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

Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films