Contribution of Lattice Scattering between Nonequivalent Valleys to Free-Carrier Infrared Absorption in Semiconductors

In a multivalley band-structure like that of the conduction band of germanium, a contribution to the absorption of infrared radiation by free carriers is made by a scattering process which does not play a role in normal transport processes but which may be of importance for hot-electron phenomena; this is the scattering between nonequivalent valleys of the conduction band. The absorption induced by this extra scattering process results in a transfer of the electrons from the $〈111〉$ valleys to the $〈100〉$ valleys or the [000] valley. A quantum-mechanical calculation was made of the partial absorption constant ${{\mu }_i}^{*}$ due to this scattering on the basis of a deformation-potential type theory. The final formula obtained for ${{\mu }_i}^{*}$ is similar to that derived previously for the partial absorption constant ${\mu }^{\mathrm{opt}}$ due to optical intravalley scattering. The physical significance of some limiting forms of ${{\mu }_i}^{*}$ at low temperatures is discussed.