# Capture into deep electronic states in semiconductors

## Abstract

This paper attempts a careful theoretical study of nonradiative electron capture by deep levels in semiconductors and has been undertaken with a view toward understanding the relevant processes, developing criteria for the choice of an appropriate set of vibronic states, and evaluating the various approximations which are commonly made in calculating capture cross sections. These points are illustrated for a specific model a one-band, one-site potential modulated in depth by a single normal mode which is solved numercially and in several approximations for various vibronic coupling strengths. The work establishes the following results: (1) A correct treatment of the cascade process through which energy is transferred to the lattice is essential in obtaining meaningful cross sections. In particular, the strength of cascade coupling in relation to the other scattering processes determines the number of vibronic levels which contribute effectively to capture and, thus, controls the magnitude and temperature dependence of the cross section. (2) Although "internal" scattering generated by the nonadiabatic terms in the local Hamiltonian can contribute to capture, "external" scattering by bulk lattice phonons may be more important. Further, such phonon scattering is related to the electronic transport properties of the material, and its contribution to capture can be calculated easily and accurately in the Condon approximation, although the latter fails for internal scattering. (3) The effectiveness of internal scattering is determined by the vibronic states used in the calculation, while an appropriate choice of the latter is dictated by the cascade process. The adiabatic states constitute a reasonably good choice. (4) Perturbation expressions for the electronic wave functions are completely inadequate, even for the weakest coupling, because the transition matrix elements depend upon the wave functions far from equilibrium. (5) The frequency changes generated by nonlinearities in the adiabatic vibronic energies produce large quantitative changes in the calculated cross sections, even for very weak coupling. Omission of a 0.4% reduction in frequency was found to overestimate the cross section by a factor of 10. (6) Calculations of transition rates between static states, although formally equivalent in perturbation expansion to those made for adiabatic states, differ greatly from the latter both because of the failure of perturbation theory and because the two sets of states describe very different physical systems. © 1983 The American Physical Society.