Many-Particle Theory of Impurity States in Polar Crystals

Abstract

An attempt is made to generalize to polar semiconductors, Kohn's many-particle approach to the theory of shallow impurity states in nonpolar crystals. Nuclear coordinates are included as dynamic variables. The impurity state is described as a linear combination of exact many-particle eigenfunctions that correspond to the motion of a polaron through the impurity-free crystal. The resulting effective dielectric constant is likewise identified as the usual static constant, by considering the interaction between an electron bound by an infinitesimal impurity charge and a small classical charge fixed at a large displacement from the impurity. Corrections to the resulting hydrogenic equation arise from the need to include real phonon states. These corrections are estimated for substances with weak electron-lattice coupling only. The corrections are found small for most III-V semiconductors. They are rather more serious for substances such as Cd${\mathrm{As}}_2$ and CdS, that have somewhat stronger coupling, suggesting a limitation to the applicability of the theory. In an Appendix an interpretation of the new formal contribution to the effective dielectric constant is given in terms of the motion of the ion cores.