Time-resolved study of electron-hole plasmas near the liquid-gas critical point in Si: Evidence for a second condensed phase.

Abstract

At low temperatures and sufficient densities, free excitons in Si and Ge undergo simultaneous gas-liquid and insulator-metal transitions into droplets of electron-hole liquid. Some previous theoretical and experimental studies have suggested that, under certain values of density and temperature, there may be separate metal-insulator and liquid-gas transitions. In the present paper, we examine the difficult transcritical region for electron-hole liquid formation in unstressed Si using time- and space-resolved photoluminescence spectroscopy. Using the latest models for the luminescence of electron-hole plasma and small excitonic complexes (EC's), we have succeeded in characterizing the complicated luminescence spectra both above and below the liquid-gas critical temperature [${\mathit{T}}_{\mathit{c}}$(LG)\ensuremath{\approxeq}24.5 K] with a relatively small number of free parameters. Near the liquid-gas critical point the luminescence spectra are analyzed as contributions from four lines: the high-density electron-hole liquid (EHL), a lower-density electron-hole plasma (EHP), free excitons (FE's), and excitonic complexes. After a sufficient thermalization time, the temperature of all phases settles to a value indistinguishable from the lattice temperature. The line shapes of FE's and EC's are calculated using previously established parameters. Using the latest band-renormalization theory, the pair density of the plasma phases (EHL and EHP) determines both the position and the shape of the spectrum.Therefore the analysis of these complex spectra is reduced to five free parameters: A single parameter describing the intensity of the FE line (the intensity of the EC line shape is linked to that of the FE using an experimentally determined scaling relation), the intensities of the two plasma components EHL and EHP, and the pair densities of these two plasmas. These parameters are sufficient to characterize the spectra over a wide range of particle density and temperature. The EHP density obtained in this way is remarkably independent of temperature and particle density, providing evidence for a second condensed phase of electron-hole plasma. The condensed liquid has a density of about one-tenth that of the ground-state electron-hole liquid and is observed both above and below the EHL critical temperature. An excitonic phase diagram for silicon is described which includes two condensed plasmas. A triple point at 18.5 K is observed where the electron-hole liquid coexists with the lower-density condensed plasma (CP) and excitonic gas. Above this temperature the CP is observed at all temperatures up to a second critical point at 45\ifmmode\pm\else\textpm\fi{}5 K. We also consider the hypothesis that the extra luminescence attributed to the CP is instead due to large excitonic complexes. Using the recently determined binding energies of large excitonic complexes and the measured gas volume, we conclude that the density of these species is too small to account for the observed luminescence.