Theory of structural properties of covalent semiconductors

Abstract

We describe a method to calculate structural properties of semiconductors from the electron-ion Hamiltonian using density-functional expressions for the total energy. The method is applied to Si using an ionic pseudopotential with a plane-wave basis and considering TO ($\ensuremath{\Gamma}$), $\mathrm{TA}(X)$, and ${C}_{11}\ensuremath{-}{C}_{12}$ lattice distortions. Harmonic and anharmonic forces and Gr\"uneisen coefficients are shown to be in reasonable agreement with experiment except that additional steps toward self-consistency appear to be essential for the very sensitive $\mathrm{TA}(X)$ mode. Charge densities for the distorted crystals show the nature of the electronic forces and the relation to phenomenological models.