Single-Layer Limit of Metallic Indium Overlayers on Si(111)

Density-functional calculations are used to identify one-atom-thick metallic In phases grown on the Si(111) surface, which have long been sought in quest of the ultimate two-dimensional (2D) limit of metallic properties. We predict two metastable single-layer In phases, one $\sqrt{7}\times \sqrt{3}$ phase with a coverage of 1.4 monolayer (ML; here 1 ML refers to one In atom per top Si atom) and the other $\sqrt{7}\times \sqrt{7}$ phase with 1.43 ML, which indeed agree with experimental evidences. Both phases reveal quasi-1D arrangements of protruded In atoms, leading to 2D-metallic but anisotropic band structures and Fermi surfaces. This directional feature contrasts with the free-electron-like In-overlayer properties that are known to persist up to the double-layer thickness, implying that the ultimate 2D limit of In overlayers may have been achieved in previous studies of double-layer In phases.

Figure 1

Formation energy as a function of In coverage obtained from different initial substrates: (a) 1.2-ML rectangular and (b) 1.0-ML hexagonal $\mathrm{In}/\mathrm{Si}(111)\text{−}(\sqrt{7}\times \sqrt{3})$, where large (small) balls represent In (Si) atoms. Additional In atoms are tried on the hollow sites of (a) and (b), and the energy of the most stable configuration in each coverage is shown in (c).

Figure 2

1.4-ML $\mathrm{In}/\mathrm{Si}(111)\text{−}(\sqrt{7}\times \sqrt{3})$. (a) Atomic structure and (b) Simulated STM image, representing the surface of constant density with $\rho =1\times {10}^{-3}e/{\AA }^3$. The experimental image was taken from Ref. [7].

Figure 3

Band structure of the $\sqrt{7}$-stripe phase. Filled (open) circles represent In-derived states containing more than 20% of charge in the protruded In atoms (more than 40% in the other In atoms). The $\sqrt{7}\times \sqrt{3}$ Brillouin zone and the calculated Fermi contours are shown in the right panel.

Figure 4

Phase boundary between the 1.4-ML $\sqrt{7}$-stripe and 1.43-ML $\sqrt{7}\times \sqrt{7}$ phases: (a) Atomic structure, (b) simulated STM image, and (c) experimental STM image taken from Ref. [7].

Figure 5

Band structure of the $\sqrt{7}\times \sqrt{7}$ phase. The $\sqrt{7}\times \sqrt{7}$ Brillouin zone (dashed lines) and the calculated Fermi contours are shown in the right panel.

Figure 6

Layer-resolved density of states per In atom for the single- and double-layer indium phases.