Electron-hole droplet transport up to near-sonic velocity in Si

Abstract

In the past, several interesting effects have been observed in conducting systems where the carrier drift velocity is made to exceed the sound velocity. Nonlinear momentum damping and phonon amplification have been demonstrated in several materials (Cds,Ge,PbTe). However, high drift velocities with a high density of carriers produce immense current densities, which cause very rapid carrier and sample heating. This heating limits such transport studies to very short current pulses. In contrast, a dense, high-mobility system of photoexcited carriers in ultrapure Si allows more complete study of the near-sonic transport regime. The electron-hole liquid which condenses at low temperatures is a highly degenerate conductor. The liquid takes the form of electron-hole droplets (EHD's) of micrometer size and fixed density. The total amount of conducting volume is thus controlled by excitation level. The low carrier density (relative to a metal) and small volume of the liquid, together with the high droplet mobility, tremendously reduce the rate of sample heating by carrier-phonon scattering, compared to a normal metal. In our experiments, with $T\ensuremath{\le}2.1$ K, the electrically neutral EHD's are accelerated by a strain-induced gradient in the semiconductor energy gap ${E}_{g}(x)$. The energy shift of the recombination luminescence peak gives the motive force per pair, ${F}_{\ensuremath{\sigma}}=\ensuremath{-}\frac{d{E}_{g}}{\mathrm{dx}}$. In this paper we report basic measurements of the EHD mobility in Si. The measured drift velocity ${v}_{d}$ is found to be proportional to ${F}_{\ensuremath{\sigma}}$ as long as ${v}_{d}$ is much less than the sound velocity $S$. We further find that the momentum damping rate, ${\ensuremath{\tau}}^{\ensuremath{-}1}=\frac{{F}_{\ensuremath{\sigma}}}{m{v}_{d}}$, increases as $S$ is approached. For ${v}_{d}<0.9S$ the observed damping is consistent with a theory describing the absorption and re-emission of thermal phonons (D'yakanov and Subashiev, 1978). At low velocity the observed droplet mobility exhibits the rapid $T$ dependence predicted by the Bloch conductivity theory for a degenerate Fermi liquid. The data show a saturation in ${v}_{d}$ at $0.9S$ that indicates a sharp increase in damping. The thermal-phonon scattering theory does not predict such a velocity limit. However, a "sound barrier," due to the Cherenkov-type emission of phonons when ${v}_{d}\ensuremath{\ge}S$, has been predicted. We propose that the observed velocity saturation is due to this effect.