Measurements of the absorption spectrum of Ge, made with high resolution, near the main absorption edge, at various temperatures between 4.2°K and 291°K, have revealed a fine structure in the absorption on the long-wavelength side of this edge. This structure has been analyzed and can be interpreted in terms of indirect transitions involving phonons with energies corresponding to temperatures of 90°K and 320°K. The initial energy dependence of the components of the absorption coefficient associated with the 320°K phonons is interpreted as being due to the formation of excitons with a binding energy 0.005 ev. The form of the corresponding spectrum of photoconductivity also indicates that excitons are being produced. Using data on intrinsic carrier density and the temperature dependence of the energy gap for band-to-band transitions, a value of 4 is found for the number of conduction-band minima in Ge and an increase of about 20% in the combined density-of-states effective mass as the temperature increases from zero up to room temperature. 90°K and 320°K therefore correspond to the energies of phonons at the edge of the Brillouin zone in the $〈111〉$ direction; these are shown to be acoustical phonons. These energies are lower than the corresponding values calculated from a Smith-type model for the vibrations of the Ge lattice. However, they are more consistent with the known Debye temperature and far infrared absorption of Ge than the calculated values.

• Received 9 April 1957

DOI:https://doi.org/10.1103/PhysRev.108.1377