量子电子学报, 2014, 31 (3): 340, 网络出版: 2014-06-03
基于高阶辛算法的纳米器件本征问题仿真
Simulation of nanodevice eigenvalue problems based on higher-order symplectic algorithm
量子光学 辛积分 时域有限差分 薛定谔方程 纳米器件本征问题 quantum optics symplectic integration time-domain finite-difference Schrdinger equation nanodevices eigenvalue problems
摘要
研究一种准确、有效的数值方法是现代纳米器件建模和优化的重要目标之一，而分析大多数纳米器件特性的起始点是确定器件的本征值和本征态。提出了一种 新算法—高阶辛时域有限差分法(Symplectic finite-difference time-domain, SFDTD(3,4))，求解含时薛定谔方程。在时间上采用三阶辛积分,空间上采用四阶差分格式, 建立了针对含时薛定谔方程数值求解的高阶辛时域有限差分算法。将高阶辛算法SFDTD(3,4)用于一维量子阱中盒中粒子和一维谐振子的仿真中，实验结果表明SFDTD(3,4)法 比传统的时域有限差分算法以及高阶时域有限差分算法更加准确，适用于对纳米器件本征问题的长时间仿真。
Abstract
Numerical solutions of Schrdinger equation have become increasingly important because of the tremendous demands for the design and optimization of nanodevices where quantum effects are significant or dominate. Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrdinger equation. A detailed numerical study on 1 D quantum eigenvalue problems is carried out. Compared with FDTD(2,2) and FDTD(2,4), the simulation results of quantum wells and harmonic oscillators strongly confirm that the explicit SFDTD scheme is well suited for a long-term simulation.
沈晶, 况晓静, 张量, 曹欣远, 陈明生, 张忠祥. 基于高阶辛算法的纳米器件本征问题仿真[J]. 量子电子学报, 2014, 31(3): 340. SHEN Jing, KUANG Xiao-jing, ZHANG Liang, CAO Xin-yuan, CHEN Ming-sheng, ZHANG Zhong-xiang. Simulation of nanodevice eigenvalue problems based on higher-order symplectic algorithm[J]. Chinese Journal of Quantum Electronics, 2014, 31(3): 340.
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