Self-Consistent Calculations of the Energy Band Structure ofMg2Si

Self-consistent calculations of the band structure of the semiconducting compound ${\mathrm{Mg}}_2$Si are presented for the nonrelativistic Hartree and Hartree-Fock (HF) independent-particle models (IPM's). The IPM's are based on a finitely periodic model of the many-electron system. Some advantages and distinctions of this model with respect to the conventional formulation are discussed. The calculations are broken into two parts. First-order core (tight-binding) functions and energies are obtained from a model in which all valence effects are neglected. The dominant valence contributions are included in the final stage of calculation where the basis consists of first-order core functions and orthogonalized plane waves. Approximations to matrix elements are described and the error is estimated. The calculations reveal that the valence-band maximum occurs at $\Gamma \left({\Gamma }_{15}\right)$ and the conduction band is many-valleyed with minima at the equivalent points $X\left(X_3\right)$. These results agree with qualitative predictions of band symmetries based on experimental charge densities and a symmetry analysis using linear combinations of atomic orbitals. A preliminary investigation indicates that the Hartree bands are in good quantitative agreement with optical data and should be a valuable aid in the interpretation of experiment. The HF-IPM results for ${\mathrm{Mg}}_2$Si are compared with results for HF calculations in free atoms.