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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.

Two framework oxide materials of the MO��� network type have been synthesized and structurally characterized by synchrotron and X-ray powder diffraction and the Rietveld method in the temperature range 25~500 K. The results show one of them to be a low thermal expansion material. Theoretical studies of negative thermal expansion (NTE) in framework oxides were conducted with two methods, geometrical modeling by Rigid Unit Mode (RUM) method and lattice dynamic calculations by free energy minimization (FEM) method, the results are compared with each other as well as with experimental observations. RUM analysis of all five types of framework oxide structures negates any simple and direct correlation between presence or absence of RUMs in a structure and the sign of its thermal expansion. Instead, results suggest that NTE of a crystalline solid can not be explained by pure geometrical considerations over its structure alone, and for a better understanding of structure-relationship in negative thermal expansion structures, specific interatomic interactions present in each one must be brought in explicitly. FEM calculation of two negative thermal expansion structures indicates on a structure by structure basis NTE could be predicted and understood within the Gruneisen model, which attributes NTE of a structure to special vibration modes in a structure that softens when the lattice shrinks. The soft NTE modes are, however, not necessarily RUM or RUM like vibration motions. / Graduation date: 2003

Graphene, a honeycomb lattice of sp2-bonded carbon atoms, has received considerable attention in the scientific community due to its unique electronic properties. Distinct symmetries of the graphene wave functions lead to unusual quantum properties, such as a unique half-integer quantum Hall effect. As an added consequence of these symmetries, back-scattering in graphene is strongly prohibited leading to long coherence lengths of carriers. These charge carriers at low energy exhibit linear energy-momentum dispersion, much like neutrinos. Thus, carriers in graphene can be described as massless Dirac fermions. Graphene grown epitaxially on semiconducting substrates offers the possibility of large-scale production and deterministic patterning of graphene for nanoelectronics. In this work, epitaxial graphene is created on SiC(0001) by annealing in vacuum. Sequential scanning tunneling microscopy (STM) and spectroscopy (STS) are performed in ultrahigh vacuum at a temperature of 4.2 K and 300 K. These atomic-scale studies address the growth, interfacial properties, stacking order, and quasiparticle coherence in epitaxial graphene. STM topographic images show the atomic structure of successive graphene layers on the SiC substrate, as well as the character of defects and adatoms within and below the graphene plane. STS differential conductance (dI/dV) maps provide spatially and energy resolved snapshots of the local density of states. Such maps clearly show that scattering from atomic defects in graphene gives rise to energy-dependent standing wave patterns. We derive the carrier energy dispersion of epitaxial graphene from these data sets by quantifying the dominant wave vectors of the standing waves for each tunneling bias.

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The object of this research was to investigate dispersion in surface phononic crystals (PnCs) for application to a newly developed passive surface acoustic wave (SAW) ozone sensor. Frequency band gaps and slow sound already have been reported for PnC lattice structures. Such engineered structures are often advertised to reduce loss, increase sensitivity, and reduce device size. However, these advances have not yet been realized in the context of surface acoustic wave sensors. In early work, we computed SAW dispersion in patterned surface structures and we confirmed that our finite element computations of SAW dispersion in thin films and in one dimensional surface PnC structures agree with experimental results obtained by laser probe techniques. We analyzed the computations to guide device design in terms of sensitivity and joint spectral operating point. Next we conducted simulations and experiments to determine sensitivity and limit of detection for more conventional dispersive SAW devices and PnC sensors. Finally, we conducted extensive ozone detection trials on passive reflection mode SAW devices, using distinct components of the time dispersed response to compensate for the effect of temperature. The experimental work revealed that the devices may be used for dosimetry applications over periods of several days.

Graphene, a single sheet of carbon atoms sp2-bonded in a honeycomb lattice, is a possible all-carbon successor to silicon electronics. Ballistic conduction at room temperature and a linear dispersion relation that causes carriers to behave as massless Dirac fermions are features that make graphene promising for high-speed, low-power devices. The critical advantage of epitaxial graphene (EG) grown on SiC is its compatibility with standard lithographic procedures. Surface X-ray diffraction (SXRD) and scanning tunneling microscopy (STM) results are presented on the domain structure, interface composition and stacking character of graphene grown on both polar faces of semi-insulating 4H-SiC. The data reveal intriguing differences between graphene grown on these two faces. Substrate roughening is more pronounced and graphene domain sizes are significantly smaller on the SiC (0001) Si-face. Specular X-ray reflectivity measurements show that both faces have a carbon rich, extended interface that is tightly bound to the first graphene layer, leading to a buffering effect that shields the first graphene layer from the bulk SiC, as predicted by ab initio calculations. In-plane X-ray crystal truncation rod analysis indicates that rotated graphene layers are interleaved in C-face graphene films and corresponding superstructures are observed in STM topographs. These rotational stacking faults in multilayer C-face graphene preserve the linear dispersion found in single layer graphene, making EG electronics possible even for a multilayer material.

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