Multilevel solution of augmented drift‐diffusion equations

Develops a finite element analysis and solution strategy for the augmented drift‐diffusion equations in semiconductors device theory using a multilevel scheme. Decouples the drift‐diffusion equations using Gummel iteration with incremental continuation in the applied voltage. Includes augmentation of the carrier mobility to address the issue of non‐local electric field effects (velocity overshoot) within the framework of the drift‐diffusion formulation. Gives comparison results with hydrodynamic and Monte Carlo models and sensitivity studies with respect to the augmentation parameter. Discretizes the equations with a special finite element method using bases of variable polynomial degree. Accomplishes solution of the resulting linear systems with a multilevel method using the basis degree as the grid level. Presents performance results and comparison studies with direct elimination.

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