Green’s-function–quantum-defect treatment of impurity photoionization in semiconductors

An analytic expression is derived for the photoionization cross section of impurity atoms in semiconductors. The use of a quantum-defect wave function for the impurity ground state permits impurity atoms to be conveniently characterized in terms of ground-state energies. The Coulomb Green's-function and time-dependent perturbation theory are used to calculate the wave function of photoexcited electrons or holes from which the photoionization cross section is obtained. The results apply to shallow or deep levels associated with carriers bound to charged impurity centers. Results for photodetachment of carriers bound to neutral impurities are obtained in the limit where the impurity charge goes to zero. Theoretical cross-section maxima are found to be in remarkably good agreement with experimental results, considering that no free parameters or empirical effective field ratios are employed.