A TETRAHEDRAL MIXED FINITE-ELEMENT METHOD FOR THE STATIONARY SEMICONDUCTOR CONTINUITY EQUATIONS

A Petrov-Galerkin mixed finite element method based on tetrahedral elements for the stationary semiconductor device continuity equations is presented. This method can be regarded as a natural extension to three dimensions of the well known Scharfetter-Gummel one-dimensional scheme. Existence, uniqueness and stability of the approximate solution are proved and an error estimate is given for an arbitrary Delaunay mesh and corresponding Dirichlet tessellation. The associated linear system is a symmetric and positive definite M-matrix. The evaluation of the terminal currents associated with the method is also discussed and it is shown that the computed terminal currents are convergent and conservative. Numerical results for a model three-dimensional device are presented to validate the theoretical results.