Abstract: The mathematical model of the semiconductor device is described by the initial boundary value problem for a system of three quasilinear partial differential equations: one of elliptic type for the electrostatic potential, the other two of convection-dominated diffusion type for the conservation of electron and hole concentrations. For 3-d semiconductor device, the electrostatic potential equation is approximated with the aid of finite volume method, while the electron and hole concentration equations are approximated with upwind finite volume schemes. Error estimate of order $O(h+\Delta t)$ in $L^{2}$-norm is obtained.

Key words: Semiconductor device, Initial boundary value problem, Upwind scheme, Finite volume method, Error estimate