Nonequilibrium Carrier Phenomena inn-Type InSb

Abstract

Four nonequilibrium carrier phenomena, namely, the hot-electron effect, injection, impact ionization, and bulk negative differential conductivity (BNDC), produce nonlinear conduction in $n$-InSb in a strongly interrelated manner. These interrelationships are shown in detail. The hot-electron effect causes more decrease in average conduction under most transport conditions than injection causes increase and thus injection is not so easily observed. As the electric field strength is increased into the impact ionization range which begins at \ensuremath{\simeq} 225 V/cm, the generation rate progressively exhibits an ${e}^{E}$, an ${e}^{\frac{1}{E}}$, and then an ${e}^{\frac{1}{{E}^{2}}}$ dependence. The distribution of the carriers in energy space shifts from a peaked distribution for $225 \mathrm{V}/\mathrm{c}\mathrm{m} \ensuremath{\lesssim}E\ensuremath{\lesssim}425 \mathrm{V}/\mathrm{c}\mathrm{m}$ to an isotropic distribution for $E\ensuremath{\gtrsim}500$ V/cm. While the carriers are in a peaked distribution, the polar-optical-phonon scattering changes from small-angle scattering to large-angle as $E$ is increased. The origin of type-$S$ BNDC is explained, as is its temporal and spatial relationship to type-$N$ BNDC. The $S$-BNDC results from the presence of copious excess carriers that are generated by impact ionization within the propagating high-field domain (HFD) associated with the Gum effect and the $N$-BNDC. A low-electric-field-strength region is responsible for the $S$-BNDC, a region that propagates in the wake of the HFD associated with type $N$. A HFD in InSb makes a single transit as a result of impact ionization within the domain. The $N$-BNDC in $n$-InSb decays in typically 10 nsec, the transit time for a HFD, whereas the $S$-BNDC persists for several hundred nanoseconds. Radiative recombination measurements show conclusively that the $S$-BNDC is caused by excess carrier generation as proposed. The decay of these excess carriers is found to be characterized by two times. The faster, \ensuremath{\sim}27 nsec, persists for typically \ensuremath{\sim}150 nsec, a much shorter duration than the $S$-BNDC decay time, and is not understood at this time. However, the longer excess-carrier decay time prevails well beyond the $S$-BNDC disappearance, a phenomenon that is explainable by the hot-electron effect.