Locally adaptive multigrid method for 3D numerical investigation of semiconductor devices

The authors present recent developments in the multigrid semiconductor device simulation program COGITO. A locally adaptive refinement strategy has been implemented. The electron and hole continuity equations have been incorporated into the solution procedure. Refinement criteria and interpolation topics are discussed in particular. The solution of a three-dimensional problem is presented. It is demonstrated that the Poisson equation in one to three dimensions for the zero-current case can be solved. Steep gradients are well resolved by adaptive refinement. The full classical equation system including the continuity equations can be solved in one dimension under a selected bias