A NECESSARY CONDITION ON DISCRETIZATION SCHEMES FOR DEVICE SIMULATION

This paper contributes to the evaluation of discretization schemes for the semiconductor device continuity equation. A simple model problem is described which provides a test any discretization scheme on simplicial grids must pass. Otherwise the scheme will fail to compute the minority charge densities in simulation problems. Many schemes published in literature do not pass this test. In a last section the relevance of the model problem to realistic devices is explained.