This is a survey of methods of analysis of the hot-electron phenomenon in semiconductors. The earliest method depended on three basic assumptions: smallness of the deviation of ƒ(p), the carrier distribution function, from ƒ0(E(p)), the distribution in energy E; the conventional relaxation-time relation between ƒ − ƒ0 and dƒ0/dE; and smallness of dƒ0/dE. More general methods are associated with giving up, successively in the reverse order, these assumptions. Procedures for obtaining and solving equations involving ƒ0 only, based on a new approach due to Levinson, are developed. An inherently precise method for calculating f and related treatment of differential mobility, which requires computer implementation and which has recently come into use, is expounded. Test calculations for the case of n-germanium are reported.
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