Finite-Difference Schemes for the Density-Gradient Equations
Finite-Difference Schemes for the Density-Gradient Equations
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密度梯度方程的有限差分格式
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Ancona
中科院分区：
文献类型：
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作者：
M. Ancona
本文推导了两种新的有限差分格式，用于求解描述半导体中量子输运的密度梯度方程，改进了简单的线性离散。第一个方案也是线性的，但包括额外的条款，以保持守恒到二阶。第二种方案是一种非线性指数拟合方法，比线性方案更复杂，但也更有效。使用涉及量子限制和隧穿的设备的例子，数值计算的方法进行评估，并显示执行得很好，允许在网格细化，特别是在隧穿问题的大幅缓解。
Two new finite-difference schemes are derived for solving the density-gradient equations describing quantum transport in semiconductors that improve on a simple linear discretization. The first scheme is also linear but includes additional terms that serve to maintain conservation to second order. The second scheme is a nonlinear exponential-fitting method that is more complicated but also more efficient than the linear schemes. The methods are evaluated numerically using device examples involving both quantum confinement and tunneling and are shown to perform quite well allowing for a substantial easing in the mesh refinement especially in tunneling problems.