Structure determination of indium-induced $\mathrm{Si}\left(111\right)\text{−}\mathrm{In}\text{−}4\times 1$ surface by LEED Patterson inversion

A low-energy electron diffraction (LEED) Patterson function (PF) with multiple incident angles is used to determine the structure of the indium-induced $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ reconstructed surface. The experimental PF maps were compared with ones calculated by both single scattering and the tensor-LEED method according to various theoretical models so that one can pick out the right one. It was found that the model proposed by Bunk et al. is the best appropriate one, from which the induced PF maps are similar to the experimental ones. Further analysis of the PF spots obtained from the experimental PF maps directly generates the same model without any presupposition. It indicates that the multiple-incidence Patterson function is an effective method to determine the surface structure. Moreover, detailed atomic positions on surface were deduced from first-principles calculations and tensor-LEED $I\text{−}V$ curve simulations. We also compared the results with those of previous investigations. Good agreement was found between them.

Figure 1

In situ REED image for the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ structure.

Figure 2

(a) LEED pattern of the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ structure at $70\mathrm{eV}$. The $4\times 1\text{unit}$ cell for one domain is outlined. (b) LEED pattern of the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ structure at $120\mathrm{eV}$. (c) Comparison between selected experimental and the best-fit theoretical $I\text{−}V$ spectra of the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ structure at normal incident angle.

Figure 3

(Color) LEED PF in the $\left(1\overline{1}0\right)$ plane from (a) the experimental LEED $I\text{−}V$ spectra taken at 15 incident angles, (b) the simulated LEED $I\text{−}V$ spectra for the SXRD model, (c) the simulated LEED $I\text{−}V$ spectra for the STM model, (d) the simulated LEED $I\text{−}V$ spectra for the TED model, and (e) the simulated LEED $I\text{−}V$ spectra for the SXRD including multiple scattering. The numbers next to the spots in (a) correspond to the atomic pairs shown in Fig. 4.

Figure 4

Top (a) and side (b) views of the atomic structure for the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ surface generated by our program.