Modeling of minority-carrier transport in nonuniformly doped silicon regions with asymptotic expansions

A comprehensive study of the modeling of minority-carrier transport and recombination in nonuniformly doped silicon regions is presented. Using the minority-carrier current density as a dependent variable, a first asymptotic succession of approximate expressions for the saturation current density is derived. This succession includes some previously proposed analytical expressions. Analogies and differences with respect to a similar-expansion recently reported in the literature are pointed out. Starting from the above-mentioned expansion, another succession is developed. The terms of this succession are shown to be more accurate, and to provide deeper-physical insight, than the other expansions. It is demonstrated that all the successions mentioned can be derived by truncation of the same series, and that the differences among the successions are only due to the truncation procedure. Comparisons between corresponding terms of the different successions are provided, and a possible estimate for the maximum error relative to the second-order term of the last succession is given