Warm-Electron Effects inn-Type Silicon and Germanium

The Boltzmann equation describing the warm-electron case is discussed and a review is given of the scattering mechanisms for $n-\mathrm{G}\mathrm{e}$ and $n-\mathrm{S}\mathrm{i}$ with relatively low doping levels. Taking into account the known band structure, the Boltzmann equation is solved by a numerical iteration method under the assumption of weak intervalley scattering. It is shown that this condition can be relaxed for special symmetry directions. The warm-electron coefficient $\beta$ has been measured in the temperature range from 77 to 250°K by an audio-frequency method based on analysis of nonlinear distortion. Good agreement between measured and calculated results is obtained using the accepted values of the deformation-potential constants.