THEORY OF NONRADIATIVE CAPTURE OF CARRIERS BY MULTIPHONON PROCESSES FOR DEEP CENTERS IN SEMICONDUCTORS

A quantum-mechanical calculation of the non-radiative transition rate by multiphonon processes is performed by employing a more direct mathe matical approach than those used by previous workers. Based on the tra p potential model proposed by Lucovsky and the optical deformation for m of electron-phonon interaction, the analytical expression for the ca rrier 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 abs olute 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 pa rticular, good fits are obtained for the temperature dependence of the experimental electron capture cross sections reported by Henry and La ng 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 rep orted by Wang et al. The results of our theory are also shown to be us eful in identifying more accurately the charge state of a deep centre.