Computation of Current-Voltage-Characteristics in a Semiconductor Device Using Arc-Length Continuation

摘要

This paper presents an algorithm for the numerical computation of current-voltage-characteristics in a semiconductor device (i.e. curves describing the dependence of the output current on the input voltage at some contacts). For certain devices (e.g. thyristors) the set of equations describing the state of the semiconductor device have multiple solutions for specific voltage ranges and snap-back phenomena occur (i.e. the current is not a single valued function of the voltage). This implies that the characteristic cannot be computed numerically by merely stepping up the voltage. The algorithm involves reparameterizing the characteristics curve by means of a parameter which approximate the arclength of the curve. Continuation in this parameter past snap-back-points does not cause serious difficulty. The authors discuss the implementation of the reparameterization and present a numerical example. (Author)