Abstract
New realistic semiempirical expressions for the two-center integrals and for the Slater-Koster parameters (SKP's) are constructed for group-IV semiconductors. These expressions provide the explicit dependences of the SKP's on the atomic characteristics, on dielectric constants in solids, and on interatomic separations. Contributions to the SKP's from the three-center and higher-order integrals are taken into account by three parameters. These expressions are valid for atomic separations as far as second-neighbor distances. The band structures of Si, Ge, and $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$ obtained using these new matrix elements are compared with other theoretical calculations and experimental optical spectra. A set of identities relating the eigenvalues at high-symmetry points under the second-neighbor approximation is also presented.
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