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

电子设备的刻度 正在接近 量子力学效应是 变得重要。 从 从实用的角度来看， 器件尺寸的减小具有 直接影响开关速度 和功耗。 一般 数值程序将是 开发解决多- 维度时间依赖性和- 独立薛定谔方程 前者使用 有效替代方向 隐式技术与 量子的傅里叶变换 机械相关函数 解决后者。 该算法 也很容易扩展到包括 存在外部 磁场 这项技术的力量将是 通过将其应用于 几个相关的问题。 首先，共振隧穿 二维波包 将对结构进行研究， 评估的依赖性 隧道时间的角度 入射率，电子波数， 以及界面的粗糙度 在典型异质结构中。 第二，传播 波包穿过交叉导线 存在时的几何形状 外部磁场将 研究以更好地了解 淬火的起源 量子霍尔效应 三是 波包传播 静电阿哈拉诺夫-玻姆 将研究干涉仪， 评估新的可行性 量子干涉仪 晶体管。 该算法将 也可以用来计算 量子限制斯塔克位移 电子和空穴， 二维激子态 量子限制结构，以及 重要步骤 光学特性 这些结构的特性。 该算法还 在该领域的潜在应用 光电子学。 发达 ADI方案也将用作 光束传播的替代方案 方法（BPM）求解菲涅耳 波动方程，并应用于 光的表征 通过各种肋骨传播 波导和渐变折射率光学器件 纤维

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.