A Theoretical Study of Quantum Ballistic Transport in Semiconductor Ring Structures

[摘要] Recent developments in microfabrication technology have enabled the manufacture of semiconductor devices in which the carriers scatter very infrequently over typical device lengths. Transport of this kind is termed ballistic, and under such conditions, coherent quantum interference phenomena become an increasingly important part of the conduction process. In particular, the conductors of such devices now assume the role of electron waveguides. Most previous attempts at modelling quantum ballistic transport have been based on one-dimensional models. However, relatively little was known about the true nature of wavepacket propagation in real structures where diffraction from apertures or around obstacles could occur. This thesis presents the first theoretical study of quantum ballistic transport in a two-dimensional quantum waveguide network. The study specifically concentrates on modelling the Aharonov-Bohm effect in ring structures, which is an exclusively quantum-mechanical effect. The method of investigation was to numerically solve the two-dimensional time-dependent Schrodinger equation for an idealised ring structure using a computer algorithm which incorporated several novel techniques. One-dimensional calculations show that one can expect a modulation depth of 100% in the oscillations in the magneto-resistance characteristic of such rings. Present oscillation amplitudes measured experimentally however fall far short of this figure, typically being about 0.1% of the background resistance in metal rings and about 10% in rings formed in the two-dimensional electron gas at a heterojunction interface. Computer simulation of wavepacket propagation in these latter structures clearly show a multi-mode structure in the wavefunction across the conductors of realistically-sized rings. It is shown that it is the transmission of more than one mode at the exit of the ring which is a major factor in reducing the amplitude of the magneto-resistance oscillations. Good agreement between the average magneto-resistance oscillation amplitude in the simulated and experimental characteristics for a ring formed at a heterojunction was obtained. The two-dimensional model can therefore be regarded as a major improvement on earlier one-dimensional models. Evidence suggesting a damping of the magneto-resistance oscillations as a result of the direct action of the magnetic field acting on the conductors is also found. It is estimated that the approximate cut-off field would be about 0.5 Tesla for the particular device modelled, which is consistent with experimental observations of a decline in the oscillation amplitude in the range 0.5-1.0 Tesla. A modification of the basic ring structure to achieve larger magneto-resistance oscillations by constricting the exit of the ring is proposed and computer simulation of wavepacket propagation through this structure shows that a substantial increase in modulation depth can be expected. The techniques developed in this thesis have therefore been able to successfully model existing quantum interference devices and also assess the likely improvement in performance of a hypothetical device. These techniques could a be applied to the modelling of wavepacket propagation in other types of sub-micron quantum-interference devices where transport can be considered to be ballistic.

[发布机构] University:University of Glasgow

[关键词] Electrical engineering