Scattering of Conduction Electrons by Lattice Vibrations in Silicon

A theoretical model which assumes intervalley lattice scattering by phonons of 630° and 190°K characteristic temperatures in addition to the usual intravalley acoustic lattice scattering has been applied to the results of measurements of electrical conductivity, Hall effect, and weak-field magnetoresistance in the 30° to 350°K temperature range in samples of nearly pure $n$-type silicon. The model gives a good quantitative description of the results when the ratios of the coupling constants for the 630° and 190° phonons to the coupling constant for acoustic scattering perpendicular to an energy-spheroid axis are, respectively, about 2.0 and 0.15. The coupling constant for acoustic scattering parallel to a spheroid axis was found in an earlier study to be about 1.5 times that for the perpendicular direction. The magnitude of the acoustic contribution to the total lattice scattering mobility, as determined empirically here, is in approximate agreement with the predictions of deformation-potential theory.