THEORY OF NON-RADIATIVE CAPTURE OF CARRIERS BY MULTIPHONON PROCESSES FOR DEEP CENTRES IN SEMICONDUCTORS

Abstract

A quantum mechanical calculation of the nonradiative transition rate by multiphonon processes is performed by employing a more direct mathematical approach than those used by previous workers. The carrier capture rate is calculated based on the trap potential model proposed by Lucovsky and the optical deformation form of electron-phonon interaction. After some transcriptions the analytical expression for the carrier capture cross section is brought to a transparent form for easy comparison with experiments. The effect due to the charge state of the deep centre is also considered. Both the absolute magnitude and the temperature dependent behaviours of the capture cross section predicted in our calculations are well supported by the experimental results of various deep centres in semiconductors. Our theory is shown to be applicable to neutral and charged centres over a wide temperature range. The electron-phonon coupling strength, Huang-Rhys factor, the average phonon energy, and the Bohr energy which reflects the charge state of a trap, all can be extracted in the fittings to experimental data. Good fits have been obtained for the experimental electron capture cross sections reported by Henry and Lang for B and A centres in GaAs. The accuracy of the Huang-Rhys factor and the phonon energy obtained for B centre is corroborated by the good fittings obtained for the photoionisation cross section data reported by Wang et al, in which we obtain its electron bound energies at various temperatures. We also show that the results of our theory are useful in identifying more accurately the charge state of a deep centre. The theory has been applied to a strong repulsive centre, the upper level of copper in germanium reported by Zhdanova et al, with some measure of success, details of which are given in Appendix B.