Multiphonon broadening of impact ionisation and Auger recombination involving traps in semiconductors

The effect of lattice coupling upon impact ionisation and Auger recombination processes involving an arbitrary number of localised states is discussed within the framework of the static coupling scheme, and new expressions for the transition rates are obtained. These results are discussed in terms of the configurational coordinate diagram which highlights the close analogy that exists between (one-electron) radiative and (two-electron) impact ionisation and Auger recombination processes involving bound states. A calculation of Auger recombination rates involving a single trap is made, and some simple approximations are developed which are found to be in good agreement with more exacting numerical calculations.