Solvable Model of a Hydrogenic System in a Strong Electric Field: Application to Optical Absorption in Semiconductors

Abstract

A model potential is proposed which, in parabolic coordinates, consists of the Coulomb potential near the origin and linear terms in the electric-field potential far from the origin. The eigenfunctions of the model potential are obtained exactly and analytically. An expression for the optical-absorption coefiicient for excitons in an electric field is derived. Selection rules for allowed and forbidden vertical transitions are obtained. Numerical calculations of the line shapes of the lowest three exciton peaks are shown to be in agreement with existing experimental data. The model predicts no asymptotic alteration of the low-frequency Franz-Keldysh edge by the Coulomb interaction and a shift to lower energies of the continuum absorption near the zero-field band gap. Comparison of the predictions of the model with those of perturbation theory in the region of the low-field exciton peaks indicates that the model does not correctly yield the positions of the peaks but does qualitatively describe their broadening and eventual disappearance in an increasing electric field. Experiments measuring the quenching field for exciton peaks in the alkali halides and rare-gas solids are proposed as a method of ascertaining the spatial extent of the associated excitons.