ANALYSIS OF A DISCRETIZATION ALGORITHM FOR STATIONARY EQUATIONS IN SEMICONDUCTOR DEVICE MODELS, III

Abstract

Given approximations to the electrostatic potential and the current densities in a semicon‐ductor device model, a method is described and analyzed for computing moments of the carrier densities, as will be used in a consistent finite‐element discretization of the full system of equations commonly adopted for such models. It is also shown how the current density distribution obtained from a Scharfetter‐Gummel method is compatible with this procedure, and leads to a global accuracy of at least first order in the mesh size. The convergence analysis depends only on the electrostatic potential and the current densities being reasonably smooth functions, and not on bounded derivatives of the carrier densities or on a limit in the change in electrostatic potential between neighbouring mesh points.

Citation

MOCK, M.S. (1984), "ANALYSIS OF A DISCRETIZATION ALGORITHM FOR STATIONARY EQUATIONS IN SEMICONDUCTOR DEVICE MODELS, III", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 3 No. 4, pp. 187-199. https://doi.org/10.1108/eb009995