Theoretical Energy-Band Parameters for the Lead Salts

Abstract

General expressions for the parabolic effective masses and $g$ factors are obtained in terms of seven undetermined parameters for a six-band model at the $L$ point of the NaCl lattice. The spin-orbit mixing of bands is treated explicitly with the result that both longitudinal and transverse components of the momentum are coupled between bands with ${L}_{6}$ symmetry and opposite parity. The six bands of interest are treated in the free-electron and tight-binding limits. The simplified expressions in the tight-binding limit, which approximate PbS, give spherical and nondegenerate valence- and conduction-band parameters. In this limit, the bands at $L$ are similar in detail to certain of the bands at $\ensuremath{\Gamma}$ in germanium and the III-V compounds. Expressions, valid over an extended range of k, are also obtained for the nonparabolic effective masses and $g$ factors. The signs of the $g$ factors are treated in detail in order to resolve the differences which have appeared in the literature.