Superlattices and Microstructures, Vol. 3, No. 4, 1987 347

INVESTIGATIONS OF THE Sb/CdTe(lOO)-(2x1) INTERFACIAL STRUCTURE WITH PHOTOEMISSION

P. John, F.M. Leibsle, T. Miller, T.C. Hsieh', and T.-C. Chiang Department of Physics and Materials Research Laboratory

University of Illinois at Urbana-Champaign Urbana, Illinois 61801

Received May 14, 1987

Clean CdTe(lOO) surfaces were generated by molecular beam epitaxy (MBE). High energy electron diffraction (HEED) and photoemission were used to determine surface quality and to make comparisons with surfaces generated via cycles of ion sputtering and annealing. Photoemission, HEED, and Auger electron spectroscopy were used to study the properties of the Sb/CdTe(lOO)-(2x1) interface. Photoemission spectra of the Cd 4d and Te 4d core levels showed no changes when Sb was deposited on the clean surface at room temperature. HEED showed that the Sb films where polycrystalline. Annealing caused the polycrystalline films to convert to a sharp (2x2) reconstructed surface. Auger spectra indicated that annealing causes desorption of all but l/2 monolayer of Sb from the surface. Photoemission spectra of the Cd 4d core level showed a significant depletion in intensity of the surface shifted component. The Sb 4d core level spectrum showed a large shift (0.72 eV) in binding energy in converting from polycrystalline to the (2x2) surface. A model is proposed for the (2x2) surface structure in which Sb atoms are bonded to two Cd atoms, and Cd atoms are bonded to only one Sb atom. In order to satisfy dangling bonds, the Sb atoms also form dimer bonds with each other.

Introduction

The interaction between group V elements and group II-VI compound semiconductor surfaces is important in the development of III-V / II-VI semiconductor heterojunctions. Some of the types of behavior one might expect would include interdiffusion of the group V atoms into the II-VI compound, clustering together of the group V atoms on the surface, or ideally, bonding of the group V atoms to the atoms on the surface of the II-VI compound. We have observed the latter type.behavior to be the case for the group V element antimony Sb on the (100) surface of the II-VI compound cadmium telluride CdTe.

In order to study the behavior of Sb atoms on the CdTe(100) surface, it is necessary to first maximize the surface quality. To do this, we have studied the molecular beam epitaxial (MBE) growth characteristics of CdTe(lOO), and compared to surfaces generated via repeated cycles of Ar ion sputtering and annealing. High-energy electron diffraction (HEED) shows that MBE generated surfaces

* present address: AT&T Bell Laboratories, Murray Hill, New Jersey

undergo the same one-domain, (2x1) reconstruction that has been observed for sputter/anneal surfaces.ls2 Photoemission results support the idea that the (2x1) surface is Cd terminated and that the (2x1) structure is induced by Cd surface dimer formation, as discussed in a previous publication.2 This

dimerization is similar to that of the well- known Si(100) surface. The procedure for generating the optimum CdTe(lOO)-(2x1) was found to be growing on the order of 1000 A of CdTe at 300°C on a sputter/anneal CdTe(lOO) substrate, and then annealing the sample at 325°C for 10 minutes.

Sb was evaporated in situ on the CdTe(lOO)-(2x1) at various substrate temperatures. For substrate temperatures up to 250°C, the Sb was found with HEED to grow three dimensionally polycrystalline. For substrate temperatures of 250°C to 350°C, the sticking coefficient for Sb was found to be zero for coverages over l/2 monolayer. The l/2 monolayer of Sb that sticks to the surface produces a (2x2) reconstruction. No three dimensional character is observed with HEED. The polycrystalline coverages could be converted to the l/2 monolayer (2x2) surface by annealing the sample at 275OC or higher. Temperatures higher than 35O'C were not

07494036/87/040347 +09 $02.00/O 0 1987 Academic Press Limited

348 Superlattices and Microstructures, Vol. 3, NO. 4, 7987

attempted so as not to damage the sample. Photoemission spectra gave no indication of Sb diffusing into the substrate CdTe, so apparently the interface is abrupt.

Experimental Details

The CdTe(100) sample is doped with In to give an n-type sample with resistivity of 2 x 10s ohm-cm. The sample was aligned using the Laue technique and then polished in this orientation. Polishing was carried out with first 0.3 p alumina, and then a mechanochemical polish with a 0.5% bromine in methanol solution. Several cycles of sputtering with 500 eV Ar+ ions and then annealing at 325'C were performed in order to generate a good (2x1) surface as determined with HEED. Substrate temperatures were measured via an chromel-alumel thermocouple attached to the sample back. MBE generated surfaces were obtained by growing CdTe on the clean sputter/anneal (2x1) surface. A single boron nitride crucible containing CdTe was used as the CdTe source after Faurie, and Million,3 and after Farrow, Jones, Williams, and Young.4 Sb was also evaporated from a boron nitride crucible. Evaporation rates were calibrated by evaporating on a water-cooled quartz-crystal thickness monitor and measuring thickness as a function of time.

Sputter/Anneal

Photoemission experiments were carried out at the Synchrotron Radiation Center of the University of Wisconsin-Madison. The University of Illinois extended range grasshopper (ERG) monochromator was utilized to select photon energies for the experiments. A hemispherical analyzer was used to analyze emitted photoelectron kinetic energies; an angle integrated approach was used for all spectra. In order to have maximum surface sensitivity,'s5 photon energies of 52, 72, and 80 eV were used for the Cd, Sb, and Te 4d core level spectra, respectively. The energy reference for these experiments was the Fermi level, as measured from a Au foil in electrical contact with the sample. The total instrumental resolution was estimated from the measured width of the Fermi level to be approximately 0.3 eV.

Binding Energy (eV)

Fig. 1 Photoemission spectra of the Cd 4d core level for two surfaces. The top spectrum was recorded for a (2x1) surface generated by MBE with the substrate at 300°C, and then 10 minutes of annealing at 325'C. The bottom spectra was recorded for a (2x1) surface generated by sputtering with 500 eV Ar ions, and then annealing at 325'C for ten minutes. Binding energies are referenced to the Fermi level. The dots are data points, and the curves are results of a least-squares fit to the data. The bulk (B) and surface (Sl and S2) components are shown.

Analyses of photoemission core level spectra were carried out by first fitting the data to a set of Voigt line-shapes (Gaussian function convolved with a Lorentzian function) on a smooth cubic polynomial background function. A detailed discussion of the fitting procedure can be found elsewhere.5-g For a given spectrum, the Gaussian and Lorentzian widths were constrained to be the same for each spin orbit component. Shifted components were constrained to have the same shape as the main component, differing only in position and intensity. For the Cd 4d core level, fitting was done assuming two surface shifted components. For the Te 4d, no shifted components were needed to fit the data for the majority of the spectra. The Sb 4d spectra

required one shifted component for room temperature coverages, and no shifted component for annealed coverages.

Results

MBE generated surfaces exhibited a one-domain (2x1) reconstruction for substrate growth temperatures 275OC to 350°C, very similar to the sputter/anneal generated surfaces. Figure 1 shows photoemission spectra of the Cd 4d core level for a sputter/anneal surface and a MBE surface. For both cases the final annealing temperature was 325°C and the substrate was held at that temperature for 10 minutes. For the MBE surface, the substrate temperature was 3OO'C during growth. The dots

Superlattices and Microstructures, Vol. 3, No. 4, 1987 349

TABLE I. Pertinent fitting parameters for photoemission spectra of the Cd 4d and Te 4d core levels for surfaces generated by various procedures. Binding energies are for the bulk contribution peak, and are referenced to the Fermi level. The branching ratio is the intensity ratio of the 4ds,, and 4d,,s components. The Gaussian and Lorentzian widths are the full widths at half maximum. S/B intensity ratio is the ratio between the surface and bulk contributions.

Sputter/Anneal MBE Surface Surface 250°C Substrate 300°C Substrate

Cd Te Cd Te Cd Te

%,2 Binding Energy (eV) 11.15 40.43 10.54 39.82 11.18 40.45 Spin-orbit Splitting (eV) 0.658 1.456 0.661 1.476 0.667 1.465 Branching Ratio 0.59 0.75 0.67 0.75 0.59 0.76 Surface Shift (eV) Sl 0.58 -- 0.57 1.00 0.60 --

s2 -0.80 -- -0.82 -- -0.81 -- Gaussian Width (eV) 0.39 0.56 0.42 0.65 0.39 0.51 Lorentzian Width(eV) 0.23 0.39 0.22 0.40 0.23 0.42 S/B Intensity Ratio Sl 0.32 -- 0.14 0.11 0.40 --

s2 0.04 -- 0.17 -- 0.05 --

indicate the recorded data; the line through the dots represents a fit to the data. Also, shown are the three components which comprise the fit (shown below the data), The line- shapes for the two surfaces are very similar, both having two surface components,' Sl and S2, shifted to higher and lower binding energy, respectively, with respect to the bulk component, B. The pertinent fitting parameters for these two surfaces are given in Table I. The only significant difference is that the Sl component is relatively larger for the MBE surface than for the sputter/anneal surface. It has been proposed that Cd dimer atoms on the surface are the source of the Sl component, and that this dimer formation generates the observed single domain, (2x1) structure.' Therefore, this increase in the relative intensity of the Sl component indicates a more developed (2x1) structure and thereby an improvement in overall surface quality. The component S2 is due to excess Cd on the Cd terminated surface.2 Figure 2 shows corresponding spectra for the Te 4d core level. For these spectra, there are no measurable surface core level shifts, and little apparent differences in line shape for the two surfaces, as seen from the fitting parameters shown in Table I. This indicates that the surface is Cd terminated for both types of preparation, as discussed in a previous pub1ication.s

Cd termination is contradictory with the results of Benson, Wagner, Torabi, and Summers for their HEED and desorption experiments." Their interpretation of their data is that the CdTe(lOO)-(2x1) is terminated with Te. Their interpretation seems to be mainly based upon

CdTe (1001-(2x1) Te 4d Cores hv = 80eV n

\

MBE Surface L.- t

\

Sputter/Annea Surface

L I I I I I I I

44 43 42 41 40 39 38 Binding Energy (eV)

Fig. 2 Same as Fig. 1 except that the results are for the Te 4d core level. The fitting resulted in just one component (the bulk component).

Superlattices and Microstructures, Vol. 3, No. 4, 1987

CdTe (lOOI- ( Ix I) Cd 4d Cores hu=52eV ??Expt.

-Fit

yy+g-q

15 14 13 I2 I I IO Binding Energy (eV)

Fig. 3 Photoemission spectra of the Cd 4d core level for a (1x1) surface generated by MBE with the substrate at 25O'C. The symbols and notations are the same as those used in Fig. 1.

the decay of the (2x1) pattern with time and the ability to regenerate the pattern by Te evaporation. We have not observed the (2x1) pattern to decay with time (several days at room temperature) and we are able to generate the (2x1) pattern by sputtering and then annealing at temperatures in the same range as those used by Benson, Wagner, Torabi, and Summers to cause degradation of the (2x1) structure (i.e. 275OC to 375'C).r" In general, we have found that the quality of the (2x1) pattern tends to increase with longer annealing time. The origin of the difference in behavior cannot be determined based on the available data. Contamination and impurity or dopant segregation are possible reasons. Photoemission and Auger spectra of our samples did not show any trace of impurity.

For substrate temperatures of 250°C and below, the MBE generated surface exhibited a rather poor (1x1) HEED pattern with pattern quality decaying with decreasing substrate temperature. The Cd and Te 4d core level spectra for a sample prepared at 25O'C are shown in Figs. 3 and 4, respectively. The fitting results are given in Table I. The decrease in surface quality is observed as

r CdTe(lOO)-(1x1) Te 4d Cores hv=80eV ??Expt. -Fit

L \

I I I I I I

44 43 42 41 40 39 Binding Energy (eV)

Fig. 4 Photoemission spectra of the Te 4d core level for a (1x1) surface generated by MBE with the substrate at 25OOC. The symbols and notations are the same as those used in Fig. 2. The fitting resulted in a small, surface shifted component in addition to the main (bulk) peak.

increased Gaussian width of both the Cd 4d and Te 4d core levels. The Sl component of the Cd 4d core level was greatly attenuated while the S2 component was enhanced. A shifted component was also present for the Te 4d core level (Fig. 4), suggesting that the surface is no longer Cd terminated. Annealing at higher temperatures (>300°C) was found to produce a (2x1) HEED pattern; core level photoemission spectra indicated that the surface quality was nearly that of the sputter/anneal surface.

Figure 5 shows Auger spectra of the CdTe(100) surface with Sb deposited upon it. The left spectrum corresponds to an Sb deposition with the CdTe substrate at 275OC. The amount of Sb atoms evaporated for this case was sufficient to generate a coverage of over 20 monolayers for a substrate at room temperature. The middle spectrum corresponds to l/2 monolayer of Sb deposited with the substrate at room temperature; the right spectrum is that of a 1 monolayer Sb coverage at room temperature. Here, we define 1 monolayer (ML) to be the number of atoms needed

1

Superlattices and Microstructures, Vol. 3, No. 4, 1987 351

- I I,

CdTe (IOO)+Sb I,

saturated (2x2) l/2 ML @ 20°C

ti Cd Cd

I ML1

Cd

t

Cd St

Cd Te I I I I Tel ,, , ,Cd, , Te, ,, I I I I I

300 400 500 ’ ’ 300 400 500 ” 300 400 500

Te

Fig. 5 Auger electron spectra of the CdTe(lOO) with Sb evaporated upon it. The left spectrum represents the saturated (2x2) structure. The middle and right spectra

Kinetic Energy (eV)

to form a single layer of Cd (or Te) in the CdTe(lOO) zincblend structure (i.e. 4.76 x lo'& atoms/cm2). Clearly, the left and middle spectra show the same Sb signal strength, while the right spectrum shows almost twice the Sb signal strength. This result indicates that the Sb coverage saturates at l/2 ML for a 275'C substrate temperature. Further studies revealed that this behavior is the same for substrate temperatures between 225OC and 350°C. For substrate temperatures below 150°C, Sb was fiound to grow in a three dimensional polycrystalline form. Here, there was no limitation on the amount of Sb that would stick to the CdTe(lOO) surface. The polycrystalline structure could be converted to the l/2 ML, (2x2) structure by annealing at temperatures of 275'C or higher. The excess Sb on the surface is apparently driven off by the annealing process. For substrate temperatures between 15O'C and 225OC, little or no Sb stuck to the surface and the substrate (2x1) reconstruction was not disturbed. Therefore, the (2x2) surface can be generated only at sufficiently high temperatures to cause the reaction and bonding of Sb to the CdTe substrate. The bonding must be fairly strong.

represent l/2 ML and 1 ML depositions, respectively, with the substrate at room

temperature.

Photoemission spectra reveal several properties of the CdTe(lOO)-Sb(2x2) structure.

Figure 6 shows the Sb 4d core level for a 10 ML deposition at room temperature before and after annealing at 275'C for 10 minutes. The annealed surface exhibits the (2x2) reconstruction and relative photoemission intensities indicate that the Sb coverage is saturated. These spectra have been analyzed by fitting to model functions as discussed above. The results are shown in the figure and in Table II. One shifted component was needed in fitting the pre-anneal spectrum; some of the atoms on the surface of Sb clusters are speculated to be the source of this shift. Apart from this small component, the only significant difference between the two spectra is the rather large shift in binding energy, 0.72 eV, after annealing. This shift in binding energy was found to be independent of the amount of Sb deposited, depending only upon an annealing temperature large enough to produce the (2x2) reconstruction. An overall core level shift of this magnitude would seem to indicate a significant change in the electronic environment of the Sb atoms, such as a change in bonding mechanism.

352 Superlattices and Microstructures, Vol. 3, No. 4, 1987

CdTe(lOO)+lO ML Sb Sb 4d Cores hv= 72eV A

IO min. 8 275°C

I I I I I I I 37 36 35 34 33 32 31

Binding Energy(eV)

Fig. 6 Photoemission spectra of the Sb 4d core level for 10 ML of Sb deposited on the CdTe(lOO)-(2x1) surface at room temperature (bottom spectra) and for the same surface after annealing for 10 minutes at 275OC (top spectrum). Binding energies are referenced to the Fermi level. The dots are data points, the curves are results of a least-square fit to the data.

.

Spectra of the Cd 4d core level for 10 ML of Sb deposited at room temperature and for zhr Sb (2x2) structure are shown in Fig. 7. The fitting results are shown in the figure and in Table II. By comparing to the spectra for the clean CdTe(lOO)-(2x1) surface (upper panel of Fig. l), one can see that the surface shifted components, Sl and S2, as well as the overall line shape, are relatively unaffected by the presence of Sb for the room temperature case. This fact indicates that the Sb is only loosely bonded to the substrate. For the Sb (2x2) surface, the intensity of the Sl component of the Cd 4d core level is greatly attenuated (see Fig. 7). Clearly, the annealing process causes the Sb atoms to bond to the surface Cd atoms, resulting in a more bulklike environment for the Cd surface atoms (Sl). The Te 4d core level spectra do not show any apparent changes in going from the clean surface (Fig. 2) to the room temperature deposited surface to the annealed (2x2) surface (Fig. 8). Also, the photoemission intensity ratios between the Cd 4d and Te 4d spectra do not significantly change in these cases. This indicates that the Sb atoms only bond to the Cd atoms that are on the surface, and that the amount of Sb that diffuses into the bulk is negligibly small, if nonzero.

From the binding energies of the Cd and Te bulk core level contributions, the change in band bending near the surface due to various surface treatments can be deduced. For the somewhat disordered low-temperature (1x1) MBE surface, the Fermi level is pinned 0.41 eV above the valence band maximum (VBM). This is significantly lower than the observed 1.02 eV above the VBM for the sputter/anneal surface and 1.05 eV above the VBM for the MBE surface. These values for the clean surface are also similar to those surfaces with Sb evaporated on them. For the as deposited at room temperature case, the Fermi level was pinned 0.90 eV above

TABLE II. Fitting parameters for photoemission spectra of the Cd 4d, Te 4d, and Sb 4d core levels for 10 ML of Sb deposited on the CdTe(lOO)-(2x1) surface at room temperature as well as for the same surface after annealing at 275°C to generate the (2x2) structure. The notations are the same as those used in Table I.

As Deposited After Annealing at Room Temperature Cd Te Sb

at 275'C Cd Te Sb

4%,2 Binding Energy (eV) 11.03 40.31 Spin-orbit Splitting (eV) 0.652 1.474 Branching Ratio 0.59 0.75 Surface Shift (eV) Sl 0.60 --

s2 -0.87 -- Gaussian Width (eV) 0.40 0.50 Lorentzian Width(eV) 0.23 0.43 S/B Intensity Ratio Sl 0.38 --

s2 0.04 --

32.16 1.255 0.68 0.55

0.33 0.29 0.04 __

11.15 40.42 32.88 0.652 1.481 1.242 0.59 0.72 0.65 0.59

-0.81 0.40 0.41 0.39 0.23 0.45 0.29 0.05 0.05 -- --

Superlattices and Microstructures. Vol. 3, No. 4, 1987

14 13 12 II IO 9 8

Binding Energy (eV)

CdTe(lOO)+lO ML Sb Cd 4d Cores P?

I I I I I I

Fig. 7 Same as Fig. 6 except that the results are for the Cd 4d core level. The symbols and notations are the same as those used in Fig. 1.

the VBM. Annealing produced a slight change in the pinning position, moving to 1.02 eV above the VBM.

Model and Discussion

Based upon the above results, we propose the following model for the Sb/CdTe(lOO)-(2x1) interface. For depositions at temperatures less than 150°C, the Sb atoms do not strongly bond to the CdTe substrate atoms, preferring to form Sb clusters upon the surface instead. These clusters are polycrystalline, with the Sb atoms attached to each other via metallic bonding characteristic of bulk Sb. The substrate surface is relatively unaffected; the Cd dimer bonds are left intact.' The annealing process causes the Sb-Sb bonds to break. The Sb atoms then either bond to available Cd atoms or evaporate off the surface. For temperatures less than 225'C, Cd atoms do not readily bond to the free Sb atoms, so all Sb atoms leave the surface. For temperatures above 225'C, the Sb atoms are able to bond to Cd atoms. This temperature is related to the energy barrier associated with the reaction path, The Sb

CdTe(lOO)+lO ML Sb Te 4d Cores hv=80 eV

I I I 1 I I I 44 43 42 41 40 39 38

Binding Energy (eV)

Fig. 8 Same as Fig. 6 except that the results are for the Te 4d core level. The symbols and notations are the same as those used in Fig. 2.

atoms that do bond to the Cd atoms behave as do In atoms on the Si(lOO)-(2x1) surface in the model proposed by Rich, et al.rl The Sb atoms are now in an sp3 binding configuration or possibly the sp3/pz hybrid configuration discussed by Mailhiot, Duke, and Chadi,r' explaining the large binding energy shift of the Sb 4d core level caused by annealing. The reduction of the relative intensity of the Cd 4d core level Sl component that is produced by the surface Cd dimer atoms indicates that these Cd atoms are in a more bulk-like environment2 In the bulk, Cd atoms are four fold coordinated. This implies that the Sb atoms bond to dimer bonded Cd atoms giving the Cd atoms a bulk like coordination. The sites occupied by the Sb atoms are illustrated in Fig. 9. Panel (a) of Fig. 9 shows the geometry of the first two layers of the clean, Cd terminated surface assuming bulk periodicity. Panel (b) shows that same surface with the addition of Cd dimer bonds, yielding the one domain, (2x1) surface reconstruction. Panel (c) indicates how the Sb atoms can bond to the Cd atoms. The surface Cd atoms are each bonded to two Te atoms (one layer below), one Cd atom

354 Superlattices and Microstructures, Vol. 3, No. 4, 1987

(a)

Cd 0 69 Sb 0 Fig. 9 Diagrams of the proposed surface structures. Only the top two substrate layers are shown (Cd on top, Te underneath), along with all Sb atoms. Panel (a) shows the Cd terminated, unreconstructed (1x1) structure, while panel (b) reflects the dimer bonds

generating the (2x1) reconstruction. Panel (c) shows the addition of l/2 ML Sb atoms and the Cd atoms to which they bond. Panel (d) indicates the Sb dimer bonds and the resulting (2x2) surface structure.

(within the same layer), and one Sb atom, ACKNOWLEDGMENTS - This material is based upon giving them the bulklike, four-fold work supported by the U.S. Department of coordination. Since an Sb atom bonds to two Cd Energy, Division of Materials Sciences, under atoms, there are only enough available sites to Contract No. DE-AC02-76ER01198. Some of the accommodate the observed l/2 ML of Sb atoms. equipment used for this research was obtained Also, since the Sb atoms can accommodate more with grants from the National Science than two bonds, the Sb atoms are able to form Foundation (Grants. No. DMR-8352083, and No. dimer bonds to reduce total energy. This is DMR-8614234). the 3M Company, Hewlett-Packard illustrated in panel (d) of Fig. 9. The end Laboratories, and E.I. du Pont de Nemours and result is a surface layer with twice the Company. The Synchrotron Radiation Center of periodicity of the bulk in both the (011) and the University of Wisconsin- Madison is (011) directions giving rise to the observed supported by the National Science Foundation (2x2) HEED pattern. under Contract No. DMR-8020164. We acknowledge

Superlattices and Microstructures, Vol. 3, No. 4, 1987 355

the use of central facilities of the Materials Research Laboratory of the University of Illinois, which is supported by the U.S. Department of Energy, Division of Materials Sciences, under Contract No. DE-AC02-76ER01198, and the National Science Foundation under Contract No. DMR-8020250.

References

1. K. Sugiyama, Journal of Crystal Growth 60, 450 (1982)

2. P. John, T. Miller, T.C. Hsieh, A.P. Shapiro, A.L. Wachs, and T.-C. Chiang, Physical Review B&, 6704 (1986)

3. J.P. Faurie and A. Million, Journal of Crystal Growth 2, 577 (1981)

4. R.F.C. Farrow, G.R. Jones, G.M. Willams, and I.M. Young, Applied Physics Letters 39, 954 (1981)

5. T.-C. Chiang, CRC Critical Reviews in Solid State and Materials Sciences, (to be published)

6. T. Miller, E. Rosenwinkel, and T.-C. Chiang, Solid State Communications 47, 935 (1983); Physical Review Bx, 570 (1984)

7. T. Miller, T.C. Hsieh, and T.-C. Chiang, Physical Review Bz, 6983 (1986)

8. T.-C. Chiang, Comments on Atomic and Molecular Physics 13, 299 (1983)

9. T. Miller, A.P. Shapiro, and T.-C. Chiang, Physical Review B3l, 7915 (1985)

10. J.D. Benson, B.K. Wagner, A. Torabi, and C.J. Summers, Applied Physics Letters 49, 1034 (1986)

11. D.H. Rich, A. Samsavar, T. Miller, H.F. Lin, T.-C. Chiang, J.-E. Sundgren, and J.E. Greene, Physical Review Letters 58, 579 (1987)

12. C. Mailhoit, C.B. Duke, and D.J. Chadi, Physical Review Letters 53, 2114 (1984); Journal of Vacuum Science and Technology A 3, 915 (1985)