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.

The shift in the $g$ tensor due to spin-orbit interactions is studied in Si and Ge. Because of crystal selection rules, the usual two-band approximation to the effective-mass sum rule is inadequate for Si and, in particular, the core state must be considered. When all important states are included, the calculations yield values in good agreement with experiment. In the case of Ge, it is found that core states do not contribute appreciably to the $g$ tensor. However, the calculated value for the shift in the transverse component of the $g$ tensor has an opposite sign to the measured one.

A certain matrix element of the deformation potential for Si is also evaluated based on the measured shift in the $g$ value due to strain. The result is compared with other deformation potentials in Si.

• Received 18 December 1961

DOI:https://doi.org/10.1103/PhysRev.126.1317