Simple modeling of intrinsic bulk lifetime in doped silicon

Based on the data in the literature, in highly-doped Si, where Auger recombination predominates, one can observe that, while minority-carrier bulk lifetime is inversely proportional to the square of doping density, diffusivity can be taken as constant. This implies that, at high dopings, diffusion length can be considered as proportional to the reciprocal of doping density. In the present work, we assume that such a dependence of diffusion length on doping holds at lower dopings as well, in the case, where Auger recombination prevails. This allows deriving a very simple expression for Auger lifetime as a function of diffusivity that is used together with a reported expression for radiative lifetime to calculate intrinsic lifetime at all dopings. The new expression for intrinsic lifetime is consistent with reported doping functions for minority-carrier diffusivity and agrees with the data of lifetime for dopings higher than 4×1017 cm-3 in both p-type Si and n-type Si. We exploit the relevant theory to show that such results are due to the fact that, at those doping levels, both diffusivity and Auger recombination are enhanced by electron-hole interaction. © 2018 Author(s).