The Theory of Hot Electrons

Abstract

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 ƒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> (E(p)), the distribution in energy E; the conventional relaxation-time relation between ƒ − ƒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and dƒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> /dE; and smallness of dƒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> /dE. More general methods are associated with giving up, successively in the reverse order, these assumptions. Procedures for obtaining and solving equations involving ƒ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> 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.