Chapter 5

Au/Si{111}

Abstract

The structure of the Si{111}√3x√3-30-Au surface has received much attention owing to the use of gold in the semiconductor industry and to the presumed relationship between the Si-√3-Au and the Si-√3-Ag surfaces. Plausible models suggested for these structures can be divided into two groups: honeycomb models and trimer models. We demonstrate conclusively that the Si-√3-Au surface contains 1-ml of Au atoms which form trimers [82]. The trimers have a 2.8 Ang. edge length, are located above fourth-layer Si atom sites, and consist of Au atoms registered on off-first-layer Si atom sites. The first layer of Si atoms is missing. The Au trimer layer is 0.56 Ang. above the second-layer Si atoms. The second-layer Si atoms are radially displaced 0.48 Ang. away from the three-fold axis. The remaining Si atoms are presumed to be in bulk sites. This structure is closely related to the structure of the Si{111}6x6-Au surface. Presented below is a description of the background information, the experimental details, and the structural analysis.

5.1 Introduction

A complex morphology is developed when thick Au films, of the order of 10 ml, are deposited on a Si{111} surface. For growth on a room-temperature substrate the interface between the bulk Si substrate and the Au film is not sharp, Si atoms migrate through the Au, and a Au/Si layer is formed on top of the Au films. For growth on a substrate above 400 C the initial interface is a 6x6 structure, islands of Au grow above this interface structure, and the tops of the islands are a reacted Au/Si surface [1]. Little is known about the structure of the interface, the bulk, and the surface of such thick Au films. Even less is known about the surface structures of near- and sub-monolayer growth of Au on Si{111}. These structures, in particular a Si{111}√3x√3-30-Au structure, are the subject of this chapter. A historical overview is presented next. For the aid of the reader, Glossary B contains definitions of the structure acronyms.

An initial LEED and AES study of the Au/Si{111} surface was completed by Bishop et. al.[83], using a Si{111} sample that was implanted with Au atoms. A √3 pattern was observed when the sample was heated to 740 C, 1/5--order spots appeared after heating to 900 C, and a 1x1 pattern appeared after heating to 1000 C.

Subsequent studies [84] - [88] led to the reporting of three structures when Au was evaporated onto the Si{111}7x7 surface and then heated to 700 C for several minutes. These structures were: a 5x1 phase at coverages reaching 2/5 ml; a mixed 5x1 and √3 surface at coverages reaching 4/5 ml; a √3 surface at coverages reaching 1-ml; and a 6x6 surface above 1-ml. The 5x1 pattern also contained weak streaks between and parallel to the rows of the fractional-order beams, which suggest [84] that the 5x1 structure was actually a disordered 5x2 phase. The √3 surface was reported [89] in varying degrees of order, i.e., containing sometimes sharp spots and diffuse rings. This was associated with the √3 structure being a disordered sub-unit of the 6x6 phase. It is difficult to establish if there was a mixed √3 and 6x6 surface, since the latter contains LEED beams of the former. With only the above information, Le Lay et. al.[85] have proposed a model for the √3 structure with a trimer centered on a H₃ site of Au atoms on off-T₄ sites (model H₃-T₄), see Figure 4.4. Other possible structures could be a trimer on a H₃ site of Au atoms on off-T₁ sites (H₃-T₁), see Figure 4.5, or a trimer on a T₄ site of Au atoms on off-T₁ sites (T₄-T₁), see Figure 4.6. These models are called simple-trimers, and there exist three other possible registrations to the Si bulk (T₄-H₃, T₁-T₄, and T₁-H₃).

Further structural studies by Oura et. al.[90], using low-energy ion scattering (LEIS), determined the structure of the Si-√3-Au to involve 1-ml of Au trimers, 2.9 Ang. on a side, located over a Si honeycomb above the Si{111}1x1 surface. The difficulty with this model is that the registration of the Si honeycomb and Au-trimer layers with respect to the bulk was not declared. The Si 2/3-ml honeycomb may be a hexagonal array of Si atoms on H₃ sites with Au trimers in either the H₃-T₁ or the H₃-T₄ configuration. In fact, there exist eight models that could be created. The Si-atom honeycomb can be composed of 2/3 ml of Si atoms in the T₁, T₄, or H₃ sites; the honeycomb can also be formed from 1/3-ml T₁-vacancies. Each of these four honeycombs may then have the Au trimer placed on T₄ or H₃ sites; T₁ or H₃ sites; T₁ or T₄ sites; or T₄ or H₃ sites, see Figures 5.1 5.2, 5.3, and 5.4 as examples. These models, called modified coplanar trimer (MCT) models, are different from the coplanar trimer models (CT) [91, 92, 93] in that the Au trimer layer is 0.3 Ang. above the Si honeycomb layer (as opposed to being coplanar). Of course, the CT models are also different from simple trimer models in that there is the extra Si layer. Other models involving honeycombs, the simple trimer, embedded Au, and immersed Au do not match Oura et. al.'s data and analysis.

Huang et. al.[94], also using LEIS, have determined a different structure. The Au atoms form a 2/3-ml honeycomb on H₃ sites, 2.0 Ang. above a Si{111}1x1 surface, see Figure 5.5. An additional 1/3-ml of gold atoms can occupy H₃ sites in the centers of the above mentioned honeycomb, 0.3 Ang. below the Au-honeycomb layer. Other Si-√3-Au surface structure models (such as Oura et. al.'s MCT, the simple trimer, embedded Au, and immersed Au atoms) did not fit Huang et. al.'s data and analysis.

A recent MEIS study by Chester et. al.[95] concluded that the Si{111}√3x√3-30-Au surface contains 1-ml of coplanar Au atoms. The Au atoms were determined not to be located on bulk Si atom sites, and large surface Si-atom displacements were found. Chester et. al.'s structural analysis ruled out a Au honeycomb structure and favored trimer-based structures. A simple trimer model (H₃-T₁), a MCT-model (with a Si top-layer vacancy honeycomb and Au trimers), and a honeycomb chained-trimer model (HCT, to be discussed later) yielded acceptable but not complete agreement with the experimental backscattering yields. Finally, a structure (lacking mirror symmetry) with twisted Au trimers above a Si missing top-layer (MTL), with Au-trimers centered on H₃ sites, and with Au atoms on off-T₁ sites was determined; this model is denoted MTL-H₃-T₁. The lack of Si atoms is a paramount conclusion of this analysis [96].

ARPES studies [97] showed that ``the surface reconstruction has the same symmetry as the ideal, unreconstructed bulk.'' Hence, all models must contain 3-fold rotation and mirror-plane symmetry.

SXD studies [98, 99] have determined, from a Patterson function map, that the Au atoms do not occupy high-symmetry (bulk) sites, but the Au layer maintains mirror symmetry. This fact rules out the honeycomb and centered-honeycomb models, which contain Au atoms on H₃ sites. A trimer-based model (2.8 Ang. on its side, untwisted, and on a relaxed Si surface) was found to be correct. However, the outermost Si atoms were found to be twisted which breaks mirror-symmetry and requires two domains so as to yield an ``effective'' mirror-symmetry. Additionally, the registration of the Au trimer was not determined. Hence, the structure was not quantitatively solved. Additionally, the 6x6 structure was determined also to be composed of Au trimer-units, indicating a close relationship between the √3 and the 6x6 phases.

STM images [100, 101, 102, 103] do not show a honeycomb array of Au atoms. Instead, large protrusions are imaged, one per rt unit-cell, at either bias polarity indicating that the protrusions are of structural origin. Dumas et. al.'s[103] STM images also contain protrusions, triangular in shape, 0.7 Ang. high, and rotated 30 deg from the √3 unit-cell edge. If these protrusions are single Au atoms, then the structure could be a 1/3-ml simple hexagonal layer. There are, however, no reports of the Si-√3-Au phase containing only 1/3-ml of Au atoms. On the other hand, if these protrusions involve several Au atoms and if the coverage is truly 1-ml, then they could each be a trimer. Overall, the STM results indicate a trimer-based structure.

Total-energy calculations, by Ding et. al.[104], have determined that, of the trimer-based models, the MTL-H₃-T₁ model is most stable, the trimer is unrotated, the Si atoms have large radial displacements, and the Au-Si plane separation is small. An alternative MTL-T₁-H₃ model was proven to be nearly as stable. Additionally, calculated charge-density contours displayed one triangular protrusion per √3 unit-cell. Hence, the results of the total-energy calculations confirm the major results of the MEIS, SXD, and STM studies.

Finally, a study of the lower-coverage 5x1 surface [105] has suggested a model involving trimers of Au atoms. Although the 5x1 and √3 surfaces are clearly different, it is quite possible that the building blocks of the surface unit-meshes are the same.

At this stage, some general remarks should be made about the applicability of the various surface techniques, remarks which are particularly important for the problem discussed here. First, the mere observation of a LEED pattern is not the determination of a structure, it is only an indication of the presence, symmetry, and size of the surface unit-mesh of a structure. Second, a qualitative model of adsorbate sites is insufficient to define a structure, the distances involved (the structure) are needed. Third, a model accepted by dynamical LEED analysis must be consistent with data from other techniques, namely, STM, that a honeycomb array is not visualized on the √3 surface; SXD, that Au atoms do not occupy H₃ sites; MEIS, that the first layer of Si atoms is missing; and SXD and ARPES, that the surface maintains bulk symmetry. Fourth, the atomic arrangement in the outermost layer is by itself not a complete determination of the surface structure; the surface layers must be correctly registered to the bulk layers. Fifth, the lack of agreement between the three ion-scattering studies [90, 94, 95] indicates that none of the proposed models may be discarded, and another surface structural technique must be applied.

The purpose of the present study was to determine the √3 structure or at least to rule out many of the proposed models for a range of structures. These models, in summary, are the Au honeycomb and centered-honeycomb models registered on H₃ sites (as Huang et. al. have determined), the Au-trimer models with various registries (as Dornisch et. al. have indicated), the MCT (modified coplanar-trimer) models which contain a Si honeycomb plus Au trimers with various registries (as Oura et. al. have determined), and the MTL (missing top-layer) models with various Au-trimer registries (as Chester et. al. and Ding et. al. have determined). A trimer-based structure appears to be most likely.

5.2 Experiment

A Si{111} sample cleaved from a larger wafer (phosphor, n-type, 8-12 Ohm cm) was used for the experiment. Prior to mounting on a goniometer, the sample was HF etched. The sample was then loosely mounted on a 0.025-mm thick Ta disk, 25 mm in diameter, with care given so that no other materials were forward of the sample surface. This sample disk was mounted on a goniometer which allows heating to 1400 C (e-beam bombardment), translation along three-perpendicular axis, rotation about two of those axes, and tilt about the third axis.

For deposition, Au foils were mounted on two separate W-coils, approximately 10 cm from the sample face. The sources were resistively heated to approximately 1000 C, yielding deposition rates on the order of 1/2 ml per minute, as determined by AES measurements. It should be noted that at 1000 C the vapor pressure of Au is approximately 5•10^-6 Torr, and heating of the sample by radiation from the Au source was negligible. Gold coverage was monitored by following the increase of the R_Au ratio, see Equation 2.6 discussed in Chapter 2, where R_inf=I^inf_Au(69) / I^inf_Si(92) = 0.93 and lambda_69=4.0 Ang. were assumed [37, 38]. Assuming a nearest-neighbor distance of 2.89 Ang., we can convert the above thickness in Angstroms to coverage in units of LE. This assumption is based on a close-packed Au layer and the lack of Au diffusion into the Si substrate.

After the initial baking of the vacuum system and outgassing of all filaments, a pressure below 2•10^-10 Torr was achieved and maintained throughout the experiment, except during Ar-ion bombardment and Au deposition.

After an initial bombardment (2 uA, 375 eV, 5•10^-5 Torr, 30 C, 60 min.) followed by an anneal (1000 C, 20 min.), a good Si{111}7x7 LEED pattern was obtained. This process was repeated once more, so as to reduce the oxygen and the carbon AES signals to the noise level, where they remained throughout the experiment, see Table 2.1. Typical values for the ratio R_C were 0.002, which corresponds to less than 1 at.% contamination [37], typical values for the ratio R_O were four times lower.

The deposition of Au on the room-temperature Si substrate gradually obscured the Si{111]7x7 LEED pattern for Au coverage up to 4 LE, and no new ordered structures were seen. Anneal of the Si{111} substrate (700 C for 10 min.), followed by slow cooling to room temperature, caused, with increasing Au coverage, the appearance of a sequence of different LEED patterns, namely, 5x1 plus very weak 5x2 streaks, 5x1 and √3x√3-30, √3x√3-30, √3x√3-30 together with 6x6, and finally 6x6, see Figure 5.6. Anneal of anyone of these structures for up to 60 min. did not produce any changes, long anneals produced only an improvement in the long-range order, as visible in the sharpness and reduced background of the LEED pattern. A clean ordered Si{111}7x7 could be regained by bombardment (1 to 2 hours), followed by 1000 to 1100 C anneal (10 to 30 min.). Anneal alone was not sufficient to remove all the Au from the AES spectra.

LEED I(V) spectra were collected for the Si{111}√3x√3-30-Au structure several times and were always found to be the same. Anneal (700 C, 10 to 120 min.) of the sample did not affect the LEED spectra. Soaking the sample in 2•10^-10 Torr vacuum (1 to 48 hr.) did not affect the LEED spectra. Si{111}√3x√3-30-Au surfaces prepared by Au deposition onto a hot (700 C) Si{111} substrate produced the same LEED spectra as the above surfaces. The presence of the 5x1 phase did not affect the fractional-beam spectra of the √3 phase. These five facts suggest that the Si-√3-Au structure is very stable.

From a set of sixty-nine LEED I(V) spectra, a final set of ten integral- and ten fractional-order beams was created after averaging degenerate beams, normalizing to constant incident-beam current, subtracting the background, and smoothing. These beams (10, 01, 11, 20, 02, 21, 12, 30, 03, 22, 1/3 1/3, 2/3 2/3, 4/3 1/3, 1/3 4/3, 4/3 4/3, 5/3 2/3, 2/3 5/3, 1/3 7/3, 7/3 1/3, and 5/3 5/3) were used in the analysis to be discussed later.

5.3 Keating Energy Analysis

A Keating energy analysis for several of the Si-√3-Au model structures was undertaken, i.e., for each model the elastic energy was minimized as a function of structural parameters. However, this analysis had only limited application in the search for the Si-√3-Au surface structure. We used it to gain insight into what were suitable models and structural parameters for a dynamical LEED intensity analysis. Two constraints were imposed upon the Keating energy analysis. First, the Au radius was assumed to be 1.40 Ang. for Au-Au bonds, and 1.30 Ang. for Au-Si bonds. Second, tetrahedral bonding was not enforced upon the Au atoms, i.e., only the bond angles of Si atoms were considered. Additionally, many of the possible models were not calculated owing to their lack of chemical simplicity or lack of mirror-plane symmetry, i.e., models that required the Si top-layer atoms to bond to six other atoms were discarded. Only the simple honeycomb model (2/3 ml) was retained from the group of models which require the Si top-layer atoms to bond to five other atoms. The twisting of trimer units, due to the violation of mirror symmetry, was not considered [106]. In particular, the structure determined by Chester et. al. [95] using ion-scattering lacks mirror symmetry and contains highly distorted Au-Si bonds, and hence was not considered. Finally, several of the models contain Si dangling-bonds which the Keating-energy analysis necessarily neglects. Hence, these models must be viewed with suspicion.

The models considered may be subdivided into five groups. The first group contains the 2/3-ml Au honeycomb and the 1-ml Au-centered honeycomb models. The other four groups contain Au trimers with various registries to the Si surface and the addition (or depletion) of Si atoms in the surface, i.e.: +2/3 ml, 0, -1/3 ml, and -1 ml of surface Si [107]. For each of the above models, we can consider six, six, two, and six, respectively, different registries of a Au-trimer layer (20 total). We have selected the plausible models for the Keating-energy analysis as followed:

1. The MCT-T₁-T₁-T₄ and MCT-T₁-T₁-H₃ models, see Figures 5.1 and 5.2, are plausible, but unlikely. Each Si adatom satisfies a T₁ dangling-bond and bonds to three Au atoms. There exists, however, an additional T₁ dangling-bond below each trimer.
2. The MCT-T₄-T₄-T₁, MCT-T₄-T₄-H₃, MCT-H₃-H₃-T₁, and MCT-H₃-H₃-T₄ models are implausible. Each Si adatom satisfies three T₁ dangling-bonds. There exists, however, only one adatom bond per three Au atoms.
3. The H₃-T₁ and T₄-T₁ models, see Figures 4.5 and 4.6, are plausible. Each T₁ dangling-bond is satisfied by one Au atom.
4. The T₁-H₃, T₁-T₄, H₃-T₄, and T₄-H₃ models, see Figure 4.4 as an example, are implausible. The first two require one T₁ dangling-bond per three Au atoms and two unsatisfied T₁ dangling-bonds. The second two require six bonds per Si-T₁ atom.
5. The MCT-T^V₁-T₁-T₄ model, see Figure 5.3, is plausible, but unlikely. There are two unsatisfied T₁ dangling-bonds, but the T₄ dangling-bonds are each satisfied by a Au trimer-atom.
6. The MCT-T^V₁-T₁-H₃ model, see Figure 5.4, is implausible. There are two unsatisfied T₁ dangling-bonds, and the T₄ dangling-bonds must each be split for two Au trimer-atoms.
7. The MTL-T₄-H₃ and MTL-T₄-T₁ models, see Figures 5.7 and 5.8, are plausible, but unlikely. The nine T₄ dangling-bonds are satisfied, but substantial reconstruction can be expected.
8. The MTL-T₁-T₄ and MTL-H₃-T₄ models are implausible. Each T₄ atom can only bond once to a Au atom. Hence, there are six unsatisfied T₄ dangling-bonds.
9. The MTL-T₁-H₃ and MTL-H₃-T₁ models, see Figures 5.9 and 5.10, are plausible. Each T₄ atom can satisfy all of its dangling-bonds.

The honeycomb (HC) model has a high energy primarily due to the need to have the first-layer Si atoms bond to two Au atoms and three second-layer Si atoms. This necessarily leads to non-tetrahedral bonding. Therefore, we excluded this and the centered honeycomb models from consideration for the LEED intensity analysis. The two simple-trimer models, T₄-T₁ and H₃-T₁, have the lowest Keating energy and achieve near optimal bond-lengths. Such simple trimer-models have been determined for other surfaces, see Appendix C. Hence, these two models were thus included in the I(V) analysis. The MCT-T^V₁-T₁-T₄ model's energy is much higher due to the relaxation of Si atoms around the vacancies. The MCT-T₁-T₁-T₄ model contains no substrate relaxation. This derives from the Si honeycomb insulating the substrate from the Au trimers. The MCT-T₁-T₁-H₃ model, results not shown, yields the same results, i.e., the Au-trimer layer becomes almost coplanar with the Si-adatom layer in order to shorten the Au-Si bond, but the adatom bond-angles become less tetrahedral. These MCT models were included in the I(V) analysis, but were considered unlikely to be solutions because they still contained unsatisfied Si dangling-bonds.

The MTL-T₄-H₃ model yielded a very high energy, owing to the large motion of the second-layer Si atoms. The MTL-T₄-T₁ model, results not shown, yielded almost identical values. Hence, these models were excluded from the LEED intensity analysis. The MTL-H₃-T₁ and the MTL-T₁-H₃ models yielded acceptable and nearly identical energies. The only large substrate motions required were the radial displacement (0.46 Ang.) of the second-layer Si atoms, in order to equilibrate the Au-Si bond lengths. As an intermediate conclusion, if we fixed the Au-trimer's size, then two simple trimer (H₃-T₁ and T₄-T₁) and two missing-top layer (MTL-H₃-T₁ and MTL-T₁-H₃) models yielded chemically feasible and low elastic-energy structures.

As an extension to the Keating energy analysis, we considered the adjustment of the Au-trimer's size for the two plausible MTL-models, see Table 5.3. When the Au trimer was allowed slightly to dilate, columns 1 and 2, we achieved a small reduction in the bond-bending term of the elastic energy. When the Au trimer was allowed to dilate by a large amount, columns 3 and 4, we achieved another energy minimum, see Figures 5.11 and 5.12. The two latter models, denoted honeycomb chained-trimer (HCT), are considered to be solutions to the Si{111}√3x√3-30-Ag structure, see Appendix D. We have excluded these HCT models from the LEED intensity analysis of the Si-√3-Au surface, because they yielded in-plane Si-Si and Au-Au distances different from those determined by Dornisch et. al.. The two former structures were named conjugate honeycomb chained-trimer (CHCT) by Ding et. al., see Figures 5.9 and 5.10. The ``conjugation'' is the radially outward-motion of the Si atoms from the H₃ center of symmetry, as opposed to the inward-motion in the honeycomb chained-trimer model (HCT). These CHCT models were considered to be the most likely solutions to the Si-√3-Au structure because they contained the most important features revealed by the MEIS, the SXD, the STM, the ARPES, and the TEC analyses, and they satisfied all the Si dangling-bonds.

5.4 LEED Intensity Analysis

The CHANGE program [108] was used to calculate the LEED I(V) spectra for the models considered. In each calculation, the following non-structural inputs were used: 43 beams in the energy range from 40 to 164 eV; 61 beams in the range from 168 to 240 eV; 4 eV energy increment; eight phase-shifts calculated non-relativistically from a relativistic Au potential and from a non-relativistic Si potential; a -(10+4i) eV inner potential; and a 0.1 Ang. root-mean-square amplitude of atomic vibrations. In each calculation, the in-plane distances of the Au and the Si atoms were fixed, and the variable parameter was the interlayer distance between the surface layer and the Si{111} bulk planes. Off-line R-factor and visual evaluations were done to compare the agreement between the calculated and experimental spectra. However, there existed numerical problems, namely, we were unable to use: 1) more than 10 phase-shifts, 2) more than 61 beams in the calculation, 3) more than eight atoms in the surface layer. The use of any of the above caused numerical instabilities in the program. The first two limitations precluded us from accurately calculating I(V) spectra above 240 eV. Our experimental data extended, however, to 360 eV. Hence, one third of our data was excluded from the analysis. The third limitation was most severe; a √3 surface typically contains three atoms per layer per unit-mesh. Hence, we were only able to consider the locations of atoms in the top two surface-layers, and we were forced to maintain lower layers at their bulk positions. Finally, each calculation required several CPU-hours on an IBM 3090-600 computer. Therefore, structural refinement was only attempted for models which yielded a modicum of initial agreement.

The following models were tested: T₄-T₁, H₃-T₁, H₃-T₄, T₁-T₄, T₄-H₃, T₁-H₃, MCT-T^V₁-T₁-T₄, MCT-T₁-T₁-T₄, MCT-T₁-T₁-H₃, MTL-T₁-H₃, and MTL-H₃-T₁. All of the models were tried with bulk-like locations for the Si atoms, with hard-ball spacings for the Au-Si distance, and with a Au trimer size of 2.8 Ang..

Each of the above models failed to yield calculated I(V) spectra which agreed with the experimental spectra, but the MTL models yielded the best results. There usually was better agreement for the 20, 02, 21, and 12 beams (which probe deeper since they emerge at higher energies) than for the 10 and 01 beams. The integral-order beams also scatter more from the bulk than the fractional-order beams. Hence, the agreement for the 20, 02, 21, and 12 beams indicated that the calculations were correctly executed, but either the proposed models or the parameter space we considered were completely incorrect.

R-factor analysis confirmed our visual assessment, that the matching was dismal and the MTL models yielded the best results. Initially, twelve beams (10, 01, 11, 20, 02, 21, 12, 1/3 1/3, 2/3 2/3, 1/3 4/3, 4/3 1/3) were used in the R-factor analysis. Typically, the best values for (1/2)R_P, r_ZJ, and R_VHT were 0.4, 0.6, and 0.6, respectively. The theory-experiment correspondence for several of the diffracted beams was promising, while for others it was ``hopeless.'' Hence, only five beams (10, 01, 11, 1/3 1/3, 2/3 2/3) were used in the subsequent R-factor analysis. We believed that it was better to improve the agreement for the ``best'' beams, and hope the worst beams would also get ``better.''

In further calculations, the size of the Au trimer and the second interlayer-spacing for several of the above models was also varied, but there was still no agreement. Calculations which twisted the MTL Au-trimers also yielded poor results and broke the mirror symmetry of the diffraction beams. Subsequently, the MTL-H₃-T₁ and MTL-T₁-H₃ models were calculated, using the parameters determined by the Keating energy analysis. There was a definite improvement in the agreement for the former model and little improvement for the latter model.

The I(V) spectra for the MTL-H₃-T₁ structure were then calculated using the parameters provided by Ding et. al.[104]. These parameters differ from those determined by the Keating energy analysis in that the Au-trimer's height is 0.56 Ang. as opposed to 0.81 Ang.. The agreement substantially improved. Variations of Au trimer-size, Au-Si interlayer spacing, and Si-Si in-plane spacing around the values determined by Ding et. al., did not improve the agreement. Additionally, calculations of the MTL-T₁-H₃ model, using Ding et. al.'s parameters, never produced acceptable levels of agreement. The MTL-T₁-H₃ and MTL-H₃-T₁ models yielded similar Keating energies and could be present in domains [109]. Therefore we averaged their calculated spectra, but we found no improvement in the level of agreement between the calculated and the experimental spectra. Hence, the MTL-H₃-T₁ structure determined by Ding et. al. was found by our LEED intensity analysis to be the correct structure.

A final set of LEED spectra was calculated with the following inputs: a) 30 to 164 eV, using 43 beams, b) 168 to 300 eV, using 61 beams, c) 2 eV energy increment, and d) 8 phase-shifts. There was no significant improvement in the visual agreement, and there were marginal changes in the R-factors. Hence, we still concluded that this structure is the ``solution.'' The important features are:

1. The Au trimer has an edge size of 2.8 Ang.. We initially chose the value specified by the x-ray analysis, since LEED is generally insensitive to small in-plane displacements. We later varied this variable, but found no significant reduction in the R-factor values.
2. The first Si-layer is missing.
3. The Au trimer is centered above the fourth-layer Si atoms.
4. The Au atoms are on off-first-layer Si atom sites.
5. The Au-trimer plane is 0.56 Ang. above of the plane of second Si-layer. This is the value specified by Ding et. al.'s total-energy calculation analysis. Variations of up to +-0.2 Ang. did not produce any significant improvement in our R-factor analysis.
6. The second Si-layer atoms are radially displaced away from the trimer center by 0.48 Ang. Variations, again, did not produce detectable improvements.
7. The interlayer spacing between the second-layer and the third-layer Si atoms is unchanged with respect to the bulk value.
8. The real part of the inner potential is -6 eV.
9. We have not determined if there is a symmetric out-of-plane motion of the fourth-layer Si atoms.
10. We have not determined if there is a radial motion of the third-layer Si atoms.
11. The Au-Si distances are 2.405 Ang. and 2.416 Ang. Without the radial displacement of the second-layer Si atoms the Au-Si bonds would be of unequal length, namely, two would be highly compressed and one would be highly expanded.

The visual agreement between the experimental and theoretical (for the optimized structure) spectra can be examined in Figures 5.13, 14, 15, 16, 17, and 18. Corresponding R-factors are listed in Table 5.4. Generally, the agreement is not ``outstanding'', but it is significantly better than for any other attempted structure. We expect that the agreement may improve if calculations using twelve atoms in the surface layer could be done, because this would allow for the radial motion of third-layer Si atoms, the buckling of the fourth-layer, etc.... to be explored. Additionally, we have yet to explore the twisting of the second-layer Si atoms.

5.5 Discussion

The 1/3 1/3, 10, and 01 beams for the 6x6 and √3 surfaces have remarkably similar LEED I(V) spectra, see Figure 5.19. This fact indicates that the two surfaces are similar in structure, in agreement with two STM studies [100, 101] which have determined the √3 to be an ordered sub-unit of the 6x6 structure. Nogami et. al.[100] state that there was a continuous gradient of Au atoms between the two structures, that separate domains of the two structures were not seen, that the √3 surface evolved with coverage by placing extra Au atoms in domain walls, that the √3 domains decreased in size by forming more domain walls, and that the 6x6 was formed from a mesh of walls dividing sub-units of local √3 structures. Huang et. al.[94], also state that the 6x6 surface yields LEIS spectra essentially identical to those of the √3 surface. Thus, we conclude that the Si{111}√3x√3-30-Au phase is the precursor of the Si{111}6x6-Au phase.

In regard to the √3 surface, there exist in the literature, see Appendix D, several model structures that have been applied to both the Si{111}√3x√3-30-Au and -Ag surfaces. This linkage is most likely due to the isoelectronic properties of Au and Ag. However, the growth of thin films of Au and Ag on Si is very different. For instance, Ag islands grow on the partially exposed and sharp Si-√3-Ag interface, whereas Au islands grow on a diffuse Si6x6-Au interface and the island tops contain Si atoms [1]. Additionally, the fractional-beam LEED I(V) spectra of the Si{111}√3x√3-30-Au surface, which are the most sensitive to the structure, are different from those of the Si{111}√3x√3-30-Ag surface, see Figures 5.20 and 5.21. This means that the Si{111}√3x√3-30-Au surface is not the same as the ``all-Si-√3 vacancy'' structure as concluded for the Si{111}√3x√3-30-Ag surface by Fan et. al.[31].

The problem is, however, that there is a consensus in the literature that the Si-√3-Ag surface has the HCT (MTL-H₃-T₁) structure, as determined by Ding et. al.[110]. Also, given that the Si-√3-Au surface has the CHCT (MTL-H₃-T₁) structure, as determined by Ding et. al.[104], we decided to explore the HCT model as solution of the Si-√3-Ag structure. Calculated LEED I(V) spectra using Ding et. al.'s values for the HCT-model can be examined in Figures 5.20 and 5.21. The corresponding R-factors are 0.37, 0.34, and 0.36 for (1/2)R_P, r_ZJ, and R_VHT, respectively. Attempts to refine the agreement proved fruitless. Averaging of calculated spectra for the two plausible HCT-models (MTL-H₃-T₁ and MTL-T₁-H₃) did not produce any improvement. Finally, we could not reconcile the in-plane distances (Au-Au, Ag-Ag, Si-Si, Au-Si, Ag-Si) of the HCT and CHCT models in such a way that Au could have a HCT structure and that Ag could have a CHCT structure on Si{111}. We have only determined that Au has a CHCT structure and Ag does not have a HCT structure.

Additional complications arise when discussing Au or Ag on Ge{111} surfaces. There are no reports of structure studies for Ge-√3-Au, but Dornisch et. al.[111] have recently reported the Ge-√3-Ag surface to have a Patterson map which is identical to the map for Si-√3-Au. Hence, Ge-√3-Ag may have the MTL-H₃-T₁ or MTL-T₁-H₃ configuration, with the reported twisting of second-layer Ge atoms. We have pursued elastic-energy calculations for for this system, and found the same results as for Si-√3-Au. We have pursued the preparation of Ge-√3-Ag surfaces, the collection of I(V) spectra, and the intensity analysis. However, we are unable to verify the structure of Ge-√3-Ag at this time [112].

In conclusion, the Si{111}√3x√3-30-Au surface is a trimer-based structure. The surface is missing the first layer of Si atoms. The Au atoms are registered on first-layer Si atom sites, form trimers centered on fourth-layer Si atoms sites, and are 0.56 Ang. above the second-layer Si atoms. These second-layer Si atoms relax radially away from the Au trimer by 0.48 Ang. We denote this structure MTL-H₃-T₁. The MTL-T₁-H₃ structure is equally stable (as determined by a Keating energy analysis), but is not the correct structure. The stability of either model is also demonstrated by the lack of Si dangling-bonds, as opposed to many previously proposed configurations. Finally, the related HCT-model for Si{111}√3x√3-30-Ag and CHCT-model for Ge{111}√3x√3-30-Ag have not been confirmed by our LEED intensity analyses.