In this project, we introduce a type of microscopy which produces correlated topography and fluorescence lifetime images with nanometer resolution. This technique combines atomic force microscopy (AFM) and time resolved confocal fluorescence microscopy to conduct biological and materials research. This method is used to investigate nanophotonic effects on single fluorophores, including quantum dots and fluorescent molecules. For single fluorescent molecules, we investigate the effects of quenching of fluorescence with the probe of an atomic force microscope which is combined and synchronized with a confocal fluorescence lifetime microscope. For quantum dots, we investigate the correlation between the topographic and fluorescence data. With this method of combining an atomic force microscope with a confocal microscope, it is anticipated that there will be applications in nanomaterial characterization and life sciences; such as the determination of the structure of small molecular systems on surfaces, molecular interactions, as well as the structure and properties of fluorescent nanomaterials.

Spin-orbit interactions are important in determining nuclear structure. They lead to a shift in the energy levels in the nuclear shell model, which could explain the sequence of magic numbers in nuclei. Also in nucleon-nucleon scattering, the large nucleon polarization observed perpendicular to the plane of scattering needs to be explained by adding the spin-orbit interactions in the potential. Their effects change the equation of state and other properties of nuclear matter. Therefore, the simulation of spin-orbit interactions is necessary in nuclear matter.

The auxiliary field diffusion Monte Carlo is an effective and accurate method for calculating the ground state and low-lying exited states in nuclei and nuclear matter. It has successfully employed the Argonne v6' two-body potential to calculate the equation of state in nuclear matter, and has been applied to light nuclei with reasonable agreement with experimental results. However, the spin-orbit interactions were not included in the previous simulations, because the isospin-dependent spin-orbit potential is difficult in the quantum Monte Carlo method. This work develops a new method using extra auxiliary fields to break up the interactions between nucleons, so that the spin-orbit interaction with isospin can be included in the Hamiltonian, and ground-state energy and other properties can be obtained.

This dissertation is focused on material property exploration and analysis using computational quantum mechanics methods. Theoretical calculations were performed on the recently discovered hexahydride materials A2SiH6 (A=Rb, K) to calculate the lattice dynamics of the systems in order to check for structural stability, verify the experimental Raman and infrared spectrospcopy results, and obtain the theoretical free energies of formation. The electronic structure of the systems was calculated and the bonding and ionic properties of the systems were analyzed. The novel hexahydrides were compared to the important hydrogen storage material KSiH3. This showed that the hypervalent nature of the SiH62- ions reduced the Si-H bonding strength considerably. These hydrogen rich compounds could have promising energy applications as they link to alternative hydrogen fuel technology. The carbide systems Li-C (A=Li,Ca,Mg) were studied using \emph{ab initio} and evolutionary algorithms at high pressures. At ambient pressure Li2C2 and CaC2 are known to contain C22- dumbbell anions and CaC2 is polymorphic. At elevated pressure both CaC2 and Li2C2 display polymorphism. At ambient pressure the Mg-C system contains several experimentally known phases, however, all known phases are shown to be metastable with respect to the pure elements Mg and C. First principle investigation of the configurational space of these compounds via evolutionary algorithms results in a variety of metastable and unique structures. The binary compounds ZnSb and ZnAs are II-V electron-poor semiconductors with interesting thermoelectric properties. They contain rhomboid rings composed of Zn2Sb2 (Zn2As2) with multi-centered covalent bonds which are in turn covalently bonded to other rings via two-centered, two-electron bonds. Ionicity was explored via Bader charge analysis and it appears that the low ionicity that these materials display is a necessary condition of their multicentered bonding. Both compounds were found to have narrow, indirect band gaps with multi-valley valence and conduction bands; which are important characteristics for high thermopower in thermoelectric materials. Future work is needed to analyze the lattice properties of the II-V CdSb-type systems, especially in order to find the origin of the extremely low thermal conductivity that these systems display.

The work contained in this dissertation is focused on the optical properties of direct band gap semiconductors which crystallize in a wurtzite structure: more specifically, the III-nitrides and ZnO. By using cathodoluminescence spectroscopy, many of their properties have been investigated, including band gaps, defect energy levels, carrier lifetimes, strain states, exciton binding energies, and effects of electron irradiation on luminescence. Part of this work is focused on p-type Mg-doped GaN and InGaN. These materials are extremely important for the fabrication of visible light emitting diodes and diode lasers and their complex nature is currently not entirely understood. The luminescence of Mg-doped GaN films has been correlated with electrical and structural measurements in order to understand the behavior of hydrogen in the material. Deeply-bound excitons emitting near 3.37 and 3.42 eV are observed in films with a significant hydrogen concentration during cathodoluminescence at liquid helium temperatures. These radiative transitions are unstable during electron irradiation. Our observations suggest a hydrogen-related nature, as opposed to a previous assignment of stacking fault luminescence. The intensity of the 3.37 eV transition can be correlated with the electrical activation of the Mg acceptors. Next, the acceptor energy level of Mg in InGaN is shown to decrease significantly with an increase in the indium composition. This also corresponds to a decrease in the resistivity of these films. In addition, the hole concentration in multiple quantum well light emitting diode structures is much more uniform in the active region when Mg-doped InGaN (instead of Mg-doped GaN) is used. These results will help improve the efficiency of light emitting diodes, especially in the green/yellow color range. Also, the improved hole transport may prove to be important for the development of photovoltaic devices. Cathodoluminescence studies have also been performed on nanoindented ZnO crystals. Bulk, single crystal ZnO was indented using a sub-micron spherical diamond tip on various surface orientations. The resistance to deformation (the "hardness") of each surface orientation was measured, with the c-plane being the most resistive. This is due to the orientation of the easy glide planes, the c-planes, being positioned perpendicularly to the applied load. The a-plane oriented crystal is the least resistive to deformation. Cathodoluminescence imaging allows for the correlation of the luminescence with the regions located near the indentation. Sub-nanometer shifts in the band edge emission have been assigned to residual strain the crystals. The a- and m-plane oriented crystals show two-fold symmetry with regions of compressive and tensile strain located parallel and perpendicular to the ±c-directions, respectively. The c-plane oriented crystal shows six-fold symmetry with regions of tensile strain extending along the six equivalent a-directions.

Monte Carlo methods often used in nuclear physics, such as auxiliary field diffusion Monte Carlo and Green's function Monte Carlo, have typically relied on phenomenological local real-space potentials containing as few derivatives as possible, such as the Argonne-Urbana family of interactions, to make sampling simple and efficient. Basis set methods such as no-core shell model or coupled-cluster techniques typically use softer non-local potentials because of their more rapid convergence with basis set size. These non-local potentials are typically defined in momentum space and are often based on effective field theory. Comparisons of the results of the two types of methods are complicated by the use of different potentials. This thesis discusses progress made in using such non-local potentials in quantum Monte Carlo calculations of light nuclei. In particular, it shows methods for evaluating the real-space, imaginary-time propagators needed to perform quantum Monte Carlo calculations using non-local potentials and universality properties of these propagators, how to formulate a good trial wave function for non-local potentials, and how to perform a "one-step" Green's function Monte Carlo calculation for non-local potentials.

High electron mobility transistors (HEMTs) based on Group III-nitride heterostructures have been characterized by advanced electron microscopy methods including off-axis electron holography, nanoscale chemical analysis, and electrical measurements, as well as other techniques. The dissertation was organized primarily into three topical areas: (1) characterization of near-gate defects in electrically stressed AlGaN/GaN HEMTs, (2) microstructural and chemical analysis of the gate/buffer interface of AlN/GaN HEMTs, and (3) studies of the impact of laser-liftoff processing on AlGaN/GaN HEMTs. The electrical performance of stressed AlGaN/GaN HEMTs was measured and the devices binned accordingly. Source- and drain-side degraded, undegraded, and unstressed devices were then prepared via focused-ion-beam milling for examination. Defects in the near-gate region were identified and their correlation to electrical measurements analyzed. Increased gate leakage after electrical stressing is typically attributed to "V"-shaped defects at the gate edge. However, strong evidence was found for gate metal diffusion into the barrier layer as another contributing factor. AlN/GaN HEMTs grown on sapphire substrates were found to have high electrical performance which is attributed to the AlN barrier layer, and robust ohmic and gate contact processes. TEM analysis identified oxidation at the gate metal/AlN buffer layer interface. This thin a-oxide gate insulator was further characterized by energy-dispersive x-ray spectroscopy and energy-filtered TEM. Attributed to this previously unidentified layer, high reverse gate bias up to −30 V was demonstrated and drain-induced gate leakage was suppressed to values of less than 10−6 A/mm. In addition, extrinsic gm and ft * LG were improved to the highest reported values for AlN/GaN HEMTs fabricated on sapphire substrates. Laser-liftoff (LLO) processing was used to separate the active layers from sapphire substrates for several GaN-based HEMT devices, including AlGaN/GaN and InAlN/GaN heterostructures. Warpage of the LLO samples resulted from relaxation of the as-grown strain and strain arising from dielectric and metal depositions, and this strain was quantified by both Newton's rings and Raman spectroscopy methods. TEM analysis demonstrated that the LLO processing produced no detrimental effects on the quality of the epitaxial layers. TEM micrographs showed no evidence of either damage to the ~2 μm GaN epilayer generated threading defects.

Nitride semiconductors have wide applications in electronics and optoelectronics technologies. Understanding the nature of the optical recombination process and its effects on luminescence efficiency is important for the development of novel devices. This dissertation deals with the optical properties of nitride semiconductors, including GaN epitaxial layers and more complex heterostructures. The emission characteristics are examined by cathodoluminescence spectroscopy and imaging, and are correlated with the structural and electrical properties studied by transmission electron microscopy and electron holography. Four major areas are covered in this dissertation, which are described next. The effect of strain on the emission characteristics in wurtzite GaN has been studied. The values of the residual strain in GaN epilayers with different dislocation densities are determined by x-ray diffraction, and the relationship between exciton emission energy and the in-plane residual strain is demonstrated. It shows that the emission energy increases withthe magnitude of the in-plane compressive strain. The temperature dependence of the emission characteristics in cubic GaN has been studied. It is observed that the exciton emission and donor-acceptor pair recombination behave differently with temperature. The donor-bound exciton binding energy has been measured to be 13 meV from the temperature dependence of the emission spectrum. It is also found that the ionization energies for both acceptors and donors are smaller in cubic compared with hexagonal structures, which should contribute to higher doping efficiencies. A comprehensive study on the structural and optical properties is presented for InGaN/GaN quantum wells emitting in the blue, green, and yellow regions of the electromagnetic spectrum. Transmission electron microscopy images indicate the presence of indium inhomogeneties which should be responsible for carrier localization. The temperature dependence of emission luminescence shows that the carrier localization effects become more significant with increasing emission wavelength. On the other hand, the effect of non-radiative recombination on luminescence efficiency also varies with the emission wavelength. The fast increase of the non-radiative recombination rate with temperature in the green emitting QWs contributes to the lower efficiency compared with the blue emitting QWs. The possible saturation of non-radiative recombination above 100 K may explain the unexpected high emission efficiency for the yellow emitting QWs Finally, the effects of InGaN underlayers on the electronic and optical properties of InGaN/GaN quantum wells emitting in visible spectral regions have been studied. A significant improvement of the emission efficiency is observed, which is associated with a blue shift in the emission energy, a reduced recombination lifetime, an increased spatial homogeneity in the luminescence, and a weaker internal field across the quantum wells. These are explained by a partial strain relaxation introduced by the InGaN underlayer, which is measured by reciprocal space mapping of the x-ray diffraction intensity.

The goal of this theoretical study of infrared spectra was to ascertain to what degree molecules may be identified from their IR spectra and which spectral regions are best suited for this purpose. The frequencies considered range from the lowest frequency molecular vibrations in the far-IR, terahertz region (below ~3 THz or 100 cm-1) up to the highest frequency vibrations (~120 THz or 4000 cm-1). An emphasis was placed on the IR spectra of chemical and biological threat molecules in the interest of detection and prevention. To calculate IR spectra, the technique of normal mode analysis was applied to organic molecules ranging in size from 8 to 11,352 atoms. The IR intensities of the vibrational modes were calculated in terms of the derivative of the molecular dipole moment with respect to each normal coordinate. Three sets of molecules were studied: the organophosphorus G- and V-type nerve agents and chemically related simulants (15 molecules ranging in size from 11 to 40 atoms); 21 other small molecules ranging in size from 8 to 24 atoms; and 13 proteins ranging in size from 304 to 11,352 atoms. Spectra for the first two sets of molecules were calculated using quantum chemistry software, the last two sets using force fields. The "middle" set used both methods, allowing for comparison between them and with experimental spectra from the NIST/EPA Gas-Phase Infrared Library. The calculated spectra of proteins, for which only force field calculations are practical, reproduced the experimentally observed amide I and II bands, but they were shifted by approximately +40 cm-1 relative to experiment. Considering the entire spectrum of protein vibrations, the most promising frequency range for differentiating between proteins was approximately 600-1300 cm-1 where water has low absorption and the proteins show some differences.

Single molecules in a tunnel junction can now be interrogated reliably using chemically-functionalized electrodes. Monitoring stochastic bonding fluctuations between a ligand bound to one electrode and its target bound to a second electrode ("tethered molecule-pair" configuration) gives insight into the nature of the intermolecular bonding at a single molecule-pair level, and defines the requirements for reproducible tunneling data. Importantly, at large tunnel gaps, there exists a regime for many molecules in which the tunneling is influenced more by the chemical identity of the molecules than by variability in the molecule-metal contact. Functionalizing a pair of electrodes with recognition reagents (the "free analyte" configuration) can generate a distinct tunneling signal when an analyte molecule is trapped in the gap. This opens up a new interface between chemistry and electronics with immediate implications for rapid sequencing of single DNA molecules.

In this work, atomic force microscopy (AFM) and time resolved confocal fluorescence microscopy are combined to create a microscopy technique which allows for nanometer resolution topographic and fluorescence imaging. This technique can be applied to any sample which can be immobilized on a surface and which can be observed by fluorescence microscopy. Biological problems include small molecular systems, such as membrane receptor clusters, where very high optical resolutions need to be achieved. In materials science, fluorescent nanoparticles or other optically active nanostructures can be investigated using this technique. In the past decades, multiple techniques have been developed that yield high resolution optical images. Multiple far-field techniques have overcome the diffraction limit and allow fluorescence imaging with resolutions of few tens of nanometers. On the other hand, near-field microscopy, that makes use of optically active structures much smaller than the diffraction limit can give resolutions around ten nanometers with the possibility to collect topographic information from flat samples. The technique presented in this work reaches resolutions in the nanometer range along with topographic information from the sample. DNA origami with fluorophores attached to it was used to show this high resolution. The fluorophores with 21 nm distance could be resolved and their position on the origami determined within 10 nm. Not only did this work reach a new record in optical resolution in near-field microscopy (5 nm resolution in air and in water), it also gave an insight into the physics that happens between a fluorescent molecule and a dielectric nanostructure, which the AFM tip is. The experiments with silicon tips made a detailed comparison with models possible on the single molecule level, highly resolved in space and time. On the other hand, using silicon nitride and quartz as tip materials showed that effects beyond the established models play a role when the molecule is directly under the AFM tip, where quenching of up to 5 times more efficient than predicted by the model was found.