Minority-carrier injection into semiconductors

On the basis of the linearized transport equations (small-signal theory) it is shown that minority-carrier injection into a trap-free lifetime semiconductor leads to a local-field maximum, and hence to a hitherto unrecognized resistance increase, as long as the majority carriers have the greater mobility. This applies to any value of the injection ratio $\ensuremath{\gamma}$, where ${\ensuremath{\gamma}}_{0}$ is the fraction of current carried by minority carriers in the undisturbed bulk. The conventionally expected bulk resistance decrease makes itself felt only at relatively high current densities. It is also shown that the ratio ${A}_{n}=\frac{{\ensuremath{\tau}}_{D}}{{\ensuremath{\tau}}_{0}}$ (where ${\ensuremath{\tau}}_{D}$ is the dielectric relaxation time, and ${\ensuremath{\tau}}_{0}$ the carrier lifetime) governs the boundary between the relaxation and lifetime regimes only when the injection ratio $\ensuremath{\gamma}$ is unity. For $\frac{{\ensuremath{\tau}}_{D}}{{\ensuremath{\tau}}_{0}}=1$ we then have $\ensuremath{\Delta}N=0$, irrespective of $X$. However, when $\ensuremath{\gamma}<1$, there is no value of $\frac{{\ensuremath{\tau}}_{D}}{{\ensuremath{\tau}}_{0}}$ which gives $\ensuremath{\Delta}N=0$ everywhere, hence no simple boundary between the two conduction regimes. The equations developed are general, and can be applied to a variety of other transport problems.