MODELING OF MINORITY-CARRIER TRANSPORT IN NONUNIFORMLY DOPED SILICON REGIONS WITH ASYMPTOTIC EXPANSIONS

The minority-carrier transport and recombination in arbitrarily doped silicon regions has been studied by means of different asymptotic expa nsions. Firstly, by using the minority-carrier current density as depe ndent variable, a first asymptotic succession of approximate expressio ns for the saturation current density has been derived. This successio n includes some previously proposed analytical expressions. Analogies and differences with respect to a similar expansion recently reported in the literature are pointed out. Secondly, starting from the previou s expansion, another succession is developed. The terms of this succes sion are shown to be more accurate, and to provide deeper physical ins ight, with respect to the other expansions, In particular, the first-o rder term accurately describes the current injection in thin regions a t any value of the surface recombination velocity. It is then demonstr ated that all the mentioned successions can be derived by truncation o f the same series, and that the differences among the successions are only due to the truncation procedure. Comparisons between correspondin g terms of the different successions are provided and a possible estim ate for the maximum error relative to the second-order term of the las t succession is given. Finally, the analytical model of Selvakumar and Roulston is briefly reviewed, From the analysis of the asymptotic beh avior, a rigorous definition for the constant C-s appeabove model is p ut forward. It is then shown that, with the above definition of C-s, t he model of Selvakumar and Roulston and the integral formulation prese nted here give the same description of minority-carrier injection in t hin regions.