On the stability of finite difference schemes in transient semiconductor problems

Nonlinear instabilities of explicit and half-implicit Crank-Nicholson schemes are analyzed by perturbation techniques. The time step is found to be inversely proportional to μN, a criterion which is in good agreement with experience. Based on this result, an optimal choice between the fast half-implicit method and the fully implicit Newton method is possible, favoring the former for Gunn-diodes and Schottky-barrier field-effect transistors, and the latter for insulated-gate field-effect transistors and some bipolar transistor problems. © 1973.