The main purpose of this thesis is to justify the density functional theory of freezing in the case of a crystal with square symmetry. In the first part, I discuss the widely used technique of molecular dynamics to characterise the dynamics and statistical observables of a system undergoing a phase transition. I then outline the advantages and the main drawbacks of this technique: slow implementation and poor performance for long time scales. It is shown that order parameter or phenomenological theories of freezing paliate those problems. These theories describe the dynamics of one parameter that starts in a highly symmetric state and which symmetry is broken during the phase transition. The dynamics of the order parameter, which in our case is the time averaged density, is governed by the topology of a free energy functional. We derive such a free energy functional for two theories and explain why one of these can be applied to give freezing into arbitrary symmetry groups. The study of freezing into square symmetry and various elastic deformations of two-dimensional crystals form the last part of the thesis.

In the past two decades, significant progress in constructing physical systems of reduced dimensionality has been made. In these systems, quantum effects are observed in the electric current response to an applied bias voltage. Considerable theoretical effort has been made to understand conductance and capacitance which characterize this response. In addition to a fundamental science interest, there has been a significant technological need to build and understand small scale devices in order to maintain the current rate of progress in increasing computer performance. / In this thesis, we theoretically investigated the conductance and capacitance of mesoscopic and molecular scale systems. Our approach incorporated Landauer-Buttiker transport theory. / We developed a highly efficient method, based on the solution of the time-dependent Schrodinger equation incorporating a magnetic field, to solve the quantum scattering problem in mesoscopic nanostructures. We studied linear response capacitance in a two plate mesoscopic capacitor with one plate a quantum conductor in the ballistic scattering regime. By determining the scattering wavefunctions in the quantum plate, we were able to obtain relevant densities of states and use them to self-consistently calculate capacitance matrix coefficients for the system. We find the capacitance to be highly dependent on the external magnetic field and the number of probes attached to the quantum conductor. / To study molecular scale systems, our approach was based on Density Functional Theory within Local Density Approximation and non-equilibrium Green's functions, implemented in the simulation package McDcal. For the work in this thesis, we modified McDcal to run on parallel computer architectures. We studied the current-voltage characteristics of silicon cage nanowires sandwiched between aluminum electrodes. We successfully analyzed our results using the complex band structure of the nanowire. Finally, we studied the capacitance properties of carbon nanotube junctions. In junctions with tubes so far apart that their wavefunctions do not overlap, we studied the variation in capacitance for different relative tube positions and radii. We also studied junctions where the nanotubes are in contact but in which there is no current due to a conductance gap. In this system we find an enhancement in the value of capacitance.

We study the dynamics of an interface driven far from equilibrium in three dimensions. We first derive the equations of motion which describe this physics. Numerical results are then obtained for three models which simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We show that the three models belong to the same dynamical universality class by estimating the dynamical scaling exponents and the scaling functions. We confirm the results by a careful study of the crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this phenomenon by monitoring the surface step energy which shows a drastic jump at a finite temperature for a given driving force. At the same temperature, a finite size scaling analysis on the bond energy fluctuation shows a diverging peak.

The semiconductor ZnO has a band gap of 3.3 eV and has potential in applications as transparent and conducting layers for electronic devices. In the present work, experiments have been carried out to deposit thin films of ZnO on glass and silicon substrates by RF magnetron sputtering. The deposition experiments were performed at substrate temperatures in a range from room value to 400°C. Resistivity measurements were performed on the films. The resistivity increased as the substrate temperature was increased from room value to 400°C. The films on the silicon substrates were then processed into ZnO(n)-Si(p) heterojunctions whereas the ones on glass substrates were processed into metal-ZnO-metal MSM devices. Dark current-voltage and capacitance-voltage characteristics of the fabricated devices have been studied in order to determine the effects of substrate temperature during the deposition. In addition, post deposition heat treatment experiments were performed and the effects were examined by the electrical measurements. For the samples deposited at room temperature, the resistivity was observed to decrease drastically after a heat treatment at 150°C for 30 minutes. / Illuminated characteristics of both the heterojunctions and MSM devices were also studied in a wavelength range from 300 to 700 nm. It was observed that UV responsivity for the ZnO-Si heterojunctions shows an increase from 210 to 300°C and a large decrease at 400°C. Under illumination, the current at given voltage increases for all samples and this has been confirmed to be mainly due to the bandgap absorption. From the post deposition heat treatment experiments carried out at low temperatures, the dark current was observed to increase with heat treatment time. However, the photocurrent was also observed to increase with the heat treatment time.

In this work, we present theoretical analysis of charge transport at the molecular scale. We use a state-of-the-art theoretical tool to investigate a number of key issues of molecular electronics, paying particular attention to quantitative comparison with experimental data which have been confirmed by different labs. Our analysis allows us not only to understand the data, but also to make quantitative predictions. / We have calculated the length dependence of resistance for molecular wires, including oligophenylene thiol and alkanethiol molecules. Our results are in excellent agreement with the corresponding measured data. Our analysis provides a good understanding of charge conduction mechanism in these molecular wires. This is the first time in molecular conduction research that a parameter-free modeling agrees so well with real data. We have also studied the conformational dependence of current of a biphenyldithiol molecule in terms of the dihedral angle variations. The charge current can be tuned by this parameter, and the ratio of tuning can be as large as several hundred fold. A physical picture emerges from our analysis. / We have investigated the momentum filtering effect due to molecule orbitals. This study allows us to understand why some incoming Bloch states can conduct through the molecule, while others cannot. By adding different end-groups to the molecule, we found that conduction channels can be varied. We have also studied the gate potential control of electric current. The gate voltage shifts the resonance state of the molecule thereby inducing a current modulation. We found that the gating efficiency strongly depends on the geometry of the gate electrode. The current through a biphenyl dimethanethiol molecule is found to be switchable by applying gate voltages, and the on/off current ratio can be substantial. / Finally, using carbon nanotubes with substitutional nitrogen, we clearly demonstrate that conventional equilibrium conductance analysis was not enough to describe the whole transport features in molecular devices. A nitrogen doped zigzag nanotube showed that even a single atom substitution has increased the current flow and, for small radii tubes, narrowed the current gap. Periodical substitution makes zigzag semiconducting tubes metallic, a prediction which has been confirmed by a subsequent experiment. For an armchair metallic nanotube, doping with a single impurity reduces current. The physics of these behaviours has been addressed.

Thesis (Ph. D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1031. Adviser: Alexey Bezryadin. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1037. Adviser: John H. Weaver. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007. / Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4531. Adviser: Peter Sternberg. Title from dissertation home page (viewed Apr. 22, 2008).

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1032. Adviser: Ali Yazdani. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--The College of William and Mary, 2005. / (UnM)AAI3201111. Adviser: Gina L. Hoatson. Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0321.