Resumen de Accurate charge-integrals evaluation in two-dimensional finite-element semiconductor-device simulation
A widely used approach for solving the two‐dimensional semiconductor‐device equations through the Finite‐Element method employs a linear approximation of the electric and quasi‐Fermi potentials over a triangular mesh; this approach combines the flexibility of FE method with the simplicity of a piecewise linear representation of the unknowns. Owing to the strong dependence of carrier densities on the position, a careful evaluation of integrals involving these quantities is desirable; this problem arises, for example, when the very common Galerkin's or Ritz's method are used, and is differently treated in the Literature. In this paper it is demonstrated that, if a minor approximation on the intrinsic carrier density is done, an analytical evaluation of the above integrals over each triangular element can be performed, which takes into account the correct dependence of carrier densities on the electric and quasi‐Fermi potentials; the results may be used to avoid heavy mesh refinements, which make the solution procedure costly both in CPU time and in memory storage. Practical applications to some specific devices will be shown elsewhere; the procedure and the final formulas are presented here in a rather general way, thus allowing a possible application to different problems which may be solved with FE method.
