Spatial expansion of electron-hole plasma in Si

In this paper we report measurements of the spatial and spectral evolution of the photoluminescence resulting from nanosecond pulsed-laser excitation of silicon at low temperatures. An imaging technique employing single-photon counting provides direct measurements of the expansion rates of the electron-hole plasma with 5-ns temporal resolution. We find that for 0.5-μJ excitation energy the plasma expands from the excitation point at subsonic velocities—contrary to recent claims based on spectroscopic analysis. An alternative analysis of the recombination spectra indicates that local heating can account for the anomalously broad spectra at early times. For 50-μJ excitation, time-resolved images show that the electron-hole plasma expands as a shell into the crystal, indicating that it is driven by an intense phonon wind. The expansion velocities are found to decrease smoothly as the temperature is increased through the critical temperatures ($T_c$≊23 K) of the electron-hole liquid (EHL). A theoretical calculation of the phonon-wind-driven expansion velocity yields a temperature dependence which is in reasonable agreement with the data. At low temperatures (<10 K) and near-annealing excitation levels, the EHL expansion velocity is observed to saturate at v=5.1×${10}^5$ cm/s. We attribute this nonlinear damping to a Cherenkov-like emission of TA phonons from the EHL. Finally, we present measurements of the free-exciton diffusion coefficient for temperatures between 15 and 40 K.