Minority-carrier injection into semiconductors containing traps

The paper presents an analysis of minority-carrier injection into lifetime and relaxation semiconductors containing traps, linearized within the framework of a "small-signal theory." In that sense it parallels a previous paper on the trap-free case. The restrictive assumptions customarily made in the literature as regards injection ratio, mobility ratio, carrier lifetime, dielectric relaxation time, doping levels, and specific characteristics of the trapping centers, zero recombination rate $np=n_i^{}{}_{}{}^2$, and neglect of diffusion current, are avoided here. Explicit solutions are obtained of the carrier concentration and field profiles, and plotted for a series of interesting cases, some designed to illustrate the nature of the phenomena, some to facilitate experimental verification. The results show that the establishment of lifetime and relaxation regimes depends in a complex manner on the parameters of the system. Minority-carrier injection can result in the appearance of a field maximum and a total resistance increase, not only in the trap-free case as previously reported, but to a greatly augmented extent in the presence of traps in suitable concentrations and energetic positions. The results have a potential bearing on the interpretation of many types of electrical measurements on semiconductors and semi-insulators. The equations themselves are general (except for the restriction to small currents) and can be extended to a variety of other nonequilibrium transport effects in solids.