Advanced and mature computer simulation methods exist in fluid dynamics, elec-

tromagnetics, semiconductors, chemical transport, and even chemical and material

electronic structure. However, few general or accurate methods have been developed

for quantum photonic devices. Here, a novel approach utilizing phase-space quantum

mechanics is developed to model photon transport in ring resonators, a form of en-

tangled pair source. The key features the model needs to illustrate are the emergence

of non-classicality and entanglement between photons due to nonlinear effects in the

ring. The quantum trajectory method is subsequently demonstrated on a sequence

of elementary models and multiple aspects of the ring resonator itself.

Attaining a sufficiently large critical current density (Jc) in magnetic-barrier Josephson junctions has been one of the greatest challenges to the development of dense low-power superconductor memories. Many experimentalists have used various combinations of superconductor (S) and ferromagnetic (F) materials, with limited success towards the goal of attaining a useful Jc. This trial-and-error process is expensive and time consuming. An improvement in the fundamental understanding of transport through the ferromagnetic layers and across the superconductor-ferromagnetic interface could potentially give fast, accurate predictions of the transport properties in devices and help guide the experimental studies.

In this thesis, parameters calculated using density functional methods are used to model transport across Nb/0.8 nm Fe/Nb/Nb and Nb/3.8 nm Ni /Nb/Nb Josephson junctions. The model simulates the following transport processes using realistic parameters from density functional theory within the generalized gradient approximation: (a) For the first electron of the Cooper pair in the superconductor to cross the interface- conservation of energy and crystal momentum parallel to the interface (kll). (b) For the second electron to be transmitted coherently- satisfying the Andreev reflection interfacial boundary conditions and crossing within a coherence time, (c) For transmission of the coherent pair through the ferromagnetic layer- the influence of the exchange field on the electrons’ wavefunction and (d) For transport through the bulk and across the interfaces- the role of pair-breaking from spin-flip scattering of the electrons. Our model shows the utility of using realistic electronic-structure band properties of the materials used, rather the mean-field exchange energy and empirical bulk and interfacial material parameters used by earlier workers. [Kontos et al. Phys. Rev Lett, 93(13), 137001. (2004); Demler et al. Phys. Rev. B, 55(22), 15174. (1997)].

The critical current densities obtained from out model for Nb/0.8 nm Fe/Nb is 104 A/cm2 and for Nb/3.8 nm Ni/Nb is 7.1*104 A/cm2. These values fall very close to those observed experimentally- i.e. for Nb/0.8 nm Fe/Nb is 8*103 A/cm2 [Robinson et al" Phys. Rev. B 76, no. 9, 094522. (2007)] and for Nb/3.8 nm of Ni/Nb is 3*104 A/cm2 [Blum et al Physical review letters 89, no. 18, 187004. (2002). This indicates that our approach could potentially be useful in optimizing the properties of ferromagnetic-barrier structures for use in low-energy superconducting memories.

In this work, transport in nanowire materials and nanowire field effect transistors is studied using a full band Monte Carlo simulator within the tight binding basis. Chapter 1 is dedicated to the importance of nanowires and nanoscale devices in present day electronics and the necessity to use a computationally efficient tool to simulate transport in these devices. Chapter 2 discusses the calculation of the full band structure of nanowires based on an atomistic tight binding approach, particularly noting the use of the exact same tight binding parameters for bulk band structures as well as the nanowire band structures. Chapter 3 contains the scattering rate formula for deformation potential, polar optical phonon, ionized impurity and impact ionization scattering in nanowires using Fermi’s golden rule and the tight binding basis to describe the wave functions. A method to calculate the dielectric screening in 1D systems within the tight binding basis is also described. Importantly, the scattering rates of nanowires tends to the bulk scattering rates at high energies, enabling the use of the same parameter set that were fitted to bulk experimental data to be used in the simulation of nanowire transport. A robust and efficient method to model interband tunneling is discussed in chapter 4 and its importance in nanowire transport is highlighted. In chapter 5, energy relaxation of excited electrons is studied for free standing nanowires and cladded nanowires. Finally, in chapter 6, a full band Monte Carlo particle based solver is created which treats confinement in a full quantum way and the current voltage characteristics as well as the subthreshold swing and percentage of ballistic transport is analyzed for an In0.7Ga0.3As junctionless nanowire field effect transistor.

Measurements of the geometrical magnetoresistance of a conventional semiconductor, gallium arsenide (GaAs), and a more recently developed semiconductor, iron pyrite (FeS2) were measured in the Corbino disc geometry as a function of magnetic field to determine the carrier mobility (μm). These results were compared with measurements of the Hall mobility (μH) made in the Van der Pauw configuration. The scattering coefficient (ξ), defined as the ratio between magnetoresistance and Hall mobility (μm/μH), was determined experimentally for GaAs and natural pyrite from 300 K to 4.2 K. The effect of contact resistance and heating on the measurement accuracy is discussed.

Studying the electronic band structure is necessary to understand the physics behind electron transport in devices made of the material under consideration. Graphene has been in the limelight of ground breaking research in the recent past and will continue to be in the future, as scientists around the world have been giving special attention to this remarkable material in pursuit of advancement in the semiconductor device industry by making use of many of its fascinating properties.

Although several different approaches have been proposed for the calculation of the band structure, the empirical methods have proven to be more convenient, since we can arrive at a reasonable result close to what has been found experimentally without a huge computational trade-off by varying some relevant parameters. Moreover, a method based on a plane wave basis has been found to be extremely compatible with advanced methods for device modeling and simulation such as a semi-classical Monte Carlo. The purpose of this study is to extract fitting parameters for the calculation of band structure of graphene using the empirical pseudopotential method, which can be used for further research, such as theoretical modeling and simulation of graphene-based devices. Since various methods have been proposed for the calculation of these pseudopotentials, we will also briefly study the effect of different pseudopotentials on the band structure of bilayer graphene.

In mesoscopic physics, conductance fluctuations are a quantum interference phenomenon that comes from the phase interference of electron wave functions scattered by the impurity disorder. During the past few decades, conductance fluctuations have been studied in various materials including metals, semiconductors and graphene. Since the patterns of conductance fluctuations is related to the distributions and configurations of the impurity scatterers, each sample has its unique pattern of fluctuations, which is considered as a sample fingerprint. Thus, research on conductance fluctuations attracts attention worldwide for its importance in both fundamental physics and potential technical applications. Since early experimental measurements of conductance fluctuations showed that the amplitudes of the fluctuations are on order of a universal value (e2/h), theorists proposed the hypothesis of ergodicity, e.g. the amplitudes of the conductance fluctuations by varying impurity configurations is the same as that from varying the Fermi energy or varying the magnetic field. They also proposed the principle of universality; e.g., that the observed fluctuations would appear the same in all materials. Recently, transport experiments in graphene reveal a deviation of fluctuation amplitudes from those expected from ergodicity.

Thus, in my thesis work, I have carried out numerical research on the conductance fluctuations in GaAs nanowires and graphene nanoribbons in order to examine whether or not the theoretical principles of universality and ergodicity hold. Finite difference methods are employed to study the conductance fluctuations in GaAs nanowires, but an atomic basis tight-binding model is used in calculations of graphene nanoribbons. Both short-range disorder and long-range disorder are considered in the simulations of graphene. A stabilized recursive scattering matrix technique is used to calculate the conductance. In particular, the dependence of the observed fluctuations on the amplitude of the disorder has been investigated. Finally, the root-mean-square values of the amplitude of conductance fluctuations are calculated as a basis with which to draw the appropriate conclusions. The results for Fermi energy sweeps and magnetic field sweeps are compared and effects of magnetic fields on the conductance fluctuations of Fermi energy sweeps are discussed for both GaAs nanowires and graphene nanoribbons.

Semiconductor nanowires are important candidates for highly scaled three dimensional electronic devices. It is very advantageous to combine their scaling capability with the high yield of planar CMOS technology by integrating nanowire devices into planar circuits. The purpose of this research is to identify the challenges associated with the fabrication of vertically oriented Si and Ge nanowire diodes and modeling their electrical behavior so that they can be utilized to create unique three dimensional architectures that can boost the scaling of electronic devices into the next generation. In this study, vertical Ge and Si nanowire Schottky diodes have been fabricated using bottom-up vapor-liquid-solid (VLS) and top-down reactive ion etching (RIE) approaches respectively. VLS growth yields nanowires with atomically smooth sidewalls at sub-50 nm diameters but suffers from the problem that the doping increases radially outwards from the core of the devices. RIE is much faster than VLS and does not suffer from the problem of non-uniform doping. However, it yields nanowires with rougher sidewalls and gets exceedingly inefficient in yielding vertical nanowires for diameters below 50 nm. The I-V characteristics of both Ge and Si nanowire diodes cannot be adequately fit by the thermionic emission model. Annealing in forming gas which passivates dangling bonds on the nanowire surface is shown to have a considerable impact on the current through the Si nanowire diodes indicating that fixed charges and traps on the surface of the devices play a major role in determining their electrical behavior. Also, due to the vertical geometry of the nanowire diodes, electric field lines originating from the metal and terminating on their sidewalls can directly modulate their conductivity. Both these effects have to be included in the model aimed at predicting the current through vertical nanowire diodes. This study shows that the current through vertical nanowire diodes cannot be predicted accurately using the thermionic emission model which is suitable for planar devices and identifies the factors needed to build a comprehensive analytical model for predicting the current through vertically oriented nanowire diodes.

Since its inception about three decades ago, silicon on insulator (SOI) technology has come a long way to be included in the microelectronics roadmap. Earlier, scientists and engineers focused on ways to increase the microprocessor clock frequency and speed. Today, with smart phones and tablets gaining popularity, power consumption has become a major factor. In this thesis, self-heating effects in a 25nm fully depleted (FD) SOI device are studied by implementing a 2-D particle based device simulator coupled self-consistently with the energy balance equations for both acoustic and optical phonons. Semi-analytical expressions for acoustic and optical phonon scattering rates (all modes) are derived and evaluated using quadratic dispersion relationships. Moreover, probability distribution functions for the final polar angle after scattering is also computed and the rejection technique is implemented for its selection. Since the temperature profile varies throughout the device, temperature dependent scattering tables are used for the electron transport kernel. The phonon energy balance equations are also modified to account for inelasticity in acoustic phonon scattering for all branches. Results obtained from this simulation help in understanding self-heating and the effects it has on the device characteristics. The temperature profiles in the device show a decreasing trend which can be attributed to the inelastic interaction between the electrons and the acoustic phonons. This is further proven by comparing the temperature plots with the simulation results that assume the elastic and equipartition approximation for acoustic and the Einstein model for optical phonons. Thus, acoustic phonon inelasticity and the quadratic phonon dispersion relationships play a crucial role in studying self-heating effects.

The drive towards device scaling and large output power in millimeter and sub-millimeter wave power amplifiers results in a highly non-linear, out-of-equilibrium charge transport regime. Particle-based Full Band Monte Carlo device simulators allow an accurate description of this carrier dynamics at the nanoscale. This work initially compares GaN high electron mobility transistors (HEMTs) based on the established Ga-face technology and the emerging N-face technology, through a modeling approach that allows a fair comparison, indicating that the N-face devices exhibit improved performance with respect to Ga-face ones due to the natural back-barrier confinement that mitigates short-channel-effects. An investigation is then carried out on the minimum aspect ratio (i.e. gate length to gate-to-channel-distance ratio) that limits short channel effects in ultra-scaled GaN and InP HEMTs, indicating that this value in GaN devices is 15 while in InP devices is 7.5. This difference is believed to be related to the different dielectric properties of the two materials, and the corresponding different electric field distributions. The dielectric effects of the passivation layer in millimeter-wave, high-power GaN HEMTs are also investigated, finding that the effective gate length is increased by fringing capacitances, enhanced by the dielectrics in regions adjacent to the gate for layers thicker than 5 nm, strongly affecting the frequency performance of deep sub-micron devices. Lastly, efficient Full Band Monte Carlo particle-based device simulations of the large-signal performance of mm-wave transistor power amplifiers with high-Q matching networks are reported for the first time. In particular, a CellularMonte Carlo (CMC) code is self-consistently coupled with a Harmonic Balance (HB) frequency domain circuit solver. Due to the iterative nature of the HB algorithm, this simulation approach is possible only due to the computational efficiency of the CMC, which uses pre-computed scattering tables. On the other hand, HB allows the direct simulation of the steady-state behavior of circuits with long transient time. This work provides an accurate and efficient tool for the device early-stage design, which allows a computerbased performance evaluation in lieu of the extremely time-consuming and expensive iterations of prototyping and experimental large-signal characterization.