The asymptotes of the base current in bipolar devices

Simple analytical equations are derived for the asymptotes of the base current of a bipolar transistor. Three limiting asymptotes are considered, namely, that for a transparent emitter with a high recombination velocity, that for a transparent emitter with a low recombination velocity, and that for an opaque emitter. The asymptote equations are expressed as functions of a measurable fabrication parameter, the emitter-base junction depth. It is shown that the asymptotes can be represented graphically by logarithmic plots of base current density as a function of the emitter-base junction depth, the three asymptotes giving straight lines with gradients of -1, 0, and +1. The asymptote equations are validated by comparison with exact numerical calculations and with experimental data taken from the literature. In this way, it is shown how the asymptote equations can be used to provide valuable insight into the physical mechanisms that control the base currents of different types of bipolar transistor