Development of mathematical models of semiconductor devices for computer-aided circuit analysis

This paper describes the development and verification of mathematical models which will approximate the electrical characteristics of Zener and/or avalanche diodes and tunnel diodes. Each model consists of a circuit of discrete components with their defining equations. The equations are in a form compatible with the digital computer language which makes the models useful in analysis and design, by computer, of electronic circuits containing these devices. The Zener diode model is basically the familiar Ebers-Moll conventional diode model except that additional current sources have been added to approximate the voltage regulation when breakdown of the junction occurs. The equation for junction capacitance has been modified to model the decrease in capacitance due to avalanche in the junction. A tunnel diode model is presented which approximates the entire static characteristic, including the negative resistance region. Methods for extracting model parameters from a limited number of easily obtainable data points are developed. A method for measuring and describing junction capacitance is also presented.