高阶辛算法在典型量子器件模拟中的应用

Application of High-order Symplectic FDTD Scheme to Typical Quantum Devices

利用辛积分和高阶交错差分方法建立了求解含时薛定谔方程的高阶辛算法(SFDTD(4,4)).对空间部分的二阶导数采用四阶准确度的差分格式离散得到随时间演化的多维系统再引入四阶辛积分格式离散;探讨了SFDTD(4,4)法的稳定性,获得了含时薛定谔方程的一维以及多维的稳定性条件,并得到在含势能情况下该稳定性条件的具体表达式;借助复坐标沿伸概念,实现了SFDTD(4,4)法在量子器件模拟中的完全匹配层吸收边界条件.结合一维量子阱和金属场效应管传输的仿真,结果表明较传统的时域有限差分算法,SFDTD(4,4)有着更好的计算准确度,适用于长时间仿真.算法及相关结果可为实际量子器件的设计提供必要的参考.

Using symplectic integrators and staggered spatial differences to establish a new high-order Symplectic Finite-Difference Time-Domain scheme（SFDTD（4,4））for solving time-dependent Schr？dinger equation.The fourth-order accuracy difference scheme for the second derivative of the space segment is to obtain the time evolution of the multi-dimensional system and then introducing the fourth order symplectic integrator for discrete;the numerical stability is obtained with SFDTD（4,4）scheme,one-or multi-dimensional stability conditions for Schrdinger equation with nonzero potential energy are also derived;the perfect absorbing boundary condition of SFDTD（4,4）scheme for quantum devices is achieved by the concept of stretching coordinate.The simulated results of a one-dimensional quantum well and metal MOSFET confirm the preference of the SFDTD（4,4）scheme over the traditional finitedifference time-domain scheme.The SFDTD（4,4）scheme,which is high-order-accurate and energy conserving,is well suited for long term simulation.The results can be used as a necessary reference for the design of new quantum devices.