Calculated spin-orbit splitting of all diamond-like and zinc-blende semiconductors: Effects of p1/2 local orbitals and chemical trends

e have calculated the spin-orbit (SO) splitting $\Delta_{SO}=\epsilon (\Gamma_{8v}) - \epsilon (\Gamma_{7v})$ for all diamond-like group IV and zinc-blende group III-V, II-VI, and I-VII semiconductors using the full potential linearized augmented plane wave method within the local density approximation. The SO coupling is included using the second variation procedure, including the $p_{1/2}$ local orbitals. The calculated SO splittings are in very good agreement with available experimental data. The corrections due to the inclusion of the $p_{1/2}$ local orbital are negligible for lighter atoms, but can be as large as $\sim$250 meV for 6$p$ anions. We find that (i) the SO splittings increase monotonically when anion atomic number increases; (ii) the SO splittings increase with the cation atomic number when the compound is more covalent such as in most III-V compounds; (iii) the SO splittings decrease with the cation atomic number when the compound is more ionic, such as in II-VI and the III-nitride compounds; (iv) the common-anion rule, which states that the variation of $\Delta_{SO}$ is small for common-anion systems, is usually obeyed, especially for ionic systems, but can break down if the compounds contain second-row elements such as BSb;(v) for IB-VII compounds, the $\Delta_{SO}$ is small and in many cases negative and it does not follow the rules discussed above. These trends are explained in terms of atomic SO splitting, volume deformation-induced charge renormalization, and cation-anion $p$--$d$ couplings.