Theoretical and numerical study of nanostructures

The methods presented in this thesis were developed to study the electron propagation in nanostructures with special emphasis on semiconducting materials. The essence of nanometer-scale physics is in the phase coherence of an electron wave function over a length scale that is comparable to the size of the structure itself. In order to study the electron transport in these nanostructures we have developed numerical Path Decomposition Expansion method (NPDX). Many different techniques have been used in the study of mesoscopic systems with complex geometry including transmission matrix methods, mode matching, and tight binding Green's function techniques such as the one used by Sols et al. in the study of the quantum modulated transistor. NPDX, however, permits the study of mesoscopic structures where other techniques are either not applicable or numerically prohibitive due to the geometric complexity. In addition, the nature of NPDX algorithm permits investigation of various geometries without modifications to the algorithm itself or any significant effect on the size of the computation. The transmission (reflection) coefficients calculated with the use of NPDX can then be related to the electric conductance via Landauer's formula. We have investigated a number of structures where other methods are applicable and we have found a good agreement with NPDX. We have also investigated the effects of dissipation on electron transport in these structures. Two models of dissipation are presented. These involve localized (onsite) and extended phonons linearlyt coupled to the electron. The coupling is localized to the "cavity" region only. Due to the resonant nature of electron scattering, the greatest influence of dissipation on the scattering of electron is presumably inside the cavity region. Thus, the essential features of dissipative effects should be well captured by such spatially confined phonon models. The main advantage of the localized phonon model is that it can be solved exactly. While the extended phonon model, although it can only be solved perturbatively, is a more realistic model of dissipation. Both models exhibit significant changes in the calculated transmission probabilities due to dissipation. In addition, in the localized phonon model, the "effective" cavity size as seen by the electron is modified by the dephasing nature of electron-coupling. Thus the effects of dissipation play an important role on the electron transport in nanostructures and on their practical applications. tThe choice of linear coupling was made only for the sake of simplicity.U of I OnlyThesi