Non-linear diffusion of minority carriers

A study of the non-linear diffusion of minority carriers has been carried out. Once the starting terms have been defined, i.e. the diffusion constant depends on carrier concentration according to Webster´s formula Dp=Dp0(1+P/P+Nd) an exact first integral is found, from which a study of the influence of bulk recombination on the current gain of a transistor is made. An expression for the base control charge is also found. Finally approximate formulae are derived showing the dependence of carrier concentration on distance. Results are valid for any injection level and distance. Rittner has studied the same problem when the lifetime of minority carriers is infinite. His results are not very different from the linear theory and do not provide a good description at distances larger than the diffusion length.