| Nanostructure research is becoming an increasingly valuable tool as semiconductor devices are reduced in dimension. There is an obvious limitation to how far semiconductor devices can be scaled down before their expected behavior becomes erratic. This unpredictability will make itself evident in what is known as quantum phenomena. Classical rules will no longer govern the behavior of today's very large scale integration (VLSI) and ultra large scale integration (ULSI) circuitry.; Semiconductor quantum dots and corrugated quantum wires (quantum dot arrays) are devices that are currently being studied to learn more about this transition in classical to quantum behavior. Both devices are studied in this work. Gallium Arsenide/Aluminum Gallium Arsenide square quantum dots of varying dimension (0.2 mum to 2.0 mum) with varying quantum point contact widths are simulated to study the scaling behavior of the periodicities of the magneto-conductance fluctuations and trapped electron orbits within the dot (wavefunction scars). Arrays of quantum dots, similar to the single quantum dots, are simulated to study the effect of backscattering and how it leads to enhanced resistance in a corrugated quantum wire.; The simulation tools that have been developed and utilized in this work are discussed extensively. A three-dimensional Poisson solver, a one-dimensional Schrodinger solver, and a stabilized mode matching/two-dimensional Schrodinger solver are the tools of choice in this work.; Using the simulation tools, theoretically calculated results are used to develop a magneto-conductance fluctuation 'scaling' theory for the square quantum dots. Additional simulation results for corrugated quantum wires are used to compare existing experimental data to study the backscattering effect that is observable in a doubly-corrugated structure. A self-consistent technique that combines all of the simulation tools is utilized to determine whether the scarring of the electron wavefunction exhibits a feedback effect that prolongs the wavefunction scar over a range of magnetic fields. |
