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 electrostatic 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 by the electric potential. The concentrations and temperature are computed by the upwind-block-centered difference method. The block-centered method is used to discretize the diffusion. The upwind difference is applied to approximate the convection to avoid numerical dispersion and nonphysical oscillation. The block-centered difference simulates diffusion, concentrations, temperature, and the adjoint vector functions simultaneously. It has the local conservation of mass. An optimal order error estimates is obtained. Numerical examples are provided to show the effectiveness and viability of this method.