A TRIANGULAR MIXED FINITE-ELEMENT METHOD FOR THE STATIONARY SEMICONDUCTOR-DEVICE EQUATIONS

A Petrov-Galerkin mixed finite element method based on triangular elements for a self-adjoint second order elliptic system arising from a stationary model of a semiconductor device is presented. This method is based on a novel formulation of the corresponding discrete problem and can be regarded as a natural extension to two dimensions of the well-known Scharfetter-Gummel one-dimensional scheme. Existence, uniqueness and stability of the approximate solution are proved for an arbitrary triangular mesh and an error estimate is given for an arbitrary Delaunay triangulation and its Dirichlet tesselation. No restriction is required on the angles of the triangles in the mesh. The associated linear system has the same form as that obtained from the conventional box method with an exponentially fitted approximation to the coefficient function on each element. 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.