In this paper, we present a mathematical model with initial-boundary values and a block-centered approximation for a new semiconductor device type. Two factors, heat and magnetic influences are considered. This discussion is an important and basic simulation problem in information science. The mathematical model is formulated by four nonlinear partial differential equations (PDEs), determining four major physical variables. An elliptic equation is given for the potentials, two convection-diffusion equations are for the concentrations of electronic and hole, and a heat equation is for the temperature. The potentials affects the whole physical movement. The elliptic equation is treated by a block-centered method, and the law of conservation is preserved. The computational accuracy is improved one order. Other equations are convection-dominated, thus are approximated by block-centered differences. Furthermore, the unknowns and adjoint functions are computed at the same time. These characters play important roles in numerical computations of conductor device problems. Using the theories of priori analysis such as energy estimates, the principle of duality and mathematical inductions, an optimal estimates result is obtained. Thus, this important problem is solved.
MSC(2010) 65M06, 65N06, 65N30, 82D37