Characterization of the n=1 image state on Ni(111) with twophoton photoemissionAlex V. Hamza and Glenn D. Kubiak Citation: Journal of Vacuum Science & Technology A 8, 2687 (1990); doi: 10.1116/1.576651 View online: http://dx.doi.org/10.1116/1.576651 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/8/3?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in The observation of unoccupied quantum-well states in Bi thin film grown on Si(111) by two-photonphotoemission spectroscopy Appl. Phys. Lett. 99, 243101 (2011); 10.1063/1.3666857 Time-resolved two-photon photoemission spectroscopy of image potential states: A phenomenological approach J. Chem. Phys. 115, 4314 (2001); 10.1063/1.1388625 Electronic excited state of NO adsorbed on Cu(111): A twophoton photoemission study J. Chem. Phys. 102, 2970 (1995); 10.1063/1.468605 Imagepotentialinduced resonance on Al(111) observed by twophoton photoemission spectroscopy J. Vac. Sci. Technol. A 12, 2201 (1994); 10.1116/1.579114 Summary Abstract: Characterization of empty states on C(111) (diamond) (2×1) via angleresolved twophotonphotoemission J. Vac. Sci. Technol. A 6, 814 (1988); 10.1116/1.575136

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Characterization of the n = 1 image state on Ni(111) with two~photon photoemission

Alex V. Hamza and Glenn D. Kubiak Sandia National Laboratories, Livermore, California 94551-0969

(Received 15 September 1989; accepted 25 September 1989)

The binding energy and E(k l: ) dispersion of the n = ! image potential state have been measured on Ni( 111) using angle-resolved two-photon photoemission. The binding energy, en ~ ;, is found to be 0.8 ± 0.1 eV. The E(k ll ) dispersion relation is well described by an effective mass m* 1m, of 1.0 ± 0.1, in disagreement with earlier momentum-resolved inverse photoemission results, b~t in agreement with theoretical predictions based on a phase analysis of the n = 1 image state wave function. Two-photon photoemission spectra were also recorded for Ni(lll )-p(2 X 2 )-0, showing th~ disappearance of the image state and the emergence of a weak, broad, nondispersive feature attnbutable to two-photon photoemission from states originating near the Fermi level.

I. INTRODUCTION

Within the projected band gaps of metal surfaces exists an infinite, Rydberg-like series of electronic states converging on the vacuum level. Electrons in these so-called "image" states can be viewed as being trapped in the potential energy well formed by the barrier into the bulk on the crystal side, and the long~range image potential barrier on the vacuum side. Several reviews on both the theoretical and experimen­tal characterization of image states exist. 1,2 These states are only weakly coupled to the local properties of the surface because the maxima in the associated wave function proba­bility amplitudes are well removed from the surface layer (e.g., 2.5 and 10 A for n = 1 and n = 2, respectively3 ). Ad­ditionally, the effects of the dynamical response of the sur­face electrons on the potential have been calculated to be on the order of only 2%.3,4 For image states far from the pro­jected bulk band edges, therefore, the electron energy versus surface paranel wave-vector dispersion relation E(k

jl) is

nearly that of a free electron. When an image state lies close in energy to a projected band edge, however, the effective mass (m*) characterizing E(kil ) can be much larger or smaller than the free-electron value me . This situation has been treated with phase analysis models,5,6 which correctly predict the large values of m* determined experimentally for then = IstatesonCu(1lO)/ Ni(l1O),7 anclAg(111)8 and the small value found on Cu ( 100).8 In contrast, phase anal­ysis models do not predict the large value of m* = 1.6me

which has been reported for the n = 1 image state on Ni(111).9 This state would be expected to yield m*~1.0 me __ because it is not particularly close to a projected band edge ( - 1.5 e V below the L 1 edge at f). The purpose of this paper is to resolve this apparent discrepancy by determining with high resolution the E(k ll ) dispersion relation for the n = I image state on Ni( 111),

The unoccupied electronic band structure of Ni ( 111) has been studied previously with momentum-resolved inverse photoemission OPE) ') and angle-resolved two-photon pho­toelectron spectroscopy,lO In the former work, the image state E( kll ) dispersion was determined with a resolution of 0.8 eV, yielding an effective mass of 1.6mc _ • Individual members (n = 1,2,3'00') of the series were not resolved. The subsequent two-photon photoemission experiments were

performed with a resolution sufficient to resolve individual series members and yielded a binding energy for the n = 1 state (En _ 1) of 0.80 ± 0.03 eV. E(k 1i ) was not measured for Ni ( 111) in this work.

Subsequent examination of the Ni image state binding en­ergies and E(kll ) relations using a phase analysis modelll

suggested that an effective mass of 1.6m e _ could be recon­ciled on Ni ( 111) if the position of the n = 1 state was close to the rather fiat Ll projected bulk band edge. No quantita­tive estimates of m* were presented for Ni( 111) at the time, however. The flattening of E(k ll ) by a projected band edge was later shown to occur on Ag ( III ), which supports an n = 1 state ~O.2 eV below L j • This state disperses with m* = 1.3me _,8 a value consistent with the phase-shift modeL Within this model, the value of m* increases as the separation between band edge and image state decreases. If t~e state crosses the edge, as on Cu(1l1),12 E(k ll ) again Yields a value of m'" which is within a few percent of me _ . It is therefore puzzling that the value of m~ ~ 1 on Ni(11l) could be significantly greater than on Ag ( 111 ), even though the n = 1 state on the latter surface is- 7 times doser to the L1 edge than on Ni( 111).

In the present work, we have used angle-resolved two~ photon photoemission to determine with high resolution the binding energy and E(k'i ) dispersion relations for the n = 1 image state 011 Ni( 111). We find a value of En ~ 1 which is equal within the experimental uncertainty limits of the ear­lier two-photon work. The value of m* we extract from E( kll ) is equal to 1.0 me _ to within the experimental accu­racy, in sharp contrast to the value of 1.6me _ found using inverse photoemission. Using the phase analysis model with accepted bulk band structure parameters and the measured Ni(1ll) work function (¢Ni(1:1))' we calculate m* to be equal to the new experimental value of l.Ome _

II. EXPERIMENTAl..

The apparatus has been described in detail in an earlier paper13; only the essential components will be described here. Experiments were performed with an angle-resolved two-photon photoelectron time-of-flight (TOF) spectrom~ eter. The sample is mounted on a manipulator which precise­ly rotates both the azimuthal angle about the surface normal

2687 J. Vac. Sci. Technol. A 8 (3), May/Jun 1990 0734-2101/90/032687-05$01.00 @ 1990 American Vacuum Society 2681

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2688 A. V. Hamza and G. D. Kubiak: Characterization of the n= 1 image state on Ni(111) 2688

and the polar angle (8) such that the sample normal can be varied from 0° to ± 80° with respect to the fixed TOF collec­tion axis. Measurements of E(kn ) are performed by rotating the sample polar angle along both the r-K and r-M azi­muths (as defined by electron diffraction). The overall in­strumental resolution is ~ 100 meV at an electron kinetic energy of 5 eV.

The Ni ( 111) sample surface, oriented to ± 1°, is prepared via standard metallurgical techniques and is subsequently sputtered and annealed in an ultra-high vacuum chamber having a nominal base pressure of 7 X 10 - !! Torr. The sur­face temperature T, can be varied from 35 to 1500 K. Sample cleaning employs repetitive cycles of oxidation at P02 = 2.0X 108 Torr and Ts = 760 K to remove carbon, fol­lowed by Ar -t bombardment at Ts = 950 K to remove the resulting oxygen. Surface cleanliness is determined with Au­ger electron spectroscopy, while long-range order is verified by the existence of sharp, low-background low-energy elec­tron diffraction (LEED) images. The p (2 X 2) -0 overlayer was prepared by dosing the surface with O2 at 1 X 10 - 8 Torr while simultaneously monitoring the LEED pattern. Dosing was halted when the sharpestp(2 X 2) pattern was achieved, typically in 1 min.

Excitation and photoionization wavelengths were pro­duced using the frequency-doubled and mixed output of a Nd3 + :YAG-pumped, pulsed dye laser. In the present work, the photoexcitation and photoionization frequencies are identical (i.e., single-color, two-photon ionization). In gen­eral, however, these two frequencies are independently vari­able, as are their polarizations. Much of the recent time­resolved two-photon photoemission has been performed in this two-color mode,14--16 for example. Binding energy and dispersion measurements were made using hv = 5.063 eV (frequency-doubled DeM laser dye mixed with 1064 nm Nd3 + :YAG radiation) for the n = 1 image state. One-pho­ton photoemission spectra are obtained using light at hv = 6.49 eV, produced via stimulated Raman scattering (SRS) in H2 gas at 6 atm. Temporal pulsewidths are typical­ly 6-8 ns for frequency-doubled and frequency-doubled and mixed laser outputs, whereas radiation produced in the SRS cell exhibits a - 4 ns pulse width. The laser polarization is varied from pure s polarized to p polarized using a Babinet­Solei! compensator. Measurements of the n = 1 state were performed at laser fluences below 4 mJ cm - 2 so as to mini­mize the effects of space charge broadening and shifting of spectral features (see examples below).

iii, EXPERIMENTAL RESULTS

As a test of the experimental procedures and to establish the value of ¢Ni(lll) on the Ni(111) surface, one-photon photoemission measurements were performed as a function of (j using hv = 6.49 e V. Typical spectra acquired in p polar­ization for the [1 TOJ direction are shown in Fig. 1. The pro­jected bulk majority-spin bands of A3 symmetry can be seen just below the Fermi level EF • Establishing accurately the position of EF is difficult for Ni surfaces due to the intense emission from these nearby direct transitions. We have sim­ply defined the position of E F in these spectra by comparison

J. Vac. Sci. Techno!. A, Vol. 8, No.3, May/Jun 1990

240

200

-III ft - 160 '2 :::)

.ci -22.so

... 120 < -15.00 - j >-- -7.5° 'en 80 l c: Q) 0.00 -.5 7.50

40 15.0°

22.5° 0

-1.5 ·1 -0.5 0 0.5

Binding Energy (eV)

FIG. I. Angle-resolved one-photon photoelectron spectra recorded as a function of angle along the [110 J (rK) azimuth for clean Ni ( 111 ). A photon energy of 6.49 eV was employed in p polarization at a laser pulse energy density well below the point at which space charge effects become important «O.016pJ/cm2

).

with the published data of Himpsel, Knapp, and Eastman, 17 rather than use a gold film prepared in situ, as is commonly done. From the width of the one-photon photoelectron spec­trum a value of ¢Ni( l! I) = 5.15 e V is obtained, consistent with previous measurements. 10.17

The most intense feature seen in Fig. 1 derives from sur­face state emission. This surface state disperses downward from - 0.25 to - 0.50 eV with increasing parallel wave

vector in the r K direction between f and 0.16ksRz [kSBZ = 1.68 A -! = surface Brillouin zone (SBZ) boundary at

K], in agreement with the earlier work of Himpsel and East­man. IS The surface state dispersion measured along the

r M direction is identical to that shown in Fig. 1 to within the experimental uncertainty. The projected bulk bands of AI symmetry. which lie at - 0.9 eV, are absent from the spectra of Fig. 1 because the direct transitions to LI are not observed until hv = 6.8 eV, approximately 0.3 eV higher than used here.

To prepare a transient population in the n = 1 image state, transitions are excited from the occupied surface state dis­cussed above. The resonant photon energy connecting this state and the n = 1 image state at the center of the SBZ is 4.69 eV, as determined in the high-resolution two-photon photoemission work of Giesen et al.1O The objective of the present study is to characterize the dispersion of the image state, which requires that values of kll > 0 be accessed from the ground state. Photon energies greater than 4.69 eVare necessary, as shown in Fig. 2. Through scattering, the image state parabola is fined from the maximum energy deter­mined by the value of hv in the photoexcitation step, down to

the energy at zone center F. 19 Experimentally, the variation in binding energy as a function of kll is obtained by holding

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2689 A. V. Hamza and G. D. Kubiak: Characterization of the n = 1 image state on Ni( 111) 2689

~~~~~~~~~EF M

FIG. 2. Schematic diagram of the projected bulk band structure and the filled and empty surface states on Ni( lIl). A photon energy of 5.1 eV is used to prepare a transient population in the n = 1 image state at kil > O. Photoionization is performed with a second photon at this energy to deter­mine the E(k ll ) dispersion relation.

the excitation energy fixed and measuring the kinetic energy as a function of 8. Although such "indirect" photoemission is convenient for determining E(k ll ), its use is limited. This is a result of the increasingly rapid depopulation of the excit­ed state as the energy along the parabola is increased,14 i.e., the electron temperature cannot be increased without limit.

Figure 3 shows two-photon photoelectron kinetic energy

-m :!:::: c:

::;)

.c Lo.

<2: ->-== UJ s:: Q) -I:

400

300

100

o 3.5

e

4.0 4.5 5.0 Final State Energy (eV)

FIG. 3. Angle-resolved two-photon photoelectron kinetic energy spectra recorded as a function of angle along the {2IT] ( I'M ) azimuth for the n = 1 image state on Ni ( 11 J ). The data are plotted as a function of final state energy relative to (above) the vacuum level and each spectrum is separately normalized. The absolute intensities decrease by a factor of-l0 between f) = 0° and e = 15°. The data recorded along the [110] azimuth (not shown) are identical to within the experimental uncertainty.

J. Vac. Sci. Techno!. A, Vol. 8, No.3, May/Jun 1990

spectra obtained for the n = 1 state over a range of emission

angles in therAi" direction using hv = 5.063 eV. Theinten­sity of the n = 1 state is found to decrease by approximately a factor of 10 between kl! = 0 and Ikll l-O.4 A -1, an aspect which is not obvious from the normalized spectra shown in Fig. 3. A plot of the binding energy relative to the vacuum level (E v) versus kll is shown in Fig. 4. As is evident, the E(k ll ) relation is parabolic over the range of kil we have explored and is well described by an effective mass equal to the free-electron mass, m* = 1.0 ± 0.1m. . The value of €n~ I at zone center is 0.77 ± 0.05 eV, in agreement with both the earlier two-photon photoemission \0 and the inverse photoemission measurements.9 Our value of m* is not in agreement with the value of 1.6m,,_ found in the inverse photoemission measurements, however, as is illustrated by comparison between the data and the dashed parabola drawn in Fig. 4.

In an effort to determine whether surface contamination is the cause of the disagreement between the present determin­ation of E(ku ) and that found with inverse photoemission, we have purposely contaminated the sample with oxygen. To obtain a known and controlled surface coverage, we have exposed the sample to O2 until a p(2X2) overlayer is formed, as determined by LEED. We find that the image state is quenched; only a weak, broad peak is seen at all pho­ton energies from 4.4 to 5.5 eV. The kinetic energy of this peak can be fit to the relation K.E. = 2hv - ~Ni(lll)"P(2>;2)-O' suggesting that it derives from indirect transitions of filled states near EF excited through the con­tinuum of surface-projected bulk bands. This is analogous to the situation found previously on Pd ( 111).13

Because two-photon photoelectron spectra involve two sequential one-photon transitions, we are unable to deter­mine whether the spectra intensity of the n = 1 state vanish­es on Ni (111) -p (2 X 2) -0 because the filled initial state is quenched, or if the image state itself is quenched. In princi­ple, if only the filled state is quenched, then the image state would be difficult to detect via two-photon photoemission,

0 -0.1 - -0.2 >

G) - -0.3 » CI -0.4 ... CD

-0.5 r::: w Cl -0.6 .5 -0.7 't) c -0.8 iii

-O.g -1

Ev

m* ::: 1.0 me_

~ ~ '~~~,

'\-' ~""""

-0.4 -0.3 -0.2 -0.1 ° 0.1 0.2 0.3 0.4 k (A -1)

II

FIG. 4. Plot of the n = 1 E(k ll ) dispersion relation along the rM direc­tion. The binding energy is relative to (below) the vacuum level (E v),

Plotted for comparison are the best parabolic fit to the data lm" = me , solid line) and the parabola corresponding to a fit to the data of Ref. 9 (m* = 1.6m" ,dashed line).

•••• • , ••••••• T •• '·· "~.'.'.' •••••••• -••••••••••••••• " •••••• ~ ••••••••••••••••••• _.:.:.:.:.:.; ••• .';.; •••••• >;~ •• ' ••••• ' ••••••••••••• " •••• _ •• " •••••••••• • c •• •• " ••••••••••• _ ••• "._._ •• _ ••••• _ ••• , ••••• , ................. , •• "._._ ••• _ •••••••• , •• ' ••••••••••• Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. Download to IP: 129.49.23.145 On: Thu, 18 Dec 2014 00:08:55

2690 A. V. Hamza and G. D. Kubiak: Characterization of the n= 1 image state on Ni(111) 2690

but not necessarily difficult to detect via inverse photoemis­sion. At present we cannot conclude whether surface conta­mination causes the dispersion of the n = 1 state to flatten on Ni(lll).

Surface photoemission experiments performed with pulsed lasers can be extremely misleading due to effects caused by the high charge densities created in the departing sheet of photoelectrons, diagrammed schematically in the inset of Fig. 5. The resulting "space-charge" shifts and broadening must be carefully avoided for accurate spectro­scopic work. Figure 5 shows a progression of one-photon photoelectron spectra from the clean Ni ( 111) as a function oflaser pulse energy density. As can be seen, the width of the spectrum increases by approximately a factor of 4 between the lowest and highest pulse energy densities employed. Ex­tracting a value of the work function from the width of the spectrum at the higher pulse energies would be meaningless in this example. Moreover, attempting to interpret laser sur­face photochemistry experiments solely on the optical prep­aration of excited states, completely ignoring the presence of a high flux of reasonably energetic electrons, seems especial­ly dubious. Detailed modeling studies of such phenomena will be the subject of future publication. 20

IV. DISCUSSION

The important conclusions to be drawn from the data are that the n = 1 image state on Ni(111) exhibits a binding energy of 0.75 eV and a dispersion characterized by m* = l.Om e ..• It is recognized that the E(kll ) relations for image states are, in general, not parabolic and that the use of an effective mass to describe E( k ll ) may be questionable, For the specific case of n = Ion Ni(lll), however, the dis­persion is well fit by a parabola and we will use effective masses in the following discussion as a convenient short­hand.

Phase analysis models have been used to calculate values of En = 1 and E( kll ) on a number of surfaces. In the case of Ni(111), Garrett and Smith 11 have calculated En ~ 1 = 0.8 eV, a value very close to that observed in both the present and previous two-photon photoemission experiments. Al­though a value of m* was not presented in this model calcu­lation, the large experimental value of 1.6me reported ear­lier was referred to and was rationalized as being due to the close proximity of the n = 1 state to the almost flat top pro­jected band edge. Using the methods presented by Smith,2,6 we have estimated m* for the n = 1 state on Ni( 111) using the Ni band structure parameters described in Ref. 11. We find that phase models yield m* ~ l.Om e _ [± 10% de­pending on the exact form of the phase change upon reflec­tion off the vacuum barrier (see Ref. 6) ]. Significantly larg­er values of m* are obtained only if the image state lies within - 0.7 e V of the top band edge, but not if it lies ~ 1.5 e V from the edge as in the present case. We therefore reiterate the conclusions made in previous studies that phase analysis models yield reasonably accurate predictions of image state binding energies and dispersions. This implies that the dy­namical corrections to the image potential are small for non­zero parallel electron velocities, a view which is supported by several calculations3

,4 as discussed earlier.

J. Vac. Sci. Technol. A, Vol. 8, No.3, MaylJun 1990

250 l' I f>~~ hv:5.5geV

Vi" [,V", ~\ ' .t:: 2

00 I Lv'''"", " \ 1 Laser Energy

~ 150 /JIIIV~ \ \ . :n:'ly

rLLJICm2\

~ r)~r\ \ \ \ \~-l 48

~ 100 gf I ,rr~\I\ \ \ ----==1 15 (/. ~ ,11(i\' " '----j 24 v

] 50 __ Jii 1\L--~--=--1 ;::6 ~e. I Il _____ .~ 0038

o L ). ) J 0.016

0.0 1.0 2.0 3.0 4.0 5.0

Kinetic Energy (eV)

FIG. 5. A series of one-photon photoelectron kinetic energy spectra record­ed for a range of laser pulse energy densities, showing the effects of severe space charge distortion. The TOP tube was biased at + 1 V for these mea­surements.

There are several possible explanations for the discrepan­cy between the value of m* obtained here and that measured using inverse photoemission. The final state in inverse pho­toemission can be viewed as a temporary negative charge state, while in two-photon photoemission the departing pho­toelectron leaves behind a hole. The first possibility might be that the experimental disagreement is a manifestation of the two different final states involved in the respective tech­niques. This appears doubtful since the dispersions mea­sured with either technique are within experimental error for the n = 1 states on Cu (111 ) 12 and Ag (100).8 The second possibility is that since the inverse photoemission measure­ment spans twice the range of kll as the present measure­ment, it therefore probes that part of the dispersion curve which is close to the top bulk band edge where the dispersion is expected to flatten. If this were the case, then the inverse photoemission (IPE) data in the region from - 0.4 A-I < kll < 0.4 A- 1 should show systematically steeper dis­persion than the best overall fit to m* = 1 .6m. _ . Inspecting the data in Fig. 8 of Ref. 9 shows that this is not the case. Finally, the likely explanation for the disagreement between experiments is that the overall experimental momentum res­olution is sufficient only in the present experiments to allow an accurate determination of E(kll ). As pointed out in Ref. 10, poor momentum resolution tends to increase the appar­ent m*.

In conclusion, we find that the dispersion between - 0.4 A l<kll <0.4A- 1 forthen= iimagestateonNi(111)is characterized by m* = 1.0me _. ,in agreement with a phase analysis model but in disagreement with earlier inverse pho­toemission measurements. The binding energy is found to be Ell ~ 1 = 0.77 e V, in agreement both with previous measure­ments and with published phase analysis calculations. We therefore conclude that the n = 1 state on Ni( 111) is in no way anomalous with respect to its E(kl!) dispersion, i.e., that there is no reason to invoke the existence of large ( > 2 %) dynamical or surface corrugation effects in the de­scription of image states on metals.

ACKNOWLEDGMENTS

This work was supported by the United States Depart­ment of Energy under Contract No. DE-AC04-76DP00789.

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2691 A. V. Hamza and G. D. Kubiak: Characterization ofthe n= t image state on Ni(111} 2691

The expert technical assistance of Kurt Berger is gratefully acknowledged. We also thank Dr. N. V. Smith for encour~ agement, and Dr. D. A. Outka and Dr. D. D. Johnson for useful discussions.

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Bucksbaum, Phys. Rev. B 32, 3669 (1985). 15 R. Haight and J. A. Silberman, Phys. Rev. Lett. 62, 815 (1989). JON. J. Halas and J. Bokor, Phys. Rev. Lett. 62,1679 (1989). J7 F. J. Himpsel, J. A. Knapp, and D. E. Eastman, Phys. Rev. B 19, 2872

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(to be published).

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