Elastic properties of semiconductors using universal tight-binding parameters

Minimal-basis tight-binding theory, using free-atom term values and nearest-neighbor universal 1/${\mathit{d}}^2$ coupling, and an A/${\mathit{d}}^3$+B/${\mathit{d}}^{12}$ repulsion, is used to calculate elastic properties without further approximations. Specifically, the shear constants (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 and ${\mathit{c}}_{44}$ and the Kleinman internal-displacement parameter are calculated for diamond-structure and zinc-blende-structure semiconductors. Most are within 30% or so of experiment. Spin-orbit coupling is added and found not to make significant corrections. Addition of a Louie peripheral excited state considerably improves the conduction bands but has little effect upon the elastic properties. The transverse charge and the piezoelectric charge are calculated with the additional assumption that the only important charge transfers are between nearest neighbors. These charges are not in such good accord with experiment. Comparison with the predictions of the bond-orbital approximation to tight-binding theory for (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 and the transverse charge suggests that the errors in that approximation are comparable to those of the tight-binding theory itself, small for the elastic constant but sizable for the transverse charge.