An adaptive grid refinement strategy for the drift-diffusion equations

A method of computing the error in the solution of the semiconductor current continuity equations as well as the error in the terminal currents is proposed. An appropriate error indicator is developed based on a divergence free upwinding (finite element) discretization. The grid used for discretization is adapted to the error in the solution by dynamically adding or removing grid points in order to improve the solution and thus the terminal currents. The examples indicate that it is sufficient only for a reverse-biased p-n junction to refine the grid according to the error in the Poisson equation. In the forward biased case, it is necessary to take into account the error in the current continuity equation in order to guarantee exact terminal currents.< >