Dynamics of low-energy holes in germanium

We study inter- and intra-valence-band relaxation of germanium, both experimentally and theoretically, by saturation spectroscopy. Far-infrared laser pulses with intensities between 1 and ${10}^5$ W/${\mathrm{cm}}^2$ are applied to saturate direct heavy-hole-to-light-hole transitions. The characteristic saturation intensity ${\mathit{I}}_{\mathit{s}}$ is measured for a range of frequencies (28–174 ${\mathrm{cm}}^{\mathrm{-}1}$) and temperatures (20–100 K) and found to vary over two orders of magnitude: ${\mathit{I}}_{\mathit{s}}$ increases approximately linearly with frequency; a minimum is observed at 30 K. This complex behavior is consistent with a model of inhomogeneously broadened two-level systems that takes explicit account of, and thus quantifies, the various scattering contributions from phonons, impurities, and holes. The theory predicts a saturation-induced dip in the absorption spectrum, which is also experimentally observed and yields the dynamical time constants ${\mathit{T}}_1$=43 ps and ${\mathit{T}}_2$=1.5 ps, for energy and phase relaxation, respectively, at 31.2 ${\mathrm{cm}}^{\mathrm{-}1}$ and 40 K.