Extreme ultraviolet (XUV) transient reflectivity around the germanium M4,5 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±0.2ps attributed to the X-L intervalley scattering and a hot hole relaxation rate of 600±300fs 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 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 (66-70 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
