Modeling of epitaxial graphene functionalization

A new model for graphene epitaxially grown on silicon carbide is proposed. Density functional theory modeling of epitaxial graphene functionalization by hydrogen, fluorine, methyl and phenyl groups has been performed, with hydrogen and fluorine showing a high probability of cluster formation in high adatom concentration. It has also been shown that the clusterization of fluorine adatoms provides midgap states in formation, due to significant flat distortion of graphene. The functionalization of epitaxial graphene using larger species (methyl and phenyl groups) renders cluster formation impossible, due to the steric effect, and results in uniform coverage with the energy gap opening.     

Atomic-scale transport in epitaxial graphene

The high carrier mobility of graphene is key to its applications, and understanding the factors that limit mobility is essential for future devices. Yet, despite significant progress, mobilities in excess of the 2×10(5) cm(2) V(-1) s(-1) demonstrated in free-standing graphene films have not been duplicated in conventional graphene devices fabricated on substrates. Understanding the origins of this degradation is perhaps the main challenge facing graphene device research. Experiments that probe carrier scattering in devices are often indirect, relying on the predictions of a specific model for scattering, such as random charged impurities in the substrate. Here, we describe model-independent, atomic-scale transport measurements that show that scattering at two key defects--surface steps and changes in layer thickness--seriously degrades transport in epitaxial graphene films on SiC. These measurements demonstrate the strong impact of atomic-scale substrate features on graphene performance.     

Thermodynamics of electrons in epitaxial graphene

The chemical potential, heat capacity, and magnetic susceptibility of epitaxial graphene formed on a semiconductor substrate have been studied in the framework of the Davydov model. The limiting cases of high and low temperatures are considered.     

Substrate-induced bandgap opening in epitaxial graphene

Graphene has shown great application potential as the host material for next-generation electronic devices. However, despite its intriguing properties, one of the biggest hurdles for graphene to be useful as an electronic material is the lack of an energy gap in its electronic spectra. This, for example, prevents the use of graphene in making transistors. Although several proposals have been made to open a gap in graphene's electronic spectra, they all require complex engineering of the graphene layer. Here, we show that when graphene is epitaxially grown on SiC substrate, a gap of approximately 0.26 eV is produced. This gap decreases as the sample thickness increases and eventually approaches zero when the number of layers exceeds four. We propose that the origin of this gap is the breaking of sublattice symmetry owing to the graphene-substrate interaction. We believe that our results highlight a promising direction for bandgap engineering of graphene.     

Novel growth mechanism of epitaxial graphene on metals

Graphene, a hexagonal sheet of sp(2)-bonded carbon atoms, has extraordinary properties which hold immense promise for nanoelectronic applications. Unfortunately, the popular preparation methods of micromechanical cleavage and chemical exfoliation of graphite do not easily scale up for application purposes. Epitaxial graphene provides an attractive alternative, though there are many challenges, not least of which is the absence of any understanding of the complex atomistic assembly kinetics of graphene layers. Here, we present a simple rate theory of epitaxial graphene growth on close-packed metal surfaces. On the basis of recent low-energy electron-diffraction microscopy experiments, our theory supposes that graphene islands grow predominantly by the attachment of five-atom clusters. With optimized kinetic parameters, our theory produces a quantitative account of the measured time-dependent carbon adatom density. The temperature dependence of this density at the onset of nucleation leads us to predict that the smallest stable precursor to graphene growth is an immobile island composed of six five-atom clusters. This conclusion is supported by a recent study based on temperature-programmed growth of epitaxial graphene, which provides direct evidence of nanoclusters whose coarsening leads to the formation of graphene layers. Our findings should motivate additional high-resolution imaging experiments and more detailed simulations which will yield important input to developing strategies for the large-scale production of epitaxial graphene.     

Static conductance of electron gas in epitaxial graphene

Static conductance of epitaxial graphene formed on metal and semiconductor substrates has been considered within a simple model.     

Quasiparticle scattering off phase boundaries in epitaxial graphene

We investigate the electronic structure of terraces of single layer graphene (SLG) by scanning tunnelling microscopy (STM) on samples grown by thermal decomposition of 6H-SiC(0001) crystals in ultra-high vacuum. We focus on the perturbations of the local density of states (LDOS) in the vicinity of edges of SLG terraces. Armchair edges are found to favour intervalley quasiparticle scattering, leading to the (√3 x √3)R30° LDOS superstructure already reported for graphite edges and more recently for SLG on SiC(0001). Using the Fourier transform of LDOS images, we demonstrate that the intrinsic doping of SLG is responsible for a LDOS pattern at the Fermi energy which is more complex than for neutral graphene or graphite, since it combines local (√3 x √3)R30° superstructure and long range beating modulation. Although these features have already been reported by Yang et al (2010 Nano Lett. 10 943-7) we propose here an alternative interpretation based on simple arguments classically used to describe standing wave patterns in standard two-dimensional systems. Finally, we discuss the absence of intervalley scattering off other typical boundaries: zig-zag edges and SLG/bilayer graphene junctions.     

Electron heat conductivity of epitaxial graphene on silicon carbide

The diagonal component of the electron heat conductivity tensor of epitaxial graphene formed in a semiconductor has been investigated within a simple analytical model. It is shown that the heat conductivity sharply changes at a chemical potential close to the substrate band gap edge. Low-temperature expressions for the heat conductivity are derived.     

On renormalization of the Fermi velocity in epitaxial graphene

Renormalization of the Fermi velocity in epitaxial graphene prepared on the surfaces of semiconductor and metal substrates is considered within a simple model.     

Transfer-free electrical insulation of epitaxial graphene from its metal substrate

High-quality, large-area epitaxial graphene can be grown on metal surfaces, but its transport properties cannot be exploited because the electrical conduction is dominated by the substrate. Here we insulate epitaxial graphene on Ru(0001) by a stepwise intercalation of silicon and oxygen, and the eventual formation of a SiO(2) layer between the graphene and the metal. We follow the reaction steps by X-ray photoemission spectroscopy and demonstrate the electrical insulation using a nanoscale multipoint probe technique.     

The possibility of colossal magnetoresistance in heterostructures based on epitaxial graphene

The magnetoresistance of a heterostructure comprising parallel-connected epitaxial graphene on a metal substrate and graphene on a dielectric substrate has been studied in the framework of the Drude theory. The phenomenon of colossal magnetoresistance in this system is predicted on the basis of previous results for the conductivity of epitaxial graphene.     

Size-selective carbon nanoclusters as precursors to the growth of epitaxial graphene

The nucleation and growth mechanisms of graphene on Rh(111) via temperature-programmed growth of C(2)H(4) are studied by scanning tunneling microscopy and spectroscopy, and by density functional theory calculations. By combining our experimental and first-principles approaches, we show that carbon nanoislands form in the initial stages of graphene growth, possessing an exclusive size of seven honeycomb carbon units (hereafter labeled as 7C(6)). These clusters adopt a domelike hexagonal shape indicating that bonding to the substrate is localized on the peripheral C atoms. Smoluchowski ripening is identified as the dominant mechanism leading to the formation of graphene, with the size-selective carbon islands as precursors. Control experiments and calculations, whereby coronene molecules, the hydrogenated analogues of 7C(6), are deposited on Rh(111), provide an unambiguous structural and chemical identification of the 7C(6) building blocks.     

Suppression of inhomogeneous segregation in graphene growth on epitaxial metal films

Large-scale uniform graphene growth was achieved by suppressing inhomogeneous carbon segregation using a single domain Ru film epitaxially grown on a sapphire substrate. An investigation of how the metal thickness affected growth and a comparative study on metals with different crystal structures have revealed that locally enhanced carbon segregation at stacking domain boundaries of metal is the origin of inhomogeneous graphene growth. Single domain Ru film has no stacking domain boundary, and the graphene growth on it is mainly caused not by segregation but by a surface catalytic reaction. Suppression of local segregation is essential for uniform graphene growth on epitaxial metal films.     

Gaps in the spectrum of epitaxial graphene formed on silicon carbide polytypes

Silicon carbide NH-SiC polytypes with N = 2, 4, 6, and 8 are considered as substrates for the epitaxial formation of graphene. The density of states for the substrates is described using the Haldane-Anderson model. It is shown that this model always leads to the appearance of two gaps in the graphene spectrum, which are adjacent to the valence and conduction bands of the substrate. The gap widths are determined by the ratio of the energy of interatomic interaction in the free-standing graphene sheet and the energy of graphene-substrate interaction. If this ratio is very small, the gap widths may increase so as to jointly cover almost the entire bandgap of the substrate; on the contrary, if this ratio is extremely large, both gaps exhibit narrowing and become negligibly small.     

Mapping of local electrical properties in epitaxial graphene using electrostatic force microscopy

Local electrical characterization of epitaxial graphene grown on 4H-SiC(0001) using electrostatic force microscopy (EFM) in ambient conditions and at elevated temperatures is presented. EFM provides a straightforward identification of graphene with different numbers of layers on the substrate where topographical determination is hindered by adsorbates. Novel EFM spectroscopy has been developed measuring the EFM phase as a function of the electrical DC bias, establishing a rigorous way to distinguish graphene domains and facilitating optimization of EFM imaging.     

Influence of structural properties on ballistic transport in nanoscale epitaxial graphene cross junctions

In this paper we investigate the influence of material and device properties on the ballistic transport in epitaxial monolayer graphene and epitaxial quasi-free-standing monolayer graphene. Our studies comprise (a)?magneto-transport in two-dimensional (2D) Hall bars, (b)?temperature- and magnetic-field-dependent bend resistance of unaligned and step-edge-aligned orthogonal cross junctions, and (c)?the influence of the lead width of the cross junctions on ballistic transport. We found that ballistic transport is highly sensitive to scattering at the step edges of the silicon carbide substrate. A suppression of the ballistic transport is observed if the lead width of the cross junction is reduced from 50?nm to 30?nm. In a 50?nm wide device prepared on quasi-free-standing graphene we observe a gradual transition from the ballistic into the diffusive transport regime if the temperature is increased from 4.2 to about 50?K, although 2D Hall bars show a temperature-independent mobility. Thus, in 1D devices additional temperature-dependent scattering mechanisms play a pivotal role.