Theory of Absorption of Electromagnetic Radiation by Hopping inn-Type Silicon and Germanium

The absorption of electromagnetic radiation at 0°K in the wavelength region from 100 to 800 μ and from 500 μ to 2.5 cm in $n$-type silicon and germanium, respectively, has been investigated. Concentrations of donors up to 2×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in Si and 6×${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in Ge, and compensation ratios up to 0.2, were considered. The model used was that of photon-induced hopping of an electron between the ground states of the donors. The formula for the absorption coefficient is derived and numerical results are presented. The range of validity of our results is also discussed. Absorption coefficients of the order of ${10}^2$ ${\mathrm{cm}}^{-1\mathrm{}}$ in Si and ${10}^1$ ${\mathrm{cm}}^{-1\mathrm{}}$ in Ge were obtained.