Phonon-Broadened Impurity Spectra. I. Density of States

Abstract

The phonon-broadened densities of states associated with (a) a point charge, (b) an $S$-wave hydrogenic shallow donor, and (c) an exciton bound to a neutral defect are calculated. The electronic states are coupled to the lattice vibrations via the (a) longitudinal-optical, (b) piezoelectric, and (c) deformation-potential linear electron-phonon interactions. The major dynamical approximations consist of the use of the Debye model for the acoustical-phonon spectrum and the neglect of the mixing of electronic states by phonons. Within the framework of the model Hamiltonian the Fourier transforms of the densities of states are calculated exactly and analytically. For CdS, CdTe, and ZnS numerical calculations of the densities of states are presented. The density of states associated with a shallow donor in CdTe and ZnS exhibits, in lieu of a zero-phonon line, a Lorentzian peak whose width is proportional to temperature. The inclusion of the static shielding of the piezoelectric interaction by mobile charge carriers replaces the Lorentzian by a zero-phonon line plus two shoulders. The extensions of the calculation to donor-acceptor, band-impurity, interband, and intra-deep-impurity transitions are discussed.