Theory of structural properties of covalent semiconductors

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 ($\Gamma$), $\mathrm{TA}\mathrm{}\left(X\right)\mathrm{}$, and $C_{11}-C_{12}$ lattice distortions. Harmonic and anharmonic forces and Grüneisen 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 $\mathrm{TA}\mathrm{}\left(X\right)\mathrm{}$ mode. Charge densities for the distorted crystals show the nature of the electronic forces and the relation to phenomenological models.