  Heavily-doped semiconductor films are very promising for application in
mid-infrared plasmonic devices because the real part of their dielectric
function is negative and broadly tunable in this wavelength range. In this work
we investigate heavily n-type doped germanium epilayers grown on different
substrates, in-situ doped in the $10^{17}$ to $10^{19}$ cm$^{-3}$ range, by
infrared spectroscopy, first principle calculations, pump-probe spectroscopy
and dc transport measurements to determine the relation between plasma edge and
carrier density and to quantify mid-infrared plasmon losses. We demonstrate
that the unscreened plasma frequency can be tuned in the 400 - 4800 cm$^{-1}$
range and that the average electron scattering rate, dominated by scattering
with optical phonons and charged impurities, increases almost linearly with
frequency. We also found weak dependence of losses and tunability on the
crystal defect density, on the inactivated dopant density and on the
temperature down to 10 K. In films where the plasma was optically activated by
pumping in the near-infrared, we found weak but significant dependence of
relaxation times on the static doping level of the film. Our results suggest
that plasmon decay times in the several-picosecond range can be obtained in
n-type germanium thin films grown on silicon substrates hence allowing for
underdamped mid-infrared plasma oscillations at room temperature.

Materials Science;Other Condensed Matter