Session A37: Focus Session: Graphene: Growth, Characterization and Devices: Theory and Transport

Engineering gate-controlled potential barrier and nano-constriction in bilayer graphene

Graphene, as a material with zero net nuclear spin and a small spin-orbit coupling, is a natural candidate for building quantum-dot-based spin qubits, since electron spin coherence time can potentially be much longer compared to the prevailing GaAs-based systems. To date, graphene quantum dots have largely been realized using etch-defined nanoribbons or nano-islands. Due to fabrication-related edge defects or channel doping inhomogeneity, these etch-defined nanostructures generally suffer from randomly distributed incidental dots, causing undesirable resonance peaks in transport. To eliminate the disorder-induced localized states, we explore the possibility of electron confinement by using electric-field-controlled band gap opening in bilayer graphene. In this talk, we discuss various nanostructure designs towards this aim. We will present the transport characteristics of the dual-gated and side-gated devices, compare their performance, and analyze the gate tunability in various configurations. We will also comment on their use in quantum dots and other device applications.   

First Principle Simulations of Dual Gate Bilayer Graphene Field Effect Nanotransistors

In this work we present, via first principle calculations, a study of bilayer graphene dual-gate field effect nanotransistor. We show the $I_{ds}\times V_{ds}$ curves as a function of the channel length, back$(V_{bg})/top(V_{tg})$ gate voltages, temperature and charge excess on the system. For this study we use Landauer-B\"uttiker model with Hamiltonian generated through ab initio Density Functional Theory coupled with non-equilibrium Green's Function formalism. To investigate finite gates we implement a multigrig real space Poisson solver. Our results shows that the current can be tuned varying the strength of the electric field by setting different values of $V_{bg}(V_{tg})$ as well as modifying the channel length. We also show that the current depends on the amount of net charge in the system, controlled by the $V_{bg}(V_{tg})$ values, and the minimum of flowing current occurs when the system is neutral (charge neutrality point) only for gate lengths bigger than $4nm$. In all calculations we find a finite current due to a temperature effect associated with the Fermi-Dirac distribution. Decreasing the temperature from $300K$ to $4.5K$ the current diminishes one order of magnitude. Our study predicts that bilayer graphene dual gate field effect nanotransistors with small channel lengths $(<5nm)$ presents a upper limit for the $ON/OFF$ current ratio of $10$ for $300K$ and $100$ for $4.5K$. This ratio can be increased using larger channel lengths.   

Charge transport in dual-gated bilayer-graphene Corbino-disk

We use the Corbino-disk geometry to study the electron transport behavior of dual-gated bilayer graphene devices. Experimental exclusion of the edge states enables us to probe the bulk of bilayer graphene and its electronic properties. The temperature dependence of the maximum resistivity is found to be well described by simple thermal activation at high temperatures and variable range hopping at low temperatures, consistent with other transport studies. The electric-field-dependent band gap extracted from thermal activation is found to be in good agreement with infrared spectroscopic studies (Zhang et al. Nature 459, 820 (2009)). The similarity of our data to those of conventional dual-gated bilayer graphene devices with edges suggests that edges do not play a significant role in such devices at least for temperatures above 5 K, and points to the importance of reducing bulk disorder for improving device performance.   

Theory of the electronic and transport properties of epitaxial graphene

Advances in the epitaxial growth of graphene films on SiC have the potential to open new classes of device applications that may revolutionize the semiconductor roadmap for future decades. However, this progress will require an in-depth understanding and utilization of the electronic processes that take place at the nanoscale. In this talk I will review our recent results on the electronic and transport properties of epitaxial graphene on SiC. Using calculations from first principles, I will discuss the the role of the interface buffer layer in the tuning of the band alignment and the magnetic doping at the heterojunction; I will describe the effect of electron-phonon interactions in mono- and bi-layer graphene in determining the intrinsic carrier-phonon scattering properties of this material and thus the ultimate limit of any electronic device; finally, I will briefly discuss the thermal properties of the graphene/SiC interface, since understanding of the heat transfer properties is essential for optimal thermal management and heat removal in device applications.   

Strong Enhancement of Doping in Graphene via Substrate

Controlling the type and density of charge carriers by doping is the key step for developing graphene electronics. Based on first-principles calculations, we demonstrate that doping could be strongly enhanced in epitaxial graphene on silicon carbide (SiC) substrate. Compared to free- standing graphene, the formation energies of dopants decrease dramatically by 2 $\sim $ 8 eV. The dopants prefer to stay in the interface buffer layer between epitaxial graphene and substrate, which could tune the interface dipoles evidently. The type and density of charge carriers of epitaxial graphene layer can be effectively manipulated by suitable dopants and surface passivation. Contrasting to the direct doping of graphene, the charge carriers in epitaxial graphene layer are weakly scattered by dopants due to the spatial separation between dopants and conducting channel, in the spirit of modulation doping, which takes advantages in maintaining the high carrier mobility of graphene. Beyond controlling the charge carriers via buffer layer doping, we find that the reconstructed vacancy in the interface buffer layer breaks the spin symmetry of epitaxial graphene, which induces a half-metallic state without magnetic impurities doping.   

Magnetic impurities in graphene with defects

We theoretically study magnetic impurities in graphene with defects. The defects are described by vacancies which can be realized in graphene experimentally. The occupancy number, local moment and spin susceptibility of the impurities are calculated by quantum Monte Carlo simulations. When the Fermi energy of the system is changed by gate voltage, it is found that the behaviors of these physical quantities are very different from those in perfect graphene. The spectral density of the impurity is also studied by maximum entropy methods to explain these unusual behaviors.   

Carrier Transport in Epitaxial Multi-layer Graphene

Significant attention has been focused recently on the electrical properties of graphene grown epitaxially on SiC substrates, because it offers an ideal platform for carbon-based electronics using conventional top-down lithography techniques. The transport properties of graphene are usually studied via Hall effect measurements, which provide information on the carrier mobility and density. Hall measurements performed at a single magnetic field yield a weighted average of carrier mobility and density, and are strictly applicable to homogeneous samples. In this study, we performed variable-field Hall and resistivity measurements on epitaxial graphene, and the results were analyzed with a multi-carrier model. Good agreements were obtained between experimental data and the model, providing further evidence of multi-carrier transport in the C-face grown MLG. This work is supported by DARPA under contract FA8650-08-C-7838 through the CERA program and by the Office of Naval Research.   

Hole-channel conductivity in epitaxial graphene determined by terahertz optical Hall-effect and midinfrared ellipsometry

We report non-contact, optical determination of free-charge carrier mobility, sheet density, and effective mass parameters in epitaxial graphene at room temperature using terahertz and midinfrared ellipsometry and optical Hall-effect (generalized ellipsometry in magnetic fields) measurements. The graphene layers are grown on Si- and C-terminated semi-insulating 6H silicon carbide polar surfaces. Data analysis using classical Drude functions and multilayer modeling render the existence of a $p$-type channel with different sheet densities and effective mass parameters for the two polar surfaces. The optically obtained parameters are in excellent agreement with results from electrical Hall effect measurements.   

Quantum corrections to the conductivity in graphene

The low-temperature conductivity in electron systems is determined by two quantum corrections. They originate from the interference of electron waves scattered by impurities (weak localisation, WL) and electron-electron interaction (EEI) in the presence of disorder. In graphene, due to the chirality of charged carriers, the quantum interference is sensitive not only to inelastic, dephasing, scattering, but also to elastic, inter- and intra-valley, scattering processes. It was theoretically predicted that depending on the scattering rates of such processes, weak antilocalisation (WAL) is possible in graphene. In this work we study both magnetoresistance and the temperature dependence of the conductivity and observe a transition from WL to WAL by tuning the carrier density and temperature. We show that quantum interference in graphene can survive at temperatures up to 200 K due to weak electron-phonon scattering. We also investigate the EEI correction, which is separated from the WL correction by two methods, and show that it is also affected by intra-valley scattering. This scattering leads to a new temperature regime of EEI. We find the Fermi liquid constant to be small, -0.1, and discuss the origin of this value.   

First-principles Theory of Nonlocal Screening in Graphene

Using the quasiparticle self-consistent \emph{GW} (QS\emph{GW}) and local-density (LD) approximations, we calculate the $q$-dependent static dielectric function, and derive an effective 2D dielectric function corresponding to screening of point charges. In the $q${}$\to$0 limit, the 2D dielectric constant is found to scale approximately as the square root of the macroscopic dielectric function. Its value is $\simeq$4, in agreement with the predictions of Dirac model. At the same time, in contrast with the Dirac model, the dielectric function is strongly dependent on $q$. The QS\emph{GW} approximation is shown to describe QP levels very well, with small systematic errors analogous to bulk $sp$ semiconductors. Local-field effects are rather more important in graphene than in bulk semiconductors.   

First-Principles Investigation of Polymer Binding to Graphene and Carbon Nanotubes

The interactions between a polymer (Poly[(phenylene)-co-(9,9- bis-(6-bromohexyl)uorene)]) and graphene and carbon nanotubes are investigated by using pseudopotential planewave calculations based on density functional theory (DFT). In the quest of searching the most favorable binding configurations, the monomer under investigation is placed at different orientations on graphene. In order to obtain further insight into the binding interactions of polymer-graphene system, we also calculated the binding energy for the structure in which the polymer is attached to graphene sheet via atomic oxygen. Considering the graphene impurity, we have also further investigated the polymer approaching from the chain side onto graphene with a vacancy. However, our results demonstrated that the interaction between the (Poly[(phenylene)-co-(9,9-bis-(6-bromohexyl) uorene)]) polymer and graphene is weak, mostly dispersive, but this interaction is slightly stronger when the graphene has structural defects, like vacancies. The implications of these results to the polymer and carbon nanotube interactions also are discussed.   

Spectral and optical properties of doped graphene with charged impurities in the self-consistent Born approximation

Spectral and transport properties of doped (or gated) graphene with long range charged impurities are discussed within the self-consistent Born approximation. It is shown how, for impurity concentrations greater than the electron concentration, $n_{imp} \geq n$, a finite DOS appears at the Dirac point, the one-particle lifetime no longer scales linearly with the Fermi momentum, and the lineshapes in the spectral function become non-lorentzian. These behaviors are different from the results calculated within the Born approximation. We also calculate the optical conductivity from the Kubo formula by using the self-consistently calculated spectral function in the presence of charged impurities.