The infrared transmission of degenerate arsenic-doped germanium was measured at liquid-helium and at room temperature. The 4.2°K data were used to calculate the energy gap of the degenerate material. For this, two operations were necessary: (1) to subtract the large effect of free carrier absorption, and (2) to calculate the absorption coefficient for the case of indirect transitions between two rigid parabolic bands one of which is partially occupied. A correction of the experimental data for the calculated Burstein shift shows that the indirect gap is considerably reduced [(${93}_{-9\mathrm{}}^{+4\mathrm{}}$)×${10}^{-3\mathrm{}}$ ev for 4×${10}^{19}$ As/${\mathrm{cm}}^3$]. The data indicate that the direct gap at K = (0,0,0) is also shrunk [(60±3)×${10}^{-3\mathrm{}}$ ev for 4×${10}^{19}$ As/${\mathrm{cm}}^3$]. Evidence is shown that momentum conservation in the indirect transition does not require phonons.

• Received 11 December 1961

DOI:https://doi.org/10.1103/PhysRev.126.956