Numerical analysis of a forward-biased step-junction P-L-N diode

Exact numerical steady-state solutions are presented for a forward-biased step-junction one-dimensional p⁺-n-n⁺rectifier over a current range of 10^-2to 10⁴A/cm²The versatility of the numerical approach is demonstrated by the inclusion in the physical model of injection-dependent carrier lifetimes due to Auger recombination or injection-dependent mobilities due to electron-hole scattering. The solutions obtained are compared to those given by conventional analytical treatments at low and high injection levels. Among the major results established are the validity of the Boltzmann´s relations and of the quasi-neutrality assumption at all injection levels of interest. It is shown that at the upper end of the current range, a complete analytical solution for the whole device is intractable. However, partial analytical solutions are available for the quasi-neutral regions, and these have enabled us to obtain a better understanding of some of the numerical solutions. Examples are the early onset of non-linearity effects in the n⁺region because the minority carrier current there is small compared to the total current, and the shift in the minimum of the base carrier distribution towards the n-p⁺junction as the injection efficiency from the p⁺region into the base decreases with increasing forward bias.