The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initial-boundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously. The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

中文翻译：

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动态变化的网格上半导体器件问题的以块为中心的迎风近似

三维半导体器件的数值模拟是信息科学中的一个基本问题。该数学模型由具有四个偏微分方程的初边界非线性系统定义：一个椭圆形方程用于电势，两个对流扩散方程用于电子浓度和空穴浓度，以及一个热传导方程用于温度。第一个方程通过保守的以块为中心的方法求解。浓度和温度是通过在变化的网格上以块为中心的迎风差异方法计算的，其中，以块为中心的方法和迎风近似分别用于离散扩散和对流。在变化的网格上的计算很好地显示了PN结附近的局部特殊属性。应用迎风方案近似对流，避免了数值离散和非物理振荡。以块为中心的差异可同时计算浓度，温度及其伴随矢量函数。在计算过程中保留了局部质量守恒，这是半导体器件数值模拟中的重要规则。获得最佳阶收敛。提供了数值示例以显示效率和应用。获得最佳阶收敛。提供了数值示例以显示效率和应用。获得最佳阶收敛。提供了数值示例以显示效率和应用。