Conference-ISSS-5-Structural Study of the Si ( 553 )-Au Surface

When gold is deposited onto the Si(553) surface, a highly ordered surface with a quasi-one-dimensional electronic structure can be prepared. This Si(553)-Au surface was investigated by surface X-ray diffraction to determine the surface structure. A structure model was constructed from the Patterson function of the experimental diffracted intensities. There is one gold atom in the primitive unit cell. It substitutes for a top-layer silicon atom on the terraces. The silicon atoms near the step edge reconstruct to form a honey-comb chain. [DOI: 10.1380/ejssnt.2009.533]


I. INTRODUCTION
Metal-induced structures on semiconductor surfaces have been studied frequently because of their unusual physical properties and their potential use in nanoelectronic devices.Vicinal Si(111) surfaces can be used to create one-dimensional metallic structures [1].Onedimensional systems have unusual properties, for example, strong correlation between electrons or Peierls transitions [2].They have received considerable attention in the field of surface science recently for this reason.
The Si(553) surface is a typical example of a vicinal Si(111) surface.It is composed of terraces with (111) orientation and steps.Deposition of gold atoms onto the Si(553) surface leads to the formation of a highly ordered periodic arrangement of single steps in the [110] direction separated by about 1.5 nm wide terraces.This surface has a metallic quasi-one-dimensional band structure [3], and undergoes two metal-insulator transitions near and below room temperature [4,5].The surface shows a strong Rashba effect due to the heavy gold atoms [6].In order to understand these properties better, it is necessary to know the atomic structure.
Several structure models for the Si(553)-Au surface have been proposed to date.Ghose et al. constructed a model from X-ray diffraction results [7].The model has two gold atoms at the step edge.Other authors, however, find that the coverage of the Si(553)-Au surface corresponds to only one gold atom (e.g.[3,5,8]).In addition, this model was found to be unstable in density functional theory calculations [9].A number of other models have been proposed from first-principles calculations and scanning tunneling microscopy images [3,10,11].These models generally have a single gold atom substituting for Si on the terrace and the silicon atoms near the step edge reconstruct to form a honey-comb chain.The band structure of none of these models, however, is fully consistent with the experimental one [11].Further experimental input is therefore needed to determine the correct structure model.The purpose of this study is to determine the surface structure of the Si(553)-Au surface by X-ray diffraction.

II. EXPERIMENT
Surface X-ray diffraction was used to determine the structure of the Si(553)-Au surface.The experiment was performed at beamline 15B2 of the Photon Factory at the High Energy Accelerator Research Organization.The experimental setup consists of a six-circle diffractometer with an ultra-high vacuum chamber [12].
The Si(553)-Au surface was fabricated in-situ in the ultra-high vacuum chamber (base pressure 1.0 × 10 −10 Torr).A Si(553) wafer (P-doped, 2-4 Ωcm) was repeatedly flashed to 1270 • C by resistive heating to produce a clean surface.The RHEED pattern of the Si(553) clean surface shows a ×7 reconstruction in the [110] direction and a broad specular spot because the distance between the steps is not uniform.
Gold was deposited onto the Si(553) surface kept at 600 • C.During deposition, the RHEED pattern changes.First, the pattern gradually changes to a ×5 reconstruction in the [110] direction.At higher coverages, the ×5 reconstruction disappears again and ×2 and ×3 streaks in the same direction appear.These streaks weaken again, until a pattern with weak ×2 streaks and a sharp specular spot is observed.This pattern corresponds to the ordered Si(553)-Au surface.After deposition, the sample was annealed at 850 • C. Figure 1 shows the RHEED pattern of the ordered Si(553)-Au surface.Weak spots from a √ 3 × √ 3 reconstructed structure are also visible in this pattern.They indicate that the amount of gold was slightly larger than needed for the perfect Si(553)-Au surface.We confirmed that the coverage of the ordered Si(553)-Au surface is one gold atom per primitive unit cell by comparing with the deposition time needed to prepare a Si(111)-Au-5 × 2 surface.The surface X-ray diffraction measurement was done at room temperature with an X-ray wavelength of 1.1 Å. Rocking curves were measured at each point of the crystal truncation rods (CTRs).The diffracted intensities were obtained by integrating the peaks of the rocking curves.57 CTRs were measured for perpendicular momentum transfers L in the range from 1.7 to 14.4.Symmetryequivalent CTRs were averaged, leaving 39 CTRs with 667 data points.The surface unit cell given by Ghose et al. [7] is used in this paper.It is an orthorhombic centered unit cell with two steps per unit cell.
The quality of the surface was confirmed by X-ray diffraction.If too much or too little gold is deposited, CTRs at positions in reciprocal space different from those expected for the (553) surface appear, because facets with an orientation different from (553) develop [7].A scan in reciprocal space in the direction corresponding to the direction perpendicular to the steps showed only strong CTRs at the positions of the (553) surface.

III. RESULTS AND DISCUSSION
The experimental diffraction intensities were analyzed using the Patterson function, that is, the auto-correlation function of the electron density.It is obtained from the Fourier transform of the intensities.The peaks of the Patterson function correspond to vectors between atoms.It can therefore be used to construct a model directly from the measured intensities.In the case of the Si(553)-Au surface, the diffraction is dominated by the single heavy gold atom in the primitive unit cell, and the strong peaks can be interpreted as Au-Si vectors, analogous to the analysis done for the Si(557)-Au surface [13].This greatly simplifies the analysis of the Patterson map.
Figure 2 sion symmetry, regardless of whether the structure has inversion symmetry.Therefore, for an atom at position (x, y, z) relative to the gold atom, peaks at both (x, y, z) and (−x, −y, −z) appear, and it is necessary to choose which position is the correct one.The position of the gold atom relative to the bulk Si atoms can be determined from the peaks in the Patterson map at large negative z.The peaks at large positive z correspond to the inversion image of the bulk atoms.The black crosses in Fig. 2(a) indicate the bulk atoms.From their positions, it is found that the position of the gold atom is close to that of a Si atom in the top-most layer of the ideal surface, that is, the gold atom substitutes for a Si atom in the top layer.
First, peaks close to bulk positions were searched to determine the position of the silicon atoms at the surface.If the peaks marked with a square symbol in Fig. 2(a) are taken to originate from silicon atoms located on the left side of the gold atom, then these atoms form a continuation of the bulk lattice.This is reasonable since they lie close to or below the step to the next terrace.
The weak peak marked with an asterisk symbol lies near to the gold atom at x = 0.5, y = 0.5, z = 0 and is in the proper position for a silicon atom of the topmost bilayer bonded to the gold atom.An atom on its inversion http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology image would be in an unphysical position above the gold atom.The strong peak marked with a circle is also in the position of an atom of the topmost bi-layer bonded to the gold atom.This peak is significantly stronger than the other peaks, except for the origin, however, which indicates that this peak is a superposition of two silicon atoms located on both sides of the gold atoms.We put therefore another Si atom on its inversion image (marked with a diamond).This atom is also needed to provide a sensible connection to the atoms further right of the gold atom.
The remaining peaks in Fig. 2(a) (marked with triangles) all have positions that lead to unreasonable bonding configurations close to bulk Si atoms, if they are interpreted to be on the left side of the gold atom.On the right side of the gold atom, they form a honey-comb chain structure at the step edge.Honey-comb chains are a common feature in other gold-induced surface structures [13,14] The structure model constructed from the Patterson map is shown in Fig. 3.The gold atoms substitute for a top-layer silicon atom and form a chain in [110] direction on the terraces.The Si atoms near the step edge are reconstructing to make a honey-comb chain.These features are similar to the accepted model for the Si(557)-Au surface [13] and also to most previously proposed models for the Si(553)-Au surface [10,11].The Patterson map calculated from this model (Fig. 2(b)) is in reasonable agreement with the experimental Patterson map in Fig. 2(a).
Figure 2(c) shows for comparison the Patterson map calculated from the f2 model favored in recent firstprinciples calculations by Riikonen et al. [11].The circle marks the position of a peak in the experimental Patterson map that does not appear in Fig. 2(c), because the gold atom is closer to the step edge than in the model in Fig. 3.This model is therefore not consistent with our results.
The Patterson map in the previous X-ray diffraction study of the Si(553)-Au surface by Ghose et al. [7] has some similarities to the Patterson map in Fig. 2 (a).They interpreted the strong peak marked with a circle/diamond as a second gold atom in the unit cell.Since the amount of gold that was deposited in our experiment amounts to only one gold atom per unit cell (in agreement with other reports [3,5,8]), we believe that our interpretation that this peak is due to two silicon atoms is correct.
The model in Fig. 3 is not necessarily the only one that can explain the experimental Patterson map.If the assumption that the atoms below the topmost layer of the surface are close to their bulk positions is true, however, then the position of the step edge relative to the gold atom is determined by the peak near x = 0.33, z = 0.03 (marked with a triangle) in Fig. 2(a).In models with the gold atom closer to the step edge, a Si atom would be on the inversion image of this peak near x = 0.67, z = −0.03,which would be in an unreasonable bonding configuration with respect to the positions of the bulk atoms in the second bi-layer.For the positions of the atoms between the step edge and the gold atom, an analogous argument can be made.A possible uncertainty in the model construction is that additional atoms could be present, if they are close to the inversion image of another atom or if there is too much disorder to produce a strong peak in the Patterson map.
The present model is very similar to the f3 model by Riikonen et al. [11].In their first-principles calculations, they found that this model is one of the most stable models, but the calculated band structure is different from the experimental band structure.The atoms between the honey-comb chain at the step edge and the gold atoms rearrange in their calculations, and a double honey-comb chain structure is formed.Using the positions extracted from the Patterson map, however, we find that these atoms do not form a double honey-comb chain.It should be noted, however, that the determination of the atomic positions from the Patterson map is not very exact.A more precise determination of the atomic positions by minimization of the difference between measured and calculated structure factors is underway.

IV. CONCLUSION
We investigated the surface structure of the Si(553)-Au by X-ray diffraction at room temperature.We obtained a structure model for the Si(553)-Au surface from the Patterson function of the experimental diffraction intensities.Features of the structure model are an Au atom in the middle of the terrace and a honey-comb chain of silicon atoms at the step edge.

FIG. 2 :
FIG. 2: (a) Patterson map calculated from the experimental intensities.The symbols indicate positions of atoms in the model in Fig. 3.The dashed line shows the surface termination.(b) Patterson map calculated from the model in Fig. 3. (c) Patterson map calculated from the f2 model of Ref. 11.x and z are in reduced coordinates of the centered unit cell, the x-direction is perpendicular to the steps and z perpendicular to the surface.The y = 0 section is shown, the y = 0.5 section can be obtained by shifting x by 0.5 because the unit cell is centered.