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 tem-tinal currents are convergent and conservative. (C) 2003 IMACS. Published by Elsevier Science B.V. All fights reserved.
|Journal||Applied Numerical Mathematics|
|Publication status||Published - 2003|