Infrared Absorption in Heavily Dopedn-Type Germanium

Measurements of the infrared absorption spectrum of compensated and uncompensated heavily doped $n$-type germanium at 80, 200, and 295°K are reported. The edge absorption in the doped samples differs strongly from the edge absorption in pure germanium. Both the indirect and the direct energy gap change with doping. The change depends on the total impurity concentration $N_A+N_D$ approximately as ${(N_A+N_D)}^{\frac{1}{3}}$. For $N_A+N_D=4.7\mathrm{}\times {10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ the change of the indirect gap is about 0.07 ev, the change of the direct gap about 0.06 ev. The absorption due to indirect transitions rises more rapidly with the photon energy in $n$-type germanium than in pure germanium. This extra absorption is proportional to the free electron concentration and must be due to virtual electron-electron scattering between the $〈000〉$ and $〈111〉$ valleys.