Theory of a forward-biased diffused-junction P-L-N rectifier—Part I: Exact numerical solutions

Exact numerical solutions have been obtained for a forward-biased diffused-junction n⁺-p-p⁺silicon rectifier operating from low to high injection levels. The results indicate that under high-level injection conditions, there exists a quasi-neutral region (i.e., a region wherein the electron and hole concentrations are very nearly equal) in the device which is not confined to the lightly doped p-base region but stretches into the diffused n⁺region as the injection level increases. For the impurity profile and the Shockley-Read-Hall recombination model used, it is additionally found that the quasi-Fermi potentials for both electrons and holes are constant across a large portion of the diffused region adjoining the quasi-neutral or "effective base" region. The most significant finding, however, is that at the boundary between the effective base region and the diffused region, the hole current varies more or less directly as the carrier concentration, in contrast to the situation in a step-junction rectifier where the minority carrier current in the heavily doped regions varies as the square of the carrier concentration at the base edge. A simple analysis shows that this linear relationship can be related to the constant quasi-Fermi potentials across the diffused region. As a consequence of the aforementioned linear relationship, the injection efficiency of the diffused junction is roughly independent of the injection or current levels. It may be high or low depending on whether the concentration of recombination centers in the diffused region is small or large compared to that in the base region. This is unlike the situation in a step junction where the injection efficiency would be initially high and then degrade, as the current increases.