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

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 $\mathrm{pp}\sigma$ interaction scales as $d^{-2.6\mathrm{}}$ and the $\mathrm{ss}\sigma$ interaction as $d^{-4.6\mathrm{}}$. In the tetravalent diamond semiconductors both $s$ and $p$ interactions scale as $d^{-2\mathrm{}}$. 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.