Derivation of an analytical expression for a physical process from an experimental curve with kinks

Abstract

A technique for deriving an analytical expression describing an experimental curve with one or several kinks is proposed. Depending on the pattern of the partial processes involved in the resulting process, derivation is based on calculating either their sum or geometric mean. “Participation functions” of the processes, whose run is determined by the coordinate of the intersection point of the processes and the “accuracy parameter,” are introduced into these expressions in order to increase the approximation accuracy. The choice of these parameters provides a correspondence between the approximation accuracy and the accuracy of measuring the experimental curve. Application of this technique in analytical calculations consisting of a combination of several processes and in the derivation of an analytical expression for an experimental curve with kinks is demonstrated. The thus obtained approximating expression, characterized by clarity, a high approximation accuracy, and physical simplicity, may be used to calculate other characteristics of a semiconductor device.