| This dissertation focuses on low-dimensional electron transport phenomena in devices ranging from semiconductor electron 'billiards' to semimetal atomic clusters to gold nanoparticles. In each material system, the goal of this research is to understand how carrier transport occurs when many elements act in concert. In the semiconductor electron billiards, magnetoconductance fluctuations, the result of electron quantum interference within the device, are used as a probe of electron transport through arrays of one, two, and three connected billiards. By combining two established analysis techniques, this research demonstrates a novel method for determining the quantum energy level spacing in each of the arrays. That information in turn shows the extent (and limits) of the phase-coherent electron wavefunction in each of the devices. The use of the following two material systems, the semimetal atomic clusters and the gold nanoparticles, is inspired by the electron billiard results. First, the output of the simple, rectangular electron billiards, the magnetoconductance fluctuations, is quite generally found to be fractal. This research addresses the question of what output one might expect from a device with manifestly fractal geometry by simulating the electrical response of fractal resistor networks and by outlining a method to implement such devices in fractal aggregates of semimetal atomic clusters. Second, in gold nanoparticle arrays, the number of array elements can increase by orders of magnitude over the billiard arrays, all with the potential to stay in a similar, phase-coherent transport regime. The last portion of this dissertation details the fabrication of these nanoparticle-based devices and their electrical characteristics, which exhibit strong evidence for electron transport in the Coulomb-blockade regime. A sketch for further 'off-blockade' experiments to realize magnetoconductance fluctuations, i.e. phase-coherent electron phenomena, is presented. |
