We report on the observation of inertial-ballistic transport in nanoscale cross junctions fabricated from epitaxial graphene grown on SiC(0001). Ballistic transport is indicated by a negative bend resistance of R12,43 ~ 170 ohm which is measured in a non-local, four-terminal configuration at 4.2 K and which vanishes as the temperature is increased above 80 K.
Graphene electronics has motivated much of graphene science for the past decade. A primary goal was to develop high mobility semiconducting graphene with a band gap that is large enough for high performance applications. Graphene ribbons were thought to be semiconductors with these properties, however efforts to produce ribbons with useful bandgaps and high mobility has had limited success. We show here that high quality epitaxial graphene nanoribbons 40 nm in width, with annealed edges, grown on sidewall SiC are not semiconductors, but single channel room temperature ballistic conductors for …
We study ballistic thermal transport in three-terminal atomic nanojunctions by the nonequilibrium Green's function method. We find that there is ballistic thermal rectification in asymmetric three-terminal structures because of the incoherent phonon scattering from the control terminal. With spin-phonon interaction, we also find the ballistic thermal rectification even in symmetric three-terminal paramagnetic structures.
We show that by adding only two fitting parameters to a purely ballistic transport model, we can accurately characterize the current-voltage characteristics of nanoscale MOSFETs. The model is an extension to a ballistic model (J. Appl. Phys. 76, 4879 (1994)) and includes transmission probability and the drain-channel coupling capacitor. The latter parameter gives rise to a theoretical RON that is significantly larger than those predicted previously. To validate our model, we fabricated n-channel MOSFETs with varying channel lengths. We show the length dependence of these parameters to support …
Initiating impact ionization of avalanche breakdown essentially requires applying a high electric field in a long active region, hampering carrier-multiplication with high gain, low bias and superior noise performance. Here we report the observation of ballistic avalanche phenomena in sub-MFP scaled vertical indium selenide (InSe)/black phosphorus (BP) heterostructures. The heterojunction is engineered to avalanche photodetectors (APD) and impact ionization transistors, demonstrating ultra-sensitive mid-IR light detection (4 μm wavelength) and ultra-steep subthreshold swing, respectively. Thes…
We report direct imaging of boundary magnetization associated with antiferromagnetic domains in magnetoelectric epitaxial Cr2O3 thin films using diamond nitrogen vacancy microscopy. We found a correlation between magnetic domain size and structural grain size which we associate with the domain formation process. We performed field cooling, i.e., cooling from above to below the Néel temperature in the presence of magnetic field, which resulted in the selection of one of the two otherwise degenerate 180 degree domains. Lifting of such a degeneracy is achievable with a magnetic field alone due to…
Low-temperature experiments are performed on novel nanoscale nonlinear devices (ballistic rectifiers) as well as nano-structured artificial materials, fabricated from an InP/InGaAs quantum well wafer. A DC output is generated between the lower and upper contacts of these devices, when an AC voltage is applied between the left and right contacts. As the temperature is lowered from room temperature, the DC output voltage of the ballistic rectifiers gradually changes from negative to positive. Since the negative output at high temperatures has been well understood in the framework of the classica…
Graphene multilayers are grown epitaxially on single crystal silicon carbide. This system is composed of several graphene layers of which the first layer is electron doped due to the built-in electric field and the other layers are essentially undoped. Unlike graphite the charge carriers show Dirac particle properties (i.e. an anomalous Berry's phase, weak anti-localization and square root field dependence of the Landau level energies). Epitaxial graphene shows quasi-ballistic transport and long coherence lengths; properties which may persists above cryogenic temperatures. Paradoxically, in co…
Unlike classical heat diffusion at the macroscale, nanoscale heat transport can occur without energy dissipation because phonons can travel in straight lines for hundreds of nanometres. Despite recent experimental evidence of such ballistic phonon transport, control over its directionality, and thus its practical use, remains a challenge, as the directions of individual phonons are chaotic. Here, we show a way to control the directionality of ballistic phonon transport using silicon thin-films with arrays of holes. First, we demonstrate the formation of directional heat fluxes in the passages …
Ballistic atomic transport in narrow carbon nanotubes
Università degli Studi di Padova(帕多瓦大学);Griffith University(格里菲斯大学);Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche(意大利国家光学研究所);Istituto Nazionale di Fisica Nucleare, Sezione di Padova(意大利国家核物理研究所帕多瓦分部)
The minimization of electronics makes heat dissipation of related devices an increasing challenge. When the size of materials is smaller than the phonon mean free paths, phonons transport without internal scatterings and laws of diffusive thermal conduction fail, resulting in significant reduction in the effective thermal conductivity. This work reports, for the first time, the temperature dependent thermal conductivity of doped epitaxial 6H-SiC and monocrystalline porous 6H-SiC below room temperature probed by time-domain thermoreflectance. Strong quasi-ballistic thermal transport was observe…
We propose monolayer epitaxial graphene and hexagonal boron nitride (h-BN) as ultimate thickness covalent spacers for magnetoresistive junctions. Using a first-principles approach, we investigate the structural, magnetic and spin transport properties of such junctions based on structurally well defined interfaces with (111) fcc or (0001) hcp ferromagnetic transition metals. We find low resistance area products, strong exchange couplings across the interface, and magnetoresistance ratios exceeding 100% for certain chemical compositions. These properties can be fine tuned, making the proposed ju…
Graphene, the first true two-dimensional material still reveals the most remarkable transport properties among the growing class of two-dimensional materials. Although many studies have investigated fundamental scattering processes, the surprisingly large variation in the experimentally determined resistances associated with a localized defect is still an open issue. Here, we quantitatively investigate the local transport properties of graphene prepared by polymer assisted sublimation growth (PASG) using scanning tunneling potentiometry. PASG graphene is characterized by a spatially homogeneou…
Epitaxial $\mathrm{Co_2MnSi}$ with intrinsic magnetocrystalline anisotropy as a route to bias-field-free nonlinear half-metal magnonics at the nanoscale
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau(莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道);Université de Lorraine(洛林大学)
The intermediate transport regime in nanoscale transistors between the fully ballistic case and the quasi equilibrium case described by the drift-diffusion model is still an open modeling issue. Analytical approaches to the problem have been proposed, based on the introduction of a backscattering coefficient, or numerical approaches consisting in the MonteCarlo solution of the Boltzmann transport equation or in the introduction of dissipation in quantum transport descriptions. In this paper we propose a very simple analytical model to seamlessly cover the whole range of transport regimes in ge…
In-situ Straining of Epitaxial Freestanding Ferroic Films by a MEMS Device
Paul Scherrer Institut(保罗谢勒研究所);Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy(马克斯·玻恩非线性光学与超快光谱研究所);Politecnico di Milano(米兰理工大学);Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich(苏黎世联邦理工学院材料系介观系统实验室);National Cheng Kung University(国立成功大学);Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University(国立成功大学量子前沿研究与技术中心)
Low temperature epitaxial breakdown of inhomogeneously strained Si capping layers is investigated. By growing Si films on coherently strained GeSi quantum dot surfaces, we differentiate effects of surface roughness, strain, and growth orientation on the mechanism of epitaxial breakdown. Using atomic force microscopy and high resolution cross-sectional transmission electron microscopy we find that while local lattice strain up to 2% has a negligible effect, growth on higher-index facets such as {113} significantly reduces the local breakdown thickness. Nanoscale growth mound formation is observ…
We aim to provide engineers with an introduction to the non-equilibrium Green's function (NEGF) approach, which provides a powerful conceptual tool and a practical analysis method to treat small electronic devices quantum mechanically and atomistically. We first review the basis for the traditional, semiclassical description of carriers that has served device engineers for more than 50 years. We then describe why this traditional approach loses validity at the nanoscale. Next, we describe semiclassical ballistic transport and the Landauer-Buttiker approach to phase coherent quantum transport. …
A semi-analytical model for studying thermal transport at the nanoscale, able to accurately describe both the effect of out of equilibrium transport and the thermal transfer at interfaces, is presented. Our approach is based on the definition of pseudo local temperatures distinguishing the phonon populations according to the direction of their velocity. This formalism leads to a complete set of equations capturing the heat transfer in nanostructures even in the case of hetero-structures. This model only requires introducing a new intrinsic thermal parameter called ballistic thermal conductance…
Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's Law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's Law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement…
The silicon (Si) based spin-MOSFET (metal-oxide semiconductor field-effect transistor) is considered to be the building block of low-power-consumption electronics, utilizing spin-degrees of freedom in semiconductor devices. In this paper, we review the latest results on the spin transport in nanoscale Si-based spin-valve devices, which is important to realize the nanoscale spin-MOSFET. Our results demonstrate the importance of ballistic transport in obtaining high spin-dependent output voltage in nanoscale Si spin-valve devices.
Realizing high-performance nanoelectronics requires control of materials at the nanoscale. Methods to produce high quality epitaxial graphene (EG) nanostructures on silicon carbide are known. The next step is to grow Van der Waals semiconductors on top of EG nanostructures. Hexagonal boron nitride (h-BN) is a wide bandgap semiconductor with a honeycomb lattice structure that matches that of graphene, making it ideally suited for graphene-based nanoelectronics. Here, we describe the preparation and characterization of multilayer h-BN grown epitaxially on EG using a migration-enhanced metalorgan…
Electric-field effect control of two-dimensional electron gases (2-DEG) has enabled the exploration of nanoscale electron quantum transport in semiconductors. Beyond these classical materials, transition metal-oxide-based structures have d-electronic states favoring the emergence of novel quantum orders absent in conventional semiconductors. In this context, the LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and sizeable spin-orbit coupling is emerging as a promising platform to realize topological superconductivity. However, the fabrication of nanodevices in which the el…
Quantum spin Hall (QSH) insulators have unique electronic properties, comprising a band gap in their two-dimensional interior and one-dimensional spin-polarized edge states in which current flows ballistically. In scanning tunneling microscopy (STM), the edge states manifest themselves as a localized density of states. However, there is a significant research gap between the observation of edge states in nanoscale spectroscopy, and the detection of ballistic transport in edge channels which typically relies on transport experiments with microscale lithographic contacts. Here, we study few-laye…
Directed high-speed motion of nanoscale objects in fluids (nano swimmers) can have a wide range of applications like molecular machinery, nano robotics, drug delivery, and material assembly. Here, we report ballistic plasmonic Au nanoparticle (NP) swimmers with unprecedented speeds realized by not only optical pushing but also pulling forces from a single Gaussian laser beam. Both the optical pulling and high swimmer speeds are made possible by a unique NP-laser interaction. The Au NP excited by the laser at the surface plasmon resonance peak can generate a nanoscale bubble, which can encapsul…
Ballistic transport in nanodevices based on single-crystalline Cu thin film
Pohang University of Science and Technology(浦项科技大学);Crystal Bank Research Institute, Pusan National University(釜山大学晶体银行研究所);Sungkyunkwan University(成均馆大学);Copper Innovative Technology (CIT) Co.(铜创新技术(CIT)有限公司);Ulsan National Institute of Science and Technology(蔚山科学技术院);Mississippi State University(密西西比州立大学);Korea Advanced Institute of Science and Technology (KAIST)(韩国科学技术院);Massachusetts General Hospital and Harvard Medical School(麻省总医院和哈佛医学院);Pusan National University(釜山大学);Asia Pacific Center for Theoretical Physics(亚太理论物理中心)
The electron current density in nanoscale junctions is typically several orders of magnitude larger than the corresponding one in bulk electrodes. Consequently, the electron-electron scattering rate increases substantially in the junction. This leads to local electron heating of the underlying Fermi sea in analogy to the local ionic heating that is due to the increased electron-phonon scattering rates. We predict the bias dependence of local electron heating in quasi-ballistic nanoscale conductors, its effect on ionic heating, and discuss possible experimental tests of our results.
We study the transport properties of monolayer MX2 (M = Mo, W; X = S, Se, Te) n- and p- channel metal-oxide-semiconductor field effect transistors (MOSFETs) using full-band ballistic non-equilibrium Green's function simulations with an atomistic tight-binding Hamiltonian with hopping potentials obtained from density functional theory. We discuss the subthreshold slope, drain-induced barrier lowering (DIBL), as well as gate-induced drain leakage (GIDL) for different monolayer MX2 MOSFETs. We also report the possibility of negative differential resistance behavior in the output characteristics o…
Future of silicon-based microelectronics relies on solving the heat dissipation problem. A solution may lie in a nanoscale phenomenon known as ballistic heat conduction, which implies heat conduction without heating the conductor. But, attempts to demonstrate this phenomenon experimentally are controversial and scarce whereas its mechanism in confined nanostructures is yet to be fully understood. Here, we experimentally demonstrate quasi-ballistic heat conduction in silicon nanowires (NWs). We show that the ballisticity is strongest in short NWs at low temperatures but weakens as the NW length…
Graphene's original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in conventionally patterned graphene epitaxially grown on a silicon carbide substrate (epigraphene) are stabilized by the substrate and support a protected edge state. The edge state has a mean free path that is greater than 50 microns, 5000 times greater that the bulk states and involves a theoretically unexpected Majorana-like zero-energy non-degenerate quasiparticle that…
Radiative heat-transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. In this Letter we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes, leading to dramatically different thermal relaxation dynamics spanning over three orders of magnitude. This result could have important consequences on thermal management at …
In view of the appreciable semiconducting gap of 0.26 eV observed in recent experiments, epitaxial graphene on a SiC substrate seems a promising channel material for FETs. Indeed, it is two-dimensional - and therefore does not require prohibitive lithography - and exhibits a wider gap than other alternative options, such as bilayer graphene. Here we propose a model and assess the achievable performance of a nanoscale FET based on epitaxial graphene on SiC, conducting an exploration of the design parameter space. We show that the current can be modulated by 4 orders of magnitude; for digital ap…
We report first-principles calculations of inelastic Seebeck coefficients in an aluminum monatomic junction. We compare the elastic and inelastic Seebeck coefficients with and without local heating. In the low temperature regime, the signature of normal modes in the profiles of the inelastic Seebeck effects is salient. The inelastic Seebeck effects are enhanced by the normal modes, and further magnified by local heating. In the high temperature regime, the inelastic Seebeck effects are weakly suppressed due to the quasi-ballistic transport.
Epitaxially-grown semiconductor heterostructures give the possibility to tailor the potential landscape for the carriers in a very controlled way. In planar lattice-matched heterostructures, the potential has indeed a very simple and easily predictable behavior: it is constant everywhere except at the interfaces where there is a step (discontinuity) which only depends on the composition of the semiconductors in contact. In this paper, we show that this universally accepted picture can be invalid in nanoscale heterostructures (e.g., quantum dots, rods, nanowires) which can be presently fabricat…
Using Landau-Ginsburg-Devonshire approach and available experimental results we reconstruct the thermodynamic potential of the layered ferroelectric CuInP$_2$S$_6$ (CIPS), which is expected to be applicable a wide range of temperatures and applied pressures. The analysis of temperature dependences of the dielectric permittivity and lattice constants for different applied pressures unexpectedly reveals the critically important role of the nonlinear electrostriction in this material. With the nonlinear electrostriction included we calculated temperature and pressure phase diagrams and spontaneou…
We investigate the effect of electron-phonon inelastic scattering on shot noise in nanoscale junctions in the regime of quasi-ballistic transport. We predict that when the local temperature of the junction is larger than its lowest vibrational mode energy $eV_c$, the inelastic contribution to shot noise (conductance) increases (decreases) with bias as $V$ ($\sqrt{V}$). The corresponding Fano factor thus increases as $\sqrt{V}$. We also show that the inelastic contribution to the Fano factor saturates with increasing thermal current exchanged between the junction and the bulk electrodes to a va…
We demonstrate the temperature-mediated and completely reversible process of desorption-readsorption of water on a few layers of epitaxial graphene on a 4H-SiC(0001) substrate. We show that under ambient conditions water forms solid structures on top of the second and third layers of graphene. In the case of strained or highly defective graphene domains, these features produce strongly correlated and reproducible patterns, implying importance of the underlying defects for the initial stages of water adsorption. Hydrophobicity increases with number of graphene layers. Evolution of the water lay…
Typical measurements of nanowire devices rely on end-to-end measurements to reveal mesoscopic phenomena such as quantized conductance or Coulomb blockade. However, creating nanoscale tunnel junctions allows one to directly measure other properties such as the density of states or electronic energy distribution functions. In this paper, we demonstrate how to realize uniform tunnel junctions on InSb nanowires, where the low invasiveness preserves ballistic transport in the nanowires. The utility of the tunnel junctions is demonstrated via measurements using a superconducting tunneling probe, whi…
Nucleation processes of mixed-phase states are an intrinsic characteristic of first-order phase transitions, typically related to local symmetry breaking. Direct observation of emerging mixed-phase regions in materials showing a first-order metal-insulator transition (MIT) offers unique opportunities to uncover their driving mechanism. Using photoemission electron microscopy, we image the nanoscale formation and growth of insulating domains across the temperature-driven MIT in NdNiO3 epitaxial thin films. Heteroepitaxy is found to strongly determine the nanoscale nature of the phase transition…
We propose a model for nanoscale supercapacitor consisting of two-dimensional insulating BN layers placed between two commensurate and metallic graphene layers. First-principles Density Functional calculations of structure optimized total energy and self-consistent field potential performed on these nanoscale capacitors for different levels of charging and different number of BN layers mark the values of capacitance per unit mass, which are larger than those measured values for the supercapacitors made from other carbon based materials. Our theoretical study also compares results obtained for …
Graphene samples can have a very high carrier mobility if influences from the substrate and the environment are minimized. Embedding a graphene sheet into a heterostructure with hexagonal boron nitride (hBN) on both sides was shown to be a particularly efficient way of achieving a high bulk mobility. Nanopatterning graphene can add extra damage and drastically reduce sample mobility by edge disorder. Preparing etched graphene nanostructures on top of an hBN substrate instead of SiO2 is no remedy, as transport characteristics are still dominated by edge roughness. Here we show that etching full…
Owing to its two dimensional electronic structure, graphene exhibits many unique properties. One of them is a wave vector and temperature dependent plasmon in the infrared range. Theory predicts that due to these plasmons, graphene can be used as a universal material to enhance nanoscale radiative heat exchange for any dielectric substrate. Here we report on radiative heat transfer experiments between SiC and a SiO2 sphere which have non matching phonon polariton frequencies, and thus only weakly exchange heat in near field. We observed that the heat flux contribution of graphene epitaxially g…
Nanoscale ridges in epitaxial multilayer graphene grown on the silicon face of 4 degree off-cut 4H-SiC (0001) were found using scanning tunneling microscopy (STM). These nano-ridges are only 0.1 nm high and 25-50 nm wide, making them much smaller than previously reported ridges. Atomic-resolution STM was performed near and on top of the nano-ridges using a dual scanning technique in which forward and reverse images are simultaneously recorded. An apparent 100% enlarged graphene lattice constant is observed along the leading edge of the image for both directions. Horizontal movement of the grap…
We report an experimental noise study of intermediate sized quasi ballistic semiconducting multiwalled carbon nanotube (IS-MWCNT) devices. The noise is two orders of magnitude lower than in singlewalled nanotubes (SWCNTs) and has no length dependence within the studied range. In these channel limited devices with small or negligible Schottky barriers the noise is shown to originate from the intrinsic potential fluctuations of charge traps in the gate dielectric. The gate dependence of normalized noise can be explained better using ballistic the charge noise model rather than diffusive McWhorte…
Graphene nanoribbons and constrictions are envisaged as fundamental components of future carbon-based nanoelectronic and spintronic devices. At nanoscale, electronic effects in these devices depend heavily on the dimensions of the active channel and the nature of edges. Hence, controlling both these parameters is crucial to understand the physics in such systems. This review is about the recent progress in the fabrication of graphene nanoribbons and constrictions in terms of low temperature quantum transport. In particular, recent advancements using encapsulated graphene allowing for quantized…
Ferroic materials (ferromagnetic, ferroelectric, ferroelastic) usually divide into domains with different orientations of their order parameter. Coupling different ferroic systems creates new functionalities, for instance the electrical control of macroscopic magnetic properties including magnetization and coercive field. Here we show that ferroelastic domains can be used to control both magnetic order and magnetization direction at the nanoscale with a voltage. We use element-specific x-ray imaging to map the magnetic domains as a function of temperature and voltage in epitaxial FeRh on ferro…
Graphene is generally considered to be a strong candidate to succeed silicon as an electronic material. However, to date, it actually has not yet demonstrated capabilities that exceed standard semiconducting materials. Currently demonstrated viable graphene devices are essentially limited to micron size ultrahigh frequency analog field effect transistors and quantum Hall effect devices for metrology. Nanoscopically patterned graphene tends to have disordered edges that severely reduce mobilities thereby obviating its advantage over other materials. Here we show that graphene grown on structure…
Suspended graphene membrane presents a particular structure with fundamental interests and applications in nanomechanics, thermal transport and optoelectronics. Till now, the commonly used geometries are still quite simple and limited to the microscale. We propose here to overcome this problem by making nanostructures in suspended epitaxial bilayer graphene on a large scale and with a large variety of geometries. We also demonstrate a new hybrid thin film of SiC-graphene with an impressive robustness. Since the mechanics and thermal dissipation of a suspended graphene membrane are strongly rel…
A first-principle model is proposed to study the electrostatic properties of a double-gated silicon slab of nano scale in the framework of density functional theory. The applied gate voltage is approximated as a variation of the electrostatic potential on the boundary of the supercell enclosing the system. With the electron density estimated by the real space Green's functions, efficient multigrid and fast Fourier Poisson solvers are employed to calculate the electrostatic potential from the charge density. In the representation of localized SIESTA linear combination of atomic orbitals, the Ko…
Gallium nitride (GaN) is a typical wide-bandgap semiconductor with a critical role in a wide range of electronic applications. Ballistic thermal transport at nanoscale hotspots will greatly reduce the performance of a device when its characteristic length reaches the nanometer scale, due to heat dissipation. In this work, we developed a tip-enhanced Raman thermometry approach to study ballistic thermal transport within the range of 10 nm in GaN, simultaneously achieving laser heating and measuring the local temperature. The Raman results showed that the temperature increase from an Au-coated t…
In ballistic transport, heat carriers such as phonons travel through the solid without any scattering or interaction. Therefore, there is no temperature gradient in the solid, which seems to transport the heat without getting heated itself. Ballistic transport is typically seen in high purity crystals at either temperatures below ~10 K, or physical size below ~100 nm, where the mean free path of the carrier is larger than the solid itself. In this letter, we show evidence of ballistic transport at room temperature in lithium niobate wafers in the in-plane and cross-plane directions under both …
We propose a thermoelectric cooling device based on an atomic-sized junction. Using first-principles approaches, we investigate the working conditions and the coefficient of performance (COP) of an atomic-scale electronic refrigerator where the effects of phonon's thermal current and local heating are included. It is observed that the functioning of the thermoelectric nano-refrigerator is restricted to a narrow range of driving voltages. Compared with the bulk thermoelectric system with the overwhelmingly irreversible Joule heating, the 4-Al atomic refrigerator has a higher efficiency than a b…
Nanoscale solid-solid contacts define a wealth of material behaviours from the electrical and thermal conductivity in modern electronic devices to friction and losses in micro- and nanoelectromechanical systems. For modern ultra-high integration processor chips, power electronic devices and thermoelectrics one of the most essential, but thus far most challenging, aspects is the assessment of the heat transport at the nanoscale sized interfaces between their components. While this can be effectively addressed by a scanning thermal microscopy, or SThM, which demonstrates the highest spatial reso…
Establishing good electrical contacts to nanoscale devices is a major issue for modern technology and contacting 2D materials is no exception to the rule. One-dimensional edge-contacts to graphene were recently shown to outperform surface contacts but the method remains difficult to scale up. We report a resist-free and scalable method to fabricate few graphene layers with electrical contacts in a single growth step. This method derives from the discovery reported here of the growth of few graphene layers on a metallic carbide by thermal annealing of a carbide forming metallic film on SiC in h…