The problem of the time-step size in numerical integration of the macroscopic semiconductor equations

Values for the maximum permissible time-step size in the integration of the macroscopic semiconductor equations for various time integration methods are derived by Fourier methods. The stability criterion is a sharper form of the Neumann stability criterion, and requires that for all spatial frequencies the amplification factors be smaller than unity. The derived limits explain the increasing computational load in explicit time integration procedures for finer spatial discretization or higher doping in the element.