Radiative Capture by Impurities in Semiconductors

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Abstract
Detailed balance arguments are used to study the relationship between photo-ionization cross section and radiative-capture cross section for transitions between conduction-band states and the ground state of a localized flaw; the existence of a spectrum of excited states, of compensating impurities, and of competing processes does not impede the development of a simple relationship. This relationship can be expressed in a way which illustrates that the capture lengths of an interacting photon and an interacting electron are in inverse proportion to their respective momenta. It is noted that the reciprocity of photo-ionization and radiative recombination can be utilized either to evaluate recombination in terms of known optical properties or to deduce optical density in terms of known recombination cross sections, and examples of both procedures are given. The thermally averaged capture cross section is expressed as a weighted integral of the photo-ionization cross section with respect to energy, and it is shown how the temperature dependence of radiative recombination is related to the spectral dependence of the photo-ionization cross section.

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