Abstract: Numerical methods for transient behavior of semiconductor devices are studied.Mathematical model of a three-dimensional semiconductor device with heat conduction is described by a initial boundary value problem with four quasilinear partial differential equations.Finite difference fractional step method,characteristic finite element alternating direction method,domain decomposition method and theoretical analysis are focused on.

Key words: semiconductor device, characteristic and upwind finite difference, fractional step method, alternating-direction and domain decomposition, numerical analysis