Atomically thin two-dimensional nanomaterials such as graphene and transition metal dichalcogenides (TMDCs) have seen a rapid growth of exploration since the isolation of monolayer graphene. These materials provide a rich field of study for physics and optoelectronics applications. Many applications seek to combine a two dimensional (2D) material with another nanomaterial, either another two dimensional material or a zero (0D) or one dimensional (1D) material. The work in this thesis explores the consequences of these interactions from 0D to 2D. We begin in Chapter 2 with a study of energy transfer at 0D-2D interfaces with quantum dots and graphene. In our work we seek to maximize the rate of energy transfer by reducing the distance between the materials. We observe an interplay with the distance-dependence and surface effects from our halogen terminated quantum dots that affect our observed energy transfer. In Chapter 3 we study supercapacitance in composite graphene oxide- carbon nanotube electrodes. At this 2D-1D interface we observe a compounding effect between graphene oxide and carbon nanotubes. Carbon nanotubes increase the accessible surface area of the supercapacitors and improve conductivity by forming a conductive pathway through electrodes. In Chapter 4 we investigate effective means of improving sample quality in TMDCs and discover the importance of the monolayer interface. We observe a drastic improvement in photoluminescence when encapsulating our TMDCs with Boron Nitride. We measure spectral linewidths approaching the intrinsic limit due to this 2D-2D interface. We also effectively reduce excess charge and thus the trion-exciton ratio in our samples through substrate surface passivation. In Chapter 5 we briefly discuss our investigations on chemical doping, heterostructures and interlayer decoupling in ReS₂. We observe an increase in intensity for p-doped MoS₂ samples. We investigated the charge transfer exciton previously identified in heterostructures. Spectral observation of this interlayer exciton remained elusive in our work but provided the motivation for our work in Chapter 4. We also discuss our preliminary results on interlayer decoupling in ReS₂.

As another important features in VEELS, the plasmon excitations (including the volume plasmon and surface/interfacial plasmon) are also utilized to identify different phases and multi compositions within materials. The microstructure and electronic structure evolution of silicon-rich oxide (SRO) films as a function of the annealing temperature are investigated using TEM and VEELS. The as-deposited SiO film is found to be a single phase with only single volume plasmon presents in VEEL spectrum and almost no interfacial plasmon is observed. After the annealing (Tanneal>400°C), it begins to decomposite into Si and SiO2 and the single phase changed into cluster/matrix nanocomposites where the interfacial plasmon appears. The Si duster size and its concentration increase as the annealing temperature increases. / Firstly, the applications of VEELS in investigating the electronic structures of ZnO nanowires with different diameter and surface shapes are demonstrated. Using the momentum transferred technique, one of the interband transitions with dipole-forbidden nature is identified. Several size dependent features are found on the interband transitions and plasmon oscillations of ZnO nanowires with small diameter and circular cross section, which are mainly due to the large surface to volume ratio and existence of Oxygen dangling bonds on those ZnO wires. / Further explorations on the electronic structure in the vicinity of band gap are carried out for the ZnO nanowires doped with different dopants (Co, Er, Yb) and different dopant concentrations. In order to obtain trustworthy information in the very low energy range of VEELS a narrow zero loss peak and elimination of Cerenkov effect and surface losses are necessary, which can be realized by incorporation of the gun monochromator in the TEM and taking spectrum at a momentum transfer slightly greater than zero. Band tail states (∼2-3.3 eV) are found to be generated in the ZnO nanowires after the ion implantation and their density of states increase with the ion fluence increases. The partially removal of those defect states by the Oxygen annealing is also observed in VEELS. On the other hand, interesting mid-gap state(s), which is dopant-sensitive (as it is only observed in the rare earth (Er and Yb) doped ZnO nanowires, but not in the Co-doped ones), does not show obvious change after the O annealing. The impact of these electronic structure changes on the material properties are also discussed. / In the end of the thesis, some of the practical limitations and contradictories on the energy resolution (DeltaE), spatial resolution (Delta x), and the momentum resolution (Deltaq) when carrying out the various VEELS study are summarized. The compromise made among these resolution limits is also discussed. / In this work, the important experimental parameters and appropriate data processing methods to generate trustworthy data are discussed. Based on that, three material systems, i.e., pure ZnO nanowires, doped ZnO nanowires, and Si/SiO/SiO2 composite films are investigated. Various information on the material microstructure/electronic structure is interpreted using the VEELS data. / The valence-electron energy-loss spectroscopy (VEELS) contains information on the electronic structures of materials, including the band gap the single-electron interband transitions and the plasmon oscillations. When operating in transmission electron microscope (TEM), the excellent spatial resolution enables the VEELS not only exploring the local electronic structures of individual low dimensional nanostructured materials, but also building up correlations between the electronic structure and microstructure. In addition, the capability in carrying out the momentum transfer dependent study in VEELS allows the investigation on the dispersion of plasmons and single electron excitations in the momentum space. The optically forbidden transitions, which are not allowed in conventional optical method, can also be excited at high momentum transfer values using VEELS. / Wang, Juan = 價電子能量損失譜在低維納米材料中的應用 / 王娟. / "September 2007." / Adviser: Li Quan. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1267. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 122-133). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307. / Wang, Juan = Jia dian zi neng liang sun shi pu zai di wei na mi cai liao zhong de ying yong / Wang Juan.

by S.W. Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 76-77). / by S.W. Wong. / Title Page --- p.i / Dedication --- p.ii / Acknowledgments --- p.iii / Abstract --- p.iv / Table of Contents --- p.v / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- A Brief Introduction to Nonlinear Optics --- p.7 / Chapter Chapter 3 --- Experimental Measurement of the First Hyperpolarizability β for pNA by Hyper-Rayleigh Scattering in Solution --- p.24 / Chapter 3.1 --- Introduction --- p.24 / Chapter 3.2 --- Theory of Measurement of β by HRS --- p.26 / Chapter 3.3 --- Experimental Setup --- p.31 / Chapter 3.4 --- Preparation of Sample --- p.34 / Chapter 3.5 --- Results --- p.35 / Chapter Chapter 4 --- Studies of Depolarization Ratio in HRS --- p.44 / Chapter 4.1 --- Background --- p.44 / Chapter 4.2 --- Theory --- p.45 / Chapter 4.3 --- Results --- p.55 / Chapter 4.4 --- Discussion and Conclusion --- p.57 / Chapter Chapter 5 --- Measurement on other Nonlinear Optical Compounds --- p.63 / Chapter Chapter 6 --- Conclusion --- p.73 / References --- p.76

Xiao, Manda = 金納米晶修飾的空心介孔二氧化矽微球在表面等離子體激元調製下的光散射行為 / 肖蔓達. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references. / Abstracts in English and Chinese. / Xiao, Manda = Jin na mi jing xiu shi de kong xin jie kong er yang hua xi wei qiu zai biao mian deng li zi ti ji yuan diao zhi xia de guang san she xing wei / Xiao Manda. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgement --- p.iv / Table of Contents --- p.vi / List of Figures --- p.viii / List of Tables --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Plasmonic Properties of Noble Metal Nanocrystals --- p.1 / Chapter 1.2 --- Light Scattering from Dielectric Spheres --- p.6 / Chapter 1.3 --- Motivations and Outline of the Thesis --- p.9 / Chapter 2 --- Characterization Techniques --- p.17 / Chapter 2.1 --- Instrumentation --- p.17 / Chapter 2.2 --- Extinction Measurement of Au Nanocrystals and the HMSMSs Decorated with the Au Nanocrystals --- p.17 / Chapter 2.3 --- Sample Preparation for the TEM and SEM Characterization --- p.18 / Chapter 2.4 --- Dark-Field Imaging and Spectroscopy of the Individual Microspheres --- p.19 / Chapter 3 --- Fabrication of Hollow Mesoporous Silica Microspheres Decorated with the Au Nanocrystals --- p.25 / Chapter 3.1 --- Preparation of the Hollow Mesoporous Silica Microspheres --- p.25 / Chapter 3.2 --- Growth of the Au Nanocrystals --- p.29 / Chapter 3.3 --- Assembly of the Au Nanocrystals onto the Hollow Mesoporous Silica Microspheres --- p.32 / Chapter 4 --- Resonant Scattering Properties of the Hollow Mesoporous Silica Microspheres --- p.38 / Chapter 4.1 --- Experimental Results --- p.38 / Chapter 4.2 --- Calculation of the Scattering Spectra by Mie Theory --- p.42 / Chapter 4.3 --- Summary --- p.46 / Chapter 5 --- Resonant Scattering Properties of the Au Nanocrystal-Decorated Hollow Mesoporous Silica Microspheres --- p.49 / Chapter 5.1 --- Effect of the Plasmon Resonances of the Au Nanocrystals on the Resonant Scattering Behaviors of the HMSMSs --- p.49 / Chapter 5.2 --- Estimation of the Scattering Enhancement Factors --- p.54 / Chapter 5.3 --- Summary --- p.59 / Chapter 6 --- Summary --- p.61

In this thesis, Gallium Nitride (GaN) micro- and nanostructures were fabricated based on focused ion beam (FIB) milling. The starting wafer is an epitaxial structure containing InGaN/GaN multi-quantum wells. High crystal quality structures such as the nano-cone, nanopillar array and single pillar were fabricated based on the FIB method. During the fabrication process, various approaches were designed to minimize FIB damage caused by Gallium ion bombardment. The fabrication process for nano-cone is a combination of mask preparation by FIB with subsequent reactive ion etching (RIE). For fabricating nanopillar arrays, the nanopillars were patterned directly using FIB with an optimized beam current followed by wet etching process to remove the damage. On the other hand, the single pillar is achieved by gradually decreasing the ion beam current as the diameter of the pillar becomes smaller. The first order Raman spectra for the nanopillar array reveal a strong additional peak when the diameter of the nanopillars is less than 220 nm. This peak can also be observed in GaN pillars without MQW and is clearly assigned to the surface optical (SO) mode originated from the A1 phonon in wurtzite GaN. The frequency of this SO mode is found to be sensitive with the diameter and surface roughness of the nanopillars. Temperature-variable photoluminescence (PL) measurements show that a broadband emission in the as-grown sample split into the two well-resolved bands for nanopillars and the emission band at the higher energy side quickly thermally quenched. Room temperature PL measurements on the single pillars exhibit an increasing blue-shift of the peak emission with the decreasing of the pillar diameter. Additional simulation data and excitation power dependent PL studies confirm the observation of strain relaxation in the pillar’s MQW due to FIB fabrication. The temperature variable PL on the single pillar shows a monotonous blue shift as the temperature arises to 300 K. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

Central to the practical use of nanoscale materials is the controlled growth in technologically meaningful quantities. Many of the proposed applications of the nanomaterials potentially require inexpensive production of the building blocks. Solution-based synthetic approach offers controllability, high throughput, and scalability, which make the process attractive for the potential scale-up. Growth kinetics could be readily influenced by chemical interactions between the precursor and the solvent. In order to fully utilize its benefits, it is therefore pivotal to understand the decomposition chemistry of the precursors used in the reactions. Supercritical fluids were used as solvent in which high temperature reactions could take place. Silicon nanowires with diameters of 20~30 nm was synthesized in supercritical fluids with metal nanocrystals as seeds for the nanowire growth. To unravel the effect of silicon precursors, several silicon precursors were reacted and the resulting products were investigated. The scalability of the system is discussed based on the experimental data. The nanowires were characterized with various characterization tools, including high-resolution transmission electron microscopy and electron energy loss spectroscopy. The crystallographic signatures were analyzed through the transmission electron microscopic study, and fundamental electrical and optical properties were probed by electron energy loss spectroscopy. Carbon nanotubes were prepared by reacting carbon-containing chemicals in supercritical fluids with organometallic compounds that form metal seed particles in-situ. A batch reaction, in which the temperature control was relatively poor, yielded a mixture of multiwall nanotubes and amorphous carbon nanofilaments with a low selectivity of nanotubes in the product. When reaction parameters were translated into a continuous flow-through reaction, nanotube selectivity as well as the throughput of the total product significantly improved. Magnetic properties of various metal nanocrystals were also studied. Colloidal synthesis enables the growth of FePt and MnPt3 nanocrystals with size uniformity. The as-synthesized nanocrystals, however, had compositionally disordered soft-magnetic phases. To obtain hard magnetic layered phase, the nanocrystals must be annealed at high temperatures, which led to sintering of the inorganic cores. To prevent sintering, the nanocrystals were encapsulated with silica layer prior to annealing. Interparticle magnetic interactions were also explored using particles with varying silica thickness. / text

Nonlinear organic liquids that exhibit two-photon absorption (TPA) function as good optical limiters for sensor protection from laser pulses. L34 (4-butyl-4'-propyl-diphenylethyne) is a liquid organic compound exhibiting nonlinear optical absorption. A thiol- derivatized analog of L34 (“thiol-L34”) was prepared to bind the molecules to the surface of gold nanoparticles. Surface binding is necessary to investigate synergy between nonlinear optical absorption of gold nanoparticles and thiol-L34. Thiol-L34 was prepared in a six-step organic synthesis starting from 3-(4-bromophenyl) propionic acid. Au nanoparticles with <15 nm diameter have been prepared and sensitized with the thiol-L34 compound for assessment of their nonlinear optical behavior. Diazolylmethenes a class of metal-coordinating dyes that are similar to dipyrrins with some substitutions of nitrogen atoms in place of carbon atoms. Modification in the framework of dipyrrinoid dyes via this replacement of nitrogen for carbon atoms may lead to compounds that serve as effective agents for bioimaging and/or photodynamic therapy. Several routes to the synthesis of di-(1,2,3)-triazolylmethenes, di-(1,2,4)-triazolylmethenes, and ditetrazolylmethenes are presented.

Biological organisms, organs and tissues have evolved through natural selection diverse functional and structural traits to accomplish complex tasks. For example, small insects with tiny thermal capacitance have developed tailored spectral properties and behavioral tactics to mitigate rapid changes of body temperatures caused by environmental electromagnetic radiations; neural networks in the brain, through changing the efficacy of synapses, can recognize hidden patterns and correlations in raw data, cluster and classify them, and continuously learn and improve over time. These biological systems are a rich source of bio-inspiration for developing solutions to address engineering challenges. My thesis work focuses on the intersection between photonics and biology and explores three unique biological systems and their technological implications. Beginning with the investigation of butterfly wings, we observed that the wings contain a matrix of living structures, including mechanical and thermal sensory neural cells, hemocytes, pheromone producing organs, , and even “wing hearts”, and that these living structures carry out their specific functions over the entire life span of butterflies but are vulnerable to sustained high temperatures. We discovered that butterflies have evolved heterogeneously thickened wing cuticles and special nanostructured wing scales to locally enhance thermal emissivity so that the regions of the wings containing living structures can better dissipate heat through thermal radiation. Furthermore, we discovered that butterfly wings almost always possess enhanced reflectivity in the near-infrared, which can significantly reduce heating caused by solar radiation. This enhanced near-infrared reflectivity is found to originate from optical scattering at the porous wing scales, especially pale-colored scales underneath the surface layer of colorful ones. Besides these structural adaptations, our bioassays showed that butterflies utilize a number of behavioral strategies to avoid overheating or overcooling of their wings. We found that butterflies can use their wings as a fast and sensitive temperature monitor to detect the direction and strength of sunlight or artificial light applied onto the wings; as such, they can adapt the most suitable postures to minimize overheating of the wings if the illumination is too strong and to warm up the wings when ambident temperatures are insufficient for taking flight. Drawing inspiration from the multi-layered wing scales, which impart coloration to the wings while maintaining their high near-infrared reflectivity, we developed a double-layered, radiative-cooling coating that is able to minimize solar heating while still stay colorful. The second part of my thesis work explored nanostructured fibers and textiles as a novel solution for radiative cooling. The work was motivated by our discovery that the silk fibers produced by the caterpillars of the Madagascan moon moth (Argema mittrei) contain a high density of filamentary air voids, which enable individual fibers of the moth to strongly reflect light over the solar spectrum. This, in combination with natural polymers’ intrinsic high mid-infrared emissivity, provides the cocoons of the moth with remarkable passive radiative-cooling properties. We developed fabrication platforms to produce synthetic fibers with filamentary air voids by modifying both wet spinning and melt extrusion techniques. The melt extrusion approach, in particular, is implemented in an industry-scale fiber extrusion machine for high-throughput, high-yield production. The fabricated nanostructured fibers reproduce the prominent solar reflectivity of the Madagascan moon moth silk fibers and possess high emissivity due to the variety of chemical bonds in the synthetic polymers used. The melt-extruded fibers were twisted into yarns, which were subsequently woven and knitted into fabrics. The finished fabric samples were demonstrated to perform as effective radiative cooling devices compared to conventional white fabrics. Lastly, inspired by how neural networks in the brain form the basis of learning and motivated by how artificial neural networks are implemented in computers, we develop a novel platform of optical neural computing, a smart glass, for object recognition. Our optical neural network takes advantage of strong light-matter interactions with sub-wavelength resolutions in metasurfaces to emulate the layered computations in a biological or artificial neural network. In the simplest implementation of a single-layer smart glass, a metasurface was trained to provide 2D phase modulations that can transform the complex optical wave scattered from an input object into a characteristic intensity distribution pattern on the output plane corresponding to the identity of the object. We experimentally demonstrated the recognition of handwritten numerical digits and letters with different fonts with high accuracies using the smart glass and explored the capability of a polarization-multiplexing smart glass based on birefringent metasurfaces for performing distinct recognition tasks at orthogonal incident polarizations. This optical neural computing platform represents a new paradigm of computation operating at the speed of light with no power consumption and this physical-wave-based computation guarantees data security beyond digital encryption.

Nanocrystals are an important field of study in the 21st century. Crystallites that are nanometers in size have very different properties from their bulk analogs because quantum mechanical effects become dominant at such small length scales. When a crystallite becomes small enough, the quantum confinement of electrons in the material manifests as a size-dependence of the nanocrystal's properties. Electrical and optical properties such as absorbance, surface plasmon resonance, and photoluminescence are sensitive to the size of the nanocrystal and proffer an array of technological applications for nanocrystals in such fields as biological imaging, laser technology, solar power enhancement, LED modification, chemical sensors, and quantum computation.The synthesis of size-controlled nanocrystals is critical to using nanocrystal in applications for their size-dependent properties. The development of nanocrystal synthesis techniques has been its own entire field of study for two decades or more, and several successes have established novel, utilitarian protocols for the mass-production of nanocrystals with controlled size and very low polydispersity. However, the experimental successes are generally poorly understood and no theoretical framework exists to explain the dynamics of these processes and how to better control or optimize them. It is the goal of this thesis to develop novel theories of nanocrystal synthesis processes to describe these phenomena in theoretical detail and extract meaningful correlations and driving forces that provide the necessary insight to improve the technology and enhance our understanding of nanocrystal growth. Chapter 4, 5 and 6 comprise all the novel research conducted for this thesis, with Chapters 1, 2 and 3 serving as necessary background to understanding the current state of the art. In Chapter 4, we develop a quantitative describe of the process of size focusing, in which a population of polydisperse nanocrystals, which are useless for applications, can be made more monodisperse by the injection of new crystallizable material. We derive mass balance equations that relate the rate of new-material generation to changes in the growth patterns of the nanocrystals. Specifically, we determine that only when the rate of crystal-material production is sustained at a high level can size focusing occur and a monodisperse sample of nanocrystals be produced. Quantitative criteria are provided for how high the rate of production must be, and the quantitative effects on the nanocrystal size distribution function for various magnitudes of the production rate. The effect of the production rate on every facet of the size distribution function is evaluated analytically and confirmed numerically. Furthermore, through comparison of the theory to experimental data, it is determined that a typical nanocrystal synthesis accidentally correlates two variables that are critical to the phenomenon of size focusing. The unknowingly correlated variables have frustrated experimental investigations of the same insights we provided with theory. We recommend a new synthesis protocol that decouples the critical variables, and thus permit the quantitative control of nanocrystal size and polydispersity through theoretical relations, which can also be generalized for the a priori design and optimization of nanocrystal synthesis techniques. In Chapter 5, a theoretical investigation of the growth of surfactant-coated nanocrystals is undertaken. The surfactants create a layer around the nanocrystal that has different transport properties than the bulk solution, and therefore has a strong effect on diffusion-limited growth of nanocrystals. This effect of a surfactant layer is investigated through the lens of the LSW theory of Ostwald ripening as well as through the lens of our own theory of size focusing from Chapter 4. The quantitative effect of a surfactant layer on the various growth processes of spherical nanocrystals is determined, with the result that size focusing can potentially be enhanced by the choice of an appropriate surfactant for a particular nanocrystal material. In addition to the kinetic studies of Chapter 4 and 5, a thermodynamic investigation of surfactant-coated nanocrystals is conducted in Chapter 6, with the goal of understanding the process known as "digestive ripening". In digestive ripening, a population of polydisperse gold nanocrystals is exposed to a strongly binding surfactant, at which point the nanocrystals spontaneously shrink and become highly monodisperse. Different surfactants and different crystal materials can exhibit digestive ripening. Those same materials also have the capacity to be digested further from nanocrystals into molecular clusters that eliminate all crystalline material in favor of surfactant-crystal coordination. The outstanding question is, why does the spontaneous digestive ripening process appear to make large nanocrystals shrink to small nanocrystals, but it does not force small nanocrystals to shrink further to molecular clusters? We construct a full Gibbs free energy model, which we minimize under multiple constraints to obtain quantitative relations for what thermodynamic properties (such as the surfactant binding energy and the crystal-solvent surface energy) govern the existence and size-dependence of a thermodynamically stable nanocrystal. Through our model, we determine that a finite-size nanocrystal is only stable under two possible conditions: either the surfactant-crystal binding is stronger than the crystal-crystal binding and the system contains too few surfactants to form molecular clusters and thus "surfactant-lean" nanocrystals are created, or the surfactantsurfactant intermolecular interactions are sufficiently strong that the nanocrystal core is treated as a swollen micelle in a microemulsion and is stabilized by the surfactant tails' interactions. Quantitative equations are provided that establish what trends and values are expected for experimental results. The results are inconclusive: there is no evidence supporting either conclusion because the available experimental data is insufficient. More accurately, many thermodynamically critical parameters (like the crystal surface energy) are unknown and are practically immeasurable in experimental systems. Speaking generally, the evidence for the surfactant-lean condition is moderately better than the evidence for the microemulsion condition, but in both cases the evidence is insufficient to make a solid conclusion. We therefore use our quantitative results of the thermodynamic investigation to make recommendations to experimentalists as to what trends and what nanocrystal growth processes we expect to observe in either thermodynamic case. While our results are inconclusive in and of themselves, they will be used to highlight the exact thermodynamic driving forces of the experimental systems. We conclude by giving an overview of two new fields of study for theoretical descriptions of nanocrystal growth, specifically the growth of anisotropic nanocrystals and a practical theory for nanocrystal nucleation. Preliminary relations are constructed, with comments on what directions we expect the research to take and how the results would be useful in enhancing our understanding of nanocrystal growth behavior.

In this dissertation I present advances in the studies of artificial lattices with honeycomb topology, called artificial graphene (AG), in nano-patterned GaAs quantum wells (QWs). AG lattices with very small lattice constants as low as 40 nm are achieved for the first time in GaAs. The high quality AG lattices are created by optimized electron-beam (E-beam) lithography followed by inductively coupled plasma reactive-ion etching (ICP-RIE) process. E-beam lithography is used to define a honeycomb lattice etch mask on the surface of the GaAs QW sample and the optimized anisotropic ICP-RIE process is developed to transfer the pattern into the sample and create the AG lattices. Such high-resolution AG lattices with small lattice constants are essential to form AG miniband structures and create well-developed Dirac cones. Characterization of electron states in the nanofabricated artificial lattices is by optical experiments. Optical emission (photoluminescence) yields a determination of the Fermi energy of the electrons. A significant reduction of the Fermi energy is due to the nano-patterning process. Resonant inelastic light scattering (RILS) spectra reveal novel transitions related to the electron band structures of the AG lattices. These transitions exhibit a remarkable agreement with the predicted joint density of states (JDOS) based on the band structure calculation for the honeycomb topology. I calculate the electron band structures of AG lattices in nano-patterned GaAs QWs using a periodic muffin-tin potential model. The evaluations predict linear energy-momentum dispersion and Dirac cones, where the massless Dirac fermions (MDFs) appear, occur in the band structures. Requirements of the parameters of the AG potential to achieve isolated and well-developed Dirac cones are discussed. Density of states (DOS) and JDOS from AG band structures are calculated, which provide a basis to interpret quantitatively observed transitions of electrons involving AG bands. RILS of intersubband transitions reveal intriguing satellite peaks that are not present in the as-grown QWs. These additional peaks are interpreted as combined intersubband transitions with simultaneous change of QW subband and AG band index. The calculated JDOS for the electron transitions within the AG lattice model provide a remarkably accurate description of the combined intersubband excitations. Novel low-lying excitation peaks in RILS spectra, interpreted as direct transitions between AG bands without change in QW subband, provide a more direct insight on the AG band structures. We discovered that RILS transitions around the Dirac cones are resonantly enhanced by varying the incident photon energies. The spectral lineshape of these transitions provides insights into the formation of Dirac cones that are characteristic of the honeycomb symmetry of the AG lattices. The results confirm the formation of AG miniband structures and well-developed Dirac cones. The realization of AG lattices in a nanofabricated high mobility semiconductor offers the advantage of tunability through methods suitable for device scalability and integration. The last part of this thesis describes the growth of nanocrystalline single layer and bilayer graphene on sapphire substrates by molecular beam epitaxy (MBE) with a solid carbon source. Raman spectroscopy reveals that fabrication of single layer, bilayer or multilayer graphene crucially depends on MBE growth conditions. Etch pits revealed by atomic force microscopy indicate a removal mechanism of carbon by reduction of sapphire. Tuning the interplay between carbon deposition and its removal, by varying the incident carbon flux and substrate temperature, should enable the growth of high quality graphene layers on large area sapphire substrates.