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Expressions for the temperature dependence of the carrier mean free path for optical phonon scattering and the mean energy loss per collision are presented which predict avalanche multiplication as a function of electric field for any operating temperature once the appropriate parameters have been determined at a single temperature. This has been verified for electrons in Si by the correlation of measurements at 300°K, 213°K, and 100°K. The temperature dependence of the breakdown voltages of a variety of abrupt and linear-graded Si and Ge p-n junctions has also been predicted. The fractional change in breakdown voltage with increasing temperature is predicted to decrease with increased doping concentration and, for the same breakdown voltage, to be less for linear-graded junctions than for abrupt junctions.
Crowell et al. (Thu,) studied this question.