Auger transition rates for excitons bound to acceptors in Si and Ge

Abstract

We present calculations of the phononless Auger transition rates for excitons bound to the four common shallow acceptors (B, Al, Ga, and In) in Si and Ge. The calculated rates for the bound excitons in Si vary significantly for the different acceptors, increasing rapidly as the acceptor binding energy increases. This is in agreement with the rapid decrease with increasing acceptor binding energy of measured acceptor bound-exciton lifetimes in Si. Numerically, the calculated Auger rates are within about a factor of 3 of the measured recombination rates for the different acceptors. The dependence of the Auger rates on acceptor binding energy is due to an increased spreading in momentum space of the bound-exciton wave function. In Ge, the calculated Auger rates are orders of magnitude less than the measured free-exciton recombination rate in undoped Ge, suggesting that the phononless Auger transition is not important for acceptor bound excitons in Ge. This is consistent with the experimental observation that light doping with shallow acceptors has little effect on the lifetimes of photoexcited carriers at low temperatures in Ge; whereas, in Si the carrier lifetimes can be decreased by orders of magnitude. The principal difference between Si and Ge is that the acceptor binding energies are much greater in Si than they are in Ge.