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

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 finitedifference 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。

Numerical solutions of Schrodinger 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 Schrodinger 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.