Modelling of Quantum Transport in Nanostructures
Abstract: In this thesis, theoretical studies of the transport properties of three nanoscale systems: one-dimensional (1D) quantum wires (QWRs), zero-dimensional (0D), laterally confined, double-barrier resonant tunnelling structures (DBRTSs) and three-terminal ballistic junctions (TBJs), have been performed. In the first part of the thesis, an overview of the realization and properties of such systems is given along with a description of modelling tools used in the calculations. The second and main part of the thesis contains the original research results, summarized into seven papers. The conductance of QWRs with corrugated boundaries is investigated in Paper I with respect to the nature of the boundary roughness, geometrical parameters of the QWR and temperature. It is shown that, due to the structural imperfections, the conductance exhibits rapid fluctuations, strong, broad dips between adjacent conductance plateaus at very low temperatures and, in general, a suppression of the conductance below the values expected for an ideal QWR. The results agree with existing experimental results. Experimental studies of the transport properties of 0D quantum dots obtained by laterally confining vertical DBRTSs by means of metallic gates have shown complex, gate-dependent fine structure in the measured current-voltage (I-V) characteristics. The origin of this fine structure is theoretically studied and explained (Papers II-V) in terms of quasi-1D-0D-1D systems with a tunable lateral confinement. It is shown that, due to the low dimensionality of the emitter, dot and collector regions, complex fine structure, which is strongly dependent on Fermi energy, source-drain voltage, and gate voltage, is formed in the I-V characteristics, which may explain the experimentally observed results. A tentative comparison between experiments and theory is made in Paper IV. Three-terminal junction systems have very recently emerged as excellent candidates for use as building blocks in the formation of nanoscale electronic devices. A general formalism for the calculation of electron transport through three- terminal quantum structures is presented in Paper VI. Using this method, the transport through Y-shaped TBJ structures is studied in Paper VII. Quantum effects are shown to influence the transport properties of TBJs at low temperatures, possibly enabling new device functionality.
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