A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis

ABSTRACT A finite volume element scheme combined with upwind fractional step differences is presented on nonuniform partition to simulate numerically three‐dimensional transient problems of semiconductor device. Its mathematical model is defined by four partial differential equations (PDEs). An elliptic equation for the potential is discretized by a conservative finite volume element. Other PDEs for the concentrations and heat are treated by upwind fractional step differences. Applying the method of finite volume element, the principle of duality, the induction hypothesis, the prior error theory of differential equations and other special techniques, we give error estimates of second‐order accuracy in ‐norm. Finally, two experimental tests are given for showing possible applications in actual problems.