Acoustic-phonon emission due to localized photoexcitation of Si: Electron-hole droplets versus the phonon hot spot

Abstract

We consider theoretically the evolution of nonequilibrium carriers and phonons created by optical excitation of Si at low temperatures (T2 K) in light of recent heat-pulse experiments. At low excitation levels (\ensuremath{\le}20 W/${\mathrm{mm}}^{2}$), the detected phonons indicate a quasidiffusive propagation mode, involving anharmonic decay and elastic scattering of relatively high-frequency (\ensuremath{\ge}1 THz) phonons. At intermediate excitation densities (\ensuremath{\ge}20 W/${\mathrm{mm}}^{2}$) a transition is observed to a localized source of relatively low-frequency (\ensuremath{\le}1 THz) phonons. The threshold for this effect is much lower than that predicted for the formation of a hot spot involving only the phonon system. We interpret these data in terms of the phonons generated in the presence of electron-hole droplets. It is well known that nonequilibrium carriers emit optical and acoustic phonons in their energy relaxation and recombination. At moderate excitation densities droplets of electron-hole liquid are formed. These droplets modify both relaxation and recombination processes of photoexcited carriers due to the increased carrier-carrier scattering in the dense (3\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) liquid. Hot carriers, excited by the initial optical excitation or by Auger recombination in the droplets, transfer their kinetic energy to colder carriers in the droplets, partially bypassing the generation of optical phonons and heating the droplets. Our calculations indicate that this process can provide a mechanism for the production of a localized source of low-frequency phonons, as observed in the heat-pulse experiments.