Comparison of theoretical and empirical lifetimes for minority carriers in heavily doped silicon

Abstract The minority carriers determine essential electrical characteristics of bipolar devices and bipolar-like parasitic paths in field effect devices. The electrical behavior of such devices is frequently described by detailed device models. Compared to the other input parameters for detailed device models, the minority carrier lifetimes due to traps or defects as functions of doping density have great uncertainty. Detailed device models, which include the contributions of both Auger recombination and Shockley-Read-Hall processes to this lifetime, give correct values for the d.c. common emitter gain of npn transistors with shallow, heavily doped emitters. However, those models which include commonly used empirical expressions for the above lifetime do not predict correct values for the gain. The physical significance of these device modeling results involves competition between trapping of carriers and Auger recombination when donor densities lie within the decade of 1019 cm−3. An example of the foregoing competition is given by applying detailed device models to an npn transistor with an emitter surface concentration of 2.3 × 1020 cm−3 and with an emitter-base junction depth of 1.1 μm. A major finding in this paper is that the commonly used empirical expressions for the lifetime due to defects may not give correct results when included in detailed models of shallow, heavily doped silicon emitters.