In this paper the mechanisms of bandgap narrowing, Shockley-Read-Hall (SRH) recombination, Auger recombination, and carrier-carrier and carrier-lattice scattering are included in an exact one-dimensional model of a bipolar transistor. The transistor is used as a vehicle for studying the relative importance of each of these phenomena in determining emitter efficiency in devices with emitter junction depths of 1 µm to 8 µm. It is shown that bandgap narrowing is the dominant influence for devices with shallow emitters of 2 µm or less and that SRH recombination dominates for emitter depths greater than 4 µm. Calculations are also presented showing the effects of the emitter surface concentration and high-level injection on the current gain for devices with emitter junction depths of 1 µm to 8 µm. It is shown that there is an optimum surface concentration of 5 × 1019cm-3for the 1-µm emitter depth but no optimum under 1021cm-3for devices with emitter depths greater than 4 µm.
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Adler et al. (1976) studied this question.