Transport phenomena in nanoscale systems
In this dissertation we discuss two general problems: transport of ballistic particles in systems with rough boundaries and the interference effect of bulk and boundary scattering processes. ^ We derived a perturbative transport equation for ballistic particles in thin films with random rough walls for both quasiclassical and quantized motion across the film. The unusual non-diagonal structure of the effective scattering operator makes the transport equation different from the standard Waldmann-Snider equation when the distance between quantized levels for the motion across the film is comparable to the wall-induced perturbation. We calculate the magnitude of this anomaly for degenerate particles and Gaussian correlations of the surface inhomogeneities. ^ Outside the quantum resonance domain we derived a simple, universal surface collision operator. This operator contains all relevant information on statistical and geometrical characteristics of weak roughness and can be used as a general boundary condition on the corrugated surfaces. We apply this operator to a variety of systems including films and channels with rough walls, particles adsorbed on or bound to rough substrates, multilayer systems with randomly corrugated interfaces, etc. The main emphasis is on quantization of motion between the walls, though the quasiclassical limit is considered as well. The diffusion and conductivity coefficients, localization length, and other transport parameters are expressed analytically via the correlation functions of surface corrugation. ^ We analyze the interference processes between bulk and surface scattering. The effective collision time for scattering by random bulk and surface inhomogeneities, and the transport relaxation time are calculated beyond the Matthiessen's rule. The diagrammatic expansion includes second order diagrams for boundary scattering and full summation of bulk processes. The effective collision time is expressed via the bulk collision time and statistical parameters of the surface inhomogeneities. Calculation of the effective transport relaxation time requires the knowledge of the irreducible vertex function for the impurity scattering. In the case of a short-range impurity potential transport coefficients and transport relaxation time depend only on observable parameters: the bulk collision time, the bulk transport relaxation time, and parameters of the surface roughness. ^
Physics, Condensed Matter
Armen Boris Stepaniants,
"Transport phenomena in nanoscale systems"
Dissertations and Master's Theses (Campus Access).