Abstract: The momentary state of a semiconductor device is described with three nonlinear partial differential equations. A finite difference scheme for transient behaviors of two-dimensional semiconductor devices on grids with local refinement in time and space is constructed and studied.The electrostatic potential equation is approximated by a five-point difference scheme.The electron and the hole density equations are discretized by a modified upwind scheme.The construction uses a linear interpolation at slave nodes.An error analysis is presented and illustrated with a numerical example.