Double-Layer In Structural Model for the $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}\sqrt{7}\mathbf{\times }\sqrt{3}$ Surface

We demonstrate by using density functional calculations that the $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}\sqrt{7}\times \sqrt{3}$ surface consists of an In double layer, contrary to the prevailing idea that the In overlayer on this surface is just one atom thick and thus can be used to represent the ultimate 2D limit of metal overlayer properties. The double-layer In structure is sound energetically and microscopically and, above all, well reproduces the measured photoemission band structure that could not be fairly compared with any single-layer In model. The present double-layer model urges a reconsideration on the recent experimental claims that the In overlayer properties were pushed to a single-layer limit in this surface.

Figure 1

Single-layer model for $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}\sqrt{7}\times \sqrt{3}$-rect. (a) Optimized structure. Large (small) balls represent the In (Si) atoms. Dashed lines denotes a $\sqrt{7}\times \sqrt{3}$ unit cell. (b) STM images. Simulations represent the surface of constant density with $\rho =1\times {10}^{-3}e/{\AA }^3$ taken at the bias voltages $+0.5\mathrm{eV}$ (empty states) and $-0.5\mathrm{eV}$ (filled states). Experimental images were taken from Refs. 9, 10. (c) Band structure. Open circles represent the In-derived states which contain more than 50% of charge in the In layer. Solid lines represent the ARPES bands reported in Ref. 13. The calculated Fermi level was set to zero. For a better comparison, the ARPES bands were shifted by $+0.2\mathrm{eV}$.

Figure 2

Double-layer model for $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}\sqrt{7}\times \sqrt{3}$-rect. (a) Optimized structure. Dark balls represent the top-layer In atoms. (b) STM images taken in the same way as in Fig. 1. (c) Band structure. Open circles represent the In-derived states which contain more than 65% of charge in the In double layer.

Figure 3

Electronic structures of the In double layer. (a) Layer-resolved band structure. Dark and gray circles represent the In states which contain more than 50% of charge in the top and second In layer, respectively. (b) Charge characters of the three surface states marked in (a). The right panels show the in-plane charge distribution on the cross section marked by long dashed lines in the left panels. (c) Fermi contours (thick lines) in comparison with the ARPES data (thin lines) of Ref. 13. The contour map was obtained at $E_F+0.2\mathrm{eV}$ for a better comparison with the experiment. (d) LDOS for three different In systems: 1.2 ML, 2.4 ML, and In(001).