A finite element approach and automatic mesh generation for the resolution of Poisson's equation in reverse biased two-dimensional semiconductor devices

A finite element (FE) approach, with triangular elements, for the resolution of Poisson's equation in reverse biased semiconductors is described. An optimised successive overrelaxation method, using a space charge approximation and neglecting the exponential dependence in the potential of the carrier concentrations, yields an excellent initial guess for the resolution of the full non-linear problem by a Newton-Raphson algorithm. Various geometrical structures and interface and boundary conditions are dealt with in a natural way. An automatic mesh generation program, allowing to take full benefit of the FE method advantages, is also briefly described. An example is presented to illustrate the application of the method.