Radiative recombination of donor-acceptor pairs in polar semiconductors

A variational treatment of effective-mass electronic states is made for donor-acceptor (D-A) pairs, including the effects of electron-phonon interaction within the static approximation. The effective Hamiltonian is based on the Fr\"ohlich continuum model. Expressions for the energy levels are obtained analytically and in terms of integrals involving trigonometric functions. The variational parameters for the orbital radii and for the p-state admixtures are determined, all as a function of D-A distance R. Both pairs with equal and those with unequal radii are investigated. The electron-phonon interaction is found to decrease at small R, and the departure from spherical symmetry increases at small R. The theory is applied to the zero-phonon spectra of D-A pairs in GaP and in ZnSe, using a procedure for obtaining the static dielectric constant ε₀ from distant-pair spectra and then focusing attention on the deviations from the ideal 1/R law for nearer-pair spectra. Comparisons are made with previous theoretical work.