Discretization Scheme for the Density-Gradient Equation and Effect of Boundary Conditions
Discretization Scheme for the Density-Gradient Equation and Effect of Boundary Conditions
复制标题
密度梯度方程的离散化格式及边界条件的影响
DOI：
10.1023/a:1020764027686
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发表时间：
2002
影响因子：
2.1
通讯作者：
Yiming Li
中科院分区：
文献类型：
--
作者：
T. Tang;Xinlin Wang;Yiming Li
近年来，密度梯度理论(M.G.Ancona和H.F.Tiersten 1987，Phys.B.35(15)：7959-7965，M.G.Ancona 1990，Phys.Rev.B.42：1222)已被建立为解决诸如MOS反型层中的电荷密度分布和MOS隧道等问题的薛定谔方程的可行替代方案(M.G.Ancona 1998，J.Tech。CAD(11)，M.G.Ancona等人2000年，IEEE Transans.电子设备47：1449)。与薛定谔方法相比，DG方法的主要优点是可以灵活地扩展到多维，并且易于并入传统的漂移-扩散或流体动力求解器(C.S.Rafferty等人)。1998年，Proc.SISPAD，第137页，A.Wettstein等人。2001年，IEEE Trans.艾力克。戴夫。48：279)。然而，代表量子效应的DG项是一个单微扰项，需要特别注意离散化(X.Wang 2001，马萨诸塞大学阿默斯特分校硕士论文)。在这项工作中，我们考察了线性和非线性离散格式的有效性以及边界条件对所用格式的影响。
In recent years, the density gradient theory (DG) (M.G. Ancona and H.F. Tiersten 1987, Phys. Rev. B. 35(15): 7959–7965, M.G. Ancona 1990, Phys. Rev. B. 42: 1222) has been established as a viable alternative to the solution of the Schrödinger equation for solving problems such as charge density distribution in MOS inversion layers and MOS tunneling (M.G. Ancona 1998, J. Tech. CAD(11), M.G. Ancona et al. 2000, IEEE Trans. Electron Devices 47: 1449). Primary advantages of the DG method over the Schrödinger method are flexibility in extending to multi-dimension and easiness in incorporating into the conventional drift-diffusion or hydrodynamic solver (C.S. Rafferty et al. 1998, Proc. SISPAD, p. 137, A. Wettstein et al. 2001, IEEE Trans. Elec. Dev. 48: 279). However, the DG term that represents the quantum effects is a singular perturbation term and requires special care for discretization (X. Wang 2001, Master's thesis, University of Massachusetts, Amherst). In this work, we examine the validity of the linear vs. the nonlinear discretization scheme and the effect of boundary conditions on the scheme used.