Effects of Spin-Orbit Coupling in Si and Ge

A treatment of spin-orbit effects in some semiconductors is given using the effective-mass method and orthogonalized-plane-wave type wave functions. In this formalism, the spin-orbit splitting of valence states in the crystal is expressed directly in terms of either experimental or calculated values of the spin-orbit splitting of the atomic-core states. The calculation yields values in good agreement with experiments for the splitting at ${\Gamma }_{{25}^{\prime }}$ for Si and at both ${\Gamma }_{{25}^{\prime }}$ and $L_{3^{\prime }}$ for Ge. A demonstration is given of the enhancement of the spin-orbit splitting of valence states in the crystal over the corresponding atomic value.