Femtosecond tracking of carrier relaxation in germanium with extreme ultraviolet transient reflectivity

Abstract

Extreme ultraviolet (XUV) transient reflectivity around the germanium ${M}_{4,5}$ edge ($3d$ core-level to valence transition) at 30 eV is advanced to obtain the transient dielectric function of crystalline germanium [100] on femtosecond to picosecond time scales following photoexcitation by broadband visible-to-infrared (VIS/NIR) pulses. By fitting the transient dielectric function, carrier-phonon induced relaxations are extracted for the excited carrier distribution. The measurements reveal a hot electron relaxation rate of $3.2\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.16em}{0ex}}\mathrm{ps}$ attributed to the $X\text{\ensuremath{-}}L$ intervalley scattering and a hot hole relaxation rate of $600\ifmmode\pm\else\textpm\fi{}300\phantom{\rule{0.16em}{0ex}}\mathrm{fs}$ ascribed to intravalley scattering within the heavy hole (HH) band, both in good agreement with previous work. An overall energy shift of the XUV dielectric function is assigned to a thermally induced band gap shrinkage by formation of acoustic phonons, which is observed to be on a timescale of 4--5 ps, in agreement with previously measured optical phonon lifetimes. The results reveal that the transient reflectivity signal at an angle of ${66}^{\ensuremath{\circ}}$ with respect to the surface normal is dominated by changes to the real part of the dielectric function, due to the near critical angle of incidence of the experiment $({66}^{\ensuremath{\circ}}\text{--}{70}^{\ensuremath{\circ}})$ for the range of XUV energies used. This work provides a methodology for interpreting XUV transient reflectivity near core-level transitions, and it demonstrates the power of the XUV spectral region for measuring ultrafast excitation dynamics in solids.