A Model for the Field and Temperature

We derive a simple analytical model for the eld and temperature dependence of Shockley-Read-Hall lifetimes in silicon from a microscopic level, where the capture of carriers at recombination centers is assumed to be a multiphonon process. Strong electric elds, as often present in modern devices, cause trap assisted tunneling, i.e. the multiphonon recombination path is no longer purely vertical in a band diagram, but has a horizontal branch at an eeective energy which is given by the maximum of the transition probability. Applying reasonable approximations we calculate this eeective recombination path as a function of eld strength and temperature. Field enhancement factors of the inverse carrier lifetimes are then presented that require no integration, iteration or higher mathematical functions. The anisotropy and multi-valley nature of the silicon conduction band is carefully taken into account. We discuss all approximations and physical eeects by means of the gold acceptor level. The model is able to describe the pre-breakdown behaviour of trap tunneling leakage and is suitable for the implementation into simulation packages.