Theory of non-radiative capture of carriers by multiphonon processes for deep centres in semiconductors

Abstract

A quantum-mechanical calculation of the non-radiative transition rate by multiphonon processes is performed by employing a more direct mathematical approach than those used by previous workers. Based on the trap potential model proposed by Lucovsky and the optical deformation form of electron-phonon interaction, the analytical expression for the carrier capture cross section is brought to a transparent form for easy comparison with experiments after some transcriptions. The effect due to the charge state of the deep centre is also discussed. Both the absolute magnitude and the temperature-dependent behaviour of the capture cross section predicted in our calculations are well supported by the experimental results of various deep centres in semiconductors. In particular, good fits are obtained for the temperature dependence of the experimental electron capture cross sections reported by Henry and Lang (1977) for B and A centres in GaAs. The accuracy of the Huang-Rhys factor and the phonon energy obtained for the B centre is corroborated by the good fittings obtained for the photoionization cross section data reported by Wang et al (1984). The results of our theory are also shown to be useful in identifying more accurately the charge state of a deep centre.