Semiconductor device simulation using adaptive refinement and flux upwinding

An adaptive mesh refinement scheme and dynamic data structure were developed in conjunction with a flux-upwind Petrov-Galerkin finite-element formulation for analysis of semiconductor device equations. The electrostatic potential equation and carrier-current continuity equations are iteratively decoupled in the solution algorithm. Incremental continuation in applied bias is used to improve the nonlinear solution iteration and to produce an efficient and robust scheme. The adaptive refinement scheme also uses an element-by-element conjugate gradient solution algorithm that performs efficiently on parallel and vector processors. Sample numerical results for MOS and bipolar devices indicate the effectiveness of the flux or streamline upwind Petrov-Galerkin (FUPG) method and demonstrate its superiority over traditional Scharfetter-Gummel (SG) approaches