Photo-Ionization with Phonon Participation in Semiconductors

Abstract

When the photo-ionization spectrum of an impurity in a semiconductor is measured, it is sometimes possible to find the ionization energy by suitable interpretation of the data. In many cases this has been done by fitting to a simple power law, in the derivation of which it is assumed that phonon participation may be neglected. When there is strong electron -phonon coupling it is not clear that this approach is valid, and the interpretation of the threshold energy obtained in this way is ambiguous.

In this paper we consider a general model of electron-phonon coupling and obtain an expression for the photo-ionization cross-section as a function of photon energy. With sufficient experimental information it is possible to fit the data using this expression. Where less is known about the electronic or vibrational factors, a knowledge of the general cases allows one to decide whether a straightforward power law approximation may be used. If it is valid to interpret the data by fitting to a power law, the threshold obtained is the optical ionization energy.