Calculated Spin-Orbit Splittings of Some Group IV, III-V, and II-VI Semiconductors

The spin-orbit splittings of the valence and conduction bands of the group-IV semiconductors Si, Ge, and $\alpha -\mathrm{Sn}$, the III-V compounds AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb, and the II-VI compounds ZnS, ZnSe, ZnTe, and CdTe have been obtained at the $\Gamma$, $X$, and $L$ symmetry points in the Brillouin zone. The calculations were made using a relativistic orthogonalized plane wave (ROPW) model. The energies presented are differences in eigenvalues of the Dirac Hamiltonian where the exchange correlation potential operator was approximated by the cube root of the electron density with coefficients suggested by Slater and by Kohn, Sham, and Gaspar (KSG). The calculated values are compared with values obtained from experiments and from previous $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ calculations. The validity of the two-thirds rule for the ratio of the $L$-point to $\Gamma$-point valence-band spin-orbit splitting is examined. The effects of hydrostatic pressure on the spin-orbit splittings are also presented.