Universal band structures for group-V elements and IV-VI compound semiconductors

Abstract

The tight-binding band structures of the group-V elements As, Sb, and Bi and the IV-VI compound semiconductors have been found by the fitting of previous calculations and photoemission data. The two-center interactions are found to scale with bond length $d$. The $\mathrm{pp}\ensuremath{\sigma}$ interaction scales as ${d}^{\ensuremath{-}2.6}$ and the $\mathrm{ss}\ensuremath{\sigma}$ interaction as ${d}^{\ensuremath{-}4.6}$. In the tetravalent diamond semiconductors both $s$ and $p$ interactions scale as ${d}^{\ensuremath{-}2}$. The different scaling law reflects bonding differences; both $s$ and $p$ electrons are involved in bonding in diamond while only $p$ electrons are used in the group-V and IV-VI compound solids. The states of the group-V elements are reasonably well reproduced with only first-neighbor interactions. Second-neighbor interactions or excited ${s}^{*}$ and ${d}^{*}$ states are needed to fit the narrow gaps of the IV-VI compound semiconductors. The electronic structure of the rocksalt phase of InSb is also calculated and used to illustrate the differences in bonding between III-V and IV-VI compounds.