopants.

Our results demonstrate that it is not sufficient to in-crease the annealing temperature in order to create a high fraction of 117Cd-H pairs for the study of H-diffu-sion in GaN. Another approach could be either to protect the GaN surface during annealing or to perform the an-nealing under high external N2 pressure.

(1) S.J. Pearton, J.C. Zolper, R.J. Shul and F. Ren, J. Appl.

Phys. 86 (1999) 1 (2) A. Burchard, M. Deicher, D. Forkel-Wirth, E.E. Haller,

R. Magerle, A. Prospero and R. Stötzler, Materials Research Symposium Proc. Vol. 449 (1997) 961

(3) A. Burchard, M. Deicher, D. Forkel-Wirth, M. Knopf, R. Magerle, A. Stötzler, V.N. Fedoseyev and V.I. Mishin, Materials Research Symposium Proc. Vol. 513 (1998) 171

(4) A. Burchard, M. Deicher, D. Forkel-Wirth, E.E. Haller, R. Magerle, A. Prospero and A. Stötzler, Materials Science Forum Vol. 258-263 (1997) 1099

(5) A. Burchard, E.E. Haller, A. Stötzler, R. Weissenborn and M. Deicher, Physica B 273/274 (1999) 96

(6) G. Denninger and D. Reiser, Phys. Rev. B 55 (1997) 5073

0 20 40 60 80 1000.2

0.1

0.0

-0.1

-0.2

t (ns)

R(t

)


1.8 Behavior of doping atoms in CdCr2Se4

V. Samokhvalov, I.I. Burlakov, D. Degering and S. Unterricker (TU Bergakademie Freiberg, Institut für Angewandte Physik) in collaboration with M. Dietrich and M. Deicher ISOLDE Collaboration (CERN, Geneva, Switzerland)

If semiconductors have special magnetic features they are very attractive materials for applications in magneto electronics and magneto optics. One of the most important representatives of the spinel-type mag-netic semiconductors with the general formula AB2C4 (B=Cr) is CdCr2Se4. CdCr2Se4 is ferromagnetic below Tc=130 K. Its conductivity can be adjusted to n- or p-type by doping it with In- or Ag-atoms, respectively 1). Another doping atom could be Br, which should be sub-stituted at anion sites. By the ISOLDE on-line separator at CERN the PAC-probes 111mCd, 111Ag(111Cd), 111In(111Cd), and 77Br(77Se) can be produced and im-planted. They allow a detailed microscopic investigation of the behavior of doping atoms in this material. In such a magnetic semiconductor the electric quadrupole and also the magnetic dipole interaction can be used to char-acterize the lattice sites of the probes. From the space group of the normal spinel structure (Fd3̄m) follows that the electric field gradient (efg) vanishes at the A-sites, whereas axially symmetric efg must exist at B- and an-ion sites. In the ferromagnetic state magnetic hyperfine fields are present at all three atomic positions.

PAC results for implanted 111mCd-probes were pub-lished in the 1998 Annual Report 2). The Cd-probes are substituted as expected at the cubic Cd-sites. At 77 K a magnetic hyperfine field of 10.8(2) T was detected, which corresponds to the one detected by NMR 3).

Experiments with the probe 111In(111Cd) were carried out after recoil-implantation following (d,n)-reactions with Cd-nuclei of the host substance performed at a cy-clotron or after implantation at the ISOLDE-implanter. The implantation damage can be annealed at tempera-tures between 400 and 600°C. At room temperature, the majority of 111In(111Cd)-probes shows an axially sym-metric quadrupole interaction. The remainder is in envi-ronments with cubic symmetry. After quenching from a temperature of 600°C, the fraction of probe atoms in cu-bic environments increases considerably (Fig. 1a). In the ferromagnetic state at 77 K two Larmor frequencies �L1

= 161 Mrad/s and �L2 = 374 Mrad/s are visible (Fig. 1b). The corresponding magnetic hyperfine fields are Bhf1 = 10.9(3) T and Bhf2 = 25(2) T, respectively. The smaller field is identical to the one detected with 111mCd at the Cd-site. This means that a part of the 111In-probes

Fig. 1: PAC spectra (left) and their Fourier transforms (right) for 111In(111Cd) implanted into CdCr2Se4:a) Measured at 295 K after annealing (650°C for 15 min., quenched in H2O), b) measured in the ferromagnetic state at 77 K. An external polarizing field was applied perpendicular to the detector plane(annealing 600°C for 20 min, quenched in H2O).

0 100 200 300 4000.05

0.00

-0.05

-0.10

-0.15

T

m=295 K

0 50 100 150 2000

1

2

3

4

5

0 10 20 30 40 50 60

0.2

0.1

0.0

-0.1

-0.2

-0.3

t (ns)

0 200 400 600 800 10000

4

8

12

16

b)

a)

Fourier am

plitude (a.u.)F

ourier amplitude (a.u.)

R(t

)R

(t)

Tm=77 K

Bext

=0.1T

� (Mrad/s)


is substituted at Cd-positions with cubic site symmetry, which is also observed in the paramagnetic state (meas-urement at 295 K). The larger of the two magnetic fields obviously belongs to 111In-probes at Cr-sites. A large magnetic hyperfine field at Cr-positions is known also from NMR experiments 3). In the paramagnetic state, the 111In(111Cd)-probes at Cr-sites are influenced by the axially symmetric quadrupole interaction, which is ex-pected at B-sites.

The quadrupole interaction in CdCr2Se4 has been cal-culated from first principles by the WIEN97 code 6). At the Cr-positions with Cr-probes a value of Vzz = -1.2×101 V/m2 is obtained. In our case we have a Cd im-purity as probe atom. This situation can not be simply calculated. For an estimation we use Sternheimer cor-rections (1-�

�) for Cd and Cr according to ref. 4). (1-�

�)

is 25 and 12 in the cases of Cd and Cr, respectively. The corrected value of Vzz = -2.6×1021 V/m2 is to compare with the measured value |Vzz(Cd)| = 2.8×1021 V/m2.

In the case of 111Ag(111Cd) probes, mainly cubic en-vironments are observed after annealing the implanta-tion damage. Fig. 2 shows measurements after incom-plete annealing at 400°C. In the paramagnetic state the influence of remaining defects is present. At 77 K again the same Larmor frequency �L1 = 161 Mrad/s is visible, which is known from 111mCd-probes at Cd-sites. It is interesting that only a small damping is observed in the magnetic case. Here we have the same situation as de-scribed in ref. 2): the lattice disorder does not have such

a strong influence on the spin order as on the charge distribution and the corresponding efg. Ag clearly sub-stitutes Cd. We could not find any influence of a thermal treatment, especially quenching, on this behavior.

In the literature, the Cd-sites as well as the Cr-sites are discussed for In doping atoms 1,5). The presented in-vestigations show that depending on thermal treatments both sites can be occupied by In. In the case of Ag-at-oms only the Cd-site substitution seems to be possible. This should be considered in the discussion of n- and p- type doping behavior of In and Ag in CdCr2Se4, respectively.

We acknowledge Dr. V.E. Tezlevan (Technical Uni-versity of Moldova, Kishinev) for the growth of crystals. One of us (I.I. Burlakov) would like to thank the A. v. Humboldt foundation for a fellowship.

(1) H.W. Lehmann, Phys. Rev. 163 (1967) 488 (2) V. Samokhvalov, A. Richter, M. Dietrich, U. Zeiske,

D. Degering, S. Unterricker, A. Burchard, and M. Deicher, Annual Report 1998, Universität Konstanz, p. 53

(3) G.H. Stauss, Phys. Rev. 181 (1969) 636 (4) A.A. Gusev, I.M. Reznik, and V.A. Tsitrin, J.Phys.:

Condens. Matter 7(1995) 4855 (5) A. Rodriguez, H. Saitovich, P. Silva, J. Weberszpil,

J. Fernandes, and M.A. Continentino, Hyp. Int. 79 (1993) 937

(6) P. Blaha, K. Schwarz, and J. Luitz, WIEN97, 1999. ISBN 3-9501031-0-4

Fig. 2: PAC spectra (left) and their Fourier transforms (right) for 111Ag( 111Cd) implanted into CdCr2Se4:a) Measured at 295 K after annealing(400°C for/ 20 min.), b) measured in the ferromagnetic state at 77 K. An external polarizing field was applied perpendicular to the detector plane (annealing 400°C for 20 min).

0 100 200 300 400

0.02

0.00

-0.02

-0.04

-0.06

-0.08

b)

a)

Fourier am

plitude (a.u)F

ourier amplitude (a.u)

R(t

)

Tm = 295 K

0 50 100 150 2000

1

2

3

4

0 50 100 150 200

0.00

-0.05

-0.10

R(t

)

t (ns)

Tm = 77 K

Bext

= 0.1 T

0 200 400 600 800 10000

1

2

3

4

� (Mrad/s)


1.9 Crystalline silicon solar cells – new materials

G. Hahn, P. Geiger and E. Bucher

In the New Materials group of the chair of applied solid-state-science Prof. Bucher various crystalline sili-con materials are characterised in order to test their pos-sible potential for photovoltaic applications. Beside the characterisation of the raw material there exists a com-plete standard high efficiency solar cell processing line for fundamental investigations of completed solar cell devices. These basic investigations are necessary before the impact of an industrial type solar cell process on the material can be tested.

Important parameters of solar cell devices are the electrical properties of the charge carriers, which can be determined in temperature dependent Hall measure-ments. On the other hand lifetimes of minority charge carriers can be locally determined by the microwave detected photoconductivity decay method.

Standard characterisation of completed solar cells re-lies on illuminated and dark IV-curves, spectral response and reflection measurements as well as locally resolved LBIC (Light Beam Induced Current) measurements with the simultaneous determination of the IQE (Internal Quantum Efficiency).

RGS Silicon

RGS (Ribbon Growth on Substrate) 1) silicon is a R&D multicrystalline silicon material fabricated by the Bayer AG which aims at a very fast production process and the avoidance of sawing losses. In contrast to stan-dard multicrystalline silicon, currently used in photo-voltaics, the wafers do not need to be cut from an ingot but are crystallised in the form of approx. 300 µm thick ribbons which can be used directly for solar cell proc-essing. These features give RGS silicon a high potential for a significant cost reduction of photovoltaics.

Because of the very fast production process and a high concentration of oxygen in interstitial form the material (average grain size < 1 mm) contains crystal defects which lower the minority carrier diffusion length Ldiff to values usually < 20 µm corresponding to life-times in the order of 100 ns. Fig. 1 shows a lifetime mapping of an as grown RGS wafer.

Fig. 1: Lifetime mapping of an as grown RGS silicon wafer (11 x 8 cm2).

Mechanical V-texture

In multicrystralline silicon materials a mechanically textured surface shows benefits in three ways: The re-flectivity is reduced, because photons may have further chances to enter the cell after a first reflection (Fig. 2). On the other hand the textured surface causes an in-clined penetration of light and therefore charge carriers are created nearer to the cell surface (Fig. 2, right). The third aspect is the proximity of the emitter surface to the location of carrier generation. Especially materials with small Ldiff gain from this higher charge carrier collection probability apart from the reduced reflection losses. All effects lead to an enhanced current and therefore a higher conversion efficiency � 2).

Fig. 2: Optical generation of minority carriers in a V-shape textured silicon specimen for two different posi-tions of the laser beam illumination at a wavelength of � = 833 nm. After a first reflection the photons may have a further chance of entering the silicon.

Fig. 3 shows the simulated IQE at 833 nm for a flat and a V-textured solar cell with an assumed Ldiff of 25 µm. For the flat cell the spot of illumination is moved per-pendicular to the V-grooves. For light entering the cell in the V-bottom, the created charge carriers in average have to diffuse a longer distance to the collecting emit-ter. Therefore the IQE is lower than in the case of a flat cell. Photons entering the cell in the V-tips have a higher chance to be collected. Therefore the IQE is drastically increased compared to the flat cell with the same Ldiff. This results in an enhanced short circuit current density Jsc.

The results of the simulations in Fig. 3 can be verified by the determination of the locally resolved IQE. This is shown in Fig. 4 for a RGS solar cell with an Ldiff in the range of 25 µm. An excellent agreement with the simulation in Fig. 3 is obtained giving proof that a me-

G-opt10 cm s ( )

laser beamlaser beam

120 µm

1.0 2.7 7.1 19 51 130 360 17 -3 -1


chanical V-texture leads to higher values of Jsc in solar cells with small Ldiff.

Fig. 3: Calculated local internal quantum efficiency of a V-grooved solar cell with base diffusion length 25 µm for � = 833 nm as a function of position of illumination. The internal quantum efficiency calculated for a plane cell of the same diffusion length is plotted as a reference.

Fig. 4: Locally resolved IQE at 833 nm of a V-textured RGS solar cell. In the V-tips more carriers are collected resulting in a higher IQE. On the left a metal grid finger is visible.

Latest RGS solar cell results

An optimisation study regarding the passivating properties of atomic hydrogen in RGS material in con-junction with the concept of a mechanically textured cell surface led to cell efficiencies exceeding 12 %, with the best cell showing an independently confirmed conver-sion efficiency of 12.5 %. This is the highest value reached on RGS silicon by far and within 1999 this world record could be improved by 0.6 % absolute (best value at the end of 1998: 11.9 %).

EFG Silicon

Another multicrystalline ribbon silicon material cur-rently under investigation in our group is EFG (Edge-de-fined Film-fed Growth) silicon from ASE, Germany. In this material preparation concept which is already ap-plied commercially, the silicon wafers are fabricated via a meniscus from molten silicon 3,4). This leads to a

slower production process compared to RGS silicon, but to larger crystal grains (several cm in pulling direction) and less impurities. The electrical properties of the crystal grains can differ quite strongly as can be seen in the lifetime mapping shown in Fig. 5.

� growth direction �

Fig. 5: Lifetime mapping of an as grown EFG wafer (5 x 4 cm 2) showing lifetime variations from grain to grain.

Defects present in EFG silicon can be well passivated by atomic hydrogen. A comparison between an EFG solar cell before and after hydrogen passivation is given in Fig. 6.

Fig. 6: LBIC mapping of an EFG solar cell before (left) and after hydrogen passivation (right).

On non-textured hydrogen passivated EFG solar cells without antireflexion coating an efficiency of 9.9 % could be reached, corresponding to � = 14.4 % with a simulated antireflexion coating 5).

(1) H. Lange and I.A. Schwirtlich, J. Cryst. Growth. 104

(1990) 108 (2) G. Hahn, C. Zechner, M. Rinio, P. Fath, G. Willeke and

E. Bucher, J. Appl. Phys. 86 (1999) 7179 (3) F. V. Wald, Crystals: Growth, Properties and Applica-

tions 5, Springer-Verlag Berlin Heidelberg (1981) (4) M.J. Kardauskas, M.D. Rosenblum, B. H. Mackintosh

and J.P. Kalejs, Proc. 25th IEEE PVSEC, Washington (1996) 383

(5) P. Geiger, Diplomarbeit, Universität Konstanz (1999)

0 20 40 60 80 100 1200.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

V-tipV-bottom

Ldiff = 25 µm V-grooves untextured

loca

l IQ

E fo

r � =

833

nm

X-position of laser beam [�m]


1.10 Compound semiconductors for photovoltaics / materials for thermoelectric applications

M. Klenk and O. Schenker,U. Probst and E. Bucher (Photoluminescence measurements of CuGaSe2-films ) J. Ostreich, U. Probst and E. Bucher (Studies on CdTe thin film solar cells, Thermoelectricity)

Photoluminescence measurements of CuGaSe2-films

The best CuGaSe2 (CGS) based solar cell efficien-cies 1,2) do not reach up to now those of CuInSe2 or CuIn1-xGaxSe2

3). However, recent improvements made by the introduction of an altered buffer layer recipe 1) show that there is still a potential for further improve-ments.

The best efficiencies for all types of thin film chal-copyrite solar cells are obtained with coevaporated ab-sorber materials. Yet this process is relatively slow and needs complex control mechanisms. A simpler way which could be advantageous for industrial production is the synthesis of the absorber material from stacked ele-mental layers (SEL) of the pure elements, followed by a rapid thermal processing (RTP) step. This RTP process is already in use for CIGS layers 4), but because of the different material properties it is not clear whether the experiences gained with CIS and CIGS can be easily adopted for CGS.

CGS layers produced from stacked elemental layers by RTP

The CGS samples considered in this work were formed from sequentially evaporated precursor layers of the pure elements. As substrate material soda lime glass was used on which a molybdenum layer of approxi-mately one micron thickness was deposited by radio-frequency-sputtering. The precursors were then treated in a rapid thermal processing (RTP) step to react the elements to CGS. Typical process parameters for this step were ramp times of 10 to 20 seconds from room temperature to the maximum value of 555 °C, followed by a holding time at this temperature of six minutes. Details can be found in 5). The composition of the CGS films was adjusted by the thickness of the pure elemen-tal layers in the precursor stack and controlled by a quartz crystal monitor during evaporation.

Photoluminescence measurements

Defect levels in CGS have been studied by photolu-minescence measurements (1 m scanning monochro-mator of Czerny Turner type, frequency doubled YAG-laser, 10 K, LN-cooled Ge-detector).

First the observed interdependence of PL-spectra and composition in the lower energy range below 1.55 eV will be shortly presented, before a more detailed discus-sion will be given on the higher energy section of the spectra above this value. In Fig. 1 the PL-spectra of four samples with varying Cu/Ga-ratios are logarithmically depicted over a wide energy range. For the copper rich

materials two dominating broad and intensive peaks at about 1.26 eV and 1.0 eV can be observed whereby the peak at 1.26 eV is shifted to lower energies with reduced copper percentage. For the slightly gallium rich sample there is only one broad peak (1.17 eV) in this range with less intensity. This peak remains when the Cu/Ga-ratio is decreased but its intensity is then steadily reduced. In earlier studies on CGS single crystals 6) this broad hump was also reported and was related to the iodine used for CVT crystal growth. This interpretation is definitely not applicable to our SEL-RTP films. Schön 7) assumed however that this peak must be a superposition of at least two peaks at about 1.0 and 1.2 eV, as observed in this work for copper rich material. Because of intensity dependent shifts of the peak position he identified the peaks as donor acceptor transitions and related the signal to Cui and CuSE defects, which is again in good agree-ment with the noticed correlation to the copper content.

Fig. 1: PL-spectra over a wide energy range of four CGS films with different composition

To get some insight into the depth homogeneity of the absorber layers regarding PL–properties some films were thinned by an etching technique. Etching with bromine methanol is a known method of compound semiconductor treatment, originated in the InP process-ing 8), but was also repeatedly applied to chalcopyrite compounds 9).

When the slightly copper rich films were thinned by etching, the intensity of the lower energy peak remained constant while the peak at 1.2 eV steadily decreased.

There are several different ways to interpret the PL-spectra of chalcopyrite samples. In our case the emis-sions above 1.55 eV can be consistently explained ac-cording to a model of Massé 10), which predicts one ac-ceptor (VCu, 50 meV) and two donor levels (VSe, 80 and 110 meV). Therefore five luminescent recombinations


are then possible: Two donor- valence band (1.645 and 1.615 eV), one acceptor- conduction band (1.675 eV) and two donor-acceptor transitions (1.62 and 1.59 eV). In Fig. 2 the PL-scans of three samples of different composition are shown in the appropriate energy range, together with the mentioned transitions. There is a good correspondence of the measured and predicted peak po-sitions if a systematic shift by 0.014 eV of the measured values towards lower energies is taken into account. This could be explained if one assumes that there is internal stress due to the cooling (PL at low temperatures) of the examined Glass/Mo/CGS structure.

Fig. 2: PL-emissions above 1.55 eV of three CGS layers with different composition

The broad peak, which dominates for gallium rich CGS, appears to be mainly a superposition of the VCu-CB and the VSe–VB transition. This is also confirmed if the change of the spectra at different compositions is taken into account. At Cu/Ga-ratios larger than one, a structured PL–spectra is observed which consists pri-marily of the three vacancy to band transitions. Even in copper rich material copper vacancies exist, which is in agreement with the high formation probability of this defect. If the Cu/Ga-ratio is decreased to values below one, the copper vacancy to band signal strongly domi-nates the spectra, while the selenium vacancy to band transitions only cause the asymmetric peak shape. The respective peak position for every sample remains con-stant independent of the excitation intensity as to be expected for defect level to band transitions. This is mentioned here because in an earlier study on CGS single crystals 7) some samples behaved like this, while others showed an intensity dependent shift. This indicates that within the energy range of the main peak also a donor-acceptor pair (DAP) transition level is located.

A noticeable alteration in the PL-spectra of the etched samples is the emergence of a broad peak at 1.53 eV which is clearly a DAP. In an earlier work 11) the activa-tion energy of Gai (donor) was reported to be in the range of 110 to 120 meV. This matches perfectly with the measured signal if the slightly lower band gap of the

thin films is taken into account and the copper vacancies are taken as the corresponding acceptor level. Conse-quently the increase of interstitial gallium defects at lar-ger depth is backed by the depth profile obtained by XRF measurements.

(1) V. Nadenau, D. Hariskos, H.W. Schock, 14th Europ.

PVSEC, Barcelona (1997) p. 1250 (2) M. Saad, H. Riazi, E. Bucher, M.Ch. Lux-Steiner, Appl.

Phys. A. 62 (1996) 181 (3) M.A. Contreras, B. Egaas, K. Ramanathan, F. Hasoon,

R. Noufi, E-MRS 1999 Spring Meeting (4) F. Karg, V. Probst, H. Harms, J. Rimmasch, W. Riedl,

J. Kotschy, J. Holz, R. Teichler, O. Eibl, A. Mittwalsky, M. Kiendl, 23th IEEE Photov. Spec. Conf., Louisville (1993) p. 441

(5) O. Schenker, J.H. Schön, F. Raiser, K. Friemelt, V. Alberts, and E. Bucher, 14th Europ. PVSEC (1997) p. 1311

(6) M. Susaki, T. Miyauchi, H. Horinaka, N. Yamamoto, Jpn. J. Appl. Phys. 17 (1978) 1555

(7) J.H. Schön, O. Schenker, L.L. Kulyuk, K. Friemelt, E. Bucher, Sol. Energy Mat., 51 (1998) 371

(8) H. Löwe, P. Keppel, D. Zach, Halbleiterätzverfahren, Akademieverlag, Berlin (1990) p. 138

(9) R. Klenk, H.W. Schock, D. Cahen, T. Engelhard, E. Moons, 10th EC PVSEC, Lissabon (1991) p. 927

(10) G. Massé, J. Appl. Phys., 68 (1990) 2206 (11) F. Abou- Elfotouh, R. Noufi, D.J. Dunlavy,

L.L. Kazmerski, D. Albin, K.J. Bachmann, R. Renner, J. Vac. Sci. Technol. A6 (1988) 1515

Studies on CdTe thin film solar cells

Investigations on p-CdTe/ n-CdS-ZnO solar cells were performed in collaboration with the EU research laboratories in Ispra (Italy) and BP-solar (UK). The thin CdTe solar cells were made by electrochemical deposi-tion at BP-solar. Project target is to determine the diffu-sion length Ln of the charge carriers. In order to obtain the magnitude of Ln techniques were used that have al-ready been proven useful for silicon solar cells.

One of the two methods used implies the determina-tion of the internal quantum efficiency (IQE) by spectral response and spectral reflectance measurements. The IQE shows how many of the incoming photons are transformed in electrical energy and can be used to de-termine the Ln. This method, successfully applied to Si-technology, was now tested for CdTe solar cells.

Another way to specify the magnitude of Ln is the measurement of the current being generated by incom-ing electrons with variable energy. This method is called EBIC (electron beam induced current) and was tested successfully in 1998 at our institute for the characteriza-tion of CdTe solar cells. In the current project new ex-periences shall be made with this new technique. Some results are shown in the following:

The EBIC-signal is shown in Fig. 4 as scatter dia-gram. The obtained data were fitted by a mathematical simulation program basing on the approximation of the solar cells as Schottky diodes. The result is given by the line. Out of this approximation Ln and other important solar cell parameters can be extracted.


Fig. 3: The external quantum efficiency (EQE) and the internal quantum efficiency, derived from the spectral response and spectral reflectance measurements

Fig. 4: Fit of the EBIC-signal by the model of a Schottky-diode

Thermoelectricity

The research and optimization of ZrNiSn compounds is finished with a poster 1) at the ETS (European Ther-moelectric Society) meeting in Pardubice and a paper 2) at J. Phys.: condens. Matter. The main focus lies now at new Telluride compounds. They are very interesting for research on thermoelectrical materials; e.g. Bi2Te3 has the best thermoelectric properties (300K) at todays state of the art.

Ternary and quaternary material systems with tellurides from Sn, Sb, In, Bi, Ga, Au and Ag are under investigation. Crystals of the respective compounds are grown. The properties being relevant for thermoelectri-cal applications are measured, in specific this is the electrical conductivity �, the Seebeck coefficient S and the thermal conductivity �. These values are included in the Figure of Merit Z = S2�/� that indicates how useful a material is for thermoelectric applications. Publica-tions about the investigated compounds are planned.

(1) J. Oestreich, W. Käfer, F. Richardt, U. Probst and

E. Bucher. Proc. of the 5th european workshop on thermoelectrics, Pardubice, Czech Rep. (1999) p. 192

(2) H. Hohl, A.P. Ramirez, C. Goldmann, G. Ernst, B. Wölfing and E. Bucher, J. Phys.: condens. Matter 11 (1999) 1697

400 500 600 700 800 9000

5

10

15

20Q

uant

um e

ffici

ency

[%]

internal quantum efficiency external quantum efficiency

� [nm]


1.11 Industrial solar cell development

M. Spiegel, C. Gerhards, F. Huster, B. v. Finckenstein, T. Pernau, A. Fischer, W. Jooß, A. Hauser, P. Fath and E. Bucher

The activities of the InduS (industrial solar cell) group of the chair of Prof. Bucher focus on the devel-opment of concepts for cost reductions of crystalline Si-solar cells. To fulfill these tasks new technologies have been developed and procedures from high-efficiency processing have been simplified, which can be inte-grated into solar cell production lines.

The technology transfer from the laboratory directly into industry is guided by:

�� industrially relevant research projects (one BMWi and three European projects),

�� co-operations with 10 solar-cell-companies/material suppliers for process and cell optimization studies,

�� support of 4 equipment manufacturers for the specification of novel production systems (e.g. me-chanical surface texturization, roller printing and hy-drogen passivation) and the modification of standard production devices for throughput increase (e.g. sili-con nitride antireflection coatings (ARC)),

�� transfer of highly qualified scientists to the semiconductor/photovoltaic industry,

�� development of innovations favorable for patents (currently 1 patent announced and 4 applied for).

The following table shows the actual state of indus-trial cell production and compares it with our R&D ac-tivities.

Tab. 1: The actual state of industrial cell production compared with our R&D activities. *Technology trans-fer into cell manufacturing at sunways AG, Konstanz, took place.

Industrial standard Technology transfer

Flat solar cell surface Mechanical V-groove surface text-

urization*, Mechanical microtextur-

ing for thin cells

Homogeneous POCl3 or

paste emitter diffusion

Selective emitter structures (e.g. in

combination with roller printing of

doped paste on V-textured surfaces)

Front side ARC with TiO2 or

PECVD-SiN

Double side passivated LPCVD-

SiN coatings in combination with

efficient hydrogen bulk passivation

Metallization: screen-print-

ing, buried contact (only Cz)

Roller printing, buried contact (for

mc-Si)

For an efficient technology transfer into the industry and a close industrial education of scientists a complete pilot production line for crystalline silicon solar cells (screen printing and buried contact) was set up at our laboratory. The collaboration with our chair results in the following advantages for industry:

�� speeding up of the solar cell development, �� further development of existing industrial processes

without delaying the cell production, �� assistance on the analysis of bottlenecks within the

solar cell production (e.g. efficiency reductions due to non optimal processes) by means of solar cell/material characterization methods existing at our laboratory.

In the following the solar cell processes used in our laboratory and their industrial relevance will be described.

Mechanical surface texturization

One major concern of the PV industry is an efficient surface texturization technology for mc-Si to reduce the front surface reflection. Chemical alkaline texture etch-ing as used in industry for Cz-silicon can not efficiently be applied on mc-Si, because of the different crystal ori-entations. Therefore, a new mechanical technique has been developed with which V-grooves are cut into the wafer surface using a V-profiled cylindrical abrasive tool mounted on a high frequency spindle 1,2). A specifi-cation of the mechanical surface structuring in an indus-trial environment was worked out. On laboratory scale extensive studies on the machine parameters were car-ried out using different types of structuring tools, taking into account different tool materials, tool profiles and abrasive coatings. These experiments were the basis for the design and construction of an industrial scale ma-chine with a fully automatic wafer handling system.

Fig. 1: Reflection of a V-textured silicon surface com-pared to a flat surface (only slightly textured by NaOH etching), both coated with an ideal silicon nitride ARC.

The reflection reduction due to V-texturing is shown in Fig. 1. Due to the reduced reflection of the front sur-face and increased collection efficiency within the

400 600 800 1000 12000

5

10

15

20

25

mechanical V-textured + SiN ARC untextured (NaOH-etched) + SiN ARC

Ref

lect

ion

[%]

Wavelength [nm]


groove regions the short circuit current of screen printed cells rises by 5 % relative when mechanical instead of alkaline surface texturization is used 3). With this tech-nique an efficiency of 16.5 % on 10 * 10 cm2 screen printed mc-Si cells was obtained including mechanical V-texturing and a selective emitter structure4), which is the second highest efficiency on a large area mc-Si cell ever reported.

Additional applications 1-3) of this mechanical micro-milling process are the fast planarization or thinning of silicon wafers, the mechanical structuring of substrates (e.g. ceramic, glass) for crystalline thin-film solar cells, the parasitic junction removal, wafer recycling, and the contact formation for buried contact solar cells.

Furthermore, we currently develop a mechanical mi-crotexturing technique to reduce the saw-damage NaOH-etching time, to decrease the stress during tex-turing of thin wafers and to reduce the total front surface area and therefore the recombination loss at the surface. For the microtextured cells a shorter NaOH defect etching step is needed as compared to none microtex-tured cells as can be seen in the faster increase of the open circuit voltage VOC with NaOH etching time (Fig. 2). This is due to the fact that wafering induces a considerable deeper surface damage than our micro-milling process, which removes this damage and causes only a minor surface damage.

Fig. 2: Dependence of the open circuit voltage Voc on the NaOH-etching time. Applying a micro-texturing step prior to the etching will reduce the standard etching time by a factor of 4-5.

Emitter diffusion

The phosphorous emitter diffusion on boron doped silicon wafers is carried out in our pilot line either from the POCl3-gas phase or by the coating of the wafer by phosphorus containing pastes or liquids, followed by an annealing step. To avoid Auger recombination lower doped emitters with higher sheet resistance are pre-ferred. However the most commonly used screen print-ing metallization sets a lower limit to the surface doping concentration and the emitter depth corresponding to a sheet resistance of below 50 �/sqr. for standard screen printing processes. To overcome this obstacle basic re-search on the contact resistance has been carried out and

novel cell structures proposed including selective emit-ters (such as the combination of selectively coating the tips of a V-structured wafer with doping paste by roller printing, to define the heavy doped region). In addition the combination of cell processes, such as co-processing of the emitter and back side surface field generation by aluminum evaporation prior to P-diffusion is investi-gated, resulting in an attractive process for mc-Si due to the enhanced impurity gettering action during the diffu-sion process 5).

Hydrogen bulk passivation

Experiments have shown that the MIRHP (Micro-wave Induced Remote Hydrogen Plasma)-technique ap-plied within a standard industrial cell process results in a relative cell efficiency increase of 5-10 % on standard multicrystalline silicon 6). On cost-effective sheet silicon a performance increase up to 30 % has been reached 7). These improvements are due to the passivation of crystal defects and impurities by the incorporation of atomic hydrogen.

Silicon nitride for surface and volume passivation

Silicon nitride (SiN) films can be deposited at our laboratory by means of PECVD and LPCVD (Plasma Enhanced and Low Pressure Chemical Vapour Deposi-tion) resulting in considerable efficiency increases of mc-Si solar cells. The SiN film serves as an antireflec-tion coating and in addition provides a good surface pas-sivation as well as for the PECVD SiN an excellent bulk passivation due to the diffusion of hydrogen from the films into the cell volume during contact firing. To en-sure also a good bulk passivation for LPCVD SiN, nor-mally containing only a small H-concentration, we have incorporated the MIRHP technique into our LPCVD system. A comparison between cells only covered by an LPCVD SiN and cells were a MIRHP step is carried out prior to the LPCVD SiN process showed that the incor-poration of the MIRHP process results in an efficiency benefit of 5 % relative.

Back surface processing

When thin wafers or sheet silicon with thickness’ below 250 µm are used as base material the commonly applied Al back contact, fully covering the cell rear side, can cause a bending of the solar cells during the contact firing process. In order to avoid this disadvantage we work on the development of an industrial local back contact, with a SiN back side passivation, back side re-flector and alternatively a local back surface field, which prevents the recombination of minority carriers at the back contact. Applying these techniques 10 * 10 cm2 mc-Si solar cells (200 µm thick) with 15 % efficiency have been fabricate at our lab.

Metallization

Complete screen printing equipment (2 screen printers

0 2 4 6 8 10

540

560

580

600

620

optimum: 8-10 minoptimum: 2 min

microtexturization + NaOH-defect etching only NaOH-defect etching

V OC [m

V]

NaOH-etching time [min]


(one with optical alignment), drying and firing furnaces) has been established at our pilot line. Currently about 95 % of all commercial crystalline silicon solar cells have screen printed contacts. Fundamental properties of a thick-film paste contact are investigated in our labo-ratory. In addition screen printing is used as a reference process for the following two very promising metalliza-tion techniques, the roller printing and buried contact metallization technique.

Roller printing

As an alternative for screen printing we have con-structed together with an equipment manufacturer a first prototype for roller printing, shown in Fig. 3 8), with which the wafer metallization is carried out by self aligned fine line printing of paste on mechanical struc-tured wafers. Experiments with that prototype lead to promising results of 14.2 % efficiency on 10 * 10 cm2 mc-Si cells. Finger widths of 25 �m have been reached resulting in 2-3 % reduced finger shading as compared to standard screen-printing with 65-100 �m contact width.

Fig. 3: Roller printing technique on V-textured surfaces.

Buried contact

This metallization procedure as shown in Fig. 4, which results in highest efficiencies in monocrystalline Cz-Si silicon cell production, has been transferred in our laboratory to mc-Si 9). Within the undertaken process optimization, process steps have been implemented which are necessary to obtain high efficiencies on mc-Si cells (surface texturization, MIRHP, co-processing of emitter diffusion and back side emitter compensation by Al evaporation). Applying this technique 12.5 * 12.5 cm2 mc-Si solar cells with 15.6 % efficiency have been fabricated.

Fig. 4: Schematic drawing of a buried contact solar cell. The contact grooves are cut by a mechanical saw, the metallization is done by contactless Ni/Cu plating.

(1) G. Willeke, H. Nussbaumer, H. Bender and E. Bucher,

Solar Energy Materials and Solar Cells, 26 (1992) 345 (2) P. Fath, J. Szlufcik, J. Horzel, E. Bucher and G. Willeke,

1st World Conference on Photovoltaic Energy Conversion, Hawaii (1994) p. 1543

(3) C. Gerhards, C. Marckmann, M. Spiegel, P. Fath, G. Willeke, E. Bucher, J. Creager and S. Narayanan, Proceedings of the 2nd WCPEC, Vienna (1998) p. 1863

(4) F. Duerinckx, J. Szlufcik, J. Nijs, R. Mertens, C. Gerhards, C. Marckmann, P. Fath and G. Willeke, Proceedings of the 2nd WCPEC, Vienna (1998) p. 1836

(5) W. Jooß, G. Hahn, P. Fath, G. Willeke and E. Bucher Proceedings of the 2nd WCPEC, Vienna (1998) p. 1689

(6) M. Spiegel, P. Fath, K. Peter, B. Buck, G. Willeke and E. Bucher, Proceedings of the 13th EC Photovoltaic Solar Energy Conference, Nice (1995) p. 421

(7) M. Spiegel, C. Zechner, B. Bitnar, G. Hahn, W. Jooß, P. Fath, G. Willeke, E. Bucher, H.U. Höfs and C. Häßler, Sol. Energy Mater. Sol. Cells, 55 (1998) 331

(8) P. Fath, C. Marckmann, E. Bucher and G. Willeke 13th European Photovoltaic Solar Energy Conference, Nice (1995) p. 29

(9) R. Kühn, P. Fath, M. Spiegel, G. Willeke, E. Bucher, N. Mason and T. Bruton, Proceedings of the 14th EC Photovoltaic Solar Energy Conference, Barcelona (1997) p. 672.


1.12 Thin film silicon solar cells on low-cost metallurgical silicon substrates

K. Peter, R. Kopecek, J. Hötzel , S. Volz, P. Fath and E. Bucher in collaboration with C. Zahedi (Elkem, c/o Institute for Energy Technology, Norway) F. Ferrazza (Eurosolare, Italy) H. Riemann and E. Rupp (Institute of Crystal Growth , Germany) W. Warta and A. Eyer (Fraunhofer Institute for Solar Energy Systems, ISE, Germany)

Solar cells of thin film crystalline silicon on a low-cost substrate offer the potential for low cost, high effi-ciency, and long-term stability. In this work thin film silicon solar cells have been fabricated on UMG-Si (Up-graded Metallurgical Grade Silicon) based substrates (Fig. 1) by Liquid Phase Epitaxy (LPE) from an Indium melt at 950 °C. The UMG-Si developed at a pilot scale can be produced in a large quantity for the needs of the PV-industry.

The substrates, developed in this study, include cast multicrystalline wafers, float zone wafers, and SSP rib-bons. Large cast ingots were produced in a large indus-trial furnace. Wafering of the UMG-Si based ingots to standard sizes was carried out by a sawing machine. Although the carbon content in the UMG-Si feedstock was initially lowered, the DS (directional solidification) growth process could further reduced it. The levels of the metallic impurities in the substrate wafers were be-low the SIMS detection limits. Since the UMG-Si is a heavily doped material, the boron (B) level in the sub-strates was high (< 100 ppma) and the resistivity of the material was measured to be very low (< 30 m�cm) re-spectively. The high doping level of the substrate has confined most of the photogenerated carriers to the epi-taxial layer and minimized their loss on the substrate. Since the doping level of the epilayers was almost two orders of magnitude lower than in the substrate, no bo-ron diffusion into the grown layer may have taken place.

To obtain a doping level of 5 x 1016cm-3, 0.1 % Ga was added to the In melt. A melt back step after dipping the wafer into the indium solvent resulted in several ad-vantages: Removal of residuum oxides, surface smooth-ening, and Si supply to the melt. This meltback step cir-cumvents the addition of silicon to the solution for a continuous growth process. We used two types of LPE growth methods to deposit the Si layer. With a steady state method the growth rate was lower than 0.5 µm/min 1). Higher growth rates were achieved by ramping down the temperature. Variations in time, tem-perature and ramping resulted in different morphologies of the epilayer depending on the crystal structure. The electronic quality of the Si film strongly depends on the growth rate. By increasing the growth rate the layers change their surface morphology from a flat to a py-ramidal structure.

Solar cells fabricated on the UMG-Si based cast sub-strates have achieved VOC = 590 mV and ISC = 26.6 mA/cm2. The low FF of 63 % due to shunt formation results in a 10 % cell efficiency. Analysis of IQE (Internal Quantum Efficiency), SR (Spectral Re-

sponse) and LBIC (Light Beam Induced Current) meas-urements resulted in high effective diffusion lengths ex-ceeding the epilayer thickness in some areas. A strong contribution that could limit the solar cell performance was due to the poor material homogeneity and surface quality of the grown layers. With an optimal growth process, a higher performance of our thin film silicon solar cells on low cost substrates could be reachable.

Fig. 1: Thin LPE layer for solar cell application grown on a polycrystalline substrate from metallurgical grade silicon feedstock. The epitaxial layer on the top was gained visible after Secco etching.

In addition an alternative processing method for n-type base solar cells was pursued. The layers were grown from a pure 5N Sn solution at temperatures above 1000 °C on previously phosphor diffused UMG sub-strates. The P diffused area prevented the undesirable formation of a diode between the substrate and the LPE layer and additionally served as a back surface field (BSF) for the solar cell. One of the advantages of this alternative process is the use of the cheaper Sn solution and furthermore a simpler cell processing with an inex-pensive Al (or B) paste for the emitter diffusion and the formation of front and back contacts.

(1) R. Kopecek, K. Peter, J. Hötzel and E. Bucher, J.

Chrystal Growth 208 (2000) 289

20

m�


1.13 Novel solar cells

A. Kress (Screen printed Emitter-Wrap-Through back contact solar cells) B. Terheiden (Lamella-Silicon solar cells) A. Boueke and R. Kühn (Latest results on semitransparent POWER silicon solar cells) S. Keller, S. Scheibenstock and M. Wagner (Theoretical and experimental behaviour of monolithically integrated crystalline silicon solar cells based on the HighVo solar cell concept) W. Jooss and K. Blaschek (Back contact buried contact solar cells) P. Fath and E. Bucher

Screen printed Emitter-Wrap-Through (EWT) back contact solar cells

Unlike conventional cells, back contact solar cells have both electrodes on the rear side. This avoids shad-owing losses (summing up to 12 % for conventional cells) and facilitates considerably the connection of cells to modules. In addition the rear side emitter contributes to a higher collection probability of minority carriers generated near the cell rear. The EWT-concept is spe-cially suited for low cost silicon with diffusion lengths smaller than the device thickness. Small laser (Nd-YAG) drilled holes connect the front side emitter with the emitter contact at the cell rear. Screen printing, a re-liable and cost efficient technology in industrial practise, is applied for contact formation. Different geometryies (fingerlength, -distance and width) have been investi-gated. The advantages of the rear side emitter have been quantified with LBIC measurements (Fig. 1). The ge-ometry optimisation was assisted by 2D-computer simulations with DESSISTM. Different cell regions (busbar, fingers, etc.) were connected to a network in-cluding the series resistance of the contacts. A principle correlation between the EWT-design and observed low shunt values could be excluded by high resolution IR-thermography. The cell efficiency was increased to above 14 % by using a selective emitter, which can be realised within the EWT-concept without any further alignment steps. This is the highest efficiency world-wide reported so far for screen printed EWT-cells.

Fig. 1: LBIC measurement of an EWT-cell, arbitrary units, area 1 mm2. The small laser beam illuminates the front surface, the rear finger pattern is clearly visible due to the different collection probabilities of the rear side emitter (bright) with the connecting holes and the rear base area (dark).

A fruitful co-operation exists with BP Solarex and the Fraunhofer ISE in Freiburg within the ACE-designs project as well as with the MPI of Microstructure Physics, Halle.

Lamella-Silicon solar cells

Based on a macroscopically textured silicon substrate a novel high efficiency solar cell design for mono- and multicrystalline silicon photovoltaic devices has been developed, especially suitable for space and concentra-tion applications. It relies on cutting deep and narrow grooves with small distances between two neighbouring cuts. This results in a lamella-like appearance of the cell surface as seen in Fig. 2. The cutting is carried out with a conventional dicing saw equipped with a 15 µm thick saw blade.

After a shallow emitter diffusion and a thermal oxi-dation or silicon nitride deposition the dielectric is opened stripe-like at the top of one side of the lamellas by Shallow Angle Photolithography (SAP). The distance between the openings can be freely chosen by including lower lamellas between the ones with contacts. After a heavy phosphorous diffusion into the openings and the formation of a local back surface field the cells are met-allised by Shallow Angle Finger Evaporation (SAFE) 1) with or without SAP. This leads to very fine metal fingers.

Fig. 2: Acidic etched Lamella wafer.

The advantages of this novel solar cell concept are the very low reflection losses and the simple shallow angle photolithography with a mask-free light exposure. Furthermore, the average distance between the place of optical generation of charge carriers and the collecting


emitter is extremely small like in vertical junction solar cells 2). This leads to very high collection probabilities of charge carriers even in materials with small minority carrier diffusion lengths.

Series of monocrystalline lamella cells and reference devices have been processed investigating the impact of different contact designs, especially by varying finger distances, screen-printed and photolithographically de-fined back surface fields (BSF) and shallow angle pho-tolithography conditions. Furthermore, the process se-quence for monocrystalline float zone silicon was adapted to the demands of multicrystalline silicon.

(1) B. Terheiden, P. Fath, G. Willeke and E. Bucher, Proc.

14th EPVSEC, Barcelona, 1997 (2) J. Lindmayer and C. Wrigley, 12th IEEE PVSC, Baton

Rouge, Louisiana, 1976

Latest results on semitransparent POWER (Poly-crystalline Wafer Engineering Result) silicon solar cells 1)

Semitransparent crystalline silicon solar cells open new markets which were previously closed for photo-voltaics. They are especially suitable for applications in solar architecture (solar façades, stair cases, etc.) and for glass sliding roofs in the automobile industry. The optical transparency which results from a regular pattern of small holes in the mechanically engineered wafer can be varied in the range 0 - 30 % depending on the shape and size of the texturing tool (V-grooved or rectangular) as well as the distance between two neighboring grooves. In the case of bifacially active POWER silicon solar cells, the holes additionally lead to an electrical interconnection of the emitter on front and rear side.

The mechanical texturization technique 2) is inde-pendent of the structural properties of the starting mate-rial which may be cast or ribbon multicrystalline as well as single crystalline silicon. The grooves are created by using either a rectangular single blade (laboratory scale) or a texturization tool for industrial production, which allows the structuring of the whole wafer in only a few seconds 3).

Bifacial as well as monofacial semitransparent cell types were diffused with a 30 �/sqr. POCl3 emitter after the structuring of the wafers. A PECVD silicon nitride layer has been used as an ARC. The emitter on the rear side of the monofacial cells was removed after the SiN deposition. These cells do not have a surface passivation on the rear side and therefore show lower cell efficiencies compared to bifacial POWER cells. Finally, the screen printed metallization was fired through the antireflection coating.

Table 1 presents the results of illuminated IV measurements using the standard AM 1.5 spectrum. The 5 x 5 cm2 sized cells had a light transmittance of 18.2 % for the monofacial cells and 16 % for the bifacial cells. Maximum efficiencies of 11.2 % for monofacial POWER cells and 12.9 % for bifacial POWER cells could be obtained on monocrystalline Cz-material with

different base resistivities. On multicrystalline silicon solar cells the open circuit voltage was found to decrease somewhat to values of around 560 mV, leading to efficiencies of 10.0 % and 11.1 % for the two cell types. A little more elaborate processing including a silicon nitride with enhanced optical properties leads to the improved efficiencies in bifacial cells. Only six processing steps are necessary to produce monofacial POWER cells.

Tab. 1: IV-characteristics of different semitransparent POWER silicon solar cells. (cell area: 25 cm2).

cell type / material

FF [%]

JSC [mA/cm2]

VOC

[mV] �

[%]

untextured cell / mc

73.6 27.2 590 11.8

monofacial / mc

71.7 25.1 556 10.0

monof. / Cz (1.0 �cm)

71.2 26.2 569 10.6

monof. / Cz (0.4 �cm)

72.8 25.9 591 11.2

bifacial / mc 68.8 28.5 565 11.1 bifacial / Cz 72.9 30.3 583 12.9

Despite a semitransmittance of 18.2 %, a reduction of the collected current of only 8.1 % compared to conventional flat cells was observed on monofacially active multicrystalline devices. The good antireflection properties of the textured surface and the enhanced light-trapping of the cell geometry balance partly the optical losses due to the partial light transmittance. The open circuit voltage and the fill factor of both cell types are limited by a dominating second diode. The strongly enlarged length of the p-n-junction that enters the surface with a high recombination velocity increases the saturation current J02 of the second diode 4). Good sur-face passivation in these regions is therefore absolutely necessary to obtain high open circuit voltages as it is the case for the bifacially active cells.

The usage of base material with a reduced resistivity of 0.4 �cm decreases the limiting saturation current of the second diode by a factor of almost two for Cz-mate-rial. Those monofacial cells showed an increase in VOC by 22 mV as compared to standard 1.0 �cm material.

Due to the simpler processing 5,6), monofacial semi-transparent POWER cells seem to be more attractive for an industrial production which is undertaken by the company ‘sunways’ 7). Bifacial POWER cells, however, show a higher conversion efficiency. This can be explained by the good passivation of the rear surface of the solar cells. The emitter on the rear side covered with PECVD SiN leads to a reduced surface recombination and to a more efficient collection of minority charge carriers which are generated in the vicinity of the base contact. The spectral response in the long wavelength range is therefore strongly enhanced as compared to


monofacial semitransparent and conventional flat silicon solar cells.

(1) G. Willeke and P. Fath, 12th EPVSEC, Amsterdam

(1994) p. 766 (2) G. Willeke, H. Nussbaumer, H. Bender and E. Bucher,

Solar En. Mat. And Solar Cells 26 (1992) 345 (3) P. Fath, C. Marckmann, E. Bucher, G. Willeke,

J. Slufcik, K.De Clerq, P. Duerinckx, L. Frisson, J. Nijs and R. Mertens, 13th EPVSEC, Nice (1995) p. 29

(4) R. Kühn, A. Boueke, M. Wibral, C. Zechner, P. Fath, G. Willeke and E. Bucher, 2nd PVSEC, Wien (1998) p. 1390

(5) A. Boueke R. Kühn, M. Wibral, P. Fath, G. Willeke and E. Bucher, 2nd PVSEC, Wien (1998) p. 1709

(6) R. Kühn A. Boueke, M. Wibral, P. Fath, G. Willeke and E. Bucher, 2nd PVSEC, Wien (1998) p. 2415

(7) sunways AG, Macairestr.5, D-78467 Konstanz, Germany

hole hole

back metallization

front metallization ARCARC

emitteremitter

Fig. 3: Schematic drawings of monofacial (left) and bifacial (right) POWER cells.

Theoretical and experimental behavior of mono-lithically integrated crystalline silicon solar cells based on the HighVo solar cell concept

A new concept for the realization of monolithically integrated silicon solar cells has been presented 1-3). The concept is based on standard Si wafer technology and does not use thin film approaches. A key feature are isolation trenches dividing the wafer into several unit solar cells. Due to the imperfect isolation between unit cells UC defined on the same conductive wafer some new device aspects deviating from an ordinary se-ries connection of solar cells arise. For the theoretical description a model proposed by Valco et al. 4) has been generalized by using a two diode concept for the unit cells and by weakening the assumption of identical unit cells. The model was used to simulate the cell perform-ance in dependence on light intensity, isolation resis-tance, cell area and number of unit cells 2). As a result general design rules for these truly monolithically inte-grated solar cells are given. These design rules are quite general as they are also applicable on cells proposed in references 4 - 6. The theoretical predictions could be partially confirmed by experimental prototypes. The best cell with a total area of 21 cm2 and six unit cells exhibits an open circuit voltage of 3.5 Volts and a con-version efficiency of 12.8 % under 100 mW/cm2 AMG 1.5 illumination and standard reporting conditions.

The goal of any monolithic series connection of so-lar cells is to obtain a single photovoltaic device with output voltages not being limited by the energy band gap of the device's semiconductor material. Up to now the portable electronics market has been satisfied mainly by monolithic series interconnection of thin film solar cells although their conversion efficiency as well as their long time stability are still rather low compared to wafer-based crystalline silicon solar cells 7). For ap-plications with higher energy consumption several at-tempts to develop monolithically series connected solar cells without the help of a supporting substrate and thin silicon film technologies have been undertaken 4-6,8-10), but they all failed either physically or commercially due to the problems of cell isolation and/or cost intensive process techniques.

To achieve this goal we propose a rather simple ap-proach for defining, isolating and series connecting UCs which are very similar to standard low cost crys-talline silicon solar cells: Remove wafer material be-tween UCs by inserting trenches reaching from the cell front surface to the back surface. Remaining narrow bridges hold the device together. The trenches also de-liver a means for series connecting neighboring UCs by filling them with metal which additionally leads to an improved stability of the device. Fig. 4 and Fig. 5 illus-trate the cell design which we realized experimentally.


4 332

51

4

Fig. 4: Sketch of one Unit Cell UC and parts of the neighboring UCs. 1: silicon wafer, 2: emitter, 3: emitter contact metallization, 4: isolation trench, 5: base contact metallization.

3

1

4

5

2

Fig. 5: Cross section through the middle of the UCs from Fig 4. Series connection is achieved by printing the emitter metallization (3) through the isolation trench (4) to contact the base metallization (5) of the neighboring UC.

A key feature of the device structure is the remain-ing part of the wafer holding the UCs together. Because of the wafer resistivities usually preferred in crystalline silicon photovoltaics (about 0.3 �cm to 15 �cm) these parts represent parasitic current paths severely influ-encing the device performance. Some of the conse-quences of these current paths can be predicted from an equivalent circuit model proposed by Valco et al. 4). Yet, for a better description of our cells we extended the one diode model in Valco’s equivalent circuit to the two diode model commonly used for characterizing Si solar cells (Fig. 6). Additionally we weakened the as-sumption of identical UC parameters by using a larger set of equations.

All UCs except the one which forms the negative pole of the device in forward bias exhibit some kind of additional shunting parallel resistance Rp across the wa-fer material. In our case Rp is given by the remaining ‘bridges’. The UC representing the negative pole (UC) is not shunted because the output current has to cross the pn junction of this cell to enter or leave the device through the emitter contact. Already from the model it-self two characteristic features of monolithically series connected solar cells are obvious. First, not only for Rp reaching infinity but also for M getting large the device behavior should be similar to that of an ordinary series connection; although in the latter case for UCs altered by Rp. The main influence of Rp is a reduction

Fig. 6: Equivalent circuit model for the description of monolithically series connected solar cells. The exter-nal wires represent the monolithic series connection which is obtained in our concept through the isolation trenches. Rp is given by the remaining ‘bridges’.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-200

-150

-100

-50

0 calculated from the equivalent circuit model

ideal series connection of the illuminatedIV characteristics of one cell with Rsh = 3000 �cm2 and five cellswith Rsh = 67.31 �cm2

ideal series connection of six cellswith Rsh = 67.31 �cm2

I [m

A]

U monolithic array [V] Fig. 7: Comparison of the equivalent circuit model for six UCs and low Rp with two approximations using an ordinary series connection

of the shunt resistance of the UCs leading to an effec-tive shunt resistance Rsheff. Rsheff dominates the device behavior at low illumination intensities. Second, the asymmetry in Rp in the device leads to an interconnec-tion of non identical solar cells which also effects the cell performance (Fig. 7). For Rp < 200 �cm2 it could be shown that a small reduction of the area of UC1 with respect to the areas of the remaining UCs results in a gain in conversion efficiency which is in contrast to an ordinary series interconnection.

(1) S. Keller, P. Fath and G. Willeke, Patent application

No. PCT/DE 99/00728 (March 1999) (2) S. Keller, S. Scheibenstock, P. Fath, G. Willeke and

E. Bucher, J. Appl. Phys. 87 (2000) 1556 (3) S. Keller, S. Scheibenstock, P. Fath, G. Willeke and

E. Bucher, Technical Digest 11th International Photovoltaic Science and Engineering Conference, Sapporo City, (1999) p. 651

(4) G.J. Valco, V.J. Kapoor, J.C. Evans Jr., and A.T. Chai, Proceedings of the 15th IEEE Photovoltaic Specialists Conference, Orlando, (1981) p. 187


(5) V.J. Kapoor, G.J. Valco, G.G. Skebe, and J.C. Evans Jr., J. Appl. Phys. 57 (1985) 1343

(6) A. Goetzberger, US Patent No. 4 330 680 (May 1982). (7) H.A. Aulich, Proceedings of the 13th European Photo-

voltaic Solar Energy Conference, Nice (1995) p. 1441 (8) R.M. Swanson, US Patent No. 4 933 021 and 4 933 022

(Jun. 1990). (9) M.A. Green, US Patent No. 4 323 719 (April 1982). (10) U. Kerst and H.-G. Wagemann, Proceedings of the 14th

European Photovoltaic Solar Energy Conference, Barcelona (1997) p. 2434

Back contact buried contact solar cells

Back contact solar cells offer various advantages over conventionally designed solar cells. Investigations by solar cell manufacturers showed that module assem-bling costs could be remarkably reduced due to the back contact design. Furthermore by placing the bus-bars on the back of the cell, the active front surface can be increased because of lower shadowing losses.

On the other hand the buried contact solar cell (BCSC) process 1) enables very low shadowing losses in conjunction with high quality front grid metallization and a selective emitter structure. This results in low se-ries and contact resistance and leads to a high short cir-cuit current density.

Combining the buried contact metallization and the back contact design we are presenting a new solar cell concept, the Metallization Wrap Through (MWT) con-cept. This concept is similar to the one presented by Kerschaver et al. 2) for screen-printed metallization.

The MWT solar cell has the photo carrier collection junction and the finger contact grid on the front surface which was defined by mechanical abrasion with 15 µm wide dicing blades. The MWT cell has one laser-drilled via in each n-contacting finger to transport the current to the n-type busbar on the back surface.

Co-diffusion of Al and P plays an important role in the processing sequence of our MWT cells. It allows to economise one furnace step by forming the Al-BSF and the heavy P-diffusion (POCl3 source) of the n-type grooves, vias, edges at the same time. The n-type bus-bars on the back of the wafers are protected by masks during the Al-evaporation.

The process sequence takes advantage of the selec-tive metal deposition during the electroless plating se-quence of the buried contact process. Since metal de-posits only on metal and semiconductor surfaces but not on dielectrics, the front SiNx ARC layer ensures that metal is only deposited within the grooves on the front surface. The n-busbars and p-contacts on the rear are fully metallized simultaneously. Thus the intercon-nections i.e. the vias between the front grid and the n-contacts on the back are formed automatically during the plating step. The external p and n-contacts on the back of the cells are separated mechanically by thin sawing blades mounted on a dicing machine followed by an edge isolation step. Due to the combination of co-diffusion and mechanical contact separation no addi-tional p/n-contact definition steps are necessary in the MWT process sequence.

Fig. 8: Schematic cross-section of the MWT cell design. The view is limited to the rear side n-busbar region

Fig. 9: REM picture of a laser drilled via after electro-less metal deposition in the whole via.

MWT cells (cell size 5 x 5 cm2) were processed at the University of Konstanz on CZ solar grade silicon which was part-processed (alkaline texture etch, POCl3 emitter diffusion, LPCVD-SiNx deposition) at the pro-duction line of BP Solarex in Madrid. An efficiencies of 17.3 % for an MWT (JSC = 37.3 mA/cm2, VOC = 612 mV, FF = 75.8 %, � = 17.3 %) shows that this back contact concept is quite promising. An in-crease of 3 % in JSC was obtained compared to the con-ventionally produced reference cells (JSC = 36.3 mA/cm2, VOC = 612 mV, FF = 76.2 %, � = 16.9 %). This gain can be explained by the shad-owing loss of the front busbar. VOC is almost identical for both cell types. The fill factors of the MWT cell shows that there was sufficient metal deposition in the vias indicating the potential of the buried contact proc-ess for back contact solar cells.

(1) S.R. Wenham and M.A. Green: “Buried contact solar

cells”, United States Patent No. 4.726.850, 1988 (2) E. Van Kerschaver, R. Einhaus, J. Szlufik, J. Nijs and

R. Mertens, 2nd WCPVSEC, Wien (1998) p. 1479

ARCn++n+p+ (BSF)pAl-Si EutecticCu / Ni

n-busbar

MWTvias

p/n-contact separation


1.14 Solar cell characterization

Th. Pernau, B. Fischer, G. Kragler, S. Keller, M. Keil, P. Fath and E. Bucher

Solar cell characterization has to fulfil three major requirements: first, detailed studies of new solar cell de-signs and processes, second, revealing problems in solar cell processing and, most important, cell analysis to gain insight into the physics behind domination loss mecha-nisms.

The first stage of solar cell characterization is the measurement of dark and illuminated solar cell current-voltage curves. In the last year we built up a new solar simulator designed to measure solar cells up to 15 * 15 cm2 with currents up to 10 A. A setup for fast measurement of JSCVOC-characteristics was developed which allows us to measure IV-characteristics without the influence of series resistances.

The discrepancy in the results which arise when these three curves (dark and illuminated IV, IOCVOC) are fit-ted to the standard double diode model could in many cases be attributed to the distributed nature of the series resistance and to inhomogeneities. We developed an ap-propriate analysis programme which allows for distrib-uted effects to evaluate the three IV-measurements con-sistently with a single parameter set.

Fig. 1: Lifetime scan of a ‘ribbon growth on substrate’ (RGS) wafer (size approx. 7 * 5 cm2). The structure is determined by the growth process and is not visible to the naked eye.

Especially large area solar cells with screen printed metal contacts suffer from series resistances. We built up a probe station for contact test structures and found that the contact resistance between the silver and the p-

type emitter is the dominating source for fill factor problems followed by resistive losses due to untabbed busbars.

Current losses of solar cells due to shadowing, re-flection, as well as recombination in bulk, emitter and surfaces are analyzed by measuring the spectral re-sponse. Together with the spectral reflectance measure-ment the collection efficiency of photo-generated carri-ers, the internal quantum efficiency, is determined. Some cell types show a distinct non-linear behaviour of carrier collection. Therefore the spectral response of solar cells needs to be measured under various bias con-ditions. A new current amplifier was installed which is capable to detect the extremely small signals overlying the large bias currents. A modification of the optical setup significantly improved signal height and made measurements over larger areas possible.

Fig. 2: Experimental setup of the LBIC system. The sample, the laser diodes and the lock-in amplifiers are placed in a double-shielded housing to prevent external interference.

Another important parameter in semiconductor physics is the minority carrier lifetime. Extensive life-time studies were carried out with our microwave-de-tected photoconductance decay (µW-PCD) measurement system, which allows a spatially resolved analysis of the effective lifetime of silicon wafers. Contributions of sur-face recombination to the effective carrier lifetime of rather low quality silicon such as RGS (Fig. 1) are neg-ligible.

For larger lifetimes, however, means for an efficient surface passivation had to be found. Therefore, a chemi-cal passivation cell 1) as well as a corona charger to sup-

xy

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press surface recombination supplemented our equip-ment. By charging the non-conductive coating (e.g. thermal oxide and silicon nitride) on the silicon sample, one type of carriers in the silicon is repelled from the surface, effectively suppressing recombination at the surface. Measuring samples with and without corona charge makes the separation of bulk and surface recom-bination possible 2).

Fig. 3: LBIC measurement of a solar cell; the mul-ticrystalline base material of this solar cell was grown by liquid phase epitaxy (LPE). In contrast to standard multicrystalline material, the photocurrent near the grain boundaries is higher than inside the crystallites.

The quasi-steady-state photo-conductance (QSSPC) method 3) allows the quick measurement of the minority carrier lifetime spectrum over the excess carrier density. A single flash sweeps the light intensity over a wide range whilst the sample conductance is measured. The effective minority carrier lifetime vs. carrier density is then calculated. After programming measurement and evaluation tools, we extensively used this method for process monitoring and characterization of surface pas-sivation and emitters.

Detailed information on the recombination mecha-nisms in solar cells can be revealed with the spatially re-solved (microscopical) analysis of the photocurrent. This technique is known as light beam induced current meas-urement (LBIC)1). In the last year we completed our LBIC apparatus, which is now capable of spatial resolutions down to 0.5 µm. The light sources are diode lasers of 833 nm and 905 nm which may be focussed to spot sizes of 5 µm FWHM minimum. The photogenerated current (Range: < 1 µA) is measured via a lock-in amplifier, which allows to detect details with

diameters even below 1 µm. Parallel to the photocurrent, the spatially resolved reflection data is collected by a second lock-in amplifier.

Fig. 4: Spatially resolved reflection measurement of a solar cell with both contacts on the back side (EWT de-sign). The front side emitter is contacted through laser drilled holes (the white spots in the picture). The solar cell was made out of a CZ-type monocrystalline wafer which shows random pyramids on the surface.

By measuring the photocurrent and reflection signal spatially resolved internal and external quantum effi-ciencies can be calculated and an estimate for the local effective carrier diffusion length obtained.

Since the number of wavelengths available is limited, a critical analysis of the results and comparison with the spectral response measurement is carried out at our lab.

(1) T. Pernau: Lebensdauerbestimmung und ortsaufgelöste

Messung der Quantenausbeute an kristallinem Silizium, Diploma thesis, Universität Konstanz 1999, (http://www.ub.uni-konstanz.de/kops/volltexte/1999/304/304_1.pdf)

(2) M. Schöfthaler, Transiente Mikrowellenreflexion zur kontaktlosen Trägerlebensdauer an Silizium für Solarzellen, PhD thesis, Stuttgart, 1995

(3) R. Sinton and A. Cuevas, Appl. Phys. Lett. 69 (1996) 2510

http://www.ub.uni-konstanz.de/kops/volltexte/1999/304/304_1.pdf



1.15 Colloidal mask lithography

F. Burmeister, K. Hartel, J. Boneberg and P. Leiderer

In the last few years colloid monolayer lithography was established as an easy to use technique for the pro-duction of nanostructures of variable sizes and materials. Essentially triangular structures were produced which reflect the openings between colloidal particles in the monolayer.

In the last year a new direction was followed which focuses on the difference between colloidal masks and conventional lithographic masks:

�� The openings in the mask are separated form the surface by the particle radius.

�� The colloidal particles are spherical and transpar-ent and can therefore be used for the application with light.

Both aspects were examined, the first in order to achieve new structures, the second with respect to the use of optical nearfield effects.

The fact that the openings of the mask are well sepa-rated from the surface allows to change the angle of incidence of e.g. deposited atoms. Additionally the substrate and the mask are rotated during the evapora-tion. This leads to new structures on the surface which now depend on the angle of incidence (Fig. 1).

Fig. 1: AFM-picture of the structures resulting from an angle of incidence 25°.

In contrast to the normal angle of incidence the trian-gular structures are now connected and form a metallic network.

The optical nearfield of particles shows a strong field enhancement effect behind the particle, which is shown in Fig. 2 for a particle with the diameter of the incidence wavelength. The field intensity is increased by a factor of eight just below the particle.

In order to use this field enhancement a monolayer of 800 nm colloidal particles on a silicon wafer was illu-minated with a 100 fs laser pulse of 800 nm wavelength.

At a well defined threshold the particles are removed by local plasma formation which leads to an array of nano-holes. This effect can be used to modify arbitrary sur-faces on a nanometer scale.

Fig. 2: Calculated field enhancement near a dielectric sphere with the diameter of the incidence wavelength.

Fig. 3: Electron microscope picture of an array of nanoholes on a Si surface.

1µm


1.16 Surface structuring with ultrashort laser pulses

H.-J. Münzer, M. Mosbacher, M. Ochmann, J. Boneberg and P. Leiderer

The scientific goal of the project is to provide a method which allows the preparation of nanostructures with intensive laser pulses. A first approach that was followed during the last years was the use of the high local fields in the vicinity of a very sharp tip. And in-deed the experiments showed that upon illumination of the tip of a scanning tunneling microscope nanostruc-tures with lateral dimensions below 30 nm can be writ-ten on a surface 1). Nevertheless, these investigations made clear that the nanostructures result from the me-chanical contact between tip and surface. This contact is a direct consequence of the thermal expansion of the tip due to absorption of laser light 2). In order to clearly separate thermal effects from local field effects we chose transparent submicron spherical polystyrene parti-cles as a new approach for the realization of field enhancement.

To estimate the field enhancement we performed Mie calculations 3) of the field intensity near a dielectric sphere. A typical result for a particle with a diameter of 800 nm which is illuminated by light with a wavelength of 800 nm is presented in Fig. 1.

Fig. 1: Calculated field enhancement near a dielectric sphere in free space.

The field intensity at the light averted side of the par-ticle exhibits an enhancement by a factor of more than eight and it is localized to an area considerably smaller in diameter than �/2. These calculations suggest that spheres with a diameter �� might be used for the nano-structuring of surfaces.

To examine the feasibility of the process we system-atically investigated the formation of holes underneath irradiated particles with diameters from 320 nm-800 nm at different wavelengths from UV to near infrared and pulse duration from the fs to the ns timescale. In all these experiments we were able to create holes in the

silicon substrates used, probably due to a local plasma creation. The diameter and morphology of these struc-tures strongly depend on pulse duration and the size pa-rameter �d/� of the Mie theory.

Fig. 2: Single hole created by irradiation of an individ-ual PS sphere with a fs laser pulse.

By controlled application of the colloidal suspension we are able to deposit isolated PS spheres at any desired concentration on the substrates. These spheres now can be used for the creation of single holes (Fig. 2) whose properties can be controlled by an appropriate choice of the laser parameters.

In addition to the creation of individual holes also hole arrays can be produced by the use of a 2D colloid monolayer as focusing mask. This parallel process al-lows the structuring of large substrate areas in a single shot process.

As the colloidal masks can be applied onto various materials including polymeric, biological and semicon-ducting ones the technique seems to be feasible for the nanostructuring of these promising substrates and will be investigated further.

(1) K. Dickmann and J. Jersch, Laser und Optoelektronik 27

(1995) 76 (2) J. Boneberg, H.-J. Münzer, M. Tresp, M. Ochmann and

P. Leiderer, Appl. Phys. A 67 (1998) 381 (3) P.W. Barber and S.C. Hill, Light Scattering by Particles:

Computational Methods (World Scientific Publishing, 1989)

1 µm


1.17 Metallic nanostructures on metaldichalcogenides

A. Müller, J. Zimmermann, J. Boneberg and P. Leiderer

Island growth is a special form of growth which ap-pears when the interaction between adsorbat atoms and substrate is small compared to the interaction of adsor-bat atoms. In the case of van-der-Waals surfaces the in-teraction to the substrate is small. Thus island growth is expected. As an example the project examines this kind of growth for the system metal on metaldichalcogenide surface.

While the experiment focused on the growth behavior on homogeneous surfaces in the last years, we switched to inhomogeneous surfaces now. This is realized by highly doped crystals. Each doping site appears as a dark spot in a scanning tunneling microscopy (STM) image (Fig. 1).

Fig. 1: STM-picture of a doped WSe2 surface. Picture area is 300 nm x 200 nm.

A view with higher magnification (Fig. 2) shows that such a doping site has a lateral diameter of several na-nometers while the position of the atoms are not changed within the resolution of the STM. Therefore a possible interpretation is a local shift of surface potential due to the delocalized charge of the doping site.

Fig. 2: Magnified picture of a single doping site. The size of the picture is 8 nm x 8 nm.

In order to deduce if these doping sites affect the nu-cleation process, the area of Fig. 1 is mapped again after the deposition of about 10% of a monolayer of Au. The STM-image now shows a high density of Au-islands (Fig. 3).

Fig. 3: The area of Fig. 1 after deposition of 10% of a monolayer Au.

A comparison with Fig. 1 yields an almost 100% overlap between the island sites and the position of the doping sites (Fig. 4). Therefore one can conclude that not only topographic defects but as well electronic de-fects act as nucleation sites for island growth.

Fig. 4: Comparison of island and fomer doping position, which are marked by black points.

In principle this finding allows to study the develop-ment of nanostructures after the arrival of individual atoms.


1.18 Self-organized growth of epitaxial CoPt3 nanostructures on WSe2

A. Maier, M. Albrecht, F. Treubel, M. Maret, V. Gimple, M. Lämmlin, Ch. Niedermayer and G. Schatz in collaboration with R. Poinsot (IPCMS, GEMM, 23 rue du Loess, 67037 Strasbourg)

The magnetic properties of nanostructures as a func-tion of their size are of fundamental interest as well as of technological importance and relate to the super-paramagnetic limit for magnetic recording. Of special interest for data storage technology are the CoPt3(111) films, which present strong perpendicular anisotropy and large Kerr rotation at short wavelengths 1). Such aniso-tropy, strongly dependent on the growth temperature, was correlated with the existence of anisotropic struc-tural order effects promoted by the MBE technique 2). The highest uniaxial anisotropy energy of 1 MJ/m3 was obtained in disordered fcc films co-deposited around 400°C, while the appearance of L12-long range ordering in films deposited above 530°C caused the perpendicular anisotropy to vanish 3,4).

Here we present in-situ RHEED and STM investiga-tions of self-organized CoPt3 nanostructures grown on WSe2(0001) surfaces by co-deposition of Co and Pt at-oms under ultrahigh vacuum conditions.

For a coverage of 0.3 Å CoPt3 deposited at 300°C, hexagonal islands are produced with a relatively narrow lateral size distribution centered around 4 nm and heights ranging from 1 to 2 nm (Fig. 1). These islands consist of only about 1000 atoms.

Fig. 1: STM picture of 0.3 Å CoPt3 (about 0.1 ML) de-posited at 300°C on WSe2.

The RHEED pattern shows weak spots close to the substrate streaks, giving evidence for epitaxial growth of the CoPt3 islands (Fig. 2). For higher coverages trian-gular shapes reveal the existence of (111) facets.

Fig. 2: RHEED pictures for different coverages of CoPt3(111) deposited at 300°C.

The in-plane hysteresis loops of the nanostructures were measured using a SQUID magnetometer for tem-peratures ranging from 1.8 K to 350 K. For a coverage of 0.3 Å CoPt3 deposited at 300°C we observe a closing of the hysteresis loops between 25 and 50 K (Fig. 3) suggesting the existence of a blocking temperature be-low 50 K.

Fig. 3: Hysteresis loops for different temperatures which start to close at the blocking temperature of about 50 K.

To verify this behavior, field cooled magnetization (FCM) and zero field cooled magnetization (ZFCM) measurements will be performed. As already observed in Co nanoparticles 5) different FCM and ZFCM are expected.

(1) D. Weller, H. Brändle, G.L. Gorman, C.J. Lin and H.

Notarys, Appl. Phys. Lett. 61 (1992) 2726 (2) C. Meneghini, M.Maret, V. Parasote, M.C. Cadeville,

J.L. Hazemann, R. Cortes and S.Colonna, Eur. Phys. J. B 7 (1999) 347

(3) P.W. Rooney, A.L. Shapiro, M.Q. Tran and F. Hellman, Phys. Rev. Lett. 75 (1995) 1843

(4) M. Maret, M.C. Cadeville, R. Poinsot, A. Herr, E. Beaurepaire and C. Monier, J. Magn. Magn. Mater. 166 (1997) 45

(5) M. Respaud et. al, Phys. Rev. B 57 (1998) 2925

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1.19 Co islands on WSe2

H. Wider, M. Dippel, V. Gimple, M. Lämmlin, Ch. Niedermayer and G. Schatz

It was shown by Rettenberger that the metals Au and In form regular shaped islands on the (0001)-surface of the layered semiconductor WSe2, with a relatively sharp size distribution depending on the evaporation condi-tions 1). In order to investigate the modified intrinsic physical properties of islands in the nanometer range, WSe2 is the ideal substrate due to the fact of an inert atomic flat surface without any dangling bonds. Of par-ticular interest are the magnetic properties of islands of the 3d-elements. We have performed first experiments to produce Co islands on WSe2 to investigate the growth conditions and the structural properties. The next step will be to investigate the magnetic properties and the interaction of these islands in a SQUID magnetometer.

Fig. 1: Co islands on WSe2(0001) grown with an evapo-ration rate of 0.62 ML/min. a) At 300K with a coverage of 0.1 ML; b) at 700K with a coverage of 0.5 ML.

Fig. 1a) shows the Co islands grown at RT and an evaporation rate of 0.62 ML/min on WSe2(0001) with a nominal thickness of 0.1 ML. The island density is about 200/(1000Å)2. The exact shape of these islands is not re-solved. Fig. 2 shows the size distribution of these islands versus the island diameter. Two maxima at a diameter of 26 Å and 39 Å are obtained. If the distribution is fitted with one Gaussian distribution, the maximum is found at 29 Å with a FHMW of 20 Å. The relation between is-land diameter and height is found to be linear with a minimal island diameter of about 10 Å and a slope of the height growth of about �z = 0.25 Å per �d = 1 Å. This linear behavior must be interpreted as a Volmer-Weber growth mode, which means strong three dimensional island growth, which is already known for Co homoepi-taxy. Fig. 1b) shows Co islands on WSe2 with a cover-age of 0.5 ML, grown at 700K with the same evapora-tion rate of 0.62 ML/min. The island density is about 50/(1000Å)2. As can be seen most islands have a hex-agonal shape and they are orientated with respect to the substrate. Fig. 3 shows the size distribution and the di-ameter versus height behavior for these islands. Here also two maxima are visible, the first at about 60 Å and the second at 100 Å diameter. The maximum of a fitted single Gaussian is at 65 Å with a FHMW of 48 Å.

Again, the relation between island diameter and height is found to be linear with the same onset and slope value like in the case of the islands grown at 300 K. The ques-tion, in which atomic structure the Co is arranged in the islands is still unknown and has to be answered in fur-ther experiments.

Fig. 2: Size distribution and relation of diameter versus height of the Co islands grown at 300K.

Fig. 3: Size distribution of Co islands grown at 700K.

(1) A. Rettenberger, PhD thesis, Universität Konstanz (1998)

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1.20 A low energy muon study of the dipolar fields produced by an assembly of iron nanoclusters in silver

E.M. Forgan, T.J. Jackson and T.M. Riseman (University of Birmingham, Birmingham B15 2TT, United Kingdom) in collaboration with H.Glückler, E. Morenzoni and T. Prokscha (Paul Scherrer Institut,CH-5232 Villigen, Schweiz) R. Khasanov and H. Keller (Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland) J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig) Ch. Niedermayer, M. Pleines and G. Schatz

Low energy muons 1) were used to measure the spa-tial and temporal properties of the random dipolar fields produced by an assembly of iron nanoclusters, supported in a silver thin film matrix. The samples were prepared by C. Binns, at Leicester University. Unsupported clus-ters have been observed to follow a log normal diameter distribution, with a mean diameter of 2.8 nm and a width of 0.5 nm. We used an assembly of such iron nano-clusters supported in a non-magnetic thin film matrix. Most of the implanted muons stop at random sites in the matrix, in the regions between the clusters.

The results of our measurements on a sample con-taining clusters with an estimated median diameter of 2.8 nm are shown in Fig. 1. For transverse �SR meas-urements, shown by the circles in Fig. 1, a magnetic field of 10 mT was applied perpendicular to the surface of the sample 1). The results of zero field measurements are shown by the diamonds in Fig. 1.

Fig. 1: Muon polarization relaxation rate from trans-verse and zero field low energy �SR measurements.

At low temperatures thermal energy is insufficient to cause significant activation of the cluster moments and a static Lorentzian field distribution is obtained within the sample. In transverse �SR measurements, this causes a pure exponential damping of the muon decay spectra. At high temperatures (for this sample above 10 K 2)), ther-mal activation of the clusters' moments has a motional narrowing effect and a "stretched" exponential damping, with an exponent of 0.5, was fitted to the data. In Fig. 1, the broken line shows the average low temperature muon relaxation rate of � = 0.22 �s-1. The full line shows the results of a linear fit to the high temperature

relaxation rates. The slope of this linear fit gives an acti-vation energy of 37(4) K. From the intercept the attempt frequency for thermal activation of the cluster moments 0 = 67(15)�106 Hz is calculated 2). The diamonds in Fig. 1 show the results of zero field �SR measurements. The muon decay spectra were fitted with a Lorentzian Kubo function 3) and is seen to be consistent with the trans-verse field data.

Figure 2 shows the results of simulations of the low temperature distribution of static dipolar fields. The simulations show the field distribution as revealed by the front and back detectors in the low energy muon spec-trometer. The solid line is a Lorentzian fit to the data, with HWHM of 2.2 mT. This width corresponds to a muon relaxation rate of � = 1.8 �s-1, from which the volume concentration of iron in the sample can be determined 2).

Fig. 2: Simulation of the static dipole field due to iron nanoclusters at a concentration of 0.3 % by volume in an applied field of 10 mT. The saturation magnetization of the clusters is assumed to be 2 T in the simulations.

(1) E. Morenzoni et al., Physica B in press (2) T.J. Jackson et al., J. Phys: Cond. Matt. 12 (2000) 1399 (3) Y.J. Uemura, in Muon Science, eds. S.L. Lee, S.H.

Kilcoyne and R. Cwyinski (Institute of Physics, Bristol, 1999)


1.21 Dimensional cross-over in AuFe spin-glass studied by low energy muons

G.J. Nieuwenhuys, M.B.S. Hesselbert, F. Galli and J.A. Mydosh (Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands) in collaboration with H. Glückler, E. Morenzoni and T. Prokscha (Paul-Scherrer-Institut, CH-5232 Villigen, Switzerland) Ch. Niedermayer, M. Pleines and G. Schatz J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig E.M. Forgan (University of Birmingham, Birmingham B15 2TT, United Kingdom) R. Khasanov, H. Keller (Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland)

Since its discovery in 1972 1), the spin freezing in e.g. diluted AuFe alloys has been the subject of many dis-cussions in literature 2). The question whether the spin-glass freezing is a phase transition, with all its conse-quences, is still not fully answered. One of the important ingredients for such a discussion is the existence and the size of a characteristic length scales associated with the freezing and its dynamics. In 'normal 3D phase transi-tions' the transition temperature is a function of the shortest length of the sample as this length comes in the vicinity of the correlation length �. The finite size scal-ing of the dc-properties of spin glasses has been studied by Cowen et al. 3), and in particular for AuFe by Hoines et al. 4). They found that the freezing temperature, Tf, es-sentially approaches zero as the thickness of the films goes to zero. These experiments were measurements of the static magnetic susceptibility carried out with a SQUID magnetometer on multilayered samples. An in-vestigation of the -slow- dynamics as function of sample thickness has been performed by Sandlund et al. 5).

The slowing down of the spin system as the freezing temperature is reached from above has been the subject of a number of �SR experiments 6-9). In general it has been found that the decay of the muon polarization for T > Tf can be described by a so-called stretched expo-nential, exp[-(� t)�]. The value of � increases rapidly near Tf, while the value for � becomes 1/3.

We have investigated the muon relaxation in thin samples of AuFe 3 at.% using the low energy muon fa-cility at the Paul Scherrer Institute 10). The films have been sputter deposited on a silicon waver from the same composite target in one run and the concentration and thickness were verified using Rutherford BackScattering and Elecron Microprobe Analysis. Positive muons with energies of 1, 2.5 and 6 keV were implanted in the films of 10, 20 and 50 nm thickness, respectively. The stop-ping range was calculated using the program TRIM.SP

11), from which it was clear that in all cases more than 75 % of the muons stop in the AuFe thin film. A trans-verse field of 10 mT was used, and the runs were taken with a total of 600.000 events in the four counters.

In Fig.1 the results for the relaxation rate as a func-tion of temperature are shown. The relaxation rate was obtained from fits of the asymmetry with a stretched ex-ponential function. The result for the thickest sample (50 nm) is very similar to that obtained on bulk samples, as already reported by Schenck et al. 12). Most surprisingly, the results for the thinner samples do show not only the

expected decrease of the freezing temperature, but also the relaxation rate does not become as large as for the bulk samples. Also, the stretched exponential power, �, is not 1/3 anymore in the thinner spin glasses. These low energy �SR results indicate that the character of the spin-glass freezing changes dramatically when one of the dimensions of the sample becomes smaller than about 20 nm.

Fig. 1: Relaxation rate versus temperature for AuFe 3 at.% films of 50, 20 and 10 nm thickness.

(1) V. Canella and J.A. Mydosh, Phys. Rev. B 6 (1972) 4220 (2) J.A. Mydosh, Spin Glasses: an experimental introduc-

tion, (Taylor & Francis, London, 1993) (3) J.A. Cowen, G.G. Kelling and J. Bass, J. Appl. Phys 64

(1988) 5781 (4) L. Hoines, J.A. Cowen and J. Bass, Physica B, 309

(1994) 194-196 (5) L. Sandlund et al., Phys. Rev. B 40 (1989) 869 (6) Y. Uemura et al., Phys. Rev. B 31 (1985) 546 (7) D.E. MacLaughlin et al., Phys. Rev. Lett. 51 (1983) 927 (8) A. Keren et al., Phys. Rev. Lett. 77 (1996) 1386 (9) I. Campbell et al., Phys. Rev. Lett. 72 (1994) 1291 (10) E. Morenzoni et al., J. Appl. Phys. 81 (1997) 3340; E.

Morenzoni et al., to be published in Physica B 2000 (11) W. Eckstein, Radiation Effects and Defects in Solids

239 (1994) 130; H. Glückler et al., to be published in Physica B 2000

(12) A. Schenck et al., PSI News 1998; muSR1999, Switzer-land, 1999; to be published in Physica B (2000)

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1.22 Magnetic anisotropy and chemical long-range order in epitaxial ferrimagnetic CrPt3 films

M. Maret, M. Albrecht, J. Köhler, A. Maier, F. Treubel, E. Bucher, and G. Schatz in collaboration with R. Poinsot and C. Uhlaq-Bouillet (IPCMS, Strasbourg) J.M. Tonnerre and J.F. Berar (Lab. Crystallography, Grenoble)

The discovery of the improved short-wavelength magneto-optical properties of the Co-Pt alloy films compared with the Co/Pt multilayers has given rise to a renewal of interest in the study of the 3d transition-Pt magnetic alloys. Intensive studies in Co-Pt thin films have allowed to understand the origin of their strong perpendicular anisotropy 1,2). In the fcc CoPt3 and hcp Co3Pt films, anisotropic structural effects promoted by the MBE technique are the structural source of perpen-dicular anisotropy; such effects are established for growth temperatures around 400°C and characterized by CoPt bonds preferentially oriented out of the film plane. XMCD measurements have revealed a clear enhance-ment of the Co orbital magnetic moment along the growth direction 3).

Here we report on the magnetic and structural prop-erties of CrPt3 films. In contrast with the CoPt3 alloy which is ferromagnetic in the disordered and L12-type ordered fcc phases, bulk CrPt3 is ferrimagnetic in the L12 state and non-magnetic in the disordered state. 500 Å thick films of CrPt3 were prepared by MBE on both Pt(111) and Pt(001) buffer layers grown on Al2O3(0001) and MgO(001) substrates, respectively, either directly by co-deposition of Cr and Pt at high temperatures or after in-situ annealing of superlattices [Cr(2Å)/Pt(7.5Å)]. The epitaxial growth of the alloy as well as the L12-type long range ordering (LRO) was followed by RHEED (Fig. 1).

Fig. 1: RHEED-images of a Pt(111) buffer layer and an ordered CrPt3(111) alloy film which shows additional intermediate streaks indicating the LRO.

In CrPt3(111) films, x-ray diffraction measurements

performed on the CRG-BM02 beamline at the ESRF have allowed us to determine accurately the growth temperature dependence of the chemical order parame-ter, S, and to reveal a rhombohedral distortion of the fcc lattice such as the fcc stacking is slightly compressed along the growth direction. In films co-deposited be-tween 850°C and 900°C and superlattices annealed above 1000°C a nearly perfect L12 LRO was obtained.

The magnetic properties were studied using a SQUID magnetometer with the field applied normal and parallel to the film plane. The effective anisotropy (Keff = Ku -0.5�oMs

2) is deduced from the area enclosed between the parallel and perpendicular magnetization hysteresis loops. As in bulk alloys the chemical LRO yields a fer-rimagnetic order while the disordered films are non-magnetic. The ordered CrPt3(111) films exhibit perpen-dicular anisotropy (Keff > 0) and large remanence (Mr/Ms) which increases with the degree of LRO as shown in Fig. 2. This behavior is completely different from that observed in the ferromagnetic L12-ordered CoPt3 films which present no perpendicular anisotropy as expected from its isotropic structure.

Fig. 2: Change of the chemical LRO parameter, S, ef-fective anisotropy energy, Keff , and perpendicular re-manence, Mr/Ms , as a function of the growth tempera-ture for co-deposited CrPt3(111) films.

We suggest that the origin of perpendicular anisot-ropy in CrPt3(111) results from the arrangement of the Cr atoms with respect to the (111) planes. Owing to their large magnetic moment of 3.37 �B, oppositely directed to the small Pt moment (-0.26 �B), the Cr atoms drive the magnetization process. In the L12 fcc structure, the 6 Cr nearest neighbors around a Cr atom are arranged as second neighbors at a distance of afcc, and located in the upper and lower adjacent (111) planes. Therefore the

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overlap of their electron distribution would favor an easy axis of magnetization normal to the film plane. The ab-sence of perpendicular anisotropy in the ordered CrPt3(001) films agrees with this interpretation, since the 6 Cr neighbors are located along the [100], [010] and [001] directions. From magnetic force microscopy (MFM) measurements the magnetic domain pattern of a 450 Å thick CrPt3(111) film as-grown at 850°C consists in a network of bubbles slightly elongated of 70 nm width (Fig. 3(a)). For a thinner film (250 Å) we have ob-served an additional magnetic superstructure (Fig. 3(b)) similar to that of a stripe domain pattern which may arise due to magnetic instabilities.

Fig. 3: Topography (left) and magnetic domain pattern (right) of (a) a 450 Å thick CrPt3(111) film as-grown at 850°C and (b) a 250 Å thick CrPt3(111) film showing an additional stripe domain pattern.

(1) M. Maret, M.C. Cadeville, R. Poinsot, A. Herr, E. Beaurepaire and C. Monier, J. Magn. Magn. Mater. 166 (1997) 45

(2) C. Menegheni, M. Maret, V. Parasote, M.C. Cadeville, J-L. Hazemann, R. Cortes and S. Colonna, Eur. Phys. J. B 7 (1999) 347

(3) W. Grange, M. Maret, J.P. Kappler, J. Vogel, A. Fon-taine, F. Petroff, G. Krill, A. Rogalev, J Goulon, M. Finazzi and N. Brookes, Phys. Rev. B 58 (1998) 6298


1.23 Structure of Pt/Mn superlattices grown by molecular beam epitaxy

F. Treubel, A. Maier, M. Albrecht, M. Maret and G.Schatz in collaboration with R.Poinsot (IPCMS, GEMM,23 rue de Loess, Strasbourg)

There is great interest in the stabilization of fcc-Mn at room temperature, especially because of its theoretically predicted magnetic properties. While the 3d transition metals in the neighborhood of Mn (these are V, Cr and Fe) crystallize in the bcc bulk structure, manganese has a polymorphic character and exhibits four different structure types when heated up to the melting point. All transitions are reversible having different hysteresis loops with temperature. �-Mn, the room temperature modification, consists of 58 atoms per unit cell, �-Mn of 20. The transition temperature Ttr between these two phases is about 970 K. Both �- and �-Mn can be under-stood as complicated alloy-like structures and are the only elemental representatives of these cubic structure types. They are antiferromagnetic with Néel tempera-tures TN = 95 and <0.1 K, respectively. �- and �-Mn are high temperature modifications with the well known structure types fcc (Ttr = 1220 K) and bcc (Ttr = 1420 K), respectively. Bulk �-Mn rapidly cooled down at room temperature is tetragonally distorted and shows an antiferromagnetic state (TN = 540 K).

Tab. 1: Some physical properties of the Mn modifica-tions 1).

Structure Ttr[K] Magnetism TNéel[K]

� complex --- antiferro. 95

� complex 970 antiferro.? 0

� fcc 1220 antiferro. 540

� bcc 1420 theory ---

Fcc-Mn films have already been stabilized by mo-lecular beam epitaxy (MBE) on different substrates like Ir 2), Co 3,4), Cu 5), Ag 5) and Pd 6). We have chosen the Pt(111) surface exhibiting a rather large lattice mis-match, that could induce a ferromagnetic state of Mn. For that reason, we investigated the growth parameters and structural properties for epitaxially grown fcc Mn films. The monocristalline quality of Pt(111) and of the final Mn films was investigated with RHEED (Reflec-tion High Energy Electron Diffraction). Depending on the Mn thickness, we observed three different surface phases for a deposition temperature of 200°C:

1. For the first 12 Å (4 monolayers), Mn grows pseu-domorphically on the Pt(111) adopting its fcc structure (Fig. 1a).

2. After 12 Å, two additional streaks appear between the main ones which correspond to a two-dimensional (2D)- 33 � surface structure (Fig. 1b).

3. At 50 Å, 3D-island growth abruptly occurs indicated by the appearance of spots instead of streaks

(Fig. 1c). Additionally, these islands are faceted ((111) and (100)) with angles of 54.7° and 70.5° extracted directly from the shape of the spots.

Fig. 1: Surface phases of Mn on Pt(111) at 200°C at

different thicknesses t of Mn: a) t <12 Å: 2D-fcc. b) 12 < t < 50 Å: 2D- 33� . c) t > 50 Å: faceted clusters.

From our RHEED observations a preliminary surface phase diagram showing the stability ranges of the differ-ent observed phases is given in Fig. 2. Above 400°C a completely different growth behavior is observed, the Mn surface structure is pseudomorphic to the fcc Pt sur-face lattice. That may be explained by the formation of a 2D-fcc MnPt alloy during deposition, driven by Pt seg-regation along the advancing free surface.

To investigate the structural and physical properties on the metastable fcc Mn phase more accurately we produced a series of Mn/Pt multilayers at room-tem-perature by depositing alternately Mn and Pt with a growth rate of 0.1 Å/s. The full composition of the mul-tilayers is as follows:

Al2O3(0001) / Pt(20 Å) / [Mn(t)Pt(10 Å)]10,

where the Mn layer thickness t ranges from 6 up to 15 Å.

The variation of the in-plane lattice parameter de-duced from the RHEED patterns observed during the deposition of the [Mn(15 Å)/Pt(10 Å)]10 multilayer is shown in Fig. 3. The expected behavior has been con-

1.a)

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12<t<50 Å Mn on Pt(111)

>50 Å Mn on Pt(111)


firmed: after the first Mn monolayer growth which shows a slight extension of the surface lattice, the in-plane lattice parameter remains constant at a value of 2.796 Å with further Mn deposition until the next Pt-layer is deposited which causes a rapid decay of the lat-tice parameter down to the Pt value (2.772 Å).

Fig. 2: Surface phase diagram of Mn on Pt.

Fig. 4 shows an X-ray diffraction pattern of the [Mn(6Å)/Pt(10Å)]10 multilayer. The high-angle �-2� scan analysis yields information on the average lattice spacing in the growth direction (d111) and on the multi-layer period (� = tMn + tPt). d111 is deduced from the position of the main Bragg peak (SL0), whereas � is de-duced from the distances between the satellite and the main Bragg peak. Despite the large amount of the total thickness Kiessig fringes (SL-1, SL+1), satellite reflec-tions are clearly observed.

Fig. 3: Variation of the in-plane lattice parameter.

From the simulations of the X-ray diffraction patterns using the software program SUPREX, we have extracted the interplanar distance in the Mn layers along growth direction, d111(Mn), assuming that the interplanar distance in the Pt layer is equal to the bulk value. From Table 2, it turns out that d111

Mn is almost independent of the Mn layer thickness with a value of about 2.10 Å. This value is much smaller than expected from the in plane lattice parameter for a perfect fcc stacking (2.28 Å). From the volume of the trigonal unit cell

(arising from the distortion of the fcc-Mn) we deduced an average value for the volume per Mn atom of 14.19 Å3. This volume is larger than that obtained for Ir/Mn multilayers (2) (13.4 Å3) due to the larger Pt lat-tice parameter compared to Ir.

Fig. 4: (� - 2�) X-ray diffractogram of a Pt/Mn multi-layer produced at room temperature.

Magnetic measurements have been performed with a Superconducting Quantum Interference Device (SQUID) magnetometer. In spite of the increased vol-ume per Mn atom the Mn/Pt multilayers reveal no ferromagnetism. Probably the distorted fcc Mn phase is antiferromagnetic (Tab. 1) similar to the high tempera-ture �-Mn bulk phase.

Tab. 2: Structural properties of Mn/Pt multilayers.

Mn-thickness [Å] 6 10 12 15 d (Mn, in-plane) [Å],

RHEED 2.796 2.796 2.796 2.796

Mean d111 [Å],

XRD 2.2498 2.2414 2.2346 2.2299

d111(Mn) [Å],

SUPREX 2.100 2.095 2.100 2.090

� [Å] 13.51 16.23 17.65 20.10

Volume/atom [Å3] 14.218 14.184 14.218 14.150

(1) J. Pohl, E.U. Malang, B Scheele, J. Köhler, Ch. Lux-

Steiner, and E. Bucher, J. Vac. Sci. Technol. B 12, (1994) 1206

(2) S. Andrieu, H.M. Fischer, and M. Piecuch, Phys. Rev. B 54 (1996) 2822

(3) K. Ounadjela, P. Vennegues, Y. Henry, A. Michel, V. Pierron-Bohnes, and J. Arabski, Phys. Rev. B 49 (1994) 8561

(4) Y. Henry, V. Pierron-Bohnes, P. Vennégues, and K. Ounadjela, J. Appl. Phys. 76 (1994) 2817

(5) I.L. Grigorov, J.C. Walker, J. Appl. Phys. 83, (1998) 7010

(6) D. Tian, H. Li, S.C. Wu, and F. Jona, Phys. Rev. B 45 (1992) 3749

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1.24 Modified growth of Co on Cu(111) using In as an interlayer

H. Wider, M. Dippel, V. Gimple and G. Schatz in colaboration with J. Jaworski, J. Prokop and M. Marszalek (Institute of Nuclear Physics, Department of Nuclear Spectroscopy, Krakow, Poland)

It was demonstrated that the growth behavior of Co on Cu(111) is markedly changed with an interlayer of In in the submonolayer range 1). In order to understand this mechanism in detail and to study the dependence on the amount of the interlayer coverage, evaporation experi-ments were performed with in–situ MEED (Medium Electron Energy Diffraction) and PAC (Perturbed An-gular Correlation Spectroscopy). During the MEED ex-periments it is possible to investigate the intensity of the specular beam, which gives evidence of the underlying growth mode. By recording and analysis of the distance of the MEED spots, it is possible to observe the behavior of the in-plane interatomic distances of the top layer during growth.

Fig. 1: MEED intensities of the specular beam during the growth of Co on Cu(111), without an interlayer and with In as an interlayer of a coverage of 0.5 and 3 ML.

Fig. 1 shows the MEED specular beam reflection in-tensities during the evaporation of Co on a Cu(111) sur-face at an evaporation rate of 0.62 ML/min with and without In coverage as an interlayer at room tempera-ture. With the occurrence of monolayer oscillations for the In interlayer thicknesses of 0.5 ML and 3 ML, the curves reveal clearly the improvement of the growth be-havior, by developing a layer-by-layer growth mode. The first curve shows the intensity behavior of a 12.5 ML Co film deposited directly on an atomically flat Cu(111) surface. The drastic decrease of the specular spot intensity and the saturated value at relatively low level without any intensity oscillations proves the three-dimensional island growth of the Co. In contrast to this behavior, the Co film grown on Cu(111) with 0.5 ML of In previously deposited shows clear oscillations from a Co coverage of 3 ML up to 11 ML. Within the first

3 ML the intensity also decreases, and no oscillations or only little ones were seen. The third curve for 3 ML fi-nally shows a completely different behavior. Only weak oscillations are visible here during the first 5 – 6 ML. After that, the intensity increases dramatically, and monolayer oscillations become observable up to the 25th ML. Then the intensity remains on a saturated high level, which shows no tendency to fall for greater film thicknesses. If more Co is deposited on such surfaces, intensity oscillations of up to a total Co coverage of about 50 ML can be observed without an additional In.

Fig. 2: In-plane lattice constants during evaporation of 12 ML of Co on Cu(111) at RT. a) without an interlayer; b) with an interlayer coverage of 0.5 ML In.

At this point the question of interest is whether the In segregates to the surface partly or totally, and how much In stays at the interface or is integrated into the Co film. In this context, it is also of interest that the alloy forma-tion was observed at the Cu/Co interface, which could influence Co growth and the behavior of the In.2) Auger electron spectroscopy investigations unfortunately do not have enough sensitivity to answer these questions. These data only show that maybe part of In remains at the Cu/Co interface. The mechanism of how the In man-ages to change the growth behavior is also still un-known.

Cu(111) In3 Co28.5

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Fig. 3: AC-Spectra and their Fourier transforms for different In and Co coverages on a Cu(111) single crys-tal surface. For the interpretation see text.

To clarify this problem MEED experiments were car-ried out observing the in-plane interatomic distances of the topmost layer. Results for the growth of 12 ML Co at RT are shown in Fig.2, a) without In and b) with an In interlayer thickness of 0.5 ML. Again the data reveal a distinct difference in behavior. Without In, the Co grows pseudomorphically up to a thickness of about 5ML. That means the growth is epitaxial up to this coverage and takes over the lattice constant of the Cu substrate of 2.55 Å, which gives high mechanical stress in the Co film. Above 5 ML, the lattice constant changes within the next 4 to 5 ML to a lattice constant which should be in the region of the Co bulk value of 2.51 Å. The ques-tion whether the Co grows in the hcp or in the fcc phase, or if there is a transition, has also not been finally an-swered yet in the case of In as an interlayer. In this case (b), the behavior of the in-plane lattice constant is totally different. First, the data show a linear decrease of this value from the beginning of the growth, up to a coverage of 11 to 12 ML Co. This means that the mechanical stress in the film is reduced continuously due to the lat-tice mismatch between substrate and film. This could be the case when the In is partly integrated into the Co film and offers the Co atoms perturbed lattice sites to mini-mize the stress energy. It is also apparent that where the lattice constant saturates the value is a little larger than in the case without In. The reason for this difference has not been found in detail yet. Here, the formation of a

Cu-In alloy could play a role. Submonolayer intensity oscillations have been observed during the evaporation of In, which is consistent with the formation of CuIn2. We have hints in our data that during evaporation of In onto a pure Cu(111) surface the lattice constant in-creases by a factor of 2% within the first deposited monolayer. These investigations are difficult due to the fact that the MEED spots intensities decrease drastically for less than 1 ML.

In order to investigate dynamical changes at the atomic scale during the deposition of several elements on the Cu substrate, a very local measurement method is necessary. The PAC method meets these conditions.3) Fig. 3 shows PAC-spectra and their Fourier transforms for different In and Co coverages. Spectrum a) was taken immediately after deposition of 111In probe atoms and shows oscillations with frequencies 186 Mrad/s and 372 Mrad/s, which is characteristic for substitutional ter-race sites. (b) After deposition of 0.1 ML of natural In the PAC oscillations are strongly damped and the distri-bution of the frequencies is broadened. It seems that the radioactive probe atoms are statistically decorated with the deposited In atoms and that these modify the fieldgradients in a statistical way. Consistent with this observation is the fact, that the MEED reflection inten-sity already decreases strongly for less than 1 ML In. (c) If more than 0.4 ML of In are deposited, and in addition Co in thicknesses from 4 to 12 ML, no frequencies are visible anymore. No hints of an interface alloy or In sur-face sites are given. (d) After annealing the film for 15 min at 673 K, a signal could be detected again at 360 Mrad/s which indicates a Co surface site. From this we conclude that In probes have been incorporated near the Co/Cu interface before and a small fraction is ther-mally activated to occupy Co surface sites.

(1) H. Wider, V. Gimple, M. Dippel, J. Jaworski, J. Prokop,

M. Marszalek and G. Schatz, Annual Report Solid State and Cluster Physics, Universität Konstanz 1998

(2) W. Keppner, T. Klas, W. Körner, R. Wesche and G. Schatz, Phys. Rev. Let. 54 (1985) 2371

(3) R. Fink, R. Wesche, T. Klas, G. Krausch, R. Platzer, J. Voigt, U. Wöhrmann and G. Schatz, Surf. Sci. 225 (1990) 331

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1.25 Laser cleaning of silicon surfaces

M. Mosbacher, V. Dobler, J. Boneberg and P. Leiderer

The continuing trend of miniaturization of integrated circuits requires increasing efforts and new concepts to clean wafer surfaces from dust particles. We report on two methods based on the application of intensive laser pulses: Dry laser cleaning (DLC) where an intensive la-ser pulse hits the surface and steam laser cleaning (SLC) where additionally a thin liquid layer is condensed onto the substrate before application of the laser pulse. For the DLC method measurements of the vertical movement of the surface due to the fast thermal expan-sion are shown, which allow to determine the cleaning limits. In the case of SLC we extended the efficiency measurements into the picosecond regime.

1. Surface acceleration during dry laser cleaning

The beam of Q-switched Nd:YAG laser is frequency doubled (� = 532 nm) and guided to the silicon sub-strate. The laser energy was controlled by attenuation of the beam. The surface displacement of the silicon sub-strate was measured by a heterodyne interferometer, re-corded on a digital storage oscilloscope and derived nu-merically to obtain the acceleration. The pulse duration could be changed by varying the flash lamp energy of the Nd:YAG laser between approximately 10 ns and 20 ns (FWHM). Displacement signals were averaged over 600 shots to reduce noise.

Fig. 1: A typical result for the displacement d(t) and the acceleration a(t). The offset in time is introduced by the interferometer electronics. The interesting part for dry laser cleaning is the region between 50 ns and 60 ns with the maximal negative acceleration of amax� �3·106 g and dmax� 2.2 nm.

Fig. 1 shows a typical result of the experiment: The silicon expands during the laser pulse and reaches a plateau dmax. Ejection of particles is expected to take place during the high negative acceleration (amax).

The maximal displacement dmax and the maximal negative acceleration amax are linear functions of the in-cident laser flux (as expected theoretically). The ratio

�amax/dmax is therefore independent of the incident en-ergy density and can be used as a measure of the influ-ence of the temporal pulse shape.

Fig. 2: Dependence of �amax/dmax on the pulse width �. The dashed line is a best 1/�2 fit to the data.

The ratio �amax/dmax (see Fig. 2) increases for shorter pulse widths, but not as strong as expected for a gaus-sian temporal pulse profile (1/�2). There may be two reasons for this behavior: The pulse shape is not an ideal gaussian (rise time < fall time) and the bandwidth limit of the interferometer is reached for the shorter pulse widths.

We determined the maximal achievable surface ac-celeration during dry laser cleaning of silicon wafers 1). While the displacement is dominated only by pulse en-ergy, the acceleration shows a clear dependence on the temporal pulse shape: Shorter pulses yield higher accel-erations, therefore cleaning experiments with shorter pulses would be favorable.

This work was performed in collaboration with the University of Burgundy (Dijon/France) as part of the TMR project ERB FMRX-CT98-0188 “Modeling and Diagnostics of Pulsed Laser-Solid Interactions. Appli-cations to Laser Cleaning”.

2. Steam laser cleaning applying ps pulses

A change in the pulse duration of the cleaning laser from ns to ps leads to a more efficient heating of the liq-uid-solid interface in the steam laser cleaning process. Therefore the cleaning threshold compared to ns clean-ing may change, an effect that was quantified in our ex-periments.

For the determination of the efficiency of the process we used polystyrene colloidal particles 800 nm in di-ameter with a well defined size as model contaminants. They were deposited as isolated particles on the Si sur-face. By measuring the particle concentration via light scattering we determined quantitatively the efficiency of the ps steam laser cleaning 2). As liquid medium we

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used a water-isopropanol mixture (10% IPA) that was condensed onto the substrate just before the application of the laser pulse.

The cleaning process was carried out using two dif-ferent pump laser systems providing several different pulse durations and wavelengths: A Nd:YAG laser (��= 532 nm, FWHM= 8ns or 2.5 ns) and a pulsed dye ampli-fier seeded either with a cw dye laser beam or with a synchronously pumped mode-locked dye laser (�= 583 nm, FWHM=2.5 ns or 30 ps).

Fig. 3: Experimentally determined cleaning efficiency as a function of applied energy density polystyrene parti-cles of 800 nm diameter for ps steam laser cleaning.

For the ns steam laser cleaning a threshold of 110 mJ/cm2 was found; there was no significant influ-ence of pulse duration (2.5 and 8 ns) and wavelength (532 and 583 nm). This threshold value is identical to the universal cleaning threshold found for the removal of polystyrene spheres with diameters of 60-800 nm at ��= 532 nm, FWHM = 7 ns 3).

Decreasing the pulse length in the steam laser clean-ing process results in a considerably lower cleaning threshold. Applying pulses in the ps-regime (��= 583 nm, FWHM = 30 ps) we found a value of 20 mJ/cm2. This threshold is lower by a factor of 5 than for the ns regime due to a more efficient heating of the liquid/solid-interface. As can be seen in Fig. 3 the threshold value is far below the melting threshold of a bare Si surface that has been determined to be 220 mJ/cm2 by ps-time resolved reflectivity measurements. Important with respect to industrial applications is the fact that not only the cleaning threshold but the regime where “efficient” cleaning takes place, i.e. the fluence interval where cleaning efficiency exceeds e.g. 90%, is found at distinctly smaller laser fluences than the melt-ing threshold.

(1) V. Dobler, R. Oltra, J.P. Boquillon, M. Mosbacher, J.

Boneberg and P. Leiderer; Appl. Phys. A 69 (1999) 335 (2) M. Mosbacher, N. Chaoui, J. Siegel, V. Dobler, J. Solis,

J. Boneberg, C.N. Afonso and P. Leiderer; Appl. Phys. A 69 (1999) 331

(3) M. Mosbacher, V. Dobler, J. Boneberg and P. Leiderer; submitted to Appl. Phys. A


1.26 Range of low energy muons in Cu films

H.Glückler, E. Morenzoni, T. Prokscha (Paul Scherrer Institut,CH-5232 Villigen, Schweiz) in collaboration with M. Birke, J. Litterst, H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig) E.M. Forgan (University of Birmingham, Birmingham B15 2TT, United Kingdom) R. Khasanov, H. Keller (Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland Ch. Niedermayer, M. Pleines, G. Schatz

In 1999 we have extended our investigation of low energy muon ranges in thin metallic films on quartz glass substrates 1). In this report we present preliminary results obtained for Cu films.

Two Cu films with thickness of 68 nm and 500 nm were prepared by sputtering pure Cu onto a 50 mm diameter quartz glass disc. After the preparation the thickness of the thin film was measured by a RBS analysis 2).

TF-�SR measurements were performed in a 5 mT magnetic field at 20 K by using low energy �+ with ad-justable implantation energies E

� between 0 keV and

29.4 keV. In nonmagnetic metals like Cu, the �+ precess in an applied magnetic field with a frequency of 136 kHz/mT whereas in quartz glass muonium formation is favored. In the latter case the precession frequency is 13.9 MHz/mT. The amplitudes of these two signals are a direct measure of the fractions of �+ stopped in the metal film or in the quartz glass backing.

In Fig. 1 the observed �+-asymmetries A� for the thin

Cu film (solid symbols) and the thick Cu film (open symbols) are shown as a function of E

�. In the thin Cu

sample A� decreases from 26 % for E

� =10 keV to 5 %

for E� above 25 keV. This reflects the increasing frac-

tion of �+ thermalized in the quartz glass with increasing energy. A diamagnetic asymmetry A

�,quartzglass of 5 % is also observed in 5 mT TF-�SR measurements on uncov-ered quartz glass. This signal corresponds to the fraction of �+ which do not form Mu in quartz glass. In the thick Cu sample no energy dependence of A

� is found for E

�

above 10 keV. In both samples an almost constant A�

for energies between 3 keV and 10 keV is found. At these energies all �+ are thermalized in the Cu film. The strong decrease of A

� for energies below 3 keV can be

explained in part by the increasing fraction of �+ which are backscattered from the sample. From measurements about the backscattering behavior of protons from met-als it is known that a large fraction of backscattered par-ticles are neutralized.

To compare the measured energy dependence of A�

with predictions from range calculations, Monte Carlo simulations using the computer code TRIM.SP 3) were performed. Due to the lack of energy loss data for �+, velocity scaled energy loss data for protons were used. In the simulation, the fractions of �+ stopped in the metal and in the quartz glass for a given energy are cal-culated. Taking into account that all �+ stopped in the metal contribute to A

� whereas �+ stopped in the quartz

glass have an A�,quartzglass of 5 % we obtain the curves

shown in Fig. 1. The solid and the dotted lines represent

the predictions for the energy dependence of the �+-asymmetry for the thin and the thick Cu sample, respec-tively. As one can see in Fig. 1 the agreement between measured and calculated A

� as a function of E

� in the

thick Cu sample is excellent whereas for the thin Cu sample a small deviation between measured and calcu-lated A

� is visible for energies between 10 and 15 keV.

The measured asymmetries are smaller then the calcu-lated possibly reflecting a slightly larger projected range in Cu than predicted. Further measurements are planned to clarify this effect.

Fig 1: Energy dependence of A� in Cu films sputtered on

quartz glass. Solid symbols: thin Cu (d = 68 nm), open symbols: thick Cu (d = 500 nm). Solid line: simulated energy dependency of A

� for 68 nm Cu; dotted line: 500

nm Cu.

(1) H. Glückler et al., Physica B, in press (2) The samples were prepared by M. Horisberger, PSI; the

RBS analysis was done by M. Döbeli, PSI (3) W. Eckstein, Computer Simulation of Ion-Solid Interac-

tions (Springer Verlag, Berlin Heidelberg New York, 1991)

0 5 10 15 20 25 300

5

10

15

20

25

30A

µ+[%

]

µ+ energy [keV]


1.27 Response of the electric field gradient to an external electric field

M. Dietrich and M. Deicher in collaboration with S. Unterricker (Institut für Angewandte Physik, TU Bergakademie Freiberg, D-09596 Freiberg, Germany) J. Bartels and K. Freitag (Institut für Strahlen- und Kernphysik, Universität Bonn, D-53115 Bonn, Germany)

In solids, the electric field gradient (EFG) at a certain lattice site is determined mainly by the atoms in its near-est neighborhood, i.e. their electronic properties and the distances to each other. Therefore, variations of lattice constants lead to changes in the EFG. Lattice constants change when the temperature is varied. Such studies have been performed for numerous materials with per-turbed �-�-angular correlation spectroscopy (PAC) 1). A few papers report on the response of the EFG on hydro-static pressure 2) or the bending angle of a single crystal 3).

Another way of applying uniaxial stress can be achieved by the inverse piezoelectric effect. In polar crystals lattice constants change or atoms are shifted when an electric field is applied externally resulting in an influence on the EFG at lattice sites. We discussed the possibility of observing these slight changes with PAC recently 4). The measurements in LiNbO3 revealed only a tiny change of the EFG in dependence on the ex-ternal electric field 4).

In this report we present further studies using a dif-ferent material. The primary requirement for the success of such an experiment is a high piezoelectric constant of the material. Solids used as piezoelectric actuators with very high piezoelectric constants like SrxBa1-xNbO3 are not useful for PAC investigations because of the random occupation of the Ba sublattice by Ba and Sr atoms. This would result in a strongly damped spectrum since the probes are not exposed to an unique EFG. Therefore we have chosen BaTiO3 as an ordered material with piezo-electric constants larger than those of LiNbO3.

BaTiO3 crystallizes in the Perovskite structure and exhibits a tetragonal ferroelectric phase at room tem-perature. The single crystalline sample from ‘For-schungsinstitut für mineralische und metallische Werkstoffe - Edelsteine/Edelmetalle - GmbH’, Idar-Oberstein, had a size of 6 x 8 mm2 and a thickness of 1 mm. The polar axis along c was perpendicular to the plane. The sample had been prepared from a crystal grown with 100 ppm Co in the melt for optoelectronics use. BaTiO3 is very attractive as a material for optical and holographic storage 5) and optical waveguides 6). PAC studies in this material have been carried out with different nuclear probes for almost three decades7-9), already.

We have implanted 111In(111Cd) at the isotope sepa-rator at Bonn university with an energy of 160 keV and a dose of 2.2�1013 cm-2 and a beam spot of 5 mm di-ameter. In order to remove the implantation damage the sample has been annealed for 2.5 h at 1700 K in air. The crystal was mounted in a special Teflon holder to apply the electric field. The c-axis and consequently the sym-

metry axis of the EFG were oriented perpendicular to the detector plane. Al electrodes with a diameter of 6 mm covered the implanted area. Transformer oil with a breakdown field strength of 6 kV/mm has been used for insulation. The breakdown field strength of the sam-ple is much higher, about 40 kV/mm for nominally un-doped BaTiO3 10).

The PAC spectrum and its Fourier transform of 111In(111Cd) in BaTiO3 at ambient temperature without applied electric field are shown in Fig 1. 90(5) % of the probes are exposed to an axially symmetric EFG with the quadrupole coupling constant of Q = 34.8(1) MHz and a distribution of � Q = 1.0(1) MHz. This EFG indi-cates the occupation of the Ti-site 7). The second har-monic is not visible in the Fourier transform due to the special orientation of the crystal.

Fig. 1: PAC spectrum and its Fourier transform of 111In(111Cd) implanted into a BaTiO3 single crystal. The sample has been annealed at 1700 K for 2.5 h. The c-axis has been oriented perpendicular to the detector plane.

The first harmonics in the Fourier spectra of meas-urements with electric field applied to the sample are drawn enlarged in Fig. 2. The electric field strength is defined as positive by connecting the non-implanted side of the crystal to the positive output of the high voltage supply. A shift of the peak to higher frequencies with in-creasing electric field strength is clearly visible. The corresponding quadrupole coupling constants in depend-

0 100 200 300 400 500 6000.15

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t (ns)

R(t

)

0 50 100 150 2000

5

10

f(�

) (a

rb. u

nits

)

� (Mrad/s)


ence on the electric field strength applied are shown in Fig. 3 for all PAC spectra recorded.

Fig. 2: Normalized Fourier transforms of PAC spectra recorded with 111In(111Cd) in BaTiO3 for different ex-ternally applied electric fields of 0.0 kV/mm, +3.0 kV/mm and +4.0 kV/mm indicated by the dashed, solid and dash dotted line, respectively.

Fig. 3: Dependence of the quadrupole coupling constant �Q of 111In(111Cd) in BaTiO3 on the externally applied electric field E. The solid line represents a fit of a sec-ond order polynomial to the values measured.

The fit to the experimental values results in the func-tion

� �

νQ

2

MHz34.8(1)MHz 0.16(4) E

kV mm

MHz0.080(2) E .

2kV mm

� �

�

The linear change of the quadrupole coupling constant for BaTiO3 is � Q/�E = 0.16 MHz/kV/mm. This is 10 times the value of 0.017 MHz/kV/mm observed for LiNbO3 in our first experiment 4). This has been expected from the piezoelectric constants. The piezoelectric strain constant d33 determines the strain in c-direction S33 = d33E33 of a Perovskite structure crystal with respect to the external electric field strength E3 along c-axis. The strain constants are d33 = 3.6�10-11 C/N and 0.6�10-11 C/N for BaTiO3 11)

and LiNbO3 12), respectively, and differ by a factor of 6.

The relative changes � Q/ Q caused by the electric field strength of 1 kV/mm differ even more, by a factor of 40. The values are � Q/ Q = 4.6·10-3 (BaTiO3) and 0.11·10-

3 ( LiNbO3). It turns out that the linear contribution can be

simulated with point charge model calculations. Starting with the crystallographic determined lattice constants and atomic positions 13), the lattice contributions to the EFG at the Ti-site have been calculated. The deformation of the unit cell caused by the external electric field has been taken into account as changes in the lattice constants. The electric field along the c-axis causes a strain along both the c- and the a-axis. The relative changes for a field of 4 kV/mm are �a/a = 1.6·10-4 and �c/c = -1.4·10-4. The signs depend on the direction of the electric field with respect to the direction of the spontaneous polarization and are opposite to each other in any case. The point charge model calculations result in a purely linear dependence of the EFG on the electric field strength. An electric field of 1 kV/mm causes a relative change of the quad-rupole coupling constant of � Q/ Q = 1·10-2, twice the experimental value but the agreement is satisfactorily good.

The model does not propose a second order dependence. This may have several reasons besides the known shortcomings of the point charge model. The first order effect of an external electric field is well studied concerning the influence on lattice constants. But only little information is available concerning the influence of an external electric field on the atomic positions in the unit cell. One can imagine that the atoms are shifted relative to each other when a field is applied. The second order effect of an external electric field on lattice constants, the electrostriction, has not yet been studied completely, but it is obvious that this effect could explain the nonlinear dependence observed in this work.

(1) G.L. Catchen, W.E. Evenson and D. Alred, Phys. Rev. B

54 (1996) R3679 (2) H.H. Rinneberg, G.P. Schwartz and D.A. Shirley, Hyp.

Int. 3 (1977) 97 (3) G. Marx and R. Vianden, Physics Letters A 210 (1996)

364 (4) M. Dietrich, S. Unterricker, M. Deicher, A. Burchard

and R. Magerle, Annual Report 1995, Universität Kon-stanz, p. 75

(5) E. Kratzig, F. Welz, R. Orlowski, V. Doormann and M. Rosenkranz, Solid State Comm. 34 (1980) 817

(6) P. Moretti, P. Thevenard, G. Godefroy, R. Sommerfeld, P. Hertel and E.Krätzig, phys. stat. sol. (a) 117 (1990) K85

(7) M. Uhrmacher, V.V. Krishnamurty, K.-P. Lieb, A. López-Garcia and M. Neubauer, Z. Phys. Chem. 206 (1998) 249

(8) G.L. Catchen and R.L. Rasera, Ferroelectrics (UK) 120 (1991) 33

(9) G. Schäfer, P. Herzog and B. Wolbeck, Z. Physik A 257 (1972) 336

(10) Landolt-Börnstein III/3, Springer, Berlin (1969) (11) Landolt-Börnstein III/28a, Springer, Berlin (1990) (12) Landolt-Börnstein III/16a, Springer, Berlin (1981) (13) H.D. Megaw, Acta Cryst. 15 (1962) 972

20 25 30 35 40 45 500.0

0.2

0.4

0.6

0.8

1.0 0.0 kV/mm +3.0 kV/mm +4.0 kV/mm

f(�

) (a

rb. u

nits

)

� (Mrad/s)

-4 -2 0 2 434

35

36

37

E (kV/mm)

�Q (

MH

z)


1.28 Diffusion of muons in metallic multilayers

H. Luetkens and J. Litterst (IMNF, TU Braunschweig, D-38106 Braunschweig) in collaboration with H.Glückler, E. Morenzoni and T. Prokscha (Paul-Scherrer-Institut,CH-5232 Villigen, Schweiz) E.M. Forgan (University of Birmingham, Birmingham B15 2TT, United Kingdom) R. Khasanova and H. Keller (Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland) B. Handke, J. Korecki and T. Slezak (Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, PL-30-059 Krakow, Poland) Ch. Niedermayer, M. Pleines and G.Schatz

The development of a low energy muon source with tunable energy between a few eV and several keV opens the possibility to extend the bulk �SR technique to the study of thin films and multilayers (LE-�SR 1)). Here we report on muon diffusion in the 40 nm Au layer of an epitaxial Cr/Au/Cr trilayer. This is a basic experiment to understand the role of muon diffusion in low dimen-sional metallic systems including sticking at interfaces and the influence of small hexagonal distortion of the lattice due to epitaxial growth.

Below TN � 285 K the 10 nm Cr films are in a mag-netic state resulting in a very fast depolarization of the muon spins in their direct environment 2) while in pure Au practically no depolarization is observable. There-fore LE-�SR can yield information about muons dif-fusing from the Au layer to one of the Cr layers giving rise to depolarization of the muon spin ensemble. Addi-tionally, with this method it is for the first time possible to study muon diffusion in non-magnetic elements with-out introducing magnetic impurities into the sample. The principle of the experiment is shown in Fig. 1.

Fig. 1: Initial muon implantation profile (solid line) and time dependent muon distribution due to thermally acti-vated diffusion (dashed line). The fraction of muons reaching a Cr interface leads to a depolarization of the LE-�SR signal.

By tuning the muon implantation energy to Eimpl = 6.5 keV most of the muons stop in the Au layer giving a maximum of the observed initial asymmetry, see Fig. 2. This observation is well reproduced by the Monte Carlo code TRIM.SP 3), which is used to calcu-late the muon implantation profiles 4). While the initial asymmetry is independent of tempera-ture for the same implantation energy the depolarization rate � clearly shows the onset of muon diffusion around

125 K (Fig. 3). The increase of � reflects the faster broadening of the initial stopping distribution with in-creasing temperature. Above TN = 285 K the reduction of � indicates the magnetic phase transition of the 10 nm Cr layers 2) which occurs � 25 K below the Neel tem-perature of bulk Cr due to finite size effects.

Fig. 2: The measured asymmetry as a function of the muon implantation energy directly provides the fraction of muons which come to stop within the sandwiched gold film.

Fig 3: Temperature dependence of the depolarization rate for 6.5~keV muons.

Monte Carlo simulations of the muon diffusion proc-ess taking into account the calculated initial muon stop-ping distribution as well as sticking at interfaces are in progress. From this, quantities such as diffusion con-stants and activation energies can be obtained.

(1) E. Morenzoni, Appl. Magn. Reson. 13 (1997) 219 (2) H. Luetkens et al., Physica B, in press (3) W. Eckstein, Computer Simulation of Ion-Solid Interac-

tions (Springer, Berlin, 1991) (4) H. Glückler et al., Physica B, in press


1.29 Energy dependence of muonium formation in solid Ar, N2, Xe, and SiO2

T.Prokscha, H.Glückler and E. Morenzoni (Paul-Scherrer-Institut,CH-5232 Villigen, Schweiz) in collaboration with M. Birke, J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig) R. Khasanov and H. Keller (Physik-Institut der Universität Zürich, CH-8057 Zürich, Switzerland) Ch. Niedermayer, M. Pleines and G. Schatz

Charge differentiation in �+ or muonium (Mu) as a consequence of the slowing down of �+ in matter is of fundamental interest in the �SR method. It is also of relevance for the understanding of the moderation proc-ess of �+ in van der Waals solids like s-Ar or s-N2

1,2), which are currently most suitable to generate epithermal �+ with a mean energy of � 15 eV. These moderators are used as the source for the low-energy �+ (LE-�+) beam at PSI.

There is a lack of knowledge regarding the cross sec-tions for electron capture and electron loss at energies below 1 keV, as well as for the interaction of epithermal �+ with the spur electrons of their own ionization track. Muonium and �+ fractions have been studied only after implantation of energetic �+ 3,4).

We started LE-�SR investigations on thin s-Ar, s-N2, s-Xe films, and a quartz glass disk (SUPRASIL, SiO2), to determine the �+ and Mu fraction in these samples in dependence on the implantation energy. The layers were prepared by condensing research purity gas for 1/2 h onto the cold head of a cryostat at partial pressures of 2�10-5 mbar (s-N2), 1�10-5 mbar (s-Ar), and 3�10-6 mbar (s-Xe). This corresponds to thicknesses of 2200 nm (s-N2), 800 nm (s-Ar), and 230 nm (s-Xe), which are suffi-cient to stop the LE-�+ beam in the layers. The thick-nesses were measured offline by mounting a microbal-ance at the sample position and repeating the deposition procedure under the same conditions. The temperatures were set to 10 K (s-Ar), 13.5 K (s-N2), 30 K (s-Xe), and 20 K (SiO2).

At implantation energies between 1 and 30 keV we measured the �+ asymmetry A

� by applying an external

transverse magnetic field of 10 mT. Simultaneously the muonium signal AMu and A

� at 0.8 mT was measured.

The results for A� are shown in Fig. 1. The preliminary

analysis shows an energy independent asymmetry for s-Ar of � 12%, and � 14% for s-N2. This corresponds to �+ fractions of � 40% and � 50%, respectively, by tak-ing into account the maximum asymmetry of 27% which includes a background asymmetry of � 2% due to �+ missing the sample. The missing fraction is due to Mu formation in the layer which is confirmed by the AMu measurement at low field. The s-Xe and SiO2 data show an energy dependence of A

�: at energies below 10 keV,

A� starts to increase corresponding to a decreasing

muonium signal. At energies larger than 10 keV, A� is

constant and the �+ fraction in the sample amounts to about 10%.

The 10% �+ fraction in SiO2 is consistent with data obtained by implanting surface �+ into quartz glass at the GPS spectrometer. Investigations with surface �+ on

thick solid gas samples show a small (< 10%) �+ fraction in s-Xe 3), and only a 10 - 20% �+ fraction in s-Ar 3) and s-N2

4). This is very distinct from our data yielding larger �+ fractions.

Fig. 1: Dependence of the �+ asymmetry on the �+ im-plantation energy Ein.

Qualitatively, the s-Xe and SiO2 data are very similar as well as the s-Ar and s-N2 data. This is reflected also in the moderation properties: whereas Ar and N2 are ef-ficient moderators, Xe and SiO2, for which a higher Mu formation is observed, yield only about hundred times smaller moderation efficiencies. This indicates the cru-cial role played by the suppression of Mu formation for the moderation process.

Further systematic studies of the dependence on B- and E-fields, implantation energy, and different growing conditions during layer preparation are necessary to un-derstand the difference observed between the results obtained with surface �+ in van der Waals bulk and the results in thin layers.

(1) T. Prokscha et al., Phys. Rev. A 58 (1998) 3739 (2) E. Morenzoni, in: Muon Science (IOP Publishing, 1999) (3) R. Kiefl et al., J. Chem. Phys. 74 (1981) 309 (4) V. Storchak et al., Phys. Lett. 193 (1994) 199

10

15

µ+ asy

mm

etry

[ %

]

s-Ar

10

15

s-N2

5

10

s-Xe

5

10

0 5 10 15 20 25 30Ein [ keV ]

SiO2


1.30 Progress on the low energy ��+ apparatus

E. Morenzoni, H. Glückler, T. Prokscha and H.P. Weber (Paul Scherrer Institut,CH-5232 Villigen, Schweiz) in collaboration with J. Litterst and H. Luetkens (IMNF, TU Braunschweig, D-38106 Braunschweig) E.M. Forgan and T.J. Jackson (University of Birmingham, Birmingham B15 2TT, United Kingdom) Ch. Niedermayer, M. Pleines and G. Schatz

In the constant effort to improve the LE-�SR method, several developments of the experimental setup have been pursued in 1999. A study was performed to find the optimum choice for geometry and materials of the sam-ple environment, to achieve maximum detection effi-ciency of the decay positrons, maximum asymmetry of the �SR signal, while guaranteeing low sample tem-peratures. The absorption and scattering of the positrons interacting on their way from the sample to the scintilla-tor telescopes, as well as their detection have been in-vestigated with the GEANT program. As a consequence of this study, various components of the sample envi-ronment, such as sample holder, cold head of the cry-ostat, and the cooling shield have been modified. To re-duce the amount of interacting material and improve thermal contact critical elements have been precisely machined in very pure Aluminum instead of OFHC copper. Tests have shown that with the new setup es-sentially the same base temperature as with OFHC cop-per can be achieved. For instance for a sample insulated by a sapphire crystal 6.7 K can be obtained. It must be taken into account that the very low energy of the muons impinging on the sample does not allow the use of a cooling shield in front of it. The reduced absorption and scattering of the decay positrons in the low density ma-terial translates into an increased detection efficiency by about 30% and a relative increase of 5-10% of the signal asymmetry.

Fig. 1: View of the sample chamber, with the magnet generating a field parallel to the sample surface. The flange of the sample cryostat is also visible.

In close collaboration with the University of Bir-mingham and the PSI magnet group a special magnet was designed and built for the application of magnetic

fields parallel to the surface of the sample. The field of this magnet has to be as uniform as possible over the surface of the sample, while decreasing rapidly with dis-tance away from the sample to minimize the deflection of the incoming low energy muon beam. These specifi-cations have been fulfilled with a very compact design making use of permanent magnets and a soft iron return yoke, which is partially mounted very close to the sam-ple in the UHV region (Fig. 1). Ferrite or NdFeB per-manent magnets provide magnetic field strength of up to 20 mT with an homogeneity over the sample surface better than 1.5%. At the same time a guiding system al-lows switching on/off of the field under controlled con-ditions as it may be necessary during zero field cooling experiments. With this setup the first direct measure-ment of the magnetic field profile near the surface of a HTc superconductor in the Meissner phase and absolute determination of the magnetic penetration depth have been performed 1).

Improvements of the sample experimental chamber included the design and construction of a new shielding for the scintillator telescopes, which has reduced the positron background by more than 30%. Furthermore the gate valve chamber used for sample load has been modi-fied to reduce the sample changing time.

In view of a smooth transition to a more facility like operation, where also users external to the present low energy muon collaboration may be able to perform ex-periments, we started to implement computer control of relevant components such as the high voltage supplies of the electrostatic transport system and of the liquid nitro-gen cooling of electrostatic lenses and traps.

During the beam time at the �E3 beamline we per-formed a comparison under the same experimental con-ditions of low energy muon intensity and polarization with thick (60 mm) and thin (42 mm) production target E. Whereas the polarization is unaffected by the target change, indicating that the accepted fraction of cloud muons is independent of the target length, we experi-enced a 30 % reduction of the surface muon flux ac-cepted by the low energy muon apparatus.

(1) T.J. Jackson et al., Phys. Rev. Lett. 84 (2000) 4958


1.31 Phase transitions in two dimensional (adsorbed) layers at low temperatures

D. Löding, M. Schwarz van Doorn and P. Nielaba in collaboration with M. Reber (Dresdner Bank)

Phase transitions and quantum effects in two dimen-sional layers have been studied in great detail in the past few years 1).

After the quantification 2,3) of the behavior of mo-lecular systems with spatial rotational and translational degrees of freedom in the vicinity of phase transitions at low temperatures by path integral Monte Carlo simula-tions (PIMC) we continued our investigation of phase transitions in pure N2 and CO monolayers on graphite 4). In parallel we studied the phase behavior of N2 sub-monolayers 5).

Fig. 1: Monte Carlo-configuration of a pure CO-monolayer on graphite at low temperatures in the structure with antiferro-electrical order.

By utilizing the CRAY-T3E computer and realistic interaction potentials we were able to determine the structure of a CO monolayer at low temperatures. At low temperatures the molecular axes are parallel to the surface in the “herringbone”-structure. For pure N2 and pure CO monolayers we obtain by PIMC- simulations a 10% reduction of the transition temperature from the high temperature phase with orientational disorder to the low temperature phase with “herringbone”-structure due to quantum mechanical zero point oscillations. The or-der parameter at low temperatures is reduced by 10% as well. The experimentally observed phase transition at 5 K has been studied by PIMC as well. According to this study at low temperatures the system is in an antiferro-electric structure (Fig. 1).

With increasing Trotter index P the phase transition temperature is shifted to smaller values compared to the classical value. In the large-P limit we obtain a transi-tion temperature reduction of about 30-40% and a good agreement between the computed phase transition tem-peratures and experimental values.

Fig. 2: Distribution of the molecular axes angles in the graphite plane. Comparison of PIMC-simulations for N2- and for CO-monolayers on graphite.

From Fig. 1 it is obvious that the CO-molecular axes do not form a perfect herringbone-structure, rather the system consists of four shifted sublattices with equal molecular orientation. The deviation of the molecular axes from the ideal orientations in the herringbone-structure results in a double-maximum structure in the angle distribution function (Fig. 2), where the two maxima are at a slightly different angle as at the ideal angle �/4, which appears in the system of a N2-monolayer on graphite (Fig. 2). The structure of the low temperature phase has not yet been determined defi-nitely by experimental techniques, thus our simulation results have a certain predictive character.

For N2 submonolayers the concentration dependency of the transition temperature into the herringbone-struc-ture has been quantified as well. A reduction of the tran-sition temperature may be as large as 20% due to quan-tum delocalisation effects. Interestingly for N2-concen-trations between x=0.5 and x=0.7 at low temperatures we obtain the phenomenon, that the herringbone struc-ture is obtained by temperature reduction, but at tem-peratures about 1 K the particles in the boundary of the ordered structure leave the positions in the perfect 3 ×

3 -structure and occupy energetically favorable posi-tions due to the quadrupolar interaction, which leads in total to a positional distortion of the orientationally or-dered structure. This system feature can be quantified by the herringbone order parameter as a function of tem-perature (Fig. 3).

At a coverage of x=0.5 the order parameter decreases at very low temperatures. This behavior is present in classical simulations (P=1) but absent in PIMC simula-tions with P>4. Apparently the herringbone-structure is


stabilized by quantum effects for this coverages and temperatures as well.

Fig. 3: Herringbone order parameter as function of temperature for the system (N2)x on graphite for various x-values.

Fig. 4: N2- domain size distribution as a function of temperature in the mixed system (N2)xAr1-x for various x-values.

In mixed systems of the type (N2)xAr1-x on graphite we obtain the result, that for large x-values the herring-bone-structure is stable at low temperatures. Roughly speaking for a concentration of 10% Ar a reduction of the phase transition temperature is obtained of similar magnitude as the reduction in the pure system due to quantum effects. For smaller x-values the perfect her-ringbone-structure does not appear anymore on cooling, rather domains with local herringbone-structure appear with all three possible orientations on graphite. At the domain boundaries preferentially the spherical Ar-parti-cles are located and pin-wheel structures appear. Fig. 4 shows the domain size distributions for different tem-peratures and x-values. For x=0.9 at low temperatures very large domains are present, but already for x=0.8 and low temperatures the domain size distribution broadens, at smaller x-values the domains are compara-tively small at low temperatures.

(1) P. Nielaba, in: Computational Methods in Surface and

Colloid Science, M. Borowko (Ed.), Marcel Dekker Inc., New York (2000) p. 77

(2) M. Presber, D. Löding, R. Martonak, and P. Nielaba, Phys. Rev. B 58 (1998) 11937

(3) M. Reber, D. Löding, M. Presber, Chr. Rickward, and P. Nielaba, Comp. Phys. Commun. 121-122 (1999) 524

(4) D. Löding, PhD thesis, Universität Mainz (in preparation)

(5) M. Schwarz van Doorn, Diploma thesis, Konstanz (1999)

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1.32 Phase transitions in alloys with elastic interactions

D. Fischer and P. Nielaba in collaboration with P. Fratzl (Leoben, Austria) and J.L. Lebowitz (Rutgers University, USA)

Precipitate micro structures are important for the strength and hardness of many alloys 1,2). A number of experimental 3) and theoretical 1,4-7) investigations have shown that the development of precipitate morphologies is influenced by elastic interactions (EI) resulting from a lattice misfit between matrix and precipitates and from an externally applied elastic strain. Thus, in Nickel base superalloys cuboidal precipitates develop as a result of EI 3). These cuboids may join into large plates either spontaneously in the coarsening process or, more im-pressively, as a result of an externally applied uniaxial stress. These processes are reasonably well described by models where anisotropic elastic strains are incorporated into the kinetics of a phase separating system 1). Such models include continuum approaches as well as atom-istic computer simulations. In particular, an Ising type model has been developed 5) by Fratzl and Penrose and by Lebowitz et al. which predicts the growth of plate-like domains oriented perpendicular to the elastically soft directions, in agreement with experiment. The model fails however to reproduce some of the micro-structural details 3), like narrow channels of disordered phase effectively cutting the plates into a succession of cuboids. Simulations of Ising models (not including EI) by Lebowitz and coworkers, in which the ordered do-mains were of two types gave a precipitate morphology strongly dependent on the volume fraction of the disor-dered domain 2). This can be interpreted as due to the fact that the disordered phase has always a tendency to wet the surface of the ordered domains 2). In ref. 6 this model has been generalized by including EI resulting from a different size of the two types of atoms. By com-puter simulations the influence of the ordering tendency of the precipitates on the domain structure and the ki-netics both without and with external stress (rafting) has been studied. In the phase separation process anti-phase boundaries (APB's) appear between variants of atomi-cally ordered precipitates, as suggested in Ref. 4. In Ref. 7 the equilibrium phase diagram of this model has been computed by Monte Carlo simulations and finite size scaling techniques.

We consider a system consisting of NA atoms of type A with radii RA and NB atoms of type B with radii RB. The positions of the atoms are labeled by sites on a pla-nar square lattice L with lattice spacing a. There are N = S2 sites (N = NA+NB) and we use periodic boundary conditions. A spin variable �(p) is assigned at each site p � L, with �(p) = 1 if there is an A-atom at site p and �(p) = �1 if there is a B-atom there. The atoms, which can move off the lattice sites, are connected by elastic springs with longitudinal (L+) and transverse (T+) stiff-ness between nearest neighbors and springs with longi-tudinal stiffness (L×) between next nearest neighbors.

The different sizes of the atoms cause a lattice distor-tion, as discussed in Ref. 5. There is also a short range “chemical interaction” ,Hchem, between the atoms corre-sponding to anti-ferromagnetic (AFM) nearest and fer-romagnetic (FM) next nearest neighbor potentials 2). This has the form of an Ising Hamiltonian:

1,2

1 21,1

( ) ( )

( ) ( ( ))2

chem jp j

p j

H J a

Ja j

�

�

� �

� �

�

��

� �

� � �

��

� �

p p e

p p e e

L

L

(1)

where e1 and e2 are unit vectors in horizontal and vertical direction, respectively, and J > 0. An energy minimization over the atomic displacements for a given configuration can be performed as in Ref. 10,11,5 and the resulting total Hamiltonian is then given by:

k

p,p'

2( )

( ')

( )2

( ) ( ')2

totBZ

HJN

JN

�

�

�

�

�

� �

�

��

�

�

k

p p

k

p p

� �

L

(2)

where ( )� k� and ( )� p� are the Fourier transforms of �(p) and the effective pair potential ( )� �p - p , respectively,

i i

p p

( ) ( ) ; ( ) ( )e e� � � ��

� �� k p k pk p k p� �

and the sum over k in (2) is taken over the first Brillouin zone of the lattice L.

The effective potential ( )� p contains a long range anisotropic elastic part ( )eff

el� p which has a form simi-lar to a dipole-dipole interaction and decays like r-2 (r-3 in 3 dimensions) at large distances r. It also contains a short-range part ( )sh� p which has contributions from both the chemical and the elastic interactions. In Fourier space the potential ( )� k� , which is the sum of

( ) ( )effsh el� ��k k� � , can be calculated explicitly; see Ref.

5,6.

1 2 1 2

1( ) 2 { }

4sh J c c c c� �� k �

� (3)

2 222 1 11 2 12 1 2

211 22 12

1 2( )

2effel

D G D G D G GJ

D D D� �

� ��

�k

� � � ��

�

� � �

(4)

Here i � {1,2}, ci = cos aki, and si = sin aki, k1 and k2 being the components of the vector k along the x and y directions of the square lattice, � = (RA � RB)2/J.

The phase separation kinetics of the system has been studied by us recently 6) at a temperature, T = Tc

is/4 �


0.567 J/kB, (Tcis is the critical temperature of the two-

dimensional nearest-neighbor AFM Ising model). Three “alloys” with concentration of (large) A-atoms c = NA/N = 0.15, c = 0.25 and c = 0.35 were considered. These were all well within the two-phase region between the ordered inter-metallic alloy with stoichiometric compo-sition AB and the disordered B-rich phase.

Fig. 1: Equilibrium phase diagram (concentration c of A atoms vs. temperature T) for the model A-B alloy (cool-ing from a high temperature initial state). Two systems are studied: (a) � = 0: the triangle symbols pointing up, down and to the left give estimates for the coexistence curve between the disordered and the ordered phase at low temperatures from the maxima positions in PL(c). (triangle up: L=8, triangle left: L=16, triangle down: L=32). The triangle pointing to the right give the transi-tion points for the continuous transition from the or-dered low temperature phase to the disordered high temperature phase, obtained by the order parameter cumulant intersection method. (b) � = 2: the symbols: +, x, * give estimates for the coexistence curve between the disordered and the ordered phase at low temperatures from the maxima positions in PL(c) (+: L=8, x: L=16, *: L=32). The diamonds give the transition points for the continuous transition from the ordered low temperature phase to the disordered high temperature phase, ob-tained by the order parameter cumulant intersection method.

The full phase diagram of this model alloy has been computed 7) by finite size scaling techniques. The distri-bution functions PL(�) and PL(c) of the order parameter � and the concentration c have been computed in differ-ent subsystems with size L × L of the total system with size 128 × 128 (and 64 × 64) by cooling from initial configurations in the high temperature disordered phase. The order parameter cumulant intersection method 12) has been used for the determination of the continuous

phase transition from the ordered to the disordered phase at high temperatures. At temperatures below the tricriti-cal temperature simulations have been done at a con-centration of c = 0.25. In the subsystems of size L × L the local composition can fluctuate and at low tempera-tures PL(c) is doubly peaked with one peak at the stoichiometric composition AB of the ordered alloy and one peak at the concentration of the B-rich phase.

At high temperatures and at a fixed composition the phase transition temperature from the ordered phase to the disordered phase is computed by the cumulant inter-section method. At temperatures below the tricritical temperature PL(c) is doubly peaked. With increasing subsystem size the composition values of the maxima scale to the infinite size limit, these values are taken as the concentration values for the two coexisting phases. With increasing temperature the difference between the coexistence concentrations decreases. At the tricritical point the difference value approaches zero and at this point the line of high temperature continuous transitions begins. In Fig. 1 we present the phase diagram of the system. Here a comparison is made with the phase dia-gram of the system without elastic interactions. The lat-ter phase diagram agrees well with the phase diagram obtained by Landau 8) for the model without EI. In this case the phase diagram contains a tricritical point at a tri-critical concentration close to a value at which half of the system is ordered and the other half is disordered. As discussed by Kincaid and Cohen 9), the corresponding mean field theory provides a phase diagram with a criti-cal end point instead of a tricritical point for the interac-tion parameters chosen in the present study. The influ-ence of the elastic interactions apparently reduces the value of the critical and the tricritical temperatures by about 22% and the tricritical concentration increases by about 18%.

(1) A.G. Khachaturyan, Theory of Structural Transforma-

tions in Solids (Wiley, New York, 1983) (2) V.I. Gorentsveig, P. Fratzl, J.L. Lebowitz, Phys. Rev. 55

(1997) 2912 (3) O. Paris, M. Fährmann, E. Fährmann, T.M. Pollock and

P. Fratzl, Acta Mater. 45 (1997) 1085 (4) Y. Wang and A.G. Khachaturyan, Scripta Metall. Mater.

31 (1994) 1425 (5) P. Fratzl and O. Penrose, Acta Metall. Mater. 43

(1995)2921; P.Fratzl and O.Penrose, Acta Mater. 44, (1996) 3227; C.L. Laberge, P. Fratzl and J.L. Lebowitz, Phys. Rev. Lett. 75 (1995) 4448; C.L. Laberge, P. Fratzl and J.L. Lebowitz, Acta Mater. 45 (1997) 3949

(6) P.Nielaba, P. Fratzl and J.L. Lebowitz, J. Stat. Phys. 95 (1999) 23

(7) D. Fischer, Diploma thesis, Konstanz (1999); D. Fischer, P. Nielaba, Physica A 279 (2000) 287

(8) D.P. Landau, J. Appl. Phys. 42 (1971) 1284; D.P. Landau, Phys. Rev. Lett. 28 (1972) 449

(9) J.M. Kincaid and E.G.D. Cohen, Phys. Reports 22, 57 (1975).

(10) A.G. Khachaturyan, Soviet Phys. Crystallogr. 10, (1965) 256

(11) H.E. Cook and D. DeFontaine, Acta Metall.17 (1969) 915

(12) K. Binder, Z. Phys. B 43 (1981) 119

0 0.1 0.2 0.3 0.4 0.5

c

0

1

2

3

4

k bT /

J

λ = 0 | L = 8λ = 0 | L = 16λ = 0 | L = 32λ = 0 | cumulant

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

2.5

3

3.5

4

λ = 2 | L = 8λ = 2 | L = 16λ = 2 | L = 32λ = 2 | cumulant


1.33 Enrichment of surfaces in contact with stable binary mixtures

P. Nielaba in collaboration with H.L. Frisch (Albany, USA) and S. Puri (New Delhi, India)

There has been much interest in the temporal behav-ior of homogeneous binary mixtures in contact with a surface which has a preferential attraction for one of the components of the mixture 1,2). Typically, there are two experimentally relevant situations. Firstly, one can con-sider the case where the mixture is below the bulk criti-cal temperature Tc, so that the binary mixture undergoes phase separation. In this case, the surface becomes the origin of surface-directed spinodal decomposition waves 3), which propagate into the bulk. The second case cor-responds to a situation in which the temperature (T) of the binary mixture is greater than Tc so that the homoge-neous bulk is stable. Nevertheless, the surface becomes enriched in the preferred component, resulting in a time-dependent surface enrichment profile, which propagates into the bulk 4).

The first case mentioned above (with T < Tc) has been extensively studied, both experimentally 3,2) and numerically 1,5-7). However, because of the dominance of nonlinear effects in the late stages of phase separa-tion, the equations governing surface-directed spinodal decomposition have not proven analytically tractable. One can invoke a linear approximation to study the early stages of phase separation 8,9) but this is valid only for a limited time-range. On the contrary, for the second case mentioned above (i.e., T > Tc) with weak surface fields, the linear approximation is valid for almost all times and can be used to solve the dynamical equations exactly 10). As a matter of fact, it turns out that the linear approxi-mation provides a good description of the time-depend-ent behavior even for strong surface fields, where the order parameter values in the vicinity of the surface are sufficiently large that the linear description is no longer valid 11).

We have considered 12) the experimentally relevant situation of a stable binary mixture in contact with a sur-face which has a preference for one of the components of the mixture. In particular, we focused on the dynam-ics of surface enrichment resulting from a surface field turned on at zero time. We analytically solved this problem in the linearised approximation and used these solutions to extract the asymptotic behaviors of various characteristics of the enrichment profiles. Our numerical results indicate that some of the important predictions of linearised theory are valid even in the strongly nonlinear regime.

For details of our modeling see 5,1,12). We merely present our phenomenological model for the dynamics of a binary mixture near a surface. The bulk dynamics is governed by the usual Cahn-Hilliard (CH) equation

�2( , , )

sgn( ) ( , , )c

R ZT T R Z

�

�

�

��

��

�

�

3 21( , , ) ( , , ) ( )

2R Z R Z V Z� ��

��

� �

(1)

(Z > 0), where all quantities have been rescaled into di-mensionless units 5). In (1), � ( , , )R Z �

�

denotes the or-der parameter variable, which is proportional to the dif-ference in densities of the two species (A and B) of the binary mixture AB. The order parameter depends on dimensionless time � and space ( , )R Z

�

, with R�

denot-ing the coordinates parallel to the surface and Z denoting the coordinate perpendicular to the surface located at Z = 0. The surface is the source of a potential of strength V(Z) ( < 0), which enriches the surface in A, in our pre-sent description. We are typically interested in potentials which are flat within a certain range of the surface and decay in a power-law fashion. The surface is mimicked by two boundary conditions as follows:

1

0

( , , ) ( , , )( , 0, ) ,

Z

R Z R Z

Zh g R

� �

�

� �

�

��

� ��

� �

�

(2)

�

3 2

0

0 sgn( ) ( , , )

1( , , ) ( , , )

2

c

Z

T T R ZZ

R Z R Z

�

� �

�

��

��

�

� �

(3)

Let us consider the evolution of an initial condition consisting of fluctuations about a uniform background, viz., 0( , , ) ( , , )R Z R Z� � � ��

� �

. We linearise Eqs. (1)-(3) in the fluctuation field ( , , )R Z� �

�

, and for simplicity we restrict our considerations to the case where the order parameter field is homogeneous parallel to the surface ( ( , , ) ( , ))R Z Z� � � ��

�

. After a Laplace transform of the resulting equations we obtain 12) an

analytic solution for 0

( , ) ( , )sZ s d e Z�

� � � �

�

�

� � and the

leading asymptotic time-dependence of the m-th moment of Z as

1 1 2

2

( 1) 2 ( 2

( 1) 2( 2 )

) mm

m

m h g A hZ B

g�

�

� � � ��

� � �

� ��

(4)

Therefore, the time-dependence of the profile moments (when defined) is also similar to that in the case where there is a delta-function field at the surface 10,11).

The analytical results are strongly universal as re-gards the time-dependence of �(0,�) and <Zm> for a wide range of physical potentials. Of course, these ana-lytical results have been obtained in the context of a lin-ear theory. However, as our numerical results demon-


strate, the same behaviors arise in the nonlinear case also.

We have also solved the 1-dimensional version of our model in Eqs. (1)-(3) (with T < Tc) numerically, using a simple Euler discretisation scheme. The mesh sizes for discretisation were �� = 0.01 and �Z = 0.6. The lattice size was N = 4000 so that the lattice length L = N�Z = 2400. The boundary conditions in Eqs. (2)-(3) were ap-plied at Z = 0 and flat boundary conditions were applied at Z = L. The initial condition for all the results pre-sented here is �(Z,0) = 0, corresponding to a critical composition of the binary mixture AB without any fluctuations. The surface field is turned on at time � = 0. In our simulations, we used the power-law potential

1

1

( ) , ,

, ,n

V Z h Z

h ZZ

�

�

�

� � �

� � ��

(5)

where the cut-off � is introduced to control the diver-gence of the potential as Z � 0. In our simulations, we set � = �Z. The decay of the potential is characterized by the exponent n. The cases with n = 3 and 4 correspond to the usual cases of nonretarded and retarded Van der Waals' interactions between the surface and the pre-ferred component A.

In the “weak”-field case (h1 = 2 and n = 2,3) the satu-ration value of order parameter at the surface is suffi-ciently small (� � 0.4) that nonlinear effects are negligi-ble. In this case the numerical solution of the linearised model is nearly identical to that described above for the fully nonlinear model. The temporal evolution of pro-files is described well by the linearised model for both n = 2 and n = 3 13). It is gratifying to have a regime of fields in which there is no appreciable difference be-tween the results obtained from the nonlinear and linear models. In this regime, the analytical solutions (see above) are valid and we have then obtained a complete solution of the problem of surface enrichment with arbi-trary potentials. As the field strength is increased, we expect the validity of the linear theory to breakdown. Though this is definitely true for the time-dependent profiles, it is interesting that the diffusive behavior of various characteristics of the profile is unaffected, even in the strongly nonlinear regime. This is known for the case with a delta-function potential 11) and turns out to be valid for the case with long-ranged potentials also.

Our analytical results were obtained in the context of a linear model and predict diffusive behavior for the moments and surface value of the time-dependent en-richment profiles. The analytical results are expected to be valid in the weak-field regime, where the enrichment is sufficiently small at the surface that nonlinear effects are negligible. However, even for strong surface fields, where the enrichment profiles are considerably different from the profiles obtained from a linear model, the be-havior of various profile characteristics still remains dif-fusive. This universality over a wide range of potential functions and surface field strengths is the most relevant aspect of Ref. 12 and earlier work on delta-function sur-face fields 11).

(1) For a review of modelling and numerical simulations of

this problem, see S.Puri and H.L.Frisch, J. Phys. Condensed Matter 9 (1997) 2109

(2) For a review of experimental techniques and results for this problem, see G.Krausch, Mat. Science and Engineering Reports R14 (1995) 1

(3) R.A.L.Jones, L.J.Norton, E.J.Kramer, F.S.Bates and P.Wiltzius, Phys. Rev. Lett. 66 (1991) 1326

(4) R.A.L.Jones, E.J.Kramer, M.H.Rafailovich, J.Sokolov and S.A.Schwarz, Phys. Rev. Lett. 62 (1989) 280; R.A.L.Jones and E.J.Kramer, Phil. Mag. B 62 (1990) 129

(5) S.Puri and K.Binder, Phys. Rev. A 46 (1992) R4487; S.Puri and K.Binder, Phys. Rev. E 49 (1994) 5359; S.Puri and K.Binder, J. Stat. Phys. 77 (1994) 145; S.Puri, K.Binder and H.L.Frisch, to appear in Phys. Rev. E

(6) G.Brown and A.Chakrabarti, Phys. Rev. A 46 (1992) 4829

(7) J.F.Marko, Phys. Rev. E 48 (1993) 2861 (8) H.L.Frisch, P.Nielaba and K.Binder, Phys. Rev. E 52

(1995) 2848 (9) H.P.Fischer, P.Maass and W.Dieterich, Phys. Rev. Lett.

79 (1997) 893 (10) For the case of a delta-function surface field, this has

been done by K.Binder and H.L.Frisch, Z. Phys. B 84 (1991) 403

(11) S.Puri and H.L.Frisch, J. Chem. Phys. 79 (1993) 5560 (12) H.L. Frisch, S. Puri and P. Nielaba, J. Chem. Phys. 110

(1999) 10514 (13) We do not directly compare our numerical and analytical

results because a very fine discretisation mesh is re-quired to obtain numerical results which reasonably ap-proximate the continuum limit 9).


1.34 Elastic constants from microscopic strain fluctuations and melting of hard disks in two dimensions

P. Nielaba in collaboration with S. Sengupta (Kalpakkam, India) and K. Binder (Mainz)

One is often interested in long length scale and long time scale phenomena in solids (e.g. late stage kinetics of solid state phase transformations; motion of domain walls interfaces; fracture; friction etc.). Such phenomena are usually described by continuum theories. Micro-scopic simulations 1) of finite systems, on the other hand, like molecular dynamics, lattice Boltzmann or Monte Carlo, deal with microscopic variables like the positions and velocities of constituent particles and to-gether with detailed knowledge of interatomic poten-tials, hope to build up a description of the macro system from a knowledge of these micro variables. How does one recover continuum physics from simulating the dy-namics of N particles? This requires a “coarse-graining” procedure in space (for equilibrium) or both space and time for non-equilibrium continuum theories. Over what coarse graining length and time scale does one recover results consistent with continuum theories? We at-tempted to answer these questions 5) for the simplest nontrivial case, namely, a crystalline solid, (without any point, line or surface defects 2)) in equilibrium, at a non zero temperature far away from phase transitions. Fluc-tuations of the instantaneous local Lagrangian strain �ij(r,t), measured with respect to a static “reference” lattice, are used to obtain accurate estimates of the elas-tic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse - grained by averaging them within subsystems (of size Lb) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations <�ij�kl> as a function of Lb/L and extract elastic constants of the sys-tem in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient and gen-eral enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification.

Imagine a system in the constant NVT (canonical) ensemble at a fixed density � = N/V evolving in time t. For any “snapshot” of this system taken from this en-semble, the local instantaneous displacement field uR(t) defined over the set of lattice vectors {R} of a reference lattice (at the same density �) is

( ) ( )t t� �Ru R R (1)

where R(t) is the instantaneous position of the particle tagged by the reference lattice point R. Let us concentrate only on perfect crystalline lattices; if topological defects such as dislocations are present the analysis below needs to be modified. The instantaneous Lagrangian strain tensor �ij defined at R is then given

byRef. 2,

1

2ji i k

ijj i k j

uu u u

R R R R�

��

� � � �

� ��

(2)

The strains considered here are always small and so we, hereafter, neglect the non-linear terms in the defini-tion given above for simplicity. The derivatives are re-quired at the reference lattice points R and can be cal-culated by any suitable finite difference scheme once uR(t) is known. We are now in a position to define coarse grained variables bL

ij� which are simply averages of the strain over a sub-block of size Lb. The fluctuation of this variable then defines the size dependent compli-ance matrices S�� = 2<(�xx��yy)

2>

Fig. 1: The bulk (B) and shear (�) moduli in units of kBT/�2 for the hard disk solid. Our results for B(�) are given by � (�). The values for the corresponding quantities from Ref. 3 are given by + and ×. The line through the bulk modulus values is the analytical ex-pression obtained from the free volume prediction for the pressure. The line through our shear modulus values is obtained from the free volume bulk modulus using the Cauchy relation � = B/2�P.

Once the finite size scaled compliances are obtained the elastic constants viz. the Bulk modulus B = �P/� and the shear modulus are obtained simply using the formulae 4)

1

2B

S�

��

� (3)

12

PS

��

� � (4)


where we assume that the system is under an uniform hydrostatic pressure P.

As an example we present our results for elastic con-stants of the hard disk system in Fig. 1. Despite its sim-plicity, this system was shown to undergo a phase tran-sition from solid to liquid as the density � was de-creased. The nature of this phase transition, however, is still being debated. Early simulations 6,7) always found strong first order transitions. As computational power increased the observed strength of the first order transi-tion progressively decreased! Using sophisticated tech-niques Lee and Strandburg 8) and Zollweg and Chester 9) found evidence for, at best, a weak first order transition. On the other hand, recent simulations of hard disks 10) by Jaster, using as many as N = 65536 particles find evi-dence for a continuous, Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) transition 11) from liquid to a hexatic phase, with orientational but no translational or-der, at � = 0.899. Nothing could be ascertained, how-ever, about the expected hexatic to the crystalline solid transition at higher densities because the computations became prohibitively expensive. The solid to hexatic melting transition was estimated to occur at a density �c � .91. In Ref. 15 we investigated the melting transition of the solid phase and showed that the hard disk solid is unstable to perturbations which attempt to produce free dislocations leading to a solid � hexatic transition in accordance with KTHNY theory 11). This transition lies close to a, first order, solid to liquid melting line. We calculate quantitatively the relative positions of the first order and the KTHNY transitions in the parameter space for this system and explain why earlier simulations failed to arrive at a consensus.

Fig. 2: Typical move which attempts to change the coor-dination number and therefore the local connectivity around the central particle. Such moves were rejected in our simulation.

We have simulated a dislocation free triangular solid of hard disks using a constrained Monte Carlo algorithm (see Fig. 2). Using a block analysis scheme we calculate the finite size scaled elastic constants of this solid. From the number of times the system attempts to violate our no- dislocation constraint we can obtain (virtual) dislo-cation probabilities and hence the core energy. The ab-sence of a phase transition in our system implies that all correlation lengths remain finite and the problem of slow equilibration of defect densities is eliminated. In effect we obtain highly accurate values of the unrenor-

malized coupling constant K and the defect fugacity y which can be used as inputs to the KTHNY recursion relations. Numerical solution of these recursion relations then yields the renormalized coupling KR and hence the density and pressure of the solid to hexatic melting tran-sition.

We can draw a few very precise conclusions from our results. Firstly, a solid without dislocations is stable against fluctuations of the amplitude of the solid order parameter and against long wavelength phonons. So any melting transition mediated by phonon or amplitude fluctuation is ruled out in our system. Secondly, the core energy Ec>2.7 at the transition, so KTHNY perturbation theory is valid though numerical values of nonuniversal quantities may depend on the order of the perturbation analysis. Thirdly, solution of the recursion relations shows that a KTHNY transition at Pc = 9.39 preempts the first order transition at P1 = 9.2. Since these transi-tions, as well as the hexatic-liquid KTHNY transition lies so close to each other, the effect of, as yet unknown, higher order corrections to the recursion relations may need to be examined in the future. Due to this caveat, our conclusion that a hexatic phase exists over some re-gion of density exceeding � = .899 still must be taken as preliminary. Also, in actual simulations, cross over ef-fects near the bicritical point, where two critical lines corresponding to the liquid-hexatic and hexatic-solid transitions meet a first order liquid -solid line may com-plicate the analysis of the data, which may, in part, ex-plain the confusion which persists in the literature on this subject. In systems with softer potentials, the signa-ture of a KTHNY transition appears to be more pro-nounced 14,12).

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(13) W. Janke and H. Kleinert, Phys. Rev. Lett. 61 (1988) 2344

(14) K.Bagchi, H.C.Andersen and W.Swope, Phys. Rev. E 53 (1996) 3794

(15) S. Sengupta, P. Nielaba, nad K. Binder, Phys. Rev. E, in press


1.35 Low temperature properties of molecular solids

P. Nielaba in collaboration with Chr. Rickwardt (Landesbank Rheinland-Pfalz), M. Müser (U. Mainz), K. Binder (U. Mainz) and M. Presber (Arthur Anderson)

The study and analysis of materials properties of crystalline silicates are important since these systems are used in many industrial processes and they occur also in many natural rocks. Many interesting effects have been found by experimental techniques at temperatures well below the Debye temperature. In this temperature range quantum effects like zero point motions and corre-sponding delocalizations of atoms are important which have to be taken into account in serious theoretical studies. Usually this is done by lattice dynamics theo-ries, in the framework of the harmonic or quasiharmonic approximation. However, both near second-order struc-tural phase transitions and quite generally at higher tem-peratures the accuracy of this approach is sometimes un-certain 1), and methods that work at all conditions would be desirable. PIMC simulations 2-4) enable us to analyze the crystal low temperature thermal properties. In prin-ciple, this method yields exact quantum-statistical aver-ages (apart from statistical errors) and reduces to classi-cal statistical averages at high temperatures. In general the agreement with experimental data is much better compared to classical computations. For �-cristobalite it turns out 5) that even at temperatures as high as 600 K only with PIMC a good agreement with experimental findings is obtained. The negative thermal expansion in �-quartz however may be explained by a classical mod-eling.

Starting from the diamond lattice of silicon solids and placing between each neighbor pair of Si atoms an O atom, we arrive at a silicate which exists in nature in cu-bic symmetry: �-cristobalite. For the computation of SiO2-structures a variety of potentials are studied in the literature, for a review see ref. 7. Concerning the com-putational time it is of great advantage that apparently two-body potentials like the TTAM-potential 9) and the BKS-potential 8) describe the system properties at least as good as three body potentials.

Canonical averages <A> of an observable A in a sys-tem defined by the Hamiltonian H = Ekin+Vpot of N par-ticles in a volume V are given by:

� �1 exp( ) .A Z Sp A ��

� �� H (1)

Here Z=Sp [exp( �H)] is the partition function and � = 1/kBT is the inverse temperature. Utilizing the Trotter-product formula,

� �exp( ) lim exp( / ) exp( )/ P

kin potP

E P V P� � ��

� � �H

(2)

we obtain the path integral expression 2-4) for the parti-tion function:

� �

� �

� ��

3 / 2

( )

21

22( ) ( 1)

2 21

( )

( , , ) lim2

exp2

NP P

s

Ps

N

s sk k

k

spot

mPZ N V T d

mP

P

V

��

�

�

��

�

�

�

� �

�

� ��

� ��

��

�

r

r r

r

�

� (3)

Here, m is the particle mass, integer P is the Trotter number and rk

(s) denotes the coordinate of particle k at Trotter-index s, and periodic boundary conditions apply, the particle with Trotter-index P+1 is the same as the particle with Trotter-index 1. This formulation of the partition function allows us to perform Monte Carlo simulations for increasing values of P approaching the true quantum limit for P � �. Note that Eq. (3) does not take into account any quantum- mechanical exchange between particles (for atoms as heavy as Si and O this is an excellent approximation, though it would not work for He crystals).

Thermal averages in the ensemble with constant pres-sure p are given via the corresponding partition function

� �0

( , , ) exp ( , , )N p T dV pV Z N V T��

� � �� (4)

In order to make our results comparable with those of experiments, our PIMC simulations 5) have been per-formed in the constant pressure ensemble. Most of our simulations have been done with N = 684 particles (�-cristobalite), N = 576 (�-quartz), p = 0, and P-values up to 100. A typical PIMC data point in Fig. 1 required about 1200 CPU hours on a CRAY-T3E (single proces-sor).

At temperatures below 700 K the quantum results (see Fig. 1) for the potential energies deviate from the classical results to higher values, but for higher tem-peratures they agree with the classical values. The vol-ume of the simulation box obtained by the PIMC simu-lations (Fig. 1) agree within numerical scatter with the experimental data for all temperatures studied- in con-trast to the classical simulations. Despite the apparently high temperatures of 700 K quantum effects are very important for the thermal properties of �-cristobalite and thus quantum effects should not be neglected in simula-tions of real materials. This supports the assumption that quantum effects may still play an important role above the Debye temperature which is at about 500 K for SiO2.

According to a model of Wyckoff 11,12) for �-cristobalite the O-atoms are located in the middle of a bond connecting two Si- atoms, the Si-O-Si bond angle is 180o and the Si-O bond length 1.54 Å. In order to correct these values to obtain the actually observed angle


(between 140o and 150o) and bond lengths (Si-O: about 1.61 Å) several models have been suggested in which the O-positions deviate from the ideal middle places 13-

17). The question which of these models describes the properties of �-cristobalite best is not yet decided by experimental methods.

Fig. 1: Potential energy (a) and unit cell volume (b) for �-cristobalite, results of path integral Monte Carlo simulations (with N = 648 particles and 27 unit cells unless otherwise noted). Comparison with experimental data taken from Ref. 6. In addition simulations have been done with a “core-shell” potential 10) with an av-erage potential energy of about -43.2 eV.

According to our study 5) the temperature dependence of the Si-O and the O-O bonds have the following fea-tures:

�� The width of the distributions increases with tem-perature, the height decreases.

�� The average values increase with the tempera-ture.

�� At the same temperature the distributions ob-tained by PIMC (P=30) have larger average val-ues than the classical distributions.

�� The difference in the distributions and the aver-age values between the classical and the quantum results decrease with the temperature.

All these effects are present in the Si-Si bonds as well, however the Si-Si bond properties are significantly determined by quantum effects.

We conclude that for a realistic materials modelling the simulation by path integral Monte Carlo techniques is a useful method which should be used in future stud-ies of thermal properties of other crystals as well.

(1) G.C Rutledge, D.J. Lacks, R. Martonak and K. Binder,

J. Chem. Phys. 108 (1998) 10274 (2) R.P. Feynman and A.R. Hibbs, Quantum Mechanics and

Path Integrals (McGraw-Hill, New York, 1965); H.F. Trotter, Proc. Am. Math. Soc. 10 (1959) 545; Commun. Math. Phys. 51 (1976) 183; J.A. Barker, J. Chem. Phys. 70 (1979) 2914; K. S. Schweizer, R. M. Stratt, D. Chandler and P. G. Wolynes, J. Chem. Phys. 75 (1981) 1347; D. M. Ceperley, Rev. Mod. Phys. 67 (1995) 279

(3) P. Nielaba, in Computational Methods in Colloid and Interface Science ed. by M. Borowko (Marcel Dekker, New York, 2000) p. 77

(4) M. Presber, D. Löding, R. Martonak, and P. Nielaba, Phys. Rev. B 58 (1998) 11937; Chr. Rickwardt, M. Presber, D. Löding, M. Reber and P. Nielaba, in Path Integrals from peV to TeV, ed. by R. Casalbuoni, R. Giachetti, V. Tognetti, R. Vaia, P. Verruchi (World Scientific, Singapore, 1999) p. 446

(5) Chr. Rickwardt, PhD thesis, Mainz (1998); Chr. Rickwardt, P. Nielaba and K. Binder, in Computational Modeling and Simulation of Materials, ed. by P. Vincenzini, A. Degli Esporti (Techna, Srl, 1999), p. 411; Chr. Rickwardt, P. Nielaba, M.H. Müser and K. Binder, preprint

(6) I.P. Swainson, M.T. Dove, Phys. Chem. Minerals 22 (1995) 61

(7) K. Vollmayr, Ph.D thesis, Mainz (1995) (8) B. van Beest, G. Kramer, R. van Santen; Phys. Rev. Lett.

64 (1990) 1955 (9) S. Tsuneyuki et al., Phys. Rev. Lett. 61 (1988) 869 (10) K.-P. Schröder andJ. Sauer; J. Phys. Chem. 100 (1996)

11043 (11) R. Wyckoff, Am. J. Sci 9 (1925) 448 (12) R. Wyckoff, Z. f. Krist. 62 (1925) 189 (13) A. Wright andA. Leadbetter; Phil. Mag. 31 (1975) 1391 (14) D. Hatch, and S. Ghose; Phys. Chem. Min. 17 (1991)

554 (15) M. Dove et al., Ferroelectrics 136 (1992) 33 (16) M. Dove, A. Giddy and V. Heine; Trans. Am. Cryst.

Assoc. 27 (1992) 697 (17) A. Giddy et al., Acta Cryst. A 49 (1993) 697


1.36 Structures, phases and phase transitions in solids in reduced geometry

J. Hoffmann, W. Strepp, M. Gerstenmaier, S. Haase and P. Nielaba

An interesting effect has been found in experiments with colloidal systems 5): if colloidal particles are ex-posed to a laser beam, with increasing amplitude a crystallization and finally even a melting transition can be detected.

Fig. 1: Schematic configuration of a hard disk system in the x-y plane with external periodic potential V(x).

Fig. 2: Phase diagram of a hard disk system in external periodic potentials in the density-V0/kBT-plane. The symbols give the melting transition points according to the cumulant intersection method of the solid-order pa-rameter.

In order to be able to analyze these type of systems in greater detail, we have studied a system of hard disks 6) in an external periodic potential with amplitude V0 (Fig. 1) by Monte Carlo methods. We systematically varied the density and V0 and computed the pair correla-tion functions as well as the solid order parameter. The computed pair correlation functions are very similar to the corresponding experimental quantities. For small V0-values we obtain typical fluid correlations, for medium V0-values solid correlations and for large V0-values finally correlations of a modulated fluid, in which the particles are relatively easy to move parallel to the potential valleys. The resulting phase diagram in the density-V0-plane is shown in Fig. 2. Since the transition density for large values of V0 is higher than the smallest transition density for medium values of V0, we can con-clude that the melting transition is a ‘reentrant’ phe-nomenon.

In the last few years phase transitions in nano-pores (e.g. Vycor) have been studied intensively 7,8). Besides the spinodal decomposition studies investigations on the shift of phase transition temperatures in nano-pores with small cylinder- diameter are of great interest.

We have studied 9) phase transitions in Ar- and Ne-pore condensates by path integral Monte Carlo (PIMC) simulations in the NVT- and the NpT-ensemble using appropriate particle- and surface-potentials.

Fig. 3: Phase diagram for Ar- and Ne-pore condensates in classical and quantum simulations. The lighter Ne-particles have a reduced coexistence region.

In the PIMC simulations shifts of phase transition temperatures due to quantum delocalization effects can be quantified. This has been done for liquid-gas transi-tions 1) in two dimensions as well as for pore conden-sates 9). The influence of the pore diameter on the loca-tion of the liquid- gas critical temperature has been studied, a reduction compared to the bulk material is drastic but apparently not monotone with decreasing di-ameter. At higher densities the condensate crystallizes

side view:

top view:

d

L

x

V(x)

V0

y

x

0 0.2 0.4 0.6 0.8ρ σ3

0

0.2

0.4

0.6

0.8

1

k BT

/ε

ClassicalArgon (TO64)Neon (TO 64)


and interesting meniscus structures are present in the simulations as well as in experimental studies. The phase diagrams for Ar- and Ne-condensates are shown in Fig. 3. In the NpT ensemble solid properties have been studied as well. Due to the different influence of the wall on the system for small pore diameter we obtain cylindrical configurations and for large pore diameter configurations in which fcc- and hcp-type structures are present, see Fig. 4.

Fig. 4: Ar-configurations in a cylindrical pore in the NpT ensemble (p=0), view parallel to cylinder axis. Right: pore radius 7.5�, kBT/�=0.166, left: pore radius 10�, kBT/�=0.236.

In the experimental project A2 of the SFB 513 the island growth of Au- particles on WSe2 and on WS2 has been studied 10). In the first case the island size distribu-tion has a sharp maximum, in the second case two maxima. In the first case the height of the structures is independent on the volume, in the second case a linear relation is found. The reason for this interesting behavior is not yet understood.

In order to analyze this phenomenon we have consid-ered 11) the question if this effect may be caused by dif-ferences in the lattice parameters of the deposited parti-cles and of the surface. For simplicity we have studied a one dimensional model. With Lennard-Jones pair poten-tials the deposition and (MC) relaxation processes result in trapezoidal structures.

Taking this structure as the basis we computed the energetically favored sites (ground state) in a harmonic approximation for different lattice parameter misfits. For small misfits it turns out that a test particle can be de-posited on the side as well as on the top of the trapezoid, for large misfits a deposition at the sides is energetically favored. Thus for small misfits the islands grow in height and width, for large misfits preferentially only in width. This is similar to the experimental results.

(1) S. Haase, Diploma thesis, Konstanz (1999) (2) M. Rovere, D. Heermann and K. Binder, J. Phys.:

Condensed Matter 2 (1990) 7009 (3) S. Sengupta, P. Nielaba and K. Binder, Phys. Rev. E, in

press (4) P. Nielaba and S. Sengupta, Phys. Rev. E 55 (1997) 3754 (5) Q.-H.Wei, C. Bechinger and P. Leiderer, Phys. Rev. Lett.

81 (1998) 2606 (6) W. Strepp, Diploma thesis, Konstanz (1999) (7) Z. Zhang andA. Chakrabarti, Phys. Rev. E 50 (1994)

R4290; J.C. Lee, Phys. Rev. Lett. 70 (1993) 3599; A. Chakrabarti, Phys. Rev. Lett. 69 (1992) 1548; A.J. Liu and G.S. Grest, Phys. Rev. A 44 (1991) R7894; A.J. Liu, D.J. Durian, E. Herbolzheimer and S.A. Safran, Phys. Rev. Lett. 65 (1990) 1897; L. Monette, A.J. Liu and G.S. Grest, Phys. Rev. A 46 (1992) 7664; Z. Zhang and A. Chakrabarti, Phys. Rev. E 52 (1995) 2736; P. Huber, D. Wallacher and K. Knorr, Phys. Rev. B 60 (1999) 12657; P. Huber and K. Knorr, Phys. Rev. B 60 (1999) 12666

(8) M.W. Maddox, K.E. Gubbins, M. Sliwinska- Bartkowiak and Soong- hyuck Suh, Mol. Simulat. 17 (1997) 333; M.W. Maddox and K.E. Gubbins, J. Chem. Phys. 107 (1997) 9659; R. Radhakrishnan and K.E. Gubbins, Phys. Rev. Lett. 79 (1997) 2847; L.D. Gelb and K.E. Gubbins, Phys. Rev. E 56 (1997) 3185

(9) J. Hoffmann, PhD Thesis, Konstanz (in preparation) (10) A. Rettenberger, P. Bruker, M. Metzler, F. Mugule,

Th.W. Matthes, M. Böhmisch, J. Boneberg, K. Friemelt and P. Leiderer, Surf. Sci. 402-404 (1998) 409

(11) M. Gerstenmaier, Staatsexamensarbeit, Konstanz (1999)


1.37 Correlations and dynamic ordering processes near solid surfaces

W. Dieterich and P. Maaß

Near an interface or a free surface of a solid the atomic structure normally changes relative to the bulk structure, as a consequence of the fact that interatomic interactions near the surface are modified or disrupted. While this is a widely studied subject, only few investi-gations have been carried out with respect to surface ef-fects on two-point correlation functions determining the cross section in a surface scattering experiment.

Away from thermodynamic equilibrium, ordering and growth processes of adatoms on surfaces are of particu-lar interest, mostly in connection with molecular-beam-epitaxy (MBE) experiments which have become impor-tant in the production and design of new materials.

Several investigations have been carried out during last year in order to improve our understanding of atomic structures and correlations near solid surfaces and of surface-induced ordering and growth processes.

Ordering kinetics near surfaces of metallic alloys.

The Cu-Au system represents an example of a fcc-alloy whose ordered phases have experimentally been studied in the past in detail and which also can be de-scribed successfully in terms of simplified lattice gas models. Several special ordering phenomena are known to occur at the (001)-surface of Cu3Au which in the bulk orders in the L12 structure. These include an oscillatory segregation profile which above the bulk ordering tem-perature T0 decreases from the surface towards the bulk, and a continuous vanishing of the order parameter at T0 in the first atomic layer, despite of the fact, that the bulk material undergoes a first order phase transition. Time-resolved small angle X-ray scattering experiments at Cu3Au (001) have revealed a two-step ordering process after a temperature-quench from the disordered phase to a final temperature Tf<T0. After a rapid penetration of a segregation wave from the surface into the bulk, slow evolution of the near-equilibrium domain pattern has been observed, which consists of 4 types of ordered do-mains separated by antiphase boundaries.

Previously (see the Annual Report 1998) the essential features of these experiments could be analyzed within time-dependent Ginzburg-Landau theory 1). More recent studies were based on Monte Carlo simulations, where elementary atomic migration steps were affected by a vacancy mechanism (“ABv-model”; A=Cu; B=Au; v=vacancy). After verification of this model in compari-son with the static segregation amplitudes, the velocity of the penetrating segregation front as a function of tem-perature was extracted from the simulations.

The final penetration depths are a result of the com-petition of the ordering wave with the spontaneous growth of bulk fluctuations.

Fig. 1: Propagation of the segregation profiles �(z,t) after a temperature quench from the disordered phase (Ti>T0) to the ordered phase (Tf<T0) of Cu3Au. a) Pro-files �(z,t) for a fixed Tf = 0.97T0 b) Time-dependence of the penetration depth for different Tf. c) Penetration ve-locity at short times versus Tf.

The ordering kinetics in nonstoichiometric crystals turns out to be markedly different from the stoichiomet-ric composition, an effect which calls for experimental verification.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 20 40 60 80 100 120 140

ψ(z

,t)

Tf = 0.97 To

1000 mcs2000 mcs4000 mcs7000 mcs

10000 mcs

0

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

pene

trat

ion

dept

h in

ato

mic

laye

rs

time in mcs

Tf = 0.91 ToTf = 0.96 ToTf = 0.97 ToTf = 0.98 ToTf = 0.99 ToTf = 1.01 To

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.96 0.97 0.98 0.99 1 1.01 1.02temperature Tf in units of To

a)

b)

c)


Density functional theory

The density functional formalism (DFT) for lattice gases was developed further mainly with respect to a de-scription of ordered phases and surface effects. The as-sumption of a nearest neighbor repulsion between parti-cles on a fcc-lattice is known to yield a phase diagram which reasonably describes the experimental phase dia-gram of the Cu1-xAux system. Using a particular version of the so-called “weighted density approximation” (WDA) the phase diagram of such alloys in the regime x < 0.3 could well be reproduced (see Fig. 2), establishing the DFT as a possible alternative to the well-known cluster variation method (CVM). In surface problems, however, the DFT appears to bear essential advantages over the CVM. This was demonstrated by calculating surface-induced two particle-correlation functions in a lattice gas with nearest-neighbor attraction in a strip ge-ometry. The results of that study compare favorably with computer simulations (Fig. 3). In such problems it is es-sential to use an interaction free energy functional that conforms with the particle-hole symmetry in lattice systems. A new type of functional, the “semilinear DFT”, turned out to be appropriate in reproducing es-sential qualitative aspects in lattice gases under dimen-sional reduction 2).

Fig. 2: Phase diagram of an AxB1-x alloy on a fcc lattice with effective nearst-neighbor repulsion V>0. The tran-sition temperature (in units of V/kB) as a function of the concentration cA of A-atoms was calculated using the hybrid weighted density approximation (HWDA). For comparison we also show the CVM in tetrahedron ap-proximation. The CVM correctly predicts ordered phases of AB3 and A2B2 type, whereas in the (non-sym-metric) HWDA only AB3 type ordering occurs.

Finally we generalized the DFT to the Potts-model. Furthermore some steps were undertaken towards an extension of the DFT to a variational principle for multi-particle correlation functions. The latter aspect is of in-terest in particular in a comparison of the DFT with the general procedure in CVM theories.

Fig. 3: Lateral pair correlation function H||(x,y) in a lat-tice gas with strip geometry of width L=40 versus lateral coordinate y in the first row (x=0) and far from the sur-face (x=19) resulting from MC simulations and the se-milinear DFT. Temperatures in a) and b) are given in units of |V|/kB. Energetically neutral surfaces were as-sumed, with constant (x-independent) particle density px=0.5.

Wall induced correlations in Takahashi lattice gases

An exact formalism was developed to study the structural properties of one-dimensional lattice gases composed of particles with nearest neighbor interactions of arbitrary range (“Takahashi lattice gas”) in the pres-ence of an arbitrary confining wall potential 4). The pur-pose of these exact studies is twofold: On one hand they allow us to gain valuable insight into the behavior of higher-dimensional systems. On the other hand, it is possible to address the question for which physical quantities the canonical and grand canonical ensemble yield comparable results in such confined systems.

We derived linear recursion relations for generalized partition functions of the Takahashi lattice gas exposed to an external potential, from which thermodynamic quantities, as well as density distributions and correla-tion functions of arbitrary order can be determined. Ex-plicit results for density profiles and pair correlations near a wall were presented for various situations. In par-ticular we considered as a special case the hard rod lat-tice gas, for which a system of nonlinear coupled differ-ence equations for the occupation probabilities previ-ously derived by Robledo and Varea could be reduced to a much simpler system of independent linear equations. It was further shown that for an external potential de-scribing two hard confining walls, various central re-

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5

k BT

/ V

cA

Disorder

Disorder

AB3

A2B2

CVMHWDA

10-4

10-3

10-2

10-1

1

0 5 10 15H

||(x,

y)y

x=0

x=19

b)

T = 0.70

SLDFTMC

10-4

10-3

10-2

10-1

1

0 5 10 15

H||(

x,y)

x=0

x=19

a)

T = 0.80

SLDFTMC


gions exist in the hard rod lattice gas, where the occupa-tion probabilities are exactly constant and the multi-point correlation functions are exactly translationally in-variant in the canonical ensemble, while in the grand ca-nonical ensemble such regions do not exist.

Exact density functionals in one dimension (d=1)

Under geometrical restriction of a d-dimensional system in one direction one finally ends up with the cor-responding (d-1)-dimensional system. Exact knowledge of the statistical mechanics in reduced dimension there-fore yields an important reference for approximate theo-ries in confined systems of higher dimension. Under that aspect we further elaborated on the construction of exact density functionals for 1-d lattice gases. A general method was proposed for arbitrary nearest-neighbor in-teractions, including hard-core contributions of arbitrary size. Our procedure covers all previously known exact functionals for 1-dimensional lattice gas or fluid sys-tems, as developed predominantly in works by J. Percus et al. Our method is based on a generalized Markov-property for the probability of occupational configura-tions, where the “memory” in the conditional probabili-ties has a range given by the range of interactions 3).

The structure of the resulting grand free energy func-tional becomes most transparent in the continuum limit. It contains both the 1-particle density �(x) and the 2-particle density �(x,y) which however is coupled to �(x) via a nonlinear integral equation. Again it is possible to generalize this theory to Potts-models.

It appears that with similar ideas approximate func-tionals for d=2 and d=3 can be constructed which reduce to the exact case d=1 (and of course also to d=0) under dimensional reduction.

Nucleation on top of islands in epitaxial growth

An important process controlling the morphology of thin films grown by vapor deposition is the nucleation of stable atom clusters in the second layer on top of islands in the first layer. Smooth films growing by a layer-by-layer mode develop if stable clusters in the second layer form after coalescence of islands in the first layer, while second layer nucleation preceding island coalescence leads to a rough film morphology. The onset of second layer nucleation occurs rather sharply, when the islands in the first layer have acquired a critical mean radius Rc. Accordingly, a simple criterion for the occurrence of rough multilayer growth is that Rc is smaller than the mean distance l of islands in the first layer (in the satu-ration regime of almost constant island density before coalescence).

We developed a stochastic theory for second layer nucleation based on scaling arguments 5), by which the overall nucleation rate on top of islands and the critical island radius Rc could be determined in dependence of the relevant experimental parameters. These parameters are the incoming atom flux F, the jump rate D0 /a

2 of adatoms (with a being the jump dis-

tance on the substrate surface), and the additional step edge barrier �ES (Schwoebel barrier), which in addition to the bare surface diffusion barrier has to be sur-mounted by an adatom, when it crosses an island edge. For small critical nuclei of size i� 2 (a cluster composed of i+1 atoms is stable) the theory predicts

Rc~�� where �� D0 /Fa4, � � exp(-�ES/kBT), and the expo-nents � and �have different values depending on how � and � relate to each other. Overall there exist 4 different regimes:

( 8) /[4( 2)]

4( 2)

Regime I : 0

, 0

i i

ii

�

� �

� � �

�

� ��

� �

2( 8) /[( 2)] ( 3) /[2( 2)( 2)]

( 3)

( 2)(3 4) 3 4

Regime II:

,

i i i i i i i

i i ii i i

�

� �

� � � � � � � �

�

� � �

� ��

� �

2( 3) /[2( 2)( 2 )] /[2( 2)]

( 3) 1( 2)( 5) 5

Regime III:

,

i i i i i i i

i i ii i i

�

� �

� � � � � � �

� �

� � �

� ��

� �

/[2( 2)]

2( 2)

Regime IV: 1

, 0

i i

ii

�

� �

� �

�

� ��

� �

Fig. 4: The various scaling regions of second layer nu-cleation for a critical nucleus of size i=1 in an �-� dia-gram (see eq.(1)). The thick dashed line with slope (-6) marks the onset of smooth layer-by-layer growth and the circles refer to the onset of island coalescence found in the kinetic Monte-Carlo simulations.

The various regions I-IV for i=1 are pictured in the dynamical phase diagram shown in Fig. 4, which in ad-dition entails the transition line from rough multilayer to smooth layer-by-layer growth. Kinetic Monte Carlo simulations have been performed to test the validity of the theory, and the results from these simulations are in good agreement with the theoretical predictions (Fig. 5). Since for large step edge barriers the result (1) deviates from the predictions of a mean-field type approach pro-posed earlier 5), we suggested to reexamine various ex-

104

106

108

1010

1012

1014

10−6 10−5 10−4 10−3 10−2 10−1 100

Γ=D

0/Fa

4

α=exp[−∆Es/kBT]

I

II III

IV


periments, which employed the mean-field approach to estimate the Schwoebel barrier in some materials. Re-cently, this reexamination has been carried out 7).

Fig. 5: Critical island size Rc obtained from kinetic Monte-Carlo simulations as a function of

)TkEexp( BS /�� for i=1 (upper figure) and vari-ous ratios 4

0 / FaD�� in a range 105 to 1012 , and for i=2 (lower figure) and various � in the range 105 to 109. The regimes I-IV (see text) are indicated together with their border lines.

Further elaboration on the stochastic theory shows that the mean field approach suggested in ref. 6 becomes essentially valid for critical nuclei of size i3. For i=1 as well as for i=2 and large �ES however, the nucleation process is dominated by fluctuations that are not ac-counted for by the mean field approach. In the language of critical phenomena, one may regard i=2 as the upper critical size of the critical nucleus above which mean field theory becomes applicable. Currently we are working on an extension of the stochastic approach in order to include the lifetimes of unstable clusters with comparatively high dissociation energies.

(1) H.P. Fischer, J. Reinhard, W. Dieterich and A.Majhofer, Europhys. Letters 46 (1999) 755 (2) J. Reinhard, W. Dieterich, P. Maass and H.L. Frisch,

Phys. Rev. E 61 (2000) 422 (3) J. Buschle, P. Maass and W. Dieterich, J. Phys. A.:

Math. Gen. 33 (2000) L41 (4) J. Buschle, P. Maass and W. Dieterich, J. Stat. Phys. 99,

No. 1/2 (April 2000), in press (5) J. Rottler and P. Maass, Phys. Rev. Lett. 83 (1999) 3490 (6) J. Tersoff, A.W. Denier van der Gon and R.M. Tromp,

Phys. Rev. Lett. 72 (1994) 266 (7) J. Krug, P. Politi and Th. Michely, e-print cond/mat

9912410

10

100

10−6 10−5 10−4 10−3 10−2 10−1 100

Rc/

a


~α1/7

I

II

III IV

10

100

10−6 10−5 10−4 10−3 10−2 10−1 100

Rc/

a


~α1/5

~α3/7

I

II

IIIIV


1.38 Transport processes in glasses

P.Maaß and W. Dieterich

Ion Transport

The properties of mobile ions in glasses show many peculiarities. Dramatic variations over many orders of magnitude are observed in transport coefficients (tracer diffusion coefficients, dc-conductivity, etc.), if the con-centration of mobile ions is changed, or if one type of mobile ion is successively replaced by another type of mobile ion (mixed alkali effect). The time-dependent ion dynamics, which can be explored by various experi-mental probes (frequency-dependent conductivity, qua-sielastic neutron scattering, nuclear spin lattice relaxa-tion, internal friction) is characterized by correlation functions that in general decay much slower than simple exponential (“non-Debye relaxation”). This phenome-non is typical for transport processes in disordered systems.

Based on previous work over the past years we de-veloped a theory 1) with the aim to understand both the variations in ion mobilities upon changes in the compo-sition of mobile ions and the non-Debye dynamics within a unified description. The theory is based on the idea that different types of mobile ions encounter differ-ent structural energy landscapes in the glass. Computer simulations of a simplified lattice model deduced from the theory allow us to reproduce the experimentally ob-served changes in ion diffusivities (see Fig. 1).

Fig. 1: (a) Normalized tracer diffusion coefficients DA,B(x) of two ion types A and B as a function of their mixing ratio x=cB/(cA+cB) in a model glass with ion type specific structural energy landscapes. Long-range Cou-lomb interactions between the mobile ions were taken into account in the simulations. Full symbols refer to ion type A, open symbols to ion type B, and different symbol types refer to different temperatures. From the tem-perature dependence we determined the activation ener-gies EA,B(x) shown in (b).

Parts of the simulation results can be explained quan-titatively also by employing analytical approximation schemes. In particular, we could show how the peculiar losses found in the mechanical relaxation of ion-con-ducting glasses are linked to the ion migration. Currently

we perform extended simulations of the model (and some modifications of it) to elucidate this connection between ion mobilities and shear-stress relaxations and to get a better understanding of the scaling behavior of the frequency-dependent conductivity with respect to changes in temperature and ionic concentration.

A mixed alkali effect occurs also in crystalline ion conductors with a structure of �/�´´-alumina type. In these systems the ionic motion is confined to two-di-mensional conduction planes which are embedded in a spinel block arrangement. Using a quantitative theory proposed some time ago, we have investigated in more detail the percolative aspects of the ion migration in the conduction planes 2). A general overview on the role of percolation concepts in the field of “solid state ionics” was provided in Ref. 3.

Nearly constant dielectric loss response

In a range of sufficiently high frequencies (below typical phonon frequencies) ion conducting glasses and many other disordered low-conductivity materials show a nearly frequency-independent dielectric loss spectrum. Correspondingly, the ac-conductivity increases nearly linearly with frequency. Upon cooling, this so-called “nearly constant loss” (NCL) response extends to lower frequencies. At temperatures T � 4K it may be observ-able within many orders of magnitude in frequency.

The physical nature of the NCL-response is still un-clear. The conventional explanation adheres to the “asymmetric double well potential model (ADWP)”, which rests on the assumption of local relaxation steps subject to a broad distribution of activation barriers.

In this study we follow the idea that long-range inter-actions among dipolar centers can yield a particularly slow and highly non-exponential relaxation. As a simple model we consider the discrete hopping motion of a system of charged defects next to their associated im-mobile counterions (“dipolar lattice gas”). When these centers are placed in space in an ordered manner, their dielectric response is essentially Debye-like. However, introducing disorder in their spatial arrangement has a dramatic effect on the ac-response, as shown by Monte Carlo simulation which indeed reflect the essential fea-tures of a NCL-response (s. Fig. 2).

More detailed properties of that model are currently under study. These include scaling properties with re-spect to temperature and ion-concentration in very dilute systems, the relative importance of local (ADWP-like) disorder and positional disorder, cross-overs to a Debye-response, collective versus single-ion response and clari-fication of more technical points, e.g. the influence of the dielectric boundary conditions on the Ewald sum-mations.

0.0 0.2 0.4 0.6 0.8 1.0x

10−1

100

D(x

)/D

0

0.0 0.2 0.4 0.6 0.8 1.0x

3.0

3.5

4.0

4.5

5.0

5.5

E(x

)/v

(a) (b)


Fig. 2: Real part of the conductivity versus frequency. Filled symbols refer to a disordered dipolar lattice gas with concentration c=0.0156 of dipolar centers and at three different temperatures (from below): kBT/Vc=0.0125, 0.0188, and 0.0333, where Vc is a typi-cal Coulomb energy. The full straight line with slope 1, corresponding to a NCL-response, is shown for com-parison. The open triangles depict a conventional De-bye-like response of an ordered dipolar lattice gas at the lowest temperature (kBT/Vc=0.0125) resulting in a slope 2 as indicated by the dotted line.

Hopping in systems with site energy disorder

To describe the glassy dynamics in disordered energy landscapes we developed a novel effective medium ap-proximation for single particle hopping in lattices with site energy disorder 4,5). Although already in early theoretical formulations of the effective medium approximation fluctuations of site energies were considered formally (in particular in the context of electron transport in amorphous semiconductors), detailed investigations on the reliability and practicability of such schemes are lacking. Using our approach we calculated the frequency-dependent diffusion coefficient for various distributions of site energies and compared the results with Monte Carlo simulations. While the approximation gives a fairly good account for the overall frequency dependence, it generally fails to reproduce the correct zero-frequency limit of the diffusion coefficient. This failure, however, can be resolved by a proper rescaling of the temperature in the effective medium (see Fig. 3).

In a separate project 6) we have investigated by Monte Carlo simulations the conductivity of a Fermi lattice gas with Gaussian site disorder for a wide range of temperatures T and ionic concentrations n. This work was strongly motivated by recent measurements on ion conducting glasses which showed that conductivity spectra for various temperatures T and ionic concentrations n can be superimposed onto a common master curve by an appropriate rescaling of the conductivity and frequency. While the Fermi lattice gas model with Gaussian site energy disorder can account for the changes in ionic activation energies upon

changing n, it in general yields conductivity spectra that exhibit no scaling behavior. However, for typical n and sufficiently low T values, a fairly good data collapse was obtained analogous to that found in experiment.

Fig. 3: Real part D´(�) of the frequency-dependent dif-fusion coefficient as a function of frequency � for near-est-neighbor hopping on a simple cubic lattice with rates wi�j = � exp[-( j- i)/(2kBT)] in the presence of a uni-form distribution of site energies i with range 0� i� max. The symbols refer to the results obtained from Monte-Carlo simulations for different temperatures kBT/ max and the solid lines correspond to the tempera-ture-rescaled effective medium approximation. The de-pendence of the rescaled inverse temperature �EMA = max/kBTEMA on the true inverse temperature � = max/kBT is shown in the inset.

Aging

We investigated aging in glassy systems based on a simple model, where a point in configuration space per-forms thermally activated jumps between the minima of a random energy landscape. The model allowed us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function as they were con-jectured in theories for mean-field spin glass models. Both the exponents characterizing the scaling of the dif-ferent relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling func-tions could be obtained analytically by invoking a novel “partial equilibrium” concept. Further work on this problem is in progress.

(1) P. Maass, J. Non-Cryst. Solids 255 (1999) 35 (2) P. Maass, M. Meyer and A. Bunde, Physica A 266

(1999) 197 (3) W. Dieterich, O. Dürr, P. Pendzig, A. Bunde and A.

Nitzan, Physica A 266 (1999) 229 (4) P. Maass, B. Rinn and W. Schirmacher, Phil. Mag. B 79

(1999) 1915 (5) B. Rinn, U. Braunschweig P. Maass and W.

Schirmacher, Phys. Stat. Solidi B 218 (2000) 89 (6) M. Porto, P. Maass, M. Meyer, A. Bunde and W.

Dieterich, Phys. Rev. B 61 (2000) 6057

10-6

10-5

10-4

10-3

10-2

10-1

10-4 10-3 10-2 10-1 1

σ´(ω

)

ω

10-3

10-2

10-1

100

10-5 10-4 10-3 10-2 10-1 100 101 102

D´(

ω)

ω

2

4

6

8

1 2 3 4 5 6

βEM

A

β


2. Cluster Physics

2.1 The structure of medium sized silicon cluster anions

J. Müller and G. Ganteför in collaboration with B. Liu and K.-M. Ho (Ames Laboratory and Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA) S. Ogut and J.R. Chelikowsky (Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA) A.A. Shvartsburg and K. W. M. Siu (Department of Chemistry, York University, Toronto, Ontario, Canada M3J 1P3)

A large number of substances had been thought to displace silicon as the most important semiconductor material, but still none can compete with it as of today. Instead, the capabilities of semiconductor devices have been increased via their continuous miniaturization. This has induced a growing interest in the properties of small Si structures, including the clusters containing just a few atoms.

Fig.1: Photoelectron spectra for Sin anions (n = 8-20). Experimental scans are in thin lines, thick lines are for the DFT-LDA simulations.

Little had been known for sure about the geometries and electronic structure of medium-sized Si clusters in the 10-50 atom range. Ion mobility measurements are often too blunt as a structural probe because different isomers often have very similar mobilities 1). The other approach involves a comparison of measured electronic

properties such as electron affinities with simulations for candidate geometries. For some time, the structural op-timization of Si clusters had stalled at about the size of 10 atoms. At this point the number of possible isomers becomes too large to be treated using the then known methods: exhaustive permutation of all options by man-ual construction and simulated annealing.

A powerful tool to determine the electronic structure is Photoelectron Spectroscopy (PES) 2) that reveals the energies of molecular orbitals. In a PES experiment, size-selected cluster anions are irradiated using a fixed-wavelength laser producing photons with energy above the detachment threshold of investigated species. The distribution of kinetic energies of released electrons is measured. These data reveal the electronic structure of neutral clusters. Previously published information for the PES of Sin anions has been limited to n � 13 because of insufficiently high signal intensities for larger sizes.

Here we report a major progress in the structural characterization of medium-sized Si clusters enabled by advances in both experiment and theory. On the side of experiment, we have obtained the photoelectron spectra for Sin anions with up to 50 atoms. This has been made possible by a specially tuned Pulsed Arc Cluster Ion Source (PACIS) 3) that produces a substantially brighter ion beam than those available previously. The source features a 30 cm long extender with diameter of 4 mm, including a 4 cm long waiting room 8 mm in diameter. Liquid nitrogen circulating through this extender effi-ciently cools the clusters produced. This has allowed us to resolve multiple features in the PES, thus determining the vertical detachment energies and HOMO-LUMO gaps for medium-sized clusters. On the side of theory, a novel tool for molecular optimization, the genetic algo-rithm 4), has recently been applied to Sin species in the n � 20 size range 5). A superior power of this method has allowed us to proceed beyond the previous limit of about 10 atoms. Specifically, we have accumulated an exten-sive set of low-energy isomers for Sin anions with n � 20. All these have been optimized using the density functional theory (DFT) in both local density and gener-alized gradient approximations. Photoelectron spectra for candidate geometries have been simulated using DFT-LDA. A comparison of results with the measure-


ments has allowed us to make the structural assignments.

Fig. 2: Vertical detachment energies: measured values (solid line), calculated for the Sin anion ground states (filled circles), calculated for other low-energy Sin

- iso-mers (other symbols).

For the purpose of initial screening, we had calcu-lated the vertical detachment energies (VDEs) for a number of low-energy Sin anion isomers. These are compared with the measurements in Fig. 2. By inspec-tion, the VDEs for Sin anion ground states match the measured values for all n � 20, while other low-energy isomers fail to reproduce the measurements (with a few exceptions limited to n = 11 and 12). For species exhib-iting a reasonable agreement, the complete PES was simulated and compared with experiment. The results for n = 8 - 20 are presented in Fig. 1. Simulations for the lowest-energy geometries found by genetic algorithm are superimposed (the data for three near-degenerate isomers competing for the global minimum are shown for n = 11). The agreement between calculations and experiment is excellent except for n = 12. Since a photo-electron spectrum is highly specific to cluster structure, there is a high degree of confidence in that the lowest-energy geometries found in our calculations are actually observed in experiment. A more detailed discussion can be found in Ref. 5).

Fig. 3: HOMO-LUMO gap calculated for Sin (n � 20) species in the geometries that are lowest-energy for an-ion (solid line) and neutral (dashed line). Symbols mark the measurements for the case of anions.

The evolution of band gap (HOMO-LUMO gap) in Si clusters as a function of size is of great interest from both fundamental and applied viewpoints. These gaps can be extracted from the PES or calculated. For metal-lic species with delocalized electrons, the gap in finite particles tends to decrease with increasing cluster size. However, the gap for Sin (n � 20) neutrals varies ir-regularly in the 1 - 2 eV range without apparent decrease for larger clusters (Fig. 3).

In conclusion, we have elucidated the structure of medium-sized Si clusters using photoelectron spectros-copy. These species are basically built from the Si9 tri-capped trigonal prism (TTP) subunits 6), although some other recurrent structural patterns become important for n approaching 20. The dissociation energies of Si clus-ters drastically decrease for n > 10 7), so it is hardly sur-prising that the ion yield drops dramatically. Further-more, photoelectron spectra of larger Si clusters display peculiar features for some sizes, including n = 33 and 43. This may either reveal a HOMO-LUMO gap sub-stantially greater than that for other sizes, or indicate an unusual predominance of one geometry in the isomeric mixture. This behavior is not yet understood and is a subject of our ongoing research.

(1) R.R. Hudgins et al., J. Chem. Phys. 111 (1999) 7865 (2) H. Handschuh et al., Rev. Sci. Instrum. 66 (1995) 3838 (3) Chia-Yen Cha et al, Rev. .Sci. Instrum. 63 (1992) 5661 (4) K.M. Ho et al, Nature 392 (1982) 582 (5) A.A. Shvartsburg et al., J. Chem. Phys. 112 (2000) 4517 (6) J. Müller et al, submitted to Phys Rev. Lett. (7) A.A. Shvartsburg et al., Phys. Rev. Lett. 81 (1998) 4616

4 6 8 10 12 14 16 18 200,0

0,5

1,0

1,5

2,0

Band

gap

[eV]

Number of Atoms


2.2 Time resolved dynamics of electronic excitations in C-3

S. Minemoto, J. Müller, R. Fromherz, G. Ganteför, H.J. Münzer, J. Boneberg and P. Leiderer

The development of femtosecond lasers has made it possible to study fast dynamical processes in atoms, molecules and condensed matter. A further step forward was the combination of femtosecond lasers with pho-toelectron spectroscopy, which allowed the direct obser-vation of the reorganization of the electronic structure after photoexcitation. In such an experiment, the pump pulse triggers dynamical processes like single particle excitations or fragmentation, and with the UV-probe pulse a photoelectron spectrum is recorded at a given delay. The series of photoelectron spectra reveals the time evolution of the system with increasing pump / probe delay. Here we describe the application of this technique to study the decay of electronic excita-tions in mass selected nanoparticles and clusters, where the time scales and decay mechanisms might be differ-ent from the bulk properties as a result of the finite size of the particles.

For small aggregates with a well-defined number of atoms (clusters) it is known that the properties may vary with each additional atom. Therefore, for experiments on clusters mass separation is essential. One successful method used for the study of the ground state electronic structure of clusters is photoelectron spectroscopy of negatively charged ions 1). Recently, this technique has been combined with femtosecond lasers to study fast fragmentation processes in molecules and clusters like I2

- 2) and Au3- 3).

In the present article, we present the application of this technique to observe the time-evolution of elec-tronic excitations in mass selected clusters. As a first example, we have studied the decay of an excited state of the carbon trimer anion C3

-. Taking advantage of the new technique we determined the lifetime of this excited state directly. In addition, the photoelectron spectra re-veal the nature of the participating electronic states un-ambiguously. Especially, it was possible to directly de-termine the neutral "parent state" (see below) by de-tachment from the excited resonance proving the as-signment to a Feshbach resonance. This example de-monstrates the power of the method for studying elec-tronic excitations in larger clusters and nanoparticles.

Details of the experimental set up have been de-scribed elsewhere 1,3). The anions are generated directly in a pulsed arc cluster ion source (PACIS) and mass separated with a time-of-flight mass spectrometer. A selected bunch of anions is irradiated by the pump and probe laser pulses and the kinetic energy of the detached electrons is measured using a "magnetic-bottle"-type time-of-flight electron spectrometer. The femtosecond laser is split into pump and probe pulse, which both have equal intensities (~ 1mJ / cm2) and pulse widths (~ 300 fs).

Fig. 1 displays a comparison of two photoelectron spectra of C3

- obtained with zero delay (trace 1) and

with large delay (13 ps, trace 2) between pump and probe pulse. Both spectra have been obtained with a photon energy of h� = 3.1 eV. The spectra are normal-ized to the intensity of peak A located at a kinetic energy of 1.1 eV. This corresponds to the difference of the photon energy and the electron affinity of C3

- (EA = 1.995 eV), and peak A is assigned to direct de-tachment from the electronic ground state of C3

-. The final state is the ground state of neutral C3.

Fig. 1: Pump / probe photoelectron spectra of C3-.

Feature B is located at a kinetic energy of 2.0 eV. Its intensity with respect to the main feature A varies de-pending on the time delay between the two laser pulses. This indicates that its origin might be due to a two pho-ton process. As a first idea one would expect an increase of h� = 3.1 eV of the kinetic energy (corresponding to a kinetic energy of 4.3 eV) of an electron detached in a 2-photon process. Such a peak is observed too, but with an extremely low intensity (peak C in Fig. 1) and will be discussed later. For the 2-photon feature B an increase of 0.9 ± 0.1 eV only is observed and there are 2.2 eV of energy missing.

The photoelectron data can be understood if we as-sume the existence of an excited state of the anion lo-cated at an energy above the electron affinity. There are two different types - shape resonances and Feshbach resonances. For shape resonances, the electron is weakly bound in the potential of the neutral core by an angular momentum barrier and the decay occurs by tunneling through the barrier. The "parent state" is the state of the neutral atom (ground or excited state) and the decay of the shape resonance into this neutral state is energeti-cally allowed. For Feshbach resonances, the electron is bound with a positive electron affinity to the neutral core, which must be in an excited electronic state (the "parent state" of the Feshbach resonance). Autodetach-ment occurs via electronic autodetachment, i.e., the neutral core relaxes into its ground state transferring the energy to the additional electron which is ejected. In contrast to shape resonances, the decay occurs by con-

0 1 2 3 4 5

0

2

4

6

8

10C3

-A

Inte

nsity

[a.u

.]

Kinetic Energy [eV]

x15 C

Trace 2 13 ps

Trace 1 0 ps

B


certed action of at least two electrons resulting in con-siderably longer lifetimes.

If, in case of a Feshbach resonance, the excited anion is hit by a second photon, the additional electron is re-moved leaving the neutral in the excited "parent state" of the resonance. The kinetic energy of such an electron is increased with respect to the electron from direct photodetachment by the energy of the second photon (h� = 3.1 eV) minus the excitation energy of the neutral "parent state". Indeed, there is a known excited state of neutral C3 with the proper energy: the first excited state with an energy of 2.152 eV. We conclude that at zero delay electrons are detached from a Feshbach resonance of C3

-.

Fig. 2: Autodetachment (schematic). Three mechanisms are shown for the process of detaching an electron, to-gether with the corresponding electronic states.

There are at least three processes induced by the in-teraction with the laser beam (Fig. 2):

I. direct detachment from the ground state (1-photon, peak A): C3

- + h� � C3 + e- (Ekin = 1.0 eV) II. resonant autodetachment (1-photon, peak A):

C3- + h� � C3

-* � C3 + e- (Ekin = 1.0 eV) III. direct detachment from the excited state (2-photon,

peak B): C3

- + h�pump � C3-*

C3-* + h�probe � C3

* + e- (Ekin = 1.9 eV).

The kinetic energies of the detached electrons are given for photon energies of h�=h�pump=h�probe=3.1 eV. Processes I and II yield identical features in the electron spectra (peak A in Fig. 1), because initial and final state are the same for both 1-photon channels. The 2-photon process III results in the appearance of feature B.

Feature C in Fig. 1 can be explained by a fourth process:

IV. "shake down" detachment from the excited state (2 photon, peak C): C3

- + h�pump � C3-*

C3-*+ h�probe � C3 + e- (Ekin = 4.2 eV).

The difference between processes III and IV is the fi-nal state of the neutral C3, which is the ground state in case of process IV.

Fig. 3: Relative intensity of peak B (Fig. 1) as a function of the pump/probe delay.

In a pump / probe experiment, the lifetime of an ex-cited state can be measured directly. Fig. 3 displays the dependence of the intensity of peak B in Fig. 1 on the delay between the pump and the probe laser pulses. Ac-cording to process III, this dependence is directly related to the lifetime of the Feshbach resonance (noted C3

-*). From an exponential fit (Fig. 3) the lifetime ��of the Feshbach resonance of C3

- is determined to be

� = 2.6±0.7ps.

In conclusion, we present results of the application of time-resolved photoelectron spectroscopy to study the decay of an excited electronic state in mass selected cluster anions. As a first example, we studied the elec-tronic autodetaching process of a Feshbach resonance of C3

- and could distinguish four different channels con-tributing to the photoelectron signal. The use of charged particles allows for an accurate mass separation and in the future the method will be applied to the study of various electronic excitations in clusters and nanoparti-cles.

(1) H. Handschuh, G. Ganteför and W. Eberhardt, Rev. Sci.

Instrum. 66 (1995) 3838 (2) B.J. Greenblatt, M.T. Zanni, D.M and Neumark, Chem.

Phys. Lett. 258 (1996) 523 (3) G. Ganteför, S. Kraus and W. Eberhardt, J. Electr.

Spectr. Rel. Phen. 35 (1997) 88

vacuumlevel

continuum

bondingorbitals

C 3 -

1 � g

3 � u

direct detachment from the ground state 2 � g

auto- detachmentof the excited state2 � u

direct detachment from the excited state 2 � u

process I II III

-5 0 5 10 15 20 25 30 35

0,03

0,04

0,05

0,06

0,07

� = 2.6 ± 0.7 ps

Peak

B /

Pea

k A

[a.u

.]

Delay [ps]


2.3 Deposition of mass selected aluminum clusters

B. Klipp, M. Grass, U. Lutz, G. Ganteför, T. Schlenker, J. Zimmermann, J. Boneberg and P. Leiderer

Deposition of mass selected clusters is a new method for the preparation of well defined nanostructures on surfaces. The preparation of nanostructures on surfaces is one of the major tasks in technology and basic re-search. Applications of nanostructured surfaces are abundant and cover a wide range from heterogeneous catalysis to high density computer memories. From the point of view of basic research, many of the properties of small 3-dimensional nanostructures and 2-dimen-sional islands on surfaces are not well understood yet. E.g., there is no systematic study of the size-dependence of the electronic structure of clusters of simple metals on surfaces, although free clusters of such metals show strong variations depending on the number of delocal-ized electrons.

In the last annual report we described a new experi-mental set up including a cluster source which is oper-ated at high repetition rates (up to 1000 Hz), ion extrac-tion, mass selection using a 45° sector magnet and an ion optics to allow soft landing of clusters on a surface. With our experimental set up currents of monodispersed cluster ions of 1012 atoms per second can be achieved. The width of the kinetic energy distribution is in the range of 1 eV which is necessary to decelerate the clus-ter ion beam (“soft landing”).

Fig 1: XPS on deposited aluminum monomers.

To minimize the interaction between the substrate and the clusters we chose a graphite (HOPG = highly orien-tated pyrolytic graphite) substrate, which is an inert Van der Waals surface. In the first part of the experiment we deposit the aluminum monomer on HOPG. The amount of aluminum is 2·1014 atoms which corresponds to 10 % of a monolayer and the kinetic energy is varied from 5 eV, 10 eV to 40 eV.

The photoelectron spectra show a dramatic change between the 5 eV and the 10 eV deposition on the one hand and the 40 eV deposition on the other hand (Fig. 1). The 5 eV and 10 eV samples exhibit two peaks in the Al 2p spectra, one peak corresponding to Al-Al bonds and one corresponding to reacted Al. The Al-Al bonds indicate the formation of aluminum islands.

Fig. 2: STM-Picture: Al1 / HOPG, 5 eV deposition.

Fig. 3: STM-Picture: Al1 / HOPG, 10 eV deposition.

Deposition of aluminum monomers with a kinetic en-ergy of 40 eV, which is a few times the binding energy

82 80 78 76 74 72 70 68 66 64 62

43 % Al-Al

57 % reacted

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [eV]

EKIN = 10 eV

82 80 78 76 74 72 70 68 66 64 62

100 % reacted

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [e V]

EKIN = 40 eV

EKIN = 5 eV

82 80 78 76 74 72 70 68 66 64 62

46 % Al-Al

54 % reacted

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [eV]


of a C atom in the graphite bulk, causes sputtering of the surface and implantation of single atoms. There are no Al-Al bonds, and the amount of oxygen (not shown) is five times higher, because the sputtered surface is not inert.

The STM pictures support the interpretation of the XPS spectra. Deposition with kinetic energies below the binding energy of a C atom in graphite (e.g. 5 eV) is comparable to thermal vapor deposition. The STM pic-ture shows islands with more than 1000 atoms, which can be moved by the STM tip (Fig. 2). Deposition with kinetic energies in the range of the binding energy of a C atom in graphite (10 eV) leads to smaller islands (about 150 atoms). Few atoms with the highest energy are able to cause a defect in the surface. These defects act as nucleation sites for island growth and the islands are pinned (Fig. 3). The 40 eV deposition shows no islands at all.

Following that we deposit 2.8·1012 Al70�3 clusters on HOPG, which is the same amount of atoms as in the first part (2·1014 atoms, 10 % of a monolayer). The kinetic energies are 10 eV, 40 eV and 80 eV.

Fig. 4: XPS on deposited Al70�3 clusters.

Non of the spectra show evidence for formation of bigger islands, the Al-Al peak is smaller than the reacted Al peak. This means the islands are in the size of 70 atoms, the size of the clusters. The only difference in the 3 spectra is the bigger Al-Al peak in the 10 eV spectra (Fig. 4). This may be a hint for the formation of a few bigger island, consisting of two or three clusters or it may be, that these clusters are not pinned at the surface. If the clusters are pinned, the Al atoms on the substrate are reacted (Al-C), if the clusters are just “lying on the surface” the atoms on the surface are not reacted (Al-Al). In both cases these clusters are soft landed. STM investigations of a heated 10 eV deposition show clus-ters at surface steps, which also is an indication for mo-bile, i.e. soft landed clusters.

Fig. 5: STM picture: Al70 / HOPG , 80 eV.

The deposition of aluminum clusters consisting of 70�3 atoms with kinetic energies of 40 eV or more re-sults in single nanostructures pinned on the surface, which can be imaged by a STM with atomic resolution (Fig. 5).

82 80 78 76 74 72 70 68 66 64 62

69 % reacted31 % Al-Al

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [eV]

82 80 78 76 74 72 70 68 66 64 62

86 % reacted14 % Al-Al

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [eV]

EKIN = 10 eV

82 80 78 76 74 72 70 68 66 64 62

13 % Al-Al87 % reacted

Al 2p

Inte

nsity

[a. u

.]

Binding Energy [eV]

EKIN = 40 eV

EKIN = 80 eV


2.4 A new experimental setup for the in-situ investigation of the electronic, vibrational and chemical properties of monodisperse supported clusters

J. Müller, S. Burkart, R. Fromherz, C. Peucker, S. Boisson and G. Ganteför

Clusters deposited on surfaces have moved into the focus of interest in surface physics as a novel method to prepare nanostructured surfaces with exceptional elec-tronical and chemical properties. This development is also due to the fact that any application of clusters be-yond the utilization of cluster beams requires deposition on a substrate.

We report a new experimental setup for the in-situ in-vestigation of small monodisperse supported clusters. This instrument consists of a high intensity Pulsed Arc Cluster Ion Source (PACIS), tools for sample prepara-tion and cluster deposition under UHV conditions, and a High Resolution Electron Energy Loss Spectrometer (HREELS) for surface analysis. The setup aims to in-vestigate a whole variety of properties of supported clusters: excited electronic states like plasmon excita-tions, which determine the optical properties of the sur-face, the vibrational structure of the clusters which pro-vides access to their geometrical structure on the sur-face, and chemical properties determining the catalytic behavior. We present mass spectra of Ag, Si, and Al as well as a first measurement of HOPG substrate to dem-onstrate the capabilities of the HREELS.

Setup

Our new experimental setup is aimed to investigate small (m ~ 1000 amu) clusters supported on a substrate. Typically, the properties of clusters in this size range vary with each additional atom. Thus, it is highly desir-able to investigate monodisperse species i.e. each cluster deposited on the substrate is made up of the same num-ber n of atoms. To achieve this goal a cluster source is necessary which produces about 1015 particles of one single size in a reasonable time. At a particle current of 1 nA it takes about 1.5 h to deposit 0.1 monolayers at an area of 1 cm2. To generate the particles we employ a Pulsed Arc Cluster Ion Source (PACIS) 1) which has been developed for repetition rates up to 1000Hz. Up to three gas pulse valves and variable extenders from 10 to 50 cm length can easily be mounted to the source. As the power dissipation in the source is the crucial pa-rameter, the best exploits of clusters is achieved at oper-ating frequencies between 200 and 500 Hz. A high cur-rent power supply was developed which provides both a high voltage ignition pulse of about 300 V and 40 µs length and a high current pulse of up to 200 µs length. Because of the diode characteristic of the arc discharge it is necessary to control both the voltage and the current of this pulse.

The clusters are extracted from the gas pulse by a configuration of four differential pumping stages sepa-rated by skimmers of 4 - 8 mm diameter. They are accelerated by a collecting electrode driven at voltages

of several kV. Mass separation takes place in a sector magnet with an angle of 45° which makes the mass range up to 1000 amu accessible. After passing an addi-tional cryo-trap the clusters enter the deposition optic where they are decelerated in a homogenous electro-static field down to residual kinetic energies of 1 to 60 eV per cluster.

The UHV system comprises a deflectable 0.5 - 5 kV sputter gun and a electron impact heating unit capable to heat the sample up to 1000°C. The typical pressure at deposition is 5·10-9 mbar, 8·10-9 mbar at worst. The sample can be cooled to liquid nitrogen or liquid helium temperature if desired. After deposition the sample can be transferred under UHV conditions into the HREELS-spectrometer.

Fig. 2: Mass spectra of Si, Al, and Ag with up to 60 nA signal intensity.

The SPECS Delta 0.5 HREELS surface analysis spectrometer provides an energy resolution as low as 0.5 meV FWHM and is on the other hand capable de-tecting an energy loss up to 50 eV 2). A review on this surface analysis technique can be found in 3).

Test Results

For verification purposes mass spectra of Al, Si, and

20 40 60 80 100 120 140 160 180

0

20

40

60

Ag1+

Mass [amu]

Ag+

20 40 60 80 100 120 140 160 180

05

101520

Inte

nsity

[nA]

Al+

20 40 60 80 100 120 140 160 180

0.0

0.5

1.0

Al2O2+

Al2O+Al2

+

Al1+

O+N+

Al+

100 200 300 400 500 600

0.0

0.1

0.2

0.3

Si10-Si8

-Si7-Si6

-Si4-

Si-


Ag were recorded. Fig. 1 shows spectra which were re-corded at several repetition rates between 100 and 500 Hz . The upper plot displays a typical spectrum of Silicon cluster anions with highest intensities for Si4

-, Si6

-, and Si10-. The currents are in the 300 pA range, as

the cluster source is not yet optimized to this material. The other tested materials, Al and Ag, are considered for first deposition experiments. For Al1

+ an current of 16 nA is observed. The FWHM of this peak is 3.2 amu. An Al2 peak is observed in the presented spectrum with an intensity of 200 pA. Due to contamination of the vac-uum with O2 also Al2O+ and Al2O2

+ are also present. In case of Ag the atom could be produced with an intensity of 60 nA and a FWHM of 10.2 amu. This proves that this setup is capable – after adoption of the source to the specific material – to produce the required amount of particles for deposition experiments.

Fig. 3: A HREELS spectrum of HOPG. lower curve: complete spectrum, left scale; upper curve: enlarged energy loss features, right scale. The inset shows a typi-cal “straight through” mode spectrum with an FWHM of 2.9 meV

The HREELS spectrometer was tested with a HOPG sample. Prior to the measurement the sample was heated to 450°C for 2 hours. Fig. 2 shows an energy loss spec-trum of this material recorded with an electron energy of 30 eV. Peak A originates from the elastically scattered electrons, the asymmetric broadening A’ of this peak is caused by �-�*-transitions in the �-band of the graphite layer 4). The Peak labeled B represents the �-plasmon of the same band 4). The inset in Fig. 2 displays the typical resolution of the spectrometer in the mode used for these measurements. As a first test of the complete setup it is planned to deposit a layer of about 5·1015 Ag+ ions. Then, the successful deposition must be proved by the appearance of the Ag surface plasmon in the HREELS spectrum as described in Ref. 4.

Outlook

With the described setup we are capable to investi-gate many monodisperse cluster systems: With the proper adoption of the cluster source we have access to every metal, alloy and semiconductor material. As it is further possible to add a gaseous component to the He carrier gas it is also possible to generate reacted clusters containing e.g. Nitrogen or Carbon.

As a first series of experiments it is planned to inves-tigate silicon clusters in the size region up to 50 atoms. This is aimed to supplement our work on free Si clusters presented elsewhere in this report.

A comparable deposition setup with the complemen-tary analysis tool X-ray / Ultraviolet photoelectron spectroscopy (XPS/UPS) is already installed in our group. So we now possess the requirements for a sys-tematic and extensive investigation of small monodis-perse supported clusters.

(1) Chia-Yen Cha et al., Rev. Sci. Instrum. 63 (1992) 5661 (2) VSI (SPECS) Delta 0.5 HREELS manual v9.96 (3) H. Froizheim, in Electron Energy Loss Spectroscopy in

Electron Spectroscopy for Surface Analysis, ed. H. Ibach (Springer Verlag, 1977)

(4) C.M. Grimaud et al., Phys. Rev. B 59 (1999) 9874

-1 0 1 2 3 4 5 6 7 8 9 10

0

50k

100k

150kA

B

A'

Inte

nsity

[cts

/s]

Energy Loss [eV]

0

10

20

30

40

50

60

-6 -4 -2 0 2 4 6

020406080

100120140160

Energy Loss [meV]

Inte

nsity

[pA]


2.5 Sputtering with cluster ions

P. Gerhardt, D. Stolcic, E. Oettinger and G. Ganteför in collaboration with LS Prof. P. Leiderer, Konstanz and Fa. Carl Zeiss, Oberkochen

Sputtering with high energy atomic ions (e.g. Ar+) is a standard method for surface treatment like cleaning and polishing. At a given kinetic energy larger particles, e.g. rare gas cluster ions, deposit their kinetic energy mostly in the first few surface layers, while atoms pene-trate more deeply into the bulk. Therefore the energy dissipation and the sputtering process are different for atoms and for clusters. For clusters a higher sputter yield and an additional smoothing effect are expected 1-3). Due to this difference sputtering using high energy cluster ions might be advantageous for certain applications.

We are interested in smoothing surfaces of optical devices down to an almost perfect flat surface. Methods for polishing at this level of roughness are expensive and

time consuming and a search for cheaper and faster methods is underway. One application of extremely flat surfaces is the fabrication of optical components needed for the manufacturing of the next generation of com-puter chips.

Yet it is not quite clear whether the sputtering with clusters is suitable for this purpose. Therefore we syste-matically study the roughness of a surface sputtered with cluster ions depending on various parameters like cluster size, kinetic energy, time of exposure, ion current and angle of incidence. On the base of this information it will be decided, whether “cluster sputtering” is suitable

as a process for industrial manufacturing of high pre-cision optical components.

Our experimental setup consists of an intense cluster ion source and a target chamber. The clusters are gener-ated in a supersonic expansion and ionized by electric discharge. The cluster ions are guided through various lenses and steerers to the target. The target is set to a high potential and the cluster ions are accelerated to a kinetic energy of several 10 keV (Fig. 1). Various target materials (silicon, quartz glass, ceramics) can be ex-posed to the cluster beam and the sputtered surfaces are analyzed using interferometric and scanning probe techniques.

First we studied how the surface roughness depends on the mean cluster size. We started with large clusters

and decreased the size. The cluster ion dose was set for all data points to about 1014 cluster ions per 1 cm2.

The roughness is given by the rms (root means squa-re) value which is a measure of the mean deviation of the local height of the surface from the average height. Typical values for an evaporated gold film are about 1.5 - 2.0 nm rms. The polished surface of a silicon wa-fer, which is extremely flat, has a value of 0.2 nm rms.

We extract the rms value from Atomic Force Micro-scope pictures recorded for each of our samples. The results are shown in Fig. 2 for the sputtering of a pol-ished silicon wafer surface. In all cases, this extremely

Fig.1 : Experimental setup. The cluster ions are extracted from the supersonic beam and guided towards the target. Thesmall cluster ions are deflected using a Wien Filter.


flat surface becomes rougher after treatment. However, with decreasing cluster size the roughness decreases and, accordingly, the series of measurements will be extended to smaller clusters.

For a basic understanding of the difference of the sputter process for atoms and for clusters several addi-tional studies are planned. The light emitted from a sur-face exposed to the high energy cluster ion beam will be spectroscopically analysed. Furthermore, the change of the structure of nanostructures prepared by the use of colloid masks will hopefully shed some light on the mechanism of cluster sputtering. Finally, the shape of single impact craters created by cluster ions on a very smooth surface will be studied with a high resolution AFM and STM.

This first series of measurements on the size depend-ence clearly shows the importance of these studies. It is yet not clear, what the minimum roughness at optimum conditions will be, but the hope is to minimize the rms value below 0.1 nm, which is necessary for X-ray optics. (1) J. Matsuo et al., Nucl.Instr. and Meth. B 121 (1997) 459 (2) W. Henkes et al., J.Vac.Sci.Technol. A 13(4) (1995)

2133 (3) T.Yamaguchi et al., Nucl. Instr. and Meth. B 99 (1995)

237

Fig. 2: Systematic study of the roughness of a silicon surface sputtered with (CO2)N+ cluster ions with a kinetic energy of

30 keV. With decreasing cluster size <N> the roughness decreases. The commercially polished surface of a silicon wafer is slightly smoother (about 0.25 nm rms). For comparison, the roughness of an evaporated gold film and of asilicon surface sputtered with 60 keV atomic ions are given in the figure, too.


III. Publications and Talks

1. Publications

Group of Prof. E. Bucher

G. Aeppli, D.J. Bishop, C. Broholm, E. Bucher, S.W. Cheong, P. Dai, Z. Fisk, S.M. Hayden, R. Kleiman, T.E. Mason, et.al.: Neutron Scattering and the Search for Mechanisms of Superconductivity Physica C 318 (1999) 9

V. Alberts, J.H. Schön and E. Bucher: Material Properties and Growth Mechanism of CuInSe2 Prepared by H2Se Treatment of Metallic Alloys J. of Materials Science: Materials in Electronics 10 (1999) 469

C.A. Bolle, V. Aksyuk, F. Pardo, P.L. Gammel, E. Zeldov, E. Bucher, R. Bole, D.J. Bishop and D.R. Nelson: Observation of Mesoscopic Vortex Physics Using Micromechanical Oscillators Nature 399 (1999) 43

G. Hahn, C. Zechner, M. Rinio, P. Fath, G. Willeke and E. Bucher: Enhanced Carrier Collection Observed in Mechanically Structured Silicon with Small Diffusion Length J. Appl. Physics 86 (1999) 7179

H. Hohl, A.P. Ramirez, C. Goldmann, G. Ernst, B. Wölfing and E. Bucher: Efficient Dopants for ZrNiSn-Based Thermoelectric Materials J. Opt. Soc. Am. B. Opt. Physics 16 (1999) 1697 J. Phys.: Condens. Matter 11 (1999) 1697

M. Klenk, O. Schenker, U. Probst and E. Bucher: X-Ray Fluorescence Measurements of Thin Film Chalcopyrite Solar Cells Sol. Energy Mater. Sol. Cells 58 (1999) 299

J. Köhler, M. Albrecht, C.R. Musil and E. Bucher: Direct Growth of Nanostructures by Deposition Through an Si3N4 Shadow Mask Physica E 4 (1999) 196

A. Kress, R. Kühn, P. Fath, G. Willeke and E. Bucher: Low-Cost Back Contact Silicon Solar Cells IEEE Transactions on Electron Devices 46 (1999) 2000

J. Krustok, J.H. Schoen, H. Collan, M. Yakushev, J. Maedasson and E. Bucher: Origin of the Deep Center Photoluminescence in CuGaSe2 and CuInS2 Crystals J. Appl. Physics 86 (1999) 364

R. Kühn, A. Boueke, A. Kress, P. Fath, G. Willeke and E. Bucher: Characterization of Novel Mono- and Bifacially Active Semi-Transparent Crystalline Silicon Solar Cells IEEE Transactions on Electron Devices, 46 (1999) 2013

P.K. Mishra, V.C. Sahni, S.S. Banerjee, S. Ramakrishnan, A.K. Grover, P.L. Gammel, D.J. Bishop, E. Bucher and M.J. Higgins: Step Change in Equilibrium Magnetization Across the Peak Effect in 2H-NbSe2 Physica C, Superconductivity 322 (1999) 145

G. Nicolay, R. Claessen, F. Reinert, V.N. Strocov, S. Hüfner, H. Gao, U. Hartmann and E. Bucher: Fast Epitaxy of Au and Ag on WSe2 Surface Science 432 (1999) 95

J.H. Schön and E. Bucher: Characterization of Intrinsic Defect Levels in CuInS2 Phys. Stat. Sol. (a) 171 (1999) 511

J.H. Schön and E. Bucher: Comparison of Point Defects in CuInSe2 Single Crystals Sol. Energy Mater. Sol. Cells 57 (1999) 229

J.H. Schön, V. Alberts and E. Bucher: Control and Passivation of Vse Defect Levels in H2Se-Selenized CuInSe2 Thin Films Semicond. Sci. Technol. 14 (1999) 657

J.H. Schön, J. Oestreich, O. Schenker, H. Riazi-Nejad, M. Klenk, N. Fabre, E. Arushanov and E. Bucher: n-type Conduction in Ge-Doped CuGaSe2 Appl. Phys. Lett. 75 (1999) 2969

St. Schöttl, E.A. Schuberth, K. Flachbart, J.B. Kycia, J.I. Hong, D.N. Seidman, W.P. Halperin, J. Hufnagl and E. Bucher: Anisotropic dc Magnetization of Superconducting UPt

3 and Antiferromagnetic Ordering Below 20 mK

Phys. Rev. Lett. 83 (1999) 2378


T. Straub, T. Finteis, R. Claessen, P. Steiner, S. Huefner, P. Blaha, C.S. Oglesby and E. Bucher: Charge-Density-Wave Mechanism in 2H-NbSe2: Photoemission Results Phys. Rev. Lett. 82 (1999) 4504

T. Straub, R. Claessen, T. Finteis, P. Steiner, S. Huefner, C.S. Oglesby and E. Bucher: On the Peierls Transition in 2H-NbSe2

Physica B 261 (1999) 981

Group of Prof. W. Dieterich

J. Buschle, P. Maass and W. Dieterich: Exact density functionals in one dimension J. Phys. A.: Math. Gen. 33 (2000) L41

W. Dieterich, O. Dürr, P. Pendzig, A. Bunde and A. Nitzan: Percolation Concepts in Solid State Ionics Physica A 266 (1999) 229

H. P. Fischer, J. Reinhard, W. Dieterich and A. Majhofer: Subsurface ordering kinetics at Cu3Au (001) Europhys. Letters 46 (1999) 755

R. Kutner and P.Maass: Random Flights with Quenched Noise Amplitudes Lectures Notes in Physics vol. 519 (Springer, Heidelberg, 1999) p. 61

P. Maass: Towards a Theory for the Mixed Alkali Effect in Glasses J. Non-Cryst. Solids 255 (1999) 35

P. Maass, M. Meyer and A. Bunde: Percolation Effects in Mixed �/�´´-Alumina Crystals Physica A 266 (1999) 197

P. Maass, B. Rinn and W. Schirmacher: Hopping Dynamics in Random Energy Landscapes: An Effective Medium Approach Phil. Mag. B 79 (1999) 1915

B. Rinn, K. Zahn, P. Maass and G. Maret: Influence of Hydrodynamic Interactions on the Dynamics of Long-Range Interacting Colloidal Particles Europhys. Lett. 46 (1999) 537

J. Rottler and P. Maass: Second Layer Nucleation in Thin Film Growth Phys. Rev. Letters 83 (1999) 3490

Group of Prof. G. Ganteför

S. Burkart, N. Blessing, B. Klipp, J, Müller, G. Ganteför and G. Seifert: Experimental verification of the high stability of Al13H: a building block of a new type of cluster material Chem. Phys. Lett. 301 (1999) 546

S. Burkart, N. Blessing and G. Ganteför: Indication of a size-dependent transition from molecular to dissociative chemisorption on clusters Phys. Rev. B 60 (1999) 15639

M. Maus, G. Ganteför and W. Eberhardt: The electronic structure and the band gap of nano-sized silicon particles: competition between quantum confinement and surface reconstruction Appl. Phys. A 70 (1999) 535

Group of Prof. P. Leiderer

S. Briaudeau, Z. Demirplak, V. Dobler, J. Boneberg and P. Leiderer: Two-dimensional pressure measurement with nanosecond time resolution Appl. Phys. A 69 [Suppl.] (1999) 557

V. Dobler, R. Oltra, J.P. Boquillon, M. Mosbacher, J. Boneberg and P. Leiderer: Surface acceleration during dry laser cleaning Appl. Phys. A 69 [Suppl.] (1999) 335


J. Eisenmenger, J. Schiessling, U. Bolz, B.-U. Runge, P. Leiderer, M. Lorenz, H. Hochmuth, M. Wallenhorst and H. Dötsch: Nondestructive magneto-optical characterization of natural and artificial defects on 3'' {HTSC} wafer at liquid nitrogen temperature IEEE Trans. Appl. Sup. 9 (1999) 1840

J. Eisenmenger, J. Zimmermann, J. Schiessling, U. Bolz, B.-U. Runge and P. Leiderer: Reversible laser annealing and magneto-optical characterization of HTSC thin films Advances in solid state physics 39 (1999) 403

M. Mosbacher, N. Chaoui, J. Siegel, V. Dobler, J. Solis, J. Boneberg, C.N. Afonso and P. Leiderer: A comparison of dry and steam laser cleaning of Si wafers Appl. Phys. A 69 [Suppl.] (1999) 331

M. Mosbacher, V. Dobler, J. Boneberg and P. Leiderer: Universal threshold for the steam laser cleaning of submicron spherical particles from silicon Appl. Phys. A 70 (2000) 669

M. Ochmann, H.-J. Münzer, J. Boneberg and P. Leiderer: A circuit for measuring the gap voltage of a scanning tunneling microscope on a nanosecond time scale Rev. Sci. Instrum. 70 (1999) 2049

P. Pasquet, R. del Coso, J. Boneberg, P. Leiderer, R. Oltra and J.P. Boquillon: Laser cleaning of oxide iron layer: Efficiency enhancement due to electrochemical induced absorptivity change Appl. Phys. A 69 [Suppl.] (1999) 727

Group of Prof. G. Maret

A. Burchard, M. Deicher, V.N. Fedoseyev, D. Forkel-Wirth, R. Magerle, V.I. Mishin, D. Steiner, A. Stötzler, R. Weissenborn and Th. Wichert: Electric Field Gradients of Acceptor-Donor Pairs in Semiconductors Hyperfine Interactions 120/121 (1999) 389

A. Burchard, E.E. Haller, A. Stötzler, R. Weissenborn and M. Deicher: Annealing of Ion Implanted GaN Physica B 273-274 (1999) 96

I.D. Desnica-Frankovic, U.V. Desnica, A. Stötzler and M. Deicher: Study of Microscopic Mechanisms of Electrical Compensation of Donors in CdS by Fast Diffusors (Cu, Ag, Li or Au) Physica B 273-274 (1999) 887

U.V. Desnica, I.D. Desnica-Frankovic, R. Magerle, A. Burchard and M. Deicher: Experimental Evidence of the Self-compensation Mechanism in CdS J. Crystal Growth 197 (1999) 612

U.V. Desnica, I.D. Desnica-Frankovic, R. Magerle and M. Deicher: Compensating Defects and Electrical Activation of Donors in CdS Physica B 273-274 (1999) 907

M. Dietrich, D. Degering, J. Kortus, S. Unterricker, M. Deicher, A. Burchard and R. Magerle: Semiconductors with Structurally Determined Vacancies – PAC Studies Hyperfine Interactions 120/121 (1999) 359

M. Dietrich, A. Burchard, D. Degering, M. Deicher, J. Kortus, R. Magerle, A. Möller, V. Samokhvalov, S. Unterricker and R. Vianden: Quadrupole Interaction in Ternary Chalcopyrite Semiconductors: Experiments and Theory Z. Naturforsch. A 55 (2000) 256

J. Hamann, A. Burchard, M. Deicher, T. Filz, V. Ostheimer, F. Strasser, H. Wolf and Th. Wichert: Luminescence and Influence of Defect Concentration on Excitons in 197Hg/197Au Doped CdT Physica B 273-274 (1999) 870

C. Ronning, H. Hofsäss, A. Stötzler, M. Deicher, E.P. Carlson, P.J. Hartlieb, T. Gehrke, P. Rajagopal and R.F. Davis: Photoluminescence characterization of Mg implanted GaN Proc. MRS 1999 Fall Meeting, Symposium W: GaN and Related Alloys, Materials Research Symposium Proc. Vol. 595 (2000) in press and http://nsr.mij.mrs.org/5S1/W11.44/

A. Stötzler, R. Weissenborn and M. Deicher: Identification of Ag and Cd Photoluminescence in 111Ag Doped GaN Physica B 273-274 (1999) 144

http://nsr.mij.mrs.org/5S1/W11.44/


A. Stötzler, R. Weissenborn and M. Deicher: Identification of As, Ge and Se Photoluminescence in GaN Using Radioactive Isotopes Proc. MRS 1999 Fall Meeting, Symposium W: GaN and Related Alloys Materials Research Symposium Proc. Vol. 595 (2000) in press and http://nsr.mij.mrs.org/5S1/W12.9/

Group of Prof. P. Nielaba

D. Fischer and P. Nielaba: Phase diagram of a model alloy with lattice misfit Physica A 279 (2000) 287

H.L. Frisch, S. Puri and P. Nielaba: Enrichment of surfaces in contact with stable Binary Mixtures: The Case with Long-Ranged Surface Fields J. Chem. Phys. 110 (1999) 10514

P. Nielaba: Quantum Effects in Adsorption at Surfaces in "Computational Methods in surface and colloid Science", eds. M. Borówko, Marcel Dekker (Inc., New York, 2000) p. 77

P. Nielaba, P. Fratzl and J.L. Lebowitz: Growth of ordered domains in a computer model alloy with lattice misfit J. Stat. Phys. 95 (1999) 23

M. Reber, D. Löding, M. Presber, Chr. Rickwardt and P. Nielaba: Quantum simulations in materials science: molecular monolayers and crystals Comp. Phys. Commun. 121-122 (1999) 524

Chr. Rickwardt, P. Nielaba and K. Binder: Path integral Monte Carlo simulation of silicon and silicates in:“Computational Modeling and Simulation of Materials“, eds. P. Vincenzini, A. Degli Esporti (Techna, Srl, Italy,1999) p. 411

C. Rickwardt, M. Presber, D. Löding, M. Reber and P. Nielaba: Path Integral Monte Carlo simulations in Materials Science in “Path integrals from peV to TeV“, eds. R.Casalbuoni, R. Giachetti, V. Tognetti, R. Vaia, P. Verrucchi (World Scientific, Singapore, 1999) p. 446

S. Sengupta, P. Nielaba, M. Rao andK. Binder: Elastic constants from microscopic strain fluctuations Phys. Rev. E 61 (2000) 1072

S. Sengupta, P. Nielaba andK. Binder Elastic moduli, dislocation core energy and melting of hard disks in two dimensions Phys. Rev. E 61 (2000) 6294

Group of Prof. G. Schatz

C. Bernhard, J.L. Tallon, Ch. Niedermayer, T. Blasius, A. Golnik, E. Brücher, R.K. Kremer, D.R. Noakes, C.E. Stronach and E. J. Ansaldo: Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr2GdCu2O8 studied by muon spin rotation (µSR) and DC-magnetization Phys. Rev. B 59 (1999) 14099

T. Blasius, Ch. Niedermayer, J.L. Tallon, D.M. Pooke, A. Golnik and C. Bernhard: Evidence for a two-stage melting transition in the vortex matter of Bi2Sr2CaCu2O8+� single crystals obtained by muon spin rotation Phys. Rev. Lett. 82 (1999) 4926

T. Blasius, Ch. Niedermayer, J. Schiessling, U. Bolz, J. Eisenmenger, B.-U. Runge, P. Leiderer, J. L. Tallon, D. M. Pooke, A. Golnik, C.T. Lin and C. Bernhard: Investigations of the vortex matter in Bi2Sr2CaCu2O8�� single crystals AIP Conference Proceedings 483 (1999) p. 201

T. Blasius, Ch. Niedermayer, J. L. Tallon, D. M. Pooke, A. Golnik, D.R. Noakes, C.E. Stronach, E. J. Ansaldo, R.W. Henn, C.T. Lin and C. Bernhard: Muon spin rotation studies of the vortex matter in the high-Tc-superconductor Bi2Sr2CaCu2O8�� Acta Physica Polonica A 96 (1999) 245

http://nsr.mij.mrs.org/5S1/W12.9/


J.M. Gil, H.V. Alberto, R.C. Vilao, P.J. Mendes, L.P. Ferreira, N. Ayres de Campos, A. Weidinger, J. Krauser, Ch. Niedermayer and S.F.J. Cox: Novel muonium state in CdS Phys. Rev. Lett. 83 (1999) 5294

J.M. Gil, P.J. Mendes, L.P. Ferreira, H.V. Alberto, R.C. Vilao, N. Ayres de Campos, Y. Tomm, A. Weidinger, Ch. Niedermayer, M.V. Yakushev, R.D. Tomlinson, S.P. Cotrell and S.F.J. Cox: Modelling hydrogen in CuInSe2 and CuInS2 solar cell materials using implanted muons Phys. Rev. B 59 (1999) 1912

T. J. Jackson, C. Binns, M. Birke, E. M. Forgan, E. Morenzoni, Ch. Niedermayer, H. Glückler, A. Hofer, T. Prokscha, T. M. Riseman, A. Schatz, J. Litterst, G. Schatz and H. P. Weber: Superparamagnetic relaxation in iron nanoclusters measured by low energy muon spin rotation J. Phys. Condensed Matter 12 (2000) 1399

Ch. Niedermayer, E.M. Forgan, H. Glückler, A. Hofer, E. Morenzoni, M. Pleines, T. Prokscha, T.M. Riseman, M. Birke, T.J. Jackson, J. Litterst, M.W. Long, H. Luetkens, A. Schatz and G. Schatz: Direct Observation of a Flux Line Lattice Field Distribution across an YBa2Cu3O7�� surface by Low Energy Muons Phys. Rev. Lett. 83 (1999) 3932

Ch. Niedermayer, C. Bernhard, T. Blasius, A. Golnik, A. Moodenbaugh and J. I. Budnick: Doping dependence of the antiferromagnetic correlations in La2-xSrxCuO4 and Y1-xCaxBa2Cu3O6 Advances in Solid State Physics 39 (1999) 413

Ch. Niedermayer, T. Blasius, C. Bernhard, A. Golnik, A. Moodenbaugh and J. I. Budnick: Hole doping dependence of the antiferromagnetic correlations in La2-xSrxCuO4 and Y1-xCaxBa2Cu3O6 AIP Conference Proceedings 483 (1999) p. 292

Ch. Niedermayer: Muon Spin Rotation studies of doping in high-Tc-superconductors Acta Physica Polonica A 96 (1999) 213

T. Prokscha, M. Birke, E.M. Forgan, H. Glückler, A. Hofer, T.J. Jackson, K. Küpfer, J. Litterst, E. Morenzoni, Ch. Niedermayer, M. Pleines, T.M. Riseman, A. Schatz, G. Schatz, H.P. Weber and C. Binns: First µSR studies on thin films with a new beam of low energy positive muons at energies below 20 keV Hyperfine Interactions 120/121 (1999) 569

T. Prokscha, M. Birke, E.M. Forgan, H. Glückler, A. Hofer, T.J. Jackson, H. Luetkens, J. Litterst, E. Morenzoni, Ch. Niedermayer, M. Pleines, T.M. Riseman, A. Schatz, G. Schatz and H.P. Weber: µSR studies on thin films with low-energy muons at energies between 0 and 30 keV Proceedings of the XXXIII winter school of PNPI, St. Petersburg, Russia (1999) p. 313

C.E. Stronach, D.R. Noakes, X. Wan, Ch. Niedermayer, C. Bernhard and E.J. Ansaldo: Zero-field muon-spin-rotation study of hole antiferromagnetism in low-carrier-density Y1-xCaxBa2Cu3O6 Physica C 311 (1999) 19


2. Conference Contributions


11th Int. Photovoltaic Science and Engineering Conference (PVSEC-11) Sapporro / Japan, 10. - 24.9.99

A. Boueke, R. Kühn, P. Fath, G. Willeke and E. Bucher: Latest Results of Semitransparent POWER Silicon Solar Cells

P. Fath, N. Ohimiya, S. Bajyou, R. Busch, G. Willeke, K.H. Priewasser, H. Shiomi and E. Bucher: A Novel High Throughput Texturization System for the Crystalline Silicon Solar Cell Industry

A. Kress, P. Fath, G. Willeke and E. Bucher: Low Cost Back Contact Silicon Solar Cells

S. Keller, S. Scheibenstock, P. Fath, G. Willeke and E. Bucher: Progress in Monolithic Series Connection of Wafer Based Crystalline Silicon Solar Cells by the Novel ‘HighVo’ (High Voltage) Cell concept


DPG Frühjahrstagung Festkörperphysik 1999 Münster / Germany, 22. - 26.3.99

F. Eurich, W. Dieterich, H. P. Fischer und P. Maass: Spinodale Entmischung in dünnen Filmen

M. Kessler, J. Reinhard und W. Dieterich: Dynamische Monte-Carlo-Simulationen des ABV-Modells zu oberflächennahen Ordnungsphänomenen in Cu3Au-Legierungen

7th Int. Workshop on Disordered Systems Andalo, Trento / Italy, 1. - 4.3.99

P. Maass: New Results in the Theory of Dispersive Transport in Disordered Media

Int. Workshop on Computer-Aided Analysis of Dynamical Structures and Defects Dresden / Germany, 20. - 29.7.99

P. Maass: Spinodal Decomposition Modes in Confined Geometries

VIII Int. Conference on Hopping and Related Phenomena Murcia / Spain, 7. - 10.9.99

B. Rinn, U. Braunschweig, P. Maass and W. Schirmacher: Effective Medium Approximation for Energy Dependent Hopping on a Lattice


63. Physikertagung der DPG 1999 Heidelberg / Germany, 25. - 19.3.99

S. Burkart, N. Blessing und G. Ganteför Größenabhängiger Übergang von atomarer zu molekularer Wasserstoffchemisorption in kleinen Ti-Clustern

J. Müller, S. Burkart und G. Ganteför: Quantisierung des Valenzbandes in AunH1

--Clustern: einzelne Wasserstoffatome, die sich als Goldatom tarnen



B. Klipp, J. Müller, M. Grass und G. Ganteför: Deposition von massenselektierten Nanopartikeln

E. Oettinger, D. Stolcic und G. Ganteför: Clustersputtern: Bearbeiten und Polieren mittels Nanosandstrahlen

Clustertreffen Sassnitz auf Rügen / Germany, 27.9. - 1.10.99

N. Blessing, S. Burkart und G. Ganteför: Die elektronische Struktur von TimCm

--Clustern („Metcars“) und Rückschlüsse auf ihren Wachstumsmechanismus

S. Burkart, N. Blessing und G. Ganteför: Größenabhängiger Übergang von molekularer zu dissoziativer Wasserstoff-Chemisorption an kleinen Ti-Clustern

S. Burkart, N. Blessing, J. Müller, B. Klipp, G. Ganteför und G. Seifert: Änderung der elektronischen Struktur von Al-Clustern bei Wasserstoff-Chemisorption

S. Burkart und G. Ganteför: Einzelne Wasserstoff-Atome, die sich als Goldatom tarnen

G. Ganteför: Photoelektronenspektroskopie an massenselektierten Clusteranionen: Neue Physik bei hoher Massen- und Zeitauflösung

P. Gerhardt, D. Stolcic, E. Oettinger und G. Ganteför: Clustersputtern: Bearbeiten und Polieren mittels Nanosandstrahlen

B. Klipp, M. Grass, U. Lutz, T. Schlenker, C. Peucker und G.Ganteför: Deposition massenselektierter Aluminiumcluster auf Oberflächen

S. Minemoto, J. Müller, S. Burkart, R. Fromherz und G. Ganteför: Femtosekunden-Pump/Probe-Photoelektronenspektroskopie an massenseparierten Clusteranionen

Int. Symposium on Cluster and Nanostructure Interfaces Richmond, Virginia / USA, 25. - 28.10.99

S. Burkart, N. Blessing, B. Klipp, J. Muller, G. Ganteför and G. Seifert: The Change of the Electronic Structure of Aluminum Clusters upon Hydrogen Chemisorption

S.Burkart, N.Blessing and G.Ganteför: Size dependent transition from molecular to dissociative hydrogen chemisorption on small Ti clusters

S.Burkart, G.Ganteför, H.Groenbeck and W.Andreoni: H-chemisorption on Aun- - clusters: experiment and theory

N.Blessing, S.Burkart and G.Ganteför: The electronic structure of TinCm clusters and implications on their growth mechanism



U. Bolz, J. Eisenmenger, B.-U. Runge, J. Schiessling und P. Leiderer: Magnetische Instabilität in HTSL-Dünnschichten

M. Mosbacher V. Dobler, J. Boneberg undP. Leiderer: Reinigung kommerzieller Si-Wafer: Vergleich der Effizienzen für Dry- und Lasercleaning

EMRS'99 Strasbourg / France, 31.5. - 4.6.99

J. Siegel, M. Mosbacher, N. Chaoui, V. Dobler, J. Solis, J. Boneberg, P. Leiderer and C.N. Afonso: Influence of pulse duration on dry and steam laser cleaning efficiency of Si surfaces


Laser'99 München / Germany, 17.6.99

J. Boneberg, M. Mosbacher, V. Dobler, P. Leiderer, N. Chaoui, J. Siegel, J. Solis andC.N. Afonso: Nano- and picosecond laser cleaning of silicon surfaces

LPHYS99 Budapest / Hungary, 2 .- 6.7.99

B.-U. Runge: Magneto-optic studies of superconductors down to nanosecond time resolution

Cola'99 Göttingen / Germany, 19.-23. 7. 99

R. del Coso, M. Bruttel, J. Boneberg, P. Leiderer, J. Solis and C.N. Afonso: Nanosecond time-resolved thermal radiation measurements of Si upon ns-laser annealing

P. Pasquet, R. del Coso, J. Boneberg, P. Leiderer, R. Oltra and J.P. Boquillon: Study of optical properties of oxidized iron surfaces for modelling of laser cleaning efficiency

S.Briaudeau, Z.Demirplak, V.Dobler, J.Boneberg and P.Leiderer: Two-dimensional pressure measurements with nanosecond time resolution

M. Mosbacher, N. Chaoui, J. Siegel, V. Dobler, J. Solis, J. Boneberg, C.N. Afonso and P. Leiderer: A comparison of dry and steam laser cleaning of Si surfaces

LT22 Helsinki / Finland, 4. - 11.8.99

U. Bolz, J. Eisenmenger, J. Schiessling, B.-U. Runge and P. Leiderer: Magnetic Instability in YBa2Cu3O7-� Films



A. Stötzler, A. Burchard, R. Weissenborn und M. Deicher: Identifizierung von Defektzuständen in GaN durch radioaktive Isotope

V. Ostheimer, A. Burchard, M. Deicher, T. Filz, J. Hamann, S. Lany, H. Wolf undTh. Wichert: Einbau und Komplexbildung von Ag Atomen in CdTe

T. Filz, J. Hamann, A. Burchard, M. Deicher, V. Ostheimer, C. Schmitz, F. Strasser, H. Wolf und Th. Wichert: Identifizierung der Photolumineszenz von Akzeptor-Niveaus in II-VI Halbleitern durch Verwendung von radioaktiven Isotopen

XV Int. Symposium on Nuclear Quadrupole Interactions (XV NQI 99) Leipzig / Germany, 25. - 20.7.99

M. Dietrich, A. Burchard, D. Degering, M. Deicher, J. Kortus, R. Magerle, A. Möller, V. Samokhvalov, S. Unterricker and R. Vianden: Quadrupole Interaction in Ternary Chalcopyrite Semiconductors: Experiments and Theory

20th Int. Conference on Defects inSemiconductors (ICDS-20) Berkeley / USA, 26. - 30.7.99

A. Burchard, E.E. Haller, A. Stötzler, R. Weissenborn, and M. Deicher: Annealing of ion-implanted GaN

I.D. Desnica-Frankovic , U.V. Desnica, A. Stötzler, and M. Deicher: Study of microscopic mechanisms of electrical compensation of donors in CdS by fast diffusors (Cu, Ag, or Au)


U.V. Desnica, I.D. Desnica-Frankovic , R. Magerle, and M. Deicher: Compensating defects and electrical activation of donors in CdS

J. Hamann, A. Burchard, M. Deicher, T. Filz, V. Ostheimer, F. Strasser, H. Wolf, ISOLDE Collaboration, and Th. Wichert: Luminescence and Influence of Defect Concentration on Excitons in 197Hg/197Au doped CdTe

A. Stötzler, R. Weissenborn, and M. Deicher: Identification of Ag and Cd photoluminescence in 111Ag-doped GaN

Arbeitstreffen “Forschung mit nuklearen Sonden und Ionenstrahlen” Berlin / Germany, 6. - 8.10.99

A. Stötzler, R. Weissenborn, A. Burchard, M. Deicher und E.E. Haller: Dotierung von GaN durch Ionenimplantation: PAC- und Photolumineszenzuntersuchungen

H. Wolf, A. Burchard, M. Deicher, T. Filz, Z. Guan, J. Hamann, S. Lany, St. Lauer, V. Ostheimer, F. Strasser, and Th. Wichert: Structures and Defects in Nanocrystalline Metals and II-VI Semiconductors

9th Int. Conference on II-VI Compounds Kyoto / Japan, 1. - 5.11.99

J. Hamann, A. Burchard, M. Deicher, T. Filz, S. Lany, V. Ostheimer, F. Strasser, H. Wolf, and Th. Wichert: Identification of Ag-Acceptors in 111Ag/111Cd doped ZnTe and CdTe

Materials Research Society 1999 Fall Meeting Boston / USA, 29.11. – 3.12.99 Symposium W: GaN and Related Alloys Research

C. Ronning, H.C. Hofsäss, A. Stötzler, M. Deicher, E.P. Carlson, P.J. Hartlieb, T. Gehrke, P. Rajagopal, and R.F Davis: Photoluminescence Characterization of Mg Implanted GaN

A. Stötzler, R. Weissenborn, and M. Deicher: Identification of As, Ge and Se Photoluminescence in GaN Using Radioactive Isotopes



D. Löding und P. Nielaba: Pfadintegral Monte Carlo-Untersuchungen adsorbierter Molekülschichten auf Graphit

P. Nielaba: Quanten Monte Carlo-Simulationen in der Materialforschung

Mesoscale Modelling Manchester / UK, 20. - 29.6.99

J. Hoffmann and P. Nielaba: MC and Path-Integral MC-Simulations of Pore Condensates


1999 University of Miami Conference in High Temperature Superconductivity Miami / USA, 06.1. - 13.1.99

Ch. Niedermayer, T. Blasius, C. Bernhard, A. Golnik, A. Moodenbaugh and J. I. Budnick: Hole doping dependence of the antiferromagnetic correlations in La2-xSrxCuO4 and Y1-xCaxBa2Cu3O6

T. Blasius, Ch. Niedermayer, J. Schiessling, U. Bolz, J. Eisenmenger, B.-U. Runge, P. Leiderer, J. L. Tallon, D. M. Pooke, A. Golnik, C.T. Lin and C. Bernhard: Investigation of the vortex-matter in Bi2Sr2CaCu2O8��


Workshop on applications of low energy muons to solid state phenomena, Paul Scherrer Institut Villigen / Switzerland, 17.2 - 19.2.99

Ch. Niedermayer: Applications of muons in condensed matter physics

Treffen des Verbundes Wasserstoff und Myonen in niedrigdimensionalen Systemen München / Germany, 22.3. - 26.3.99

M. Pleines, A. Hofer, Ch. Niedermayer, G. Schatz, E.M. Forgan, T.J. Jackson, M. Long, T.M. Riseman, H. Glückler, E. Morenzoni, T. Prokscha, H.P. Weber, M. Birke, J. Litterst, H. Luetkens andA. Schatz: Status des LE µ+ Projektes und Experimente an dünnen supraleitenden Filmen


A. Maier, M. Dippel, W. Evenson, G. Filleböck, H. Wider und G. Schatz: Schmelzverhalten von Indiumclustern WSe2

Ch. Niedermayer, C. Bernhard, T. Blasius, A. Golnik, A. Moodenbaugh and J.I. Budnick: Doping dependence of the antiferromagnetic correlations in La2-xSrxCuO4 and Y1-xCaxBa2Cu3O6

XXXIV Zakopane School of Physics: Condensed matter studies by nuclear methods Zakopane / Poland, 9.5 - 15.5.99

M. Pleines, A. Hofer, Ch. Niedermayer, G. Schatz, E.M. Forgan, T.J. Jackson, M. Long, T.M. Riseman, H. Glückler, E. Morenzoni, T. Prokscha, H.P. Weber, M. Birke, J. Litterst, H. Luetkens andA. Schatz: µ+SR studies on thin HTCSC films with slow muons at energies between 0 and 30 keV

G. Schatz: Low-Dimensional Magnetism Studied with Nuclear Probes

CMNM 99, Couches Minces et Nanostructures Magnétiques Dieppe / France, 3.6 - 5.6.99

M. Maret, M. Albrecht, J. Köhler, R. Poinsot, J.M. Tonnerre, J.F. Berar and E. Bucher: Structure et magnétisme de couches minces d’alliages épitaxiés sur Pt(111)

Specialized Colloque Ampere - EPR, NMR and NQR in Solid State Physics: Recent Trends Pisa / Italy, 14.6 - 18.6.99

Ch. Niedermayer, E.M. Forgan, H. Glückler, A. Hofer, E. Morenzoni, M. Pleines, T. Prokscha, T.M. Riseman, M. Birke, T.J. Jackson, J. Litterst, M.W. Long, H. Luetkens, A. Schatz and G. Schatz: First experiments with very slow polarized muons

MOS 99, Physics and Chemistry of Molecular and Oxide Superconductors Stockholm / Sweden, 28.7. - 2.8.99

Ch. Niedermayer, T. Blasius, C. Bernhard, A. Golnik, A. Moodenbaugh and J. I. Budnick: Hole doping dependence of the antiferromagnetic correlations in La2-xSrxCuO4 and Y1-xCaxBa2Cu3O6

T. Blasius, Ch. Niedermayer, J.L. Tallon, D.M. Pooke, A. Golnik and C. Bernhard: Investigation of the vortex state in Bi2Sr2CaCu2O8�� single crystals

8th International Conference on Muon Spin Rotation, Relaxation and Resonance Les Diablerets / Switzerland 30.8 - 3.9.99

M. Birke, A. Schatz, J. Litterst, E. Morenzoni, H. Glückler, T. Prokscha, A. Hofer, M. Heuberger, Ch. Niedermayer, G. Schatz, E.M. Forgan and T.J. Jackson: LEµ+-SR measurements on thin Ni-films

T. Blasius, Ch. Niedermayer, D.M. Pooke, D.R. Noakes, C.E. Stronach, E.J. Ansaldo, A. Golnik and C. Bernhard: Low temperature vortex structures of the mixed state in underdoped Bi2Sr2CaCu2O8��


E.M. Forgan, T.J. Jackson, T.M. Riseman, H. Glückler, E. Morenzoni, T. Prokscha, H.P. Weber, A. Hofer, K.Küpfer, Ch. Niedermayer, M. Pleines, G. Schatz, M. Birke, J. Litterst, H. Luetkens, A. Schatz andC. Binns: Superparamagnetism of iron clusters studied with low energy muon spin rotation

H. Glückler, E. Morenzoni, T. Prokscha, M. Birke, E.M. Forgan, A. Hofer, T.J. Jackson, J. Litterst, H. Luetkens, Ch. Niedermayer, M. Pleines, T.M. Riseman, A. Schatz and G. Schatz: Range of low energy muons in matter

M. Pleines, M. Birke, E.M. Forgan, H. Glückler, A. Hofer, T.J. Jackson, J. Litterst, M. Long, H. Luetkens, E. Morenzoni, Ch. Niedermayer, T. Prokscha, T.M. Riseman, A. Schatz and G. Schatz: Low Energy µSR study of the field distribution of a flux line lattice crossing an YBa2Cu3O7�� surface

H. Luetkens, M. Birke, E.M. Forgan, H. Glückler, B. Handke, A. Hofer, T.J. Jackson, J. Korecki, M. Kubik, J. Litterst, E. Morenzoni, Ch. Niedermayer, M. Pleines, T. Prokscha, M. Przybylski, T.M. Riseman, A. Schatz, G. Schatz andT. Slezak: Magnetism of thin chromium films studied with LE-µ+SR

E. Morenzoni, H. Glückler, T. Prokscha, M. Birke, E.M. Forgan, A. Hofer, T.J. Jackson, J. Litterst, H. Luetkens, Ch. Niedermayer, M. Pleines, T.M. Riseman, A. Schatz andG. Schatz: Low Energy µSR at PSI: Present and future

18th European Conference on Surface Science Wien / Austria, 21.9. - 24.9.99

A. Maier, M. Dippel, W. Evenson, G. Filleböck, V. Gimple, H. Wider and G. Schatz: Melting Behavior of Indium Islands On WSe2

Arbeitstreffen “Forschung mit nuklearen Sonden und Ionenstrahlen” Berlin / Germany, 6. - 8.10.99

Ch. Niedermayer, E.M. Forgan, H. Glückler, A. Hofer, E. Morenzoni, M. Pleines, T. Prokscha, T.M. Riseman, M. Birke, T.J. Jackson, J. Litterst, M.W. Long, H. Luetkens, A. Schatz, unsG. Schatz: Erste Experimente mit niederenergetischen Myonen

TRIUMF ISAC Scientific Symposium Vancouver / Canada, 12.12.1999

G. Schatz: Surface and Interface Studies with Nuclear Probes


3. Lectures


K. Peter: LPE (Liquid Phase Epitaxy) Silicon Solar Cells Universität von Nechatel / Switzerland


W. Dieterich: Stochastische Modelle zum Ionentransport in komplexen Systemen Max Planck – Institut für Festkörperphysik, Stuttgart, 10.3.99

W. Dieterich: Spinodal decomposition: ordering and wall effects University of Tel Aviv, Tel Aviv / Israel, 22.4.99

P. Maass: Anomaler Ionentransport in Gläsern Technische Universität München, München, 1.7.99

P. Maass: Anomaler Ionentransport in Gläsern Technische Universität Berlin, Berlin, 20.7.99

P. Maass: Second Layer Nucleation in Thin Film Growth Service de Physique de l’État Condensé, CEA-Saclay, Paris / France, 14.9.99

P. Maass: Nucleation on Top of Islands in Epitaxial Growth École Polytechnique Fédérale de Lausanne (EPFL), Lausanne / Switzerland, 16.12.99


G. Ganteför: Elektronische Struktur und chemische Eigenschaften massenselektierter Mikrocluster TU-München, 20. 7. 99


J. Boneberg: Laser Cleaning of Silicon Yokneam / Israel, July 99

B.-U. Runge: Magnetooptische Untersuchungen an Hochtemperatur-Supraleitern und dünnen metallischen Filmen Seminar, Universität Bonn, 17.12.99

M. Mosbacher: Laser Cleaning of Silicon Wafers Instituto de Optica, Madrid / Spain, January 99

M. Mosbacher: Nanosecond and Picosecond Laser Cleaning Johannes Kepler Universität, Linz / Austria, October 99,


M. Deicher: Solid State Physics and Life Sciences CERN Academic Training Program “Lecture Series on Physics at ISOLDE” Geneva / Switzerland, 12.3.99


P. Nielaba: Quantensimulationen in der Materialforschung ETH Zürich, 7.12.1999


T. Blasius: Investigation of the vortex-matter in high-Tc superconductors with the technique of µSR, magneto-optics and dc magnetization measurements Seminar, Max-Planck-Institut für Festkörperphysik, Stuttgart, 12.2.99


Ch. Niedermayer: Antiferromagnetismus und Supraleitung in Hoch-Tc-Supraleitern Kolloquium, Universität Köln, 19.5.99

Ch. Niedermayer: Erste Experimente mit niederenergetischen Myonen Kolloqium, Universität Mainz, 16.11.99

G. Schatz: Niederdimensionaler Magnetismus untersucht mit nuklearen Sonden Kolloquium, Universität Wittemberg-Halle und MPI Mikrostrukturphysik, Halle / Germany, 14.1.99

G. Schatz: Ionenstrahltechniken zur Analyse von Oberflächen, Festkörpern und Polymeren Vorlesung, Graduiertenkolleg Universität Ulm, 3.2.99


4. Theses


M. Albrecht: Strukturelle und physikalische Eigenschaften von 3d-Übergangsmetallfilmen auf Ru(0001) und

Pt(111) und alternative Wege zur Nanostrukturierung

PhD thesis, May 1999

T. Bistritschan: Low temperature growth of poly crystalline silicon by hot wire chemical vapor deposition

Diploma thesis, September 1999

G. Hahn: RGS-Silizium – Materialanalyse und Solarzellenprozessierung

PhD thesis, June 1999

(http://www.ub.uni-konstanz.de/kops/volltexte/1999/303/303_1.pdf)

G. Hanna: Hochleistungs-CIGS-Solarzellen mit gradiertem Bandabstand

Diploma thesis, April 1999

V. Mornhinweg: Numerische Modellierung der elektromagnetischen Felder in offenen Laser-Kavitäten

Diploma thesis, Novenber 1999

T. Pernau: Lebensdauerbestimmung und ortsaufgelöste Messung der Quantenausbeute an kristallinen Silizium

Diploma thesis, March 1999


M. Pfeiffer: Die Finite-Differenzen-Methode zur Lösung Floquet-transformierter Mawellgleichungen im

Zeitbereich mit Anwendung in der Simulation periodischer optoelektronischer Bauelemente

Diploma thesis, May 1999


A. Tikart: Verlustanalyse und Optimierung von Emitter Wrap-Through Silizium Solarzellen

Diploma thesis, January 1999

S. Scheibenstock: Monolithisch intergriete kristalline Silizium-Solarzellen

Diploma thesis, August 1999


U. Braunschweig: Hopping-Transport in ungeordneten Energielandschaften

Staatsexamensarbeit, November 1999

J. Buschle: Statistische Mechanik für eindimensionale Gittergase mit Randfeldern – exakte Ergebnisse

Diploma thesis, March 1999

J. Reinhard: Korrelationen und Ordnungskinetik an planaren Oberflächen von Legierungsmodellen

PhD thesis, December 1999


J. Rottler: Wachstumsprozesse an Oberflächen und Nukleation der zweiten Lage




C. Peucker: Aufbau einer Hochleistungs-Clusterionenquelle

Staatsexamensarbeit, November 1999







P. Löffler: Untersuchung der Wachstumssequenzen kleiner Cluster

PhD thesis, November 1999



F. Burmeister: Nanolithographie mit kolloidalen Masken

PhD thesis, June 1999

Z. Demirplak: Optimierung einer zweidimensionalen optischen Druckmeßmethode zur Charakterisierung von

Stoßwellen

Diploma thesis, January 1999

J. Eisenmenger: Reversible Laserstrukturierung und magnetooptische Charakterisierung von

Hochtemperatursupraleiter-Dünnschichten

PhD thesis, January 1999

R. Fromherz: Laserinduzierte Bewegung von STM-Spitzen

Diploma thesis, April 1999

C. Häfner: Zeitaufgelöste MOKE-Untersuchungen an dünnen Magnetfilmen


U. Huber: Streuung von Oberflächenplasmonen an Kolloidpartikeln

Diploma thesis, May 1999

M. Ochmann: Plasmonnahfeldmikroskopie – evaneszente Lichtstreuung an einer metallischen Spitze

PhD thesis, November 1999

S. Rottmair: Herstellung und Charakterisierung von Nanostrukturen mittels Kolloidmonolagenlithografie

Staatsexamensarbeit, June 1999


D. Fischer: Phasendiagramm einer binären Modelllegierung mit elastisscher Wechselwirkung:

eine Monte Carlo-Studie

Diploma thesis, December 1999

M. Gerstenmaier: Modellierung von Wachstumskinetik auf eindimensionalen periodischen Oberflächen

Staatsexamensarbeit, December 1999

S. Haase: Pfadintegral Monte Carlo Untersuchungen zu Mischungen einfacher Quantenfluide

Diploma thesis, September 1999

M. Schwarz van Doorn: Quanten-Monte-Carlo-Simulationen von N2 Teilchen auf Graphit


W. Strepp: Monte Carlo Simulationen zu Phasenumwandlungen in Harte-Kugel-Systemen in äußeren

(periodischen) Potentialen



T. Blasius: Strukturelle und dynamische Eigenschaften der Vortex-Materie in Hochtemperatur-Supraleitern

PhD thesis, December 1999





V. Gimple: Untersuchungen zur Surfactantwirkung von Indium beim Wachstum von Kobalt auf Kupfer (111)

Diploma thesis, November 1999

M. Wendlandt: Equilibrium Structures in Thin Films of Binary Polymer Blends

Diploma thesis, February 1999


IV. Staff and Guests

Groups:

Professor Dr. Ernst Bucher Phone: +49-(0)-7531-88-2073 Fax: +49-(0)7531-88-3895 E-mail: [email protected] WWW: http://www.uni-konstanz.de/FuF/Physik/Bucher/lshome.htm Secretary: Angela Schellinger, Phone: +49-(0)7531-88-2086

Professor Dr. Wolfgang Dieterich Phone: +49-(0)-7531-88-3816 Fax: +49-(0)7531-88-3760 E-mail: [email protected] Secretary: Renate Beck, Phone: +49-(0)7531-88-3815

Professor Dr. Gerd Ganteför Phone: +49-(0)-7531-88-2067 Fax: +49-(0)-7531-88-3091 E-mail: [email protected] WWW: http://scampi.physik.uni-konstanz.de/ Secretary: Carina Hahn, Phone: +49-(0)-7531-88-3783

Professor Dr. Paul Leiderer Phone: +49-(0)-7531-88-3793 Fax: +49-(0)-7531-88-3091 E-mail: [email protected] WWW: http://www.uni-konstanz.de/FuF/Physik/Leiderer/homede.htm Secretary: Christiane Ehmann, Phone: +49-(0)-7531-88-3792

Professor Dr. Georg Maret Phone: +49-(0)-7531-88-4151 Fax: +49-(0)-7531-88-3090 E-mail: [email protected] WWW: http://hera.physik.uni-konstanz.de/Start.htm Secretary: Christiane Bustamante, Phone: +49-(0)-7531-88-3864

Professor Dr. Peter Nielaba Phone: +49-(0)-7531-88-4259 Fax: +49-(0)-7531-88-4462 E-mail: [email protected] WWW: http://www.uni-konstanz.de/nielaba/ Secretary: Yolanda Fischer, Phone: +49-(0)-7531-88-4272

Professor Dr. Günter Schatz Phone: +49-(0)-7531-88-3540 Fax: +49-(0)-7531-88-3090 E-mail: [email protected] WWW: http://www.agschatz.physik.uni-konstanz.de/ag/index.htm Secretary: Christiane Bustamante, Phone: +49-(0)-7531-88-3864


http://www.uni-konstanz.de/FuF/Physik/Bucher/lshome.htm



http://scampi.physik.uni-konstanz.de/


http://www.uni-konstanz.de/FuF/Physik/Leiderer/homede.htm


http://hera.physik.uni-konstanz.de/Start.htm


http://www.uni-konstanz.de/nielaba/


http://www.agschatz.physik.uni-konstanz.de/ag/index.htm


Scientific Staff

The letters in parentheses indicate the group: (Bu) = Bucher (Di) = Dieterich (Ga) = Ganteför (Le) = Leiderer (Ma) = Maret (Ni) = Nielaba (Sc) = Schatz

Dr. M. Albrecht (Sc) Manfred [email protected]

N. Blaschek (Bu) [email protected]

Dr. T. Blasius (Sc) [email protected]

U. Böck (Le) [email protected]

U. Bolz (Le) [email protected]

Priv. Doz. Dr. J. Boneberg (Le) [email protected]

A. Boueke (Bu) [email protected]

T. Braun (Le) [email protected]

M. Braxmaier (Le) [email protected]

Dr. St. Briaudeau (Le)

S. Burkart (Ga) [email protected]

Dr. F. Burmeister (Le) [email protected]

J. Buschle (Di) [email protected]

R. del Coso (Le)

Priv. Doz. Dr. M. Deicher (Ma) [email protected]

Z. Demirplak (Ni)

Dr. M. Dietrich (Ma) [email protected]

M. Dippel (Sc) [email protected]

V. Dobler (le) [email protected]

O. Dürr (Di) [email protected]

F. Eurich (Di) [email protected]

K. Faika (Bu) [email protected]

Dr. P. Fath (Bu) [email protected]

B. v. Finckenstein (Bu) [email protected]

B. Fischer (Bu) [email protected]

D. Fischer (Ni) [email protected]

R. Fromherz (Le) [email protected]

P. Geiger (Bu) [email protected]

Ch. Gerhards (Bu) [email protected]

P. Gerhardt (Ga) [email protected]

M. Gerstenmaier (Ni) [email protected]

V. Gimple (Sc) [email protected]

S. Haase (Ni) [email protected]

C. Häfner (Le) [email protected]

G. Hahn (Bu) [email protected]

mailto:Manfred [email protected]

































K. Hartel (Le) [email protected]

A. Hauser (Bu) [email protected]

St. Heinrichs (Di) [email protected]

M. Heuberger (Sc) [email protected]

T. Höhr (Di) [email protected]

J. Hötzel (Bu) [email protected]

J. Hoffmann (Ni) [email protected]

H. Hoppe (Sc) [email protected]

U. Huber (Le)

F. Huster (Bu) [email protected]

W. Jooß (Bu) [email protected]

St. Keller (Bu) [email protected]

M. Kessler (Di) [email protected]

M. Klenk (Bu) [email protected]

B. Klipp (Ga) [email protected]

J. Köhler (Bu) [email protected]

R. Kopecek (Bu) [email protected]

A. Kreß (Bu) [email protected]

R. Kühn (Bu) [email protected]

M. Lämmlin (Sc) [email protected]

D. Löding (Ni) [email protected]

Dr. P. Löffler (Ga)

U. Lutz (Ga)

Priv. Doz. Dr. P. Maaß (Di) [email protected]

U. Mack (Ni) [email protected]

A. Maier (Sc) [email protected]

Dr. M. Maret (Sc) [email protected]

M. Mosbacher (Le) [email protected]

A. Müller (Le) [email protected]

J. Müller (Le) [email protected]

H.-J. Münzer (Le) [email protected]

Priv. Doz. Dr. Ch. Niedermayer (Sc) [email protected]

Dr. M. Ochmann (Le) [email protected]

J. Oestreich (Bu) [email protected]

E. Oettinger (Ga) [email protected]

P. Pasquet (Le)

Th. Pernau (Bu) [email protected]

Dr. K. Peter (Bu) [email protected]

C. Peuker (Ga) [email protected]

M. Pleines (Sc) [email protected]

D. Pohl (Le)

Dr. U. Probst (Bu) [email protected]

J. Reinhard (Di) [email protected]

H. Riazi-Nejad (Bu) [email protected]









































B. Rinn (Di) [email protected]

J. Rottler (Di) [email protected]

S. Rottmaier (Le) [email protected]

Dr. B.-U. Runge (Le) [email protected]

F. Scheffler (Di) [email protected]

St. Scheibenstock (Bu) [email protected]

A. Schellinger (Bu) [email protected]

O. Schenker (Bu) [email protected]

J. Schiessling (Le) [email protected]

Th. Schlenker (Le)

M. Schwarz van Doorn (Ni) [email protected]

D. Sontag (Bu) [email protected]

Dr. M. Spiegel (Bu) [email protected]

A. Stötzler (Ma) [email protected]

D. Stolcic (Ga) [email protected]

W. Strepp (Ni) [email protected]

B. Terheiden (Bu) [email protected]

F. Treubel (Sc) [email protected]

S. Volz (Bu) [email protected]

M. Wagner (Bu) [email protected]

R. Weissenborn (Ma) [email protected]

H. Wider (Sc) [email protected]

O. Yavas (Le)

J. Zimmermann (Le)

Technical Staff

W. Betz (Le)

Ch. Goldbach (Le)

A. Fischer (Bu)

H. Görig (Le)

M. Keil (Bu)

G. Kragler (Bu)

St. Kühne (Bu)

J. Lax (Ma)

Ch. Marckmann (Bu)

W. Möbius (Ma)

H. Riazi Nejad (Bu)

F. Richard (Bu)

Guests

Prof. Dr. V. Alberts Johannesburg / South Africa 1.2.99 – 30.4.2000

Prof. E. Ansaldo Saskatoon / Canada 27.8. - 22.9.99

Prof. N. Ayres de Campos Coimbra / Portugal 20.12. - 21.12.99























Johan Bekker Johannesburg / South Africa 1.6. – 31.7.99

4.11. – 22.12.99

Prof. Binder Universität Mainz 26.1. - 27.1.99

Prof. Dr. J. P. Bouchaud S.P.E.C. Saclay / France 22.6. – 23.6.99

Prof. J.I. Budnick Storrs / USA 16.2. - 21.2.99

26.6. - 5.7.99

7.12. - 16.12.99

M. Chenene Johannesburg / South Africa 1.4. – 31.5.99

Prof. W.E. Evenson Brigham Young University, Provo / USA 1.8.98 – 1.8.99

Prof. Dr. H. L. Frisch Albany / USA 7.7. – 19.7.99

Prof. J. Gil Coimbra/Portugal 20.12. - 21.12.99

Prof. Dr. L. Kulyuk Kishenev / Moldavien 1.7. – 31.8.99

Dr. M. Lekka Institute of Nuclear Physics, Cracow / Poland 30.6. – 23.7.99

Dr. A. Majhofer Warschau / Poland 16.8. – 29.8.99

Dr. M. Marszalek Institute of Nuclear Physics, Cracow / Poland 30.6. – 23.7.99

Dr. S. Minemoto University of Tokyo /Japan 1.4. - 1.10.99

Dr. D.M. Pooke Lower Hutt / New Zealand 26.7. - 28.7.99

Dr. Mathias Presber Arthur Andersson 12.1.-22.1.99

Dr. Martina Reber Dresdner Bank 22.11.-23.11.99

Prof. Surajit Sengupta Madras / India and Mainz 10.5.-12.0.99

16.6.-18.6.99

23.11.-26.11.99

Prof. R.L. Rasera Baltimore County / USA 25.5. - 4.6.99

Prof. J.-M. Triscone Genf / Switzerland 5.5. - 6.5.99

Annual Report 1999 - uni-konstanz.de

Documents

Transcript of Annual Report 1999 - uni-konstanz.de