An improved approach to the Shockley–Read–Hall recombination in inhomogeneous fields of space-charge regions

The rate formula of Shockley–Read–Hall (SRH) recombination is generalized for multiphonon transitions in an inhomogeneous electric field. A three-band model and Fermi statistics are used. The thermal generation and recombination at deep centers is tunnel assisted, if it occurs in the electric field of space-charge layers. Trap tunneling without phonon assistance turns out to be an exceptional case as well as the exclusive thermal multiphonon transition at zero field strength. Generally, every single recombination act is a combination of thermal capture and tunneling into the trap. A background of the order of an interband tunnel length contributes to the local rate. In the Boltzmann case the well known form of the SRH rate is derived, but with spatially variable lifetimes. Their position dependence directly reflects the shape of the electric field strength, if the traps are uniformly distributed. Depending on the external parameters, the calculation of the SRH current density leads to I-U characteristics, which exhibit interesting substructures in the case of certain discrete trap configurations. The theory is applied to a Hg0.8Cd0.2Te n+p junction and a GaAs surface potential.