An upwind-block-centered finite difference method for a semiconductor device of heat conduction and its numerical analysis

The mathematical model is formulated by a nonlinear system of initial-boundary problem including four partial differential equations: an elliptic equation for elec-trostatic potential, two convection-diffusion equations for electron concentration and hole concentration, a heat conduction equation for temperature. The electric field potential is solved by the conservative block-centered method, and the first order of the accuracy is improved. The concentrations and temperature are computed by the upwind-block-centered difference method. The block-centered method is used to discretize the diffusion terms. The upwind difference is applied to approximate the convection parts without numerical dispersion or nonphysical oscillation. The block -centered difference simulates the concentrations, temperature and their adjoint vector functions simultaneously. The local conservation of mass is preserved. An optimal order error estimates is obtained. Finally, numerical examples show the effectiveness and viability of this method.(c) 2022 Published by Elsevier B.V.