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

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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.