Charge Density and Structural Properties of Covalent Semiconductors

We propose a practical scheme to calculate structural energies in crystalline semiconductors. The method is applied to Si to calculate changes in charge densities and harmonic energies for $\mathrm{TO}\left(\Gamma \right)$, $\mathrm{TA}\mathrm{}\left(X\right)\mathrm{}$, and $C_{11}-C_{12}$ distortions. Cubic anharmonic terms are also found for $\mathrm{TO}\left(\Gamma \right)$. For the shear modes a proper description of the electron-electron interaction is found to be vital. Electronic charge densities demonstrate the importance of dynamic redistribution of valence charge in covalent semiconductors.