Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations Original Research Article

This paper presents and analyzes an exponentially fitted tetrahedral finite element method for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. This finite element method is based on a set of piecewise exponential basis functions constructed on a tetrahedral mesh. The method is shown to be stable and can be regarded as an extension to three dimensions of the well-known Scharfetter–Gummel method. Error estimates for the approximate solution and its associated flux density are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux density and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative.