Hot-carrier dynamics in Ge on single picosecond timescales: Comparing Raman and reflectivity experiments with a self-consistent kinetic model

Abstract

Through comparisons of picosecond Raman and transient reflection experiments with a comprehensive kinetic model of photo-excited carrier and lattice dynamics in Ge, we demonstrate the ability of these techniques to probe subtle aspects of non-equilibrium carrier dynamics in group IV materials at moderate injected carrier densities. Using material parameters taken from the literature, the temporal evolution of the non-equilibrium optical phonon population generated by the relaxation of photo-excited electrons and holes is obtained by solving a coupled set of Boltzmann equations for the electron and hole particle and thermal currents. The results of the calculation agree, in absolute terms, with the experimentally observed evolution of the non-equilibrium optical phonon population. The calculation also predicts that the hot plasma initially diffuses rapidly away from the sample surface, on a 5 picosecond timescale, and subsequently diffuses much slower as the carrier temperature decays to the lattice temperature, and the density gradient diminishes due to the hot carriers which have already migrated into the material. This prediction is verified by comparison of the calculated change in reflectivity due to the plasma, and picosecond reflectivity measurements performed at room temperature with 575 nm pulses.