Free-Carrier Absorption inn-Type Ge

The structure of the conduction band of Ge is completely taken into account in calculating the cross section in second-order Born approximation. The second-order matrix element contains first-order matrix elements of electron-photon interaction (derived for anisotropic mass) and of electron-scatterer interaction. Scatterers considered are ionized impurities and phonons belonging to all six branches of the vibrational spectrum. Deformation parameters of electron-phonon interaction are chosen to agree with other experiments. An excellent fit to high-temperature data (450°K), where impurity effects are very small, is obtained without adjusting any parameters. Contributions to the cross section from processes involving scattering by longitudinal and transverse long-wavelength acoustic phonons are comparable; their combined effect is matched by energetic-phonon effects when $T\gtrsim 300°$K. In this temperature range, when $40\mu \gtrsim \lambda \gtrsim 10\mu$, contributions from all phonon processes are virtually indistinguishable in their temperature and wavelength (${\lambda }^2$) dependence. Predicted cross sections are too low by 20-30% at 293°K, and by a factor of 2-4 at 78°K. The low-temperature results are in apparent disagreement with theoretical results of Fan, Spitzer, and Collins. It is suggested that their theory leads to an overstimate in the impurity calculation, and that impurity effects have not yet been explained.