Acoustic mode with time-dependent phase velocity in photoexcited semiconductors.

Using the Boltzmann equation, we study the collective modes of a photoexcited electron-hole plasma in a direct-gap, small-electron-mass semiconductor in which the electron distribution is evolving with time. In this situation, we find that there exists an acoustic mode of the electron-hole plasma with a time-dependent hase velocity. The phase velocity is approximately given by ${\mathrm{\ensuremath{\omega}}}_{\mathit{p},}$h/${\mathit{q}}_{\mathrm{s}\mathrm{c},}$e(t), where ${\mathrm{\ensuremath{\omega}}}_{\mathit{p},}$h is the hole plasma frequency and ${\mathit{q}}_{\mathrm{s}\mathrm{c},}$e(t) is the screening wave vector of the electron distribution ${\mathit{f}}_{\mathit{e}}$(v,t). As the electron distribution cools, the ${\mathit{q}}_{\mathrm{s}\mathrm{c},}$e(t) increases and hence the phase velocity of the mode decreases with time.