Cross section of multiphonon-emission carrier capture at deep centers in compound semiconductors

A quantum-mechanical theory is developed for the multiphonon-emission carrier capture at deep centers in compound semiconductors, taking into account the non-Condon effect. A general formula which directly connects the Fourier transform of the interaction Hamiltonian with the transition probability is deduced in the non-Condon scheme for a single frequency and linear coupling case. Model calculations show that the non-Condon effect brings about stronger temperature dependence of the capture probability than that derived by the use of the Condon approximation. This indicates the importance of the non-Condon effect in nonradiative transitions. A model potential for a deep center is also proposed, which can account for a large magnitude of capture cross section frequently observed at deep centers. According to the proposed model potential, which includes the effect of lattice distortion, a large cross section is attributed to the "resonance" of the Bloch state with the bound state. The importance of lattice distortion is specifically pointed out. The theory presented here predicts variations of the magnitude of cross section as well as the strong temperature dependence, both being distinct features observed at deep centers in III-V compounds such as GaAs and GaP.