Theory of the Infrared Absorption of Carriers in Germanium and Silicon

The Drude-Zener theory of optical absorption by free carriers is applied to the infrared absorption of $n$-type germanium and $p$-type silicon. Average effective masses so determined are: for electrons in germanium ${〈\left(\frac{m^{*}}{m}\right)〉}_{\mathrm{Av}}$ ranges from 0.11 to 0.22; for holes in silicon ${〈\left(\frac{m^{*}}{m}\right)〉}_{\mathrm{Av}}$ ranges from 0.19 to 0.55. The average effective mass values of electrons in germanium are in good agreement with those measured by cyclotron resonance. The infrared absorption bands of $p$-type germanium are explained on the basis of transitions of holes between three energy bands lying near the top of the valence band. This band structure is suggested by cyclotron resonance experiments. Application of the theory to $p$-type silicon leads to the prediction of an absorption peak near $25\mu$ and two lesser ones near $33\mu$.