A distributed memory parallel element-by-element scheme for semiconductor device simulation Original Research Article

A domain decomposition and parallel element-by-element (EBE) scheme is developed for semiconductor device simulation modeled by the drift-diffusion (DD) equations. A classical Gummel iterative decoupling of the potential and carrier transport equations is applied on an unstructured triangulation. The distributed memory EBE scheme is formulated for a Galerkin finite element approximation of the nonlinear Poisson problem, and a modified Scharfetter–Gummel method is used for the carrier transport problem. The resulting sequences of symmetric and nonsymmetric linear systems are solved via preconditioned Krylov methods. Unstructured triangular grids are used to permit grading of the mesh, which is then partitioned to processor subdomains with appropriate data structures for message passing. Details of the parallel algorithm and data structure are provided. The scheme is implemented in Fortran90 with MPI and performance results are presented for a representative MOSFET on an IBM SP, a CRAY T3E, and an SGI/CRAY Origin2000.