Bandgap narrowing and emitter efficiency in heavily doped emitter structures revisited

The developments of heavy doping effects and of bandgap narrowing (BGN) concepts during the last two decades are critically discussed. The differences between the real bandgap reduction ΔE_g and the apparent electrical bandgap reduction ΔG are once more set forth, showing the precise meaning of the density-of-states and degeneracy contributions to ΔG. From these concepts, the author indicated previously that for negligible recombination the minority-carrier emitter current (J_pe ) is given by a Mertens-type results. It is shown in this work that in the presence of surface and (or) bulk recombination (Auger and SRH) the result of C.R. Selvakumar and D.J. Roulston is recovered; however, the electrical field in the emitter and the effective intrinsic density of carriers are not those used by Selvakumar and Roulston (1987) but, on the contrary, these quantities are given by the detailed expressions of the author´s previous work (see A.H. Marshak and C.M. Van Vliet, 1984)