Zero-phonon recombination spectra of donor-acceptor pairs in GaP and ZnSe: Model-impurity-potential approach

Abstract

The influence of central-cell corrections on electron-hole recombination energies of donor-acceptor (DA) pairs in III-V and II-VI semiconductors is investigated. A variational treatment of the DA complex is developed in the framework of the effective-mass theory, including the effects of interaction between the charge carriers and the longitudinal-optical phonons within the static approximation. The effective-mass Hamiltonian of the DA pair, based on Fr\ohlich's continuum theory, allows for central-cell corrections by means of a suitable impurity model potential adjusted to experiment in the case of isolated impurities. The orbital radii of the electron and hole wave function, its departure from spherical symmetry, and the DA-pair energy are given as a function of the donor-acceptor separation $R$. The central-cell correction is found to decrease appreciably at small $R$. The results are compared with previous theoretical work and experiments on zero-phonon spectra of DA pairs in ZnSe and in GaP. It is shown that the central-cell correction cannot be neglected in order to explain the radiative DA-pair recombination energies. The model potential adopted in the present work reproduces the general trend of the $R$-dependent electron-hole recombination energies deduced from DA-pair spectra involving dopants of various depth.