Carrier diffusion in semiconductors subject to large gradients of excited carrier density

Under conditions of intense optical pumping or electrical injection it is possible to excite such a dense plasma of electrons and holes that these carriers interact among themselves much more rapidly than they interact with the lattice phonons. In this circumstance there will be established a temperature of excited carriers, $T_e$, much larger than the temperature of the lattice, $T_L$, for periods of time sufficient for many effects to be observed. In the accompanying paper it is shown that the temperature dependence of the forbidden band gap is then described by ${\Delta E}_{\mathrm{cv}}(T_e,T_L)={\Delta H}_{\mathrm{cv}}\left(T_L\right)-T_e{\Delta S}_{\mathrm{cv}}\left(T_L\right)$. With $T_e\gg T_L$, this means that anomalously large changes in the band gap will occur and, if also there are large gradients of $T_L$ present in the sample, there will be very large gradients in the band gap. This means there will be very large gradients in the chemical potentials of the excited electrons and holes. As the band gap tends to be least where the carriers are most dense and $T_L$ the greatest, these chemical potential gradients oppose the normal outward diffusion of the excited carriers. We find that, under certain conditions, this effect may be sufficient to produce "negative diffusivity" or carrier self-confinement.