Wave functions and optical cross sections associated with deep centers in semiconductors

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Abstract
Analytical impurity wave functions associated with deep levels in semiconductors (e.g., GaAs:O, GaP:O) are calculated, using a pseudopotential scheme in which a realistic and convergent model is employed to represent the host-crystal band structure and the impurity potentials. The effects determining the form of the wave function are studied with a view to establishing a relationship between the position of a deep level in the gap and the localization of the wave function. It was found that the localization is not a sensitive function of the impurity energy measured from the nearest band edge. The optical impurity-to-band cross sections involving deep levels are computed as a function of photon energy and temperature. The electronphonon interaction is taken into account within the strong-coupling model of Huang and Rhys. A relatively simple formula is derived which can be applied to interpret optical cross sections associated with deep centers dominated by a short-range potential. Numerical results are presented for state one and two of GaP:O, and the threshold energies, the magnitude of the Franck-Condon effect, and the temperature dependence are determined. A brief discussion is given of optical cross sections associated with deep centers in GaAs and Si.