Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations
The authors extend the triangular finite elements to tetrahedral elements in three dimensions for the semiconductor continuity equations. The continuous problem is first formulated as a weak one using a weighted inner product. The wave problem is then approximated by a Bubnov-Galerkin finite element method based on a set of novel basis functions. The basis functions are piecewise exponential, and thus the method can be regarded as an extension of the Scharfetter-Gummel scheme to 3 dimensions. This method is proved to be stable in the sense that the corresponding bilinear form is coercive, and the errors in a weighted energy norm for the approximate electron and hole concentrations are shown to be of \(O(h)\) order. Finally, a method for the evaluation of the terminal currents is presented, and the computed terminal currents from this method are shown to be convergent and conservative.
scientific article; zbMATH DE number 1956717
scientific article