Photoemission and energy loss spectroscopy on semiconductor surfaces

Surface Science 48 (197.5) 44-58 Q North-Holland Publishing Company

PHOTOEMISSION SEMICONDUCTOR

AND ENERGY LOSS SPECTROSCOPY

ON

SURFACES

J.E. ROWE and H. IBACH* Bell Laborurories, Murray Hill3 New Jersey 079 74, USA

and

H. FROITZHEIM 2. Physikalisches Institut der Technischen

Hochschule,

Aachen,

Germany

The application of multiple experimental techniques to silicon surface studies is discussed. Two specific cases are considered: the chemisorption of oxygen on silicon at coverages up to one monolayer and the intrinsic surface states on cleaved and on annealed Si (111) surfaces. It is shown that by combining electron energy loss spectroscopy and ultraviofet photoemission spectroscopy, one can obtain an approximate energy level model for both occupied and unoccupied states

1. Introduction An understanding of the electronic energy levels of surface atoms is of fundamental importance in a wide range of surface phenomena. A number of new techniques for measuring surface characteristics have been developed over the last decade [ 1,2f. However, the detailed application of these techniques is at the present time in a rapid stage of development. Basic structural parameters such as surface atom bond lenths and bond angles are in general not yet known. Therefore it is useful to correlate experimental results from a variety of different methods in order to begin to understand surface electronic structure. In this paper we report the application of multiple experimental techniques to the same sample surface prepared in ultrahigh vacuum (UHV) p - lo-lo torr. Two different surfaces are considered: the silicon (111) surface with a chemisorbed layer of oxygen and the clean (111) surfaces of silicon prepared by vacuum cleavage or by annealing. The electron states of adsorbed oxygen were found to be essentially independent of surface coverage up to 0 = 1 mono* Also 2. Physikaiisches Institut der Technischen Hochschuie, Aachen, Germany; present address: Kernfors~hung~niage, Jitlich, Germany.

LE. Rowe et al,/Photoemission

and energy loss spectroscopy

4.5

PHOTCM FROh4

RESONANCE LAMP

ELECTRONSFROM VEWF’ORT

Fig. 1. Schematic diagram of the multiple technique apparatus (at Bell Laboratories) used for low resolution ELS, LEED, Auger and photoemission with a resonance lamp. The sample rotates on a 11.5 cm radius to be sequentially positioned at each experimental measurement port.

layer and were quite different from bulk silicon dioxide [3]. The two clean surfaces both have intrinsic surface states but the distribution and energies of surface states are quite different on the two clean surfaces. The preparation of these surfaces was controlled by using Auger electron spectroscopy (AES) and low energy electron diffraction (LEED) to monitor the surface chemical composition and surface crystal structure respectively. The electronic structure of these surfaces was investigated by ultraviolet photoemission spectroscopy (UPS) and by electron energy loss spectroscopy (ELS). To a first approximation, UPS reveals peaks in the density of occupied states and ELS yields transition energies. Thus a combination of UPS and ELS reveals information about the unoccupied as well as occupied electronic states.

2. Experimental

techniques

Most of the experiments were performed in an ionpumped stainless steel UHV system shown schematically in fig. 1. The base pressure was - 5 X IO-l1 torr with the liquid nitrogen titanium sublimation pump cooled. The sample is mounted 11.5 cm off axis and rotates in front of separate ports for each measurement. The LEED optics were operated in a conventional mode and used to visually observe the symmetry of the spot pattern. A single-pass PHI IO-234G Auger analyzer was used for AES and ELS. The AES data was obtained as the first derivative dN/dE of the elec-

46

J.E. Rowe et al./Photoemission

and energy loss spectroscopy

tron energy distribution while for ELS the negative second derivative -d2N/dE2 was used. A PHI 1S-250 double-pass analyzer operated in the retard (constant resolution) mode was used for UPS. The photon source was a windowless microwavepowered resonance lamp with differential pumping which has been described elsewhere [4]. The lamp was operated at a pressure of - 1.5 torr with He. Ne or Ar to provide photon energies tiw = 21.2 eV, 16.8 eV or 11.7 eV respectively. Photoelectron counting rates were typically - 3 X IO4 cps so that UPS data were recorded in a single scan at 0.1 eV per point separation and one second integrating time. The counts were stored in digital form in a PDP-8/L minicomputer which was also used to controle the voltages of the double-pass analyzer. Further data processing such as digital smoothing or computing the difference between two UPS curves could be done on line with the PDP-8/L. The primary reference level for UPS is the initial state corresponding to the vacuum level Evac= 0.The point E = -Rw was determined from the photoemission spectra by a linear extrapolation of the low energy side of the slow scattered electron peak. To insure collection of even the lowest kinetic energy electrons a small (0- 1 eV) negative bias was applied to the sample to overcome any contact potential differences. The necessary voltage compensation was estimated from the energy of secondary electrons produced at the analyzer grids with a higher bias. The estimated error in determining the reference level is less than LO.2 eV. For UPS from clean silicon samples it is more convenient to shift the energy by the photoelectric threshold energy so that the energy zero occurs at the valence band maximum. This was done using published values of the threshold energies [5]. Clean silicon surfaces were prepared by conventional argon bombardment and annealing or by UHV cleavage in a multiple cleavage sample holder which has been previously described [26]. The LEED patterns for the cleaved (111) surfaces usually showed a clear single domain, 2X1 superlattice with no indication of spot splitting due to cleavage steps. The annealed (111) surfaces had the well-known 7X 7 LEED pattern with a low background (diffused scattering) intensity, provided the annealing temperature was above 1000 “K and the cooling rate was sufficiently low (< lOO”K/min) that small lattice disorder was not quenched into the room temperature surface. In addition to the apparatus described above a number of high resolution ELS experiments were performed at the 2. Physikalisches lnstitut der Technischen Hochschule, Aachen using refined a model of the spectrometer previously described [6]. This spectrometer is shown in fig .2 and allows the angle of incidence to be changed from O-90” and for specular reflection from 45-90”. The angular resolution in the plane of incidence is 0.7” and perpendicular to this plane the angular aperture is about 2”. The monochromator and analyzer consist of 127” cylindrical electrostatic deflectors with a mean radius of 35 mm. Further details of this spectrometer are described elsewhere [6].

41

LE. Rowe et al./Photoemission and energy loss spectroscopy

Fig. 2. Schematic diagram of the high resolution ELS aparatus (at the 2. Physikalisches Institut der Technischen Hochschule, Aachen, Germany).

3. Studies

of oxygen adsorption on silicon

3.1. ELS experiments Electron energy loss spectroscopy by the bulk loss function,

- Im

measures characteristic

excitations

described

(1)

W(q,a)l,

and by the surface loss function, -Im

{l/[e(q,a)

+ 111,

(2)

for excitation energy, EL = hw, and momentum p = Aq. For low primary energies, Ep = 50 - 200 eV, the details of inelastic scattering are not yet completely understood. However, previous work has shown that to a good approximation, one may let q + 0 and use the optical dielectric function E(O,W) [3,7]. Thus one expects to observe bulk transitions similar to optical absorption which measures Im [E(U)] instead of Im (I/e). This is shown in fig. 3 where the negative second derivative of the electron energy distribution is given for E, = 100 eV. Three different surface conditions are

48

LE. Rowe et al.~Pho~~emiss~on and energy loss spectroscopy

‘0.4 i

cl

i,

/ 4

8 ENERGY,

MONOLAYER OF OXYGEN

I

12 EL (eV)

L

16

; 3

Fig. 3. Second derivative electron energy loss spectra at Ep = 100 eV for silicon (111) surfaces after (a) Ar+-ion bombardment, (b) annealed to produce a sharp 7X7 LEED pattern, and (c) at 0 = 0.4 monolayers of adsorbed oxygen, corresponding to (a) clean silicon but disordered due to Arf ion bombardment, (b) clean annealed silicon (11 I) with a 7X7 LEED pattern, and the after adsorption of 0.4 monolayer of oxygen. The bulk transitions found in these curves are the E, interb~d transition near 3.5 eV, the E, interband transition near 5 eV, the bulk plasmon oxcillation near 17 eV and the surface plasmon oscillation near 11 eV. In addition, there are surface state transitions S, , S, and Sg near 2 eV, 8 eV, and 15 eV, respectively, which are reduced in intensity by oxygen adsorption [8]. The apparent increase in S, is due to the presence of an oxygen-induced transition as shown in fig. 4 where ELS results for several oxygen coverages, 0, are given. The E, and .!Yzbulk interband transitions are also apparently enhanced due to nearby oxy gen transitions. At approximately one-fourth of a monolayer of oxygen the surfaceplasmon loss peak splits into two peaks which increase their separation with increasing coverage. This is due to an oxygen transition near 11 eV which is essentially the same energy as the silicon surface plasmon transition. A more detailed analysis has been previously given [ 31. shown

49

J.E. Rowe et a~.~~hotoemissionand energy loss spectroscopy

% Si(111)+02 A

CLEAN

ENERGY

LOSS

kVl

Fig. 4. Second derivative electron energy loss spectra for increasing coverage of oxygen adsorp tion at primary energy Ep - 100 eV. The oxygen coverage B is given in monolayers where 0 = 1 corresponds to a saturation of the rapid chemisorption stage.

3.2. URS experiments In ultraviolet

photoemission

spectrsocopy

the measured

spectrum

is given by

where Aw is the photon energy causing transitions from the initial state energies Ei to the final state energies Ef and E is the photoelectron energy. \I’$* is the square of a momentum matrix element representing the optical transition strength and T(Ef> is the probability of escape into the solid angle of the photoelectron analyzer. In this paper we shall assume that all these factors are approximately constant SO that only the summation over the initial state delta function 6 (E - Ei) is important. If this is true, then UPS measures the density of occupied states within the escape depth of the photoelectron. For many surface problems the available data suggest

50

J.E. Rowe et al./Photoemission

and energy loss spectroscop)

+ 02 .2

ev

CLEAN 7x7 8=0.26

e =0.52

4 i

8:l.O , -20

/ -15

/

1

-10 E - EVA,

-5

1 0

(eV)

Fig. 5. Photoemission spectra of silicon (111) surfaces at photon energy ??w = 21.2 eV for resolution AE = 0.4 eV. Curve 1 is the clean surface spectrum multiplied by a factor of two and curves 2-4 are differences between the oxygen exposed surface and the clean surface for increasing coverage. Four oxygen (2~) orbitals are indicated by the vertical lines at -8.3 eV, -11.9 eV, -15.1 eV and -18.4 eV with respect to the vacuum level.

that the density of states is the most important factor if a large angular-aperture analyzer is used and the photons are incident at oblique incidence [9] so that strong angular emission effects [ 10,111 and polarization selection rules in IPifl 2 are approximately averaged over. Fig. 5 shows the UPS curve for a clean silicon (111) 7X7 surface. Data for various coverages of adsorbed oxygen (see curves 2-4) are shown as difference spectra between the adsorbed and clean surfaces. The photoyield from the oxygen associated states at 8 = 1 monolayer is about 5 times that of the clean surface. Four peaks are observed at -8.3 eV, - 11.9 eV, - 15.1 eV and - 18.4 eV with respect to the vacuum level for adsorbed oxygen. The energies of these peaks are independent of coverage for 0 < 1 and it is concluded that oxygen adsorbs in a single binding state. This is in agreement with observations of the vibrational spectrum [ 121. 3.3. Energy level model Having established the energies of the surface orbitals and the transition energies, one may try to combine this information and possibly arrive at some conclusions

LE. Rowe et al./Photoemission

and energy loss spectroscopy

51

0

t

x =4.6 eV

3.5 ev

I 1 1Iev

-8.3

-12

Z

k 7.2ev

si to2

11.9

4

-15.1

-16

Fig. 6. Approximate energy level diagram for chemisorbed oxygen on a silicon surface obtained by combining the UPS initial state peaks and the ELS transitions (shown as vertical lines). The inserts show the band bending at the surface and the conduction band density of states for amorphous silicon.

about the final states that are involved in the observed electronic transitions. Such an attempt is made in fig. 6 for three of the observed transitions with UPS peaks shown as broad lines. The insert in fig. 6 displays the density of states of amorphous silicon [ 13 3 and the surface band bending. the electron affinity was determined by a linear extrapolation of the valence band photoemission density of states for the initially covered surface. The conduction band density of states is structureless, apart from the step at the bottom, due to the lack of long range order [ 131. The energy loss spectrum (fig. 4) shows the oxygen transitions as peaks rather than steplike shapes. Therefore, the final state must have a well defined energy. We believe that this final state is an exciton near the bottom of the conduction band. The origin of the 5.0 eV transition is not yet understood, but it may be due to transitions from the broad UPS band (-8.3 to -10.5 eV) to the same excitonic final state as the 3.5,7.2, and 11 eV transitions. It is surprising that no transition is observed from the - 18.4 eV state. This might be a result of the much larger width (approximately a factor of two) compared to the - 15.1 eV state (fig. 5) which would reduce the second derivative signal by a factor of four. A deeper initial state is usually lifetime-broadened considerably since the lifetime broadening increases rapidly with increasing transition energy.

52

J.E. Rowe et a~.~Photoem~ssio~ and energy loss spectroscopy

from

0

2

L Energy

bulk

data

,

I

,

6

8

10

eV

I ass

Fig, 7. High resolution ELS results for clean cleaved silicon (111) 2X 1 at a pimarY energy Eo = 50 eV and angle of incidence B = 56”. The surface state transitions are labeled So, S 1 and S2 while the bulk transitions are labeled El and Ez. The optical loss function is shown as a dotted line.

4. Studies of intrinsic

surface states

4. I. ELS experiments In the discussion of fig. 3 we remarked that intrinsic surface state transitions SI , S2 and S, are observed by ELS on the Si( 1 I 1) 7X7 surface [8]. Similar transitions have been observed on the Si (111) 2X1 cleaved surface with S, and S, shifted to higher energies by 0.5 eV and 0.7 eV respectively while S2 is shifted to lower energy by 0.6 eV. The Si (100) 2X1 annealed surface has somewhat broadened S2 and S, transitions with S, , S2 and S3 again shifted due to the different surface structure. The Sl transitions have been assigned to initial surface states (dangling bond states) near the top of the valence band and final states which are probably bulk conduction bands 1141. The S, and S, transitions are due to initial surface states of strengthened back-bond character [ 151. A high resolution energy-loss spectrum of cleaved Si(ll1) 2X1 is shown in fig. 7. This was obtained with the spectrometer at Aachen shown in fig. 2. In addition to the transitions E, , E,, SI and S2 previously observed with low resolution, the much stronger surface to surface state transition So is observed at 0.52 eV. This transition has been previously observed with optical internal reflection techniques by Chiarotti and co-workers [ 161 and it is probably much stronger and narrower than S, , Sz and S, because both initial and final states are localized at the surface and do not allow

J.E. Rowe et al./Photoemission and energy loss spectroscopy

cleaved

Si (111)2=1

0

1

2

53

‘3

Energy

4

5

ev

loss

Fig. 8. Comparison of high resolution ELS results for cleaved Si(ll1) 2X 1 and annealed Si (111) 7X7 surfaces. Note the absence of the So transition for the 7X7 surface and the shift of the S1 transition by 0.45 eV to lower energy as compared to the 2X1 surface.

decay into bulk states. Also shown in fig. 7 as a dashed line is the surface loss function [see eq. (2)] computed from bulk optical data [ 171. The agreement with HRELS is good; this indicates that long wavelength excitations predominate even at a primary energy of 50 eV. Fig. 8 shows high resolution ELS results for both cleaved Si (111) 2X 1 and annealed Si (111) 7X7. The S, transition shifts from 2.15 eV on the 2X1 surface to 1.75 eV on the 7X7 surface and the So transition essentially disappears since a decrease of intensity by a factor of 100 would still give an experimentally detectable peak. 4.2. UPS experiments The first UPS measurements of surface states were made on cleaved Si (111) 2X 1 surfaces [ 18,191. More recent measurements by UPS and INS have observed surface states on annealed Si (111) 7X7 and (100) 2X 1 as well as a number of Ge surfaces [5, 9,141. In this paper we report on only the Si (111) surfaces since the ELS results of the previous section were also on these two surfaces and because the bulk effects should be the same for both while the surface states should differ [5,14]. This is shown in fig. 9 which shows the UPS data at photon energy Aw = 11.7 eV for the 2X1 and 7X7 surfaces. The peaks D, and D2 are bulk direct transition peaks [18,19] and occur at approximately the same energy on both surfaces. The peaks A, and B, are dangling bond and back bond surface states which occur at different energies, about 0.5 eV lower on the cleaved 2X 1 surface than on the annealed 7X7 surface [5]. The A, state on the 7X7 surface has two components separated by 0.8 eV with the

54

J.E. Rowe et al./Photoemission

and energy loss spectroscopy

PHOTOEMISSION

CLEAVED (111)

-8

r

* 11 rev

‘;\

2x1

(a)

hw

-6

-4

-2

O’EF

Fig. 9. Photoemission spectra at photon energy ffw = 11.7 eV for the cleaved Si (111) 2x 1 and annealed Si (111) 7X7 surfaces with the energy zero taken at the Fermi level EF. The bulk direct transitions

D1 and D2 occur at the same energy energies.

on both surfaces

but the surface

state transitions

Ar and B1 are at different

energy part having a metallic Fermi edge at 0 eV. This was previously observed more than ten years ago by Gobeli and Allen [20] who assigned it either to surface state emission or bulk emission from the valence band at the surface. Their much lower photon energy sampled a greater escape depth of photoelectrons but they favored the surface state model. The emission from the 2X1 surface state A, goes to zero at E, so that this surface is a two dimensional semiconductor or insulator while the 7X7 surface is a two dimensional metal. The irreversible phase transition from the 2X 1 to 7X7 surfaces is shown in the UPS results of fig. 10 taken at ftw = 21.2 eV. The estimated bulk contribution [5] is indicated by shaded areas which are common to all three curves. It is clear from fig. 10 that emission from the cleaved 2X 1 surface is essentially bulk-like except for the surface state A1 near -0.5 eV with respect to the bulk valence band maximum. The back bond surface states on this surface occur at lower energies. After annealing to -380 “C for 5 min the transition structure (curve b) is obtained with only higher

J.E. Rowe et al./Photoemission

h

and energy loss spectroscopy

(a)

55

2X1 STRUCTURE

(b) TRANSITION STRUCTURE

(C)

-6

7x7 STRUCTURE

-4

-2

INITIAL

ENERGY (eV)

0 = Ev

Fig. 10. Photoemission spectra at photon energy fiw = 21.2 eV showing the irreversible phase transition from the cleaved 2X1 structure to the annealed 7X7 structure. The energy zero is taken at the top of the bulk valence band, E,, and the estimated bulk contribution is shown as a shaded area.

order LEED beams. The dangling bond states have shifted to 0.0 eV and new back bond states at -1.5 eV and -3.6 eV appear [15,15]. These latter peaks become much stronger on the 7X7 surface. This indicates that even though the 7X7 surface has metallic-like emission and dangling bond states with increased energy, the total electronic energy is lower than the 2X1 surface since the stronger backbond states on the 7X7 surface occur at lower energy. It is of some interest to compare UPS with a more surface sensitive technique such as ion neutralization spectroscopy [21] (INS) in order to verify the surface features observed by UPS. Such a comparison is shown in fig. 11 for the Si 7X7 surface for INS using He+ ions and UPS using He1 photons. This surface is particularly interesting for INS since two spearate distributions are measured which do not communicate or fold together as integral

56

J.E. Rowe et aI.~Photoemiss~ot~and energy loss spectroscopy

21.2 ev

-10

-0

-6

-4

ENERGY W/l

-2

lo 1 Eve

Fig. 11. Comparison of ultra~olet photoe~~sion spectroscopy at Ew = 21.2 eV, curve (a), and ion neutralization spectroscopy for the silicon 7X7 surface. The UPS results have been given a smail arbitrary energy shift (-0.3 eV) with respect to the non-fold energy zero for better alignment with INS results. The position of the valence band maximum E,B is shown by a vertical line.

discussed by Hagstrum and Becker [22,23 J. The curve (b) is obtained from their fig. 3 by superimposing the two unfold functions on the same energy scale [23]. The UPS curve (a) is shifted to align most of the features with the INS results. From the known ,!YFof UPS [S] we find that the INS zero differs by -0.2 eV which is within the uncertainties of both experiments. The photoelectron escape depth at 2 1.2 eV is estimated to be 4-6 a which appears to be only slightly larger (a factor of two) than the INS sampling depth [2 11. A more detailed comparison of INS and UPS on Si (111) surfaces is in progress 1241. 4.3. Approximate

energy level model

As in the studies of oxygen adsorption, one of the main goals of these experiments was to combine ELS and UPS in order to derive experimentally an approximate energy level model for the 2X1 and 7X7 surfaces. This is shown in fig. 12 where

J.E. Rowe et ab/Photoemission and energy loss spectroscopy

57

SILICON EV

-2

-1

0

EC

1

il 2

ENERGY (ev)

Fig. 12. Approximate density of states for bulk silicon and for the cleaved and annealed surfaces. The energy zero is taken at the bulk valence band maximum. The relative energy positions from one curve to another are at present uncertain to N.2.5 eV while the positions of structure within each curve are accurate to ~0.1 eV.

the energy zero is chosen at the bulk valence band maximum. The position of the Fermi level is i-O.35 5 0.15eV for both surfaces. The transition So must span E, so it is assigned to initial states slightly above the bulk valence band to final states at the photoconductance threshold observed by Miiller and Month [25]. The S, transition occurs from lower initial states to a bulk conduction band final state. On the annealed 7X7 surface two dangling bond states A, and A1 are observed at low photon energies which merge into a single broad peak at 2 1.2 eV. The UPS data [ 14,201 show a metallic edge at EF and the ELS data at low energies are consistent with a metallic Drude-like diefectric function. Since the S, transition and photoemission peak Al shift by -0.5 eV, it seems reasonable to assign the final state of S, to bulk conduction band which is the same for both surfaces.

5. Conclusions We have attempted to show in this paper the severa advantages of a multiple experiment approach to studying solid surfaces. In particular, by combining ELS and

58

J.E. Rowe et al./Photoemission

and energy lass spectroscopy

UPS it is possible to derive an approximate energy level model for both occupied and unoccupied states. It is obvious that many more details such as matrix elements, escape depths and angular effects must be considered before an accurate description of surface electronic levels is attained. However, the approximate schemes for oxygen adsorption and for clean silicon surfaces discussed above may serve to stimulate further experimental and theoretical studies.

References [ 1] Modern Methods of Surface Analysis, Eds. P. Mark and J.D. Levine (North-Holland, Amsterdam, 1971). Published in Surface Sci. 34 (1973). [2] P.F. Kane and G.R. Larrabee, Characterization of Solid Surfaces (Plenum. New York, 1974). [ 3] H. Ibach and J.E. Rowe, Phys. Rev. B 9 (1974) 1951: Phys Rev. B (to be published). [4] J.E. Rowe, S.B. Christman and E.E. Chaban, Rev. Sci. Instr. 44 (1973) 1675. [5] J.E. Rowe and H. Ibach, Phys. Rev. Letters 32 (1974) 421. [6] H. Froitzheim and H. Ibach, to be published. [7] H. Ibach, 34th Physical Electronics Conference, Murray Hill, N.J. (unpublished). (81 J.E. Rowe and H. lbach, Phys. Rev. Letters 31 (1973) 102. [9] J.E. Rowe. to be published. [lo] N.V. Smith and M.M. Traum, Phys. Rev. Letters 31 (1973) 1247. [ll] A. Liebsch, Phys. Rev. Letters 32 (1974) 1203. [12] H. Ibach, K. Horn, R. Dorn and H. Liith, Surface Sci. 38 (1973) 433 [13] F.C. Brown and O.P. Rustgi, Phys. Rev. Letters 28 (1972) 497. [ 141 J.E. Rowe, Phys. Letters 46A (1974) 400. [lS] J.A. Appelbaum and D.R. Hamann, Phys. Rev. Letters 31 (1973) 106. [16] G. Chiarotti, S. Nannarone, R. Pastore and P. Chiaradia, Phys. Rev. B4 (1971) 3398. [ 171 H.R. Philipp and H. Ehrenreich, Phys. Rev. 129 (1963) 1550. ]18] D.E. Eastman and W.D. Grobman, Phys. Rev. Letters 28 (1972) 1378. [ 191 L.F. Wagner and W.E. Spicer, Phys. Rev. Letters 28 (1972) 1381. [ZO] F.G. Allen and G.W. Gobeli, J. Appl. Phys. 35 (1964) 597. 1211 H.D. Hagstrum, Phys. Rev. 150 (1966) 495. 1221 H.D. Hagstrum and G.E. Becker, Phys. Rev. B 8 (1973) 1580. 1231 H.D. Hagstrum and GE. Becker, Phys. Rev. B 8 (1973) 1592. f24] H.D. Hagstrum. to be published. [25] W. Miiller and W. Month, Phys. Rev. Letters 27 (1971) 250. 1261 H. lbach and J.E. Rowe, Surface Sci. 43 (1974) 481.