A quantum regularization of the one-dimensional hydrodynamic model for semiconductors
A quantum regularization of the one-dimensional hydrodynamic model for semiconductors
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DOI：
10.57262/ade/1356651347
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发表时间：
2000-01
影响因子：
1.4
通讯作者：
Myo Thein Gyi;A. Jüngel
中科院分区：
文献类型：
--
作者：
Myo Thein Gyi;A. Jüngel
分析了包含量子玻姆势的等温定态流体力学方程。一维方程的电子电流密度和粒子密度耦合自洽的泊松方程的电势。量子修正可以解释为经典流体力学方程的色散正则化。物理动机的Dirichlet和Neumann边界条件的电子密度的规定。证明了在足够小的电流密度下强解的存在性和唯一性。此外，经典极限（标度普朗克常数消失）和零空间电荷极限（标度德拜长度消失）。证明是基于电子密度的变量变换，产生一个四阶椭圆方程的新变量。作为经典极限的副产品，得到了该流体动力系统亚音速解的存在性。最后，数值例子表明，对于“大”电流密度，快速振荡的粒子密度发生缩放普朗克常数趋于零。
The steady-state hydrodynamic equations for isothermal states including the quantum Bohm potential are analyzed. The onedimensional equations for the electron current density and the particle density are coupled self-consistently to the Poisson equation for the electric potential. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations. Physically motivated Dirichlet and Neumann boundary conditions for the electron density are prescribed. The existence and uniqueness of strong solutions for sufficiently small current densities are proven. Furthermore, the classical limit (vanishing scaled Planck constant) and the zero-space-charge limit (vanishing scaled Debye length) are performed. The proofs are based on a transformation of variable for the electron density, yielding a fourth-order, elliptic equation for the new variable. As a by-product of the classical limit, the existence of subsonic solutions to the hydrodynamic system is obtained. Finally, numerical examples are presented showing that for “large” current densities, fast oscillations in the particle density occur as the scaled Planck constant tends to zero.