RIA:Analysis of Electrical and Optical Properties of QuantumConfined Structures Using an Alternating Direction Implicit Algorithm

电子设备的规模正在接近量子力学效应变得重要的水平。从实用的角度来看，器件尺寸的减小对开关速度和功耗有直接的影响。一个一般的数值程序将发展，以解决多维时间依赖和独立薛定谔方程。前者采用一种有效的可选方向隐式技术，结合量子力学相关函数的傅里叶变换求解后者。该算法也很容易扩展到包括外部磁场的存在。该技术的力量将通过将其应用于几个相关问题来证明。首先，研究了波包在二维结构中的共振隧穿，以评估隧穿时间与入射角、电子波数、以及典型异质结构中界面的粗糙度。第二,为了更好地理解量子霍尔效应猝灭的起源，将研究波包在外部磁场存在下通过交叉线几何形状的传播。第三，研究了波包在静电Aharanov-Bohm干涉仪中的传播，以评估新提出的量子干涉仪晶体管的可行性。该算法还将用于计算电子和空穴的量子受限斯塔克位移，以及二维量子受限结构中的激子态。这是表征这些结构光学特性的重要一步。该算法在光电子学领域也有潜在的应用前景。开发的ADI方案也将被用作波束传播方法（BPM）的替代方案，以解决菲涅耳波方程。并应用于光通过各种肋波导和渐变折射率光纤的传播特性。

The scales of electronic devices are approaching the level where quantum mechanical effects are becoming important. From a practical point of view, the reduction of device size has a direct impact on switching speed and power consumption. A general numerical procedure will be developed to solve the multi- dimensional time-dependent and - independent Schrodinger equation. The former is solved using an efficient Alternative Direction implicit technique coupled with a Fourier transform of the quantum mechanical correlation function to solve the latter. The algorithm is also readily extended to include the presence of an external magnetic field. The power of the technique will be demonstrated by applying it to several problems of relevance. First, the resonant tunneling of wavepacket in two-dimensional structures will be investigated to assess the dependence of the tunneling time on the angle of incidence, the electron wavenumber, and the roughness of the interfaces in a typical heterostructure. Second, the propagation of wavepackets through crossed wires geometries in the presence of an external magnetic field will be studied to better understand the origin of the quenching of the quantum Hall effect. Third, the propagation of wavepacket in Electrostatic Aharanov-Bohm interferometers will be studied to assess the feasibility of newly proposed Quantum Interferometers Transistors. The algorithm will also be used to calculate the quantum-confined Stark shifts for both electrons and holes and the excitonic states in two-dimensional quantum-confined structures, and important step towards the characterization of the optical properties of these structures. The proposed algorithm has also potential applications in the field of optoelectronics. The developed ADI scheme will also be used as an alternative to the Beam Propagation Method (BPM) to solve the Fresnel wave equation, and applied to the characterization of light propagation through various Rib waveguides and graded index optical fibers.