Interaction of intense picosecond pulses of 2.7-μmphotons with germanium

Computer simulations of the propagation of intense picosecond laser pulses of 2.7-$\mu \mathrm{m}$ photons through germanium have been performed to determine the extent of carrier creation and carrier heating that occurs for a variety of pulse widths and intensities. We use the model of germanium introduced by Elci, Scully, Smirl, and Matter, appropriately modified for our situation to describe the dynamics of the electron-hole plasma created by the pulse. With 2.7-$\mu \mathrm{m}$ photons, two-photon absorption is necessary to create carriers and holes. The carrier heating occurs from free-carrier absorption, the two-photon absorption, and intervalence-band one-photon absorption. The lattice is heated when the carriers lose energy during phonon-assisted relaxation. We study the propagation of a fixed pulse through a single cell. No beam deformation is included in these simulations. A set of rate equations is solved to obtain the electron temperature and chemical potentials and the phonon temperatures both as the pulse passes through the sample and after it has passed. These parameters are used to determine the evolution of the carrier density and the energy content of the plasma. We find that electron temperatures of 15 000 K and carrier densities of ${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$ can be reached with Gaussian pulses with peak intensities of ${10}^4$ MW/${\mathrm{cm}}^2$sec. The essential mechanism for electron heating is the one-photon intervalence-band absorption. When it is ignored, the plasma heating is negligible. Substantial heating of the lattice occurs at these intensities when the conventional electron-phonon coupling is employed. The heating is sufficient to cause damage by melting. The relevance of these results to laser annealing and laser-induced damage are discussed.