Semiconductor equations
Semiconductor equations
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DOI：
10.1007/978-3-7091-6961-2
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
P. Markowich;C. Ringhofer;C. Schmeiser
中科院分区：
文献类型：
--
作者：
P. Markowich;C. Ringhofer;C. Schmeiser
半导体中电荷输运的数学模型是近年来应用数学中一个十分活跃的研究领域。漂移扩散方程是模拟半导体器件电学行为的最常用的模型，目前在数学上已得到很好的理解。因此，数值方法已经开发，这使得合理有效的计算机模拟在许多情况下的实际意义。目前，漂移锡永模型的研究具有高度的专业性。它集中在探索可能更有效的离散化方法（如混合有限元，流线扩散），非线性迭代和线性方程求解器的性能的改善，并在三维应用。随着半导体器件的不断小型化，漂移扩散模型不能很好地描述超集成器件中的电荷输运，因此近年来模型研究的重点发生了转变。漂移扩散模型（所谓的流体动力学模型）的扩展正在研究中的亚微米MOS晶体管中的热电子效应的建模，和超级计算机技术已经有可能采用动力学模型（半经典玻尔兹曼泊松和维格纳泊松方程）的某些高度集成的设备的模拟。
In recent years the mathematical modeling of charge transport in semi conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simula tion of the electrical behavior of semiconductor devices, are by now mathe matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffu sion model is of a highly specialized nature. It concentrates on the explora tion of possibly more efficient discretization methods (eg mixed finite elements, streamline diffusion), on the improvement of the performance of nonlinear iteration and linear equation solvers, and on three dimensional applications. The ongoing miniaturization of semiconductor devices has prompted a shift of the focus of the modeling research lately, since the drift diffusion model does not account well for charge transport in ultra integrated devices. Extensions of the drift diffusion model (so called hydrodynamic models) are under investigation for the modeling of hot electron effects in submicron MOS-transistors, and supercomputer technology has made it possible to employ kinetic models (semiclassical Boltzmann-Poisson and Wigner Poisson equations) for the simulation of certain highly integrated devices.