Relativistic Effects on the Electronic Band Structure of Compound Semiconductors

The effects of the three relativistic interaction terms, mass-velocity, Darwin, and spin-orbit coupling, on the electronic levels of covalent-bond compound semiconductors BN, SiC, AlP, and GaAs have been investigated. Quantitative relativistic shifts and spin-orbit splittings of the appropriate Bloch states at $\Gamma$, $X$, and $L$ points in the Brillouin zone have been obtained using orthogonalized-plane-wave crystal wave functions. Comparisons between available experimental data and calculations of the spin-orbit splittings of GaAs show a maximum discrepancy of 11%. The inclusion of the relativistic shifts of the energy levels did not change very significantly the band structure obtained by the nonrelativistic calculations. These effects increase, however, as the atomic numbers of the constituent atoms increase.