Infrared Absorption in $n$-Type Germanium

Theory of absorption by free carriers is given taking into account the effects of scattering by impurities and by lattice vibrations. Experimental results are reported for $n$-type germanium samples of various carrier and impurity concentrations. The measurements were made in the temperature range between 78°K and 450°K, covering a wavelength region from 5 to 38 microns. At the high-temperature end, the absorption is proportional to the carrier concentration, lattice scattering being the dominant effect. At 78°K, the absorption per unit carrier concentration consists of a constant part and a part proportional to the impurity concentration. The absorption increases with wavelength more rapidly at the low temperature. The frequency and temperature dependences of absorption in the various samples are in good agreement with the theory. Quantitative agreement can be obtained by using an effective mass $m^{*}\eqsim 0.1m$.