Ming Ruan

Yike Hu

Zelei Guo

Rui Dong

James Palmer

John Hankinson

Claire Berger

Walt A De Heer

Epitaxial graphene on silicon carbide: Introduction to structured graphene

We present an introduction to the rapidly growing field of epitaxial graphene on silicon carbide, tracing its development from the original proof-of-concept experiments a decade ago to its present, highly evolved state. The potential of epitaxial graphene as a new electronic material is now being recognized. Whether the ultimate promise of graphene-based electronics will ever be realized remains an open question. Silicon electronics is based on single-crystal substrates that allow reliable patterning on the nanoscale, which is an absolute requirement for any new electronic material. That is why epitaxial graphene is based on single-crystal silicon carbide. We also present recent results on nanopatterned graphene produced by etching the silicon carbide before annealing so that the graphene structures are produced in their final shapes. This avoids post annealing patterning, which is known to greatly affect transport properties on the nanoscale. Creating such structured graphene is an elegant method for avoiding pervasive patterning problems.

Introduction

The exceptional properties of graphite and graphitic materials are well known [1][START_REF] Fitzer | Carbon Reinforcements and Carbon/Carbon Composites[END_REF][START_REF] Thostenson | [END_REF] and have been exploited in several industries: For example, the next generation of commercial airliners will be made primarily of graphite composites. Graphite has the highest melting point of any material, and its sp [START_REF] Fitzer | Carbon Reinforcements and Carbon/Carbon Composites[END_REF] bonds are among the strongest in nature. In a series of articles in the 1930s on the nature of the chemical bond, Linus Pauling focused on the sp [START_REF] Fitzer | Carbon Reinforcements and Carbon/Carbon Composites[END_REF] bonds in what is now called graphene, showing that they are directional, rigid, and chemically stable, so that a free graphene sheet is fl at and chemically inert. [START_REF] Pauling | The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry[END_REF] This is also why curved structures such as fullerenes and nanotubes tolerate high strain without collapsing. Thus, it was not surprising that the early suspensions of graphene sheets made by Boehm et al. were stable. 5 In the past decade, there has been a great focus on the chemical and electronic properties of monolayer graphite, or graphene. 6,7 Yet, this significant increased interest in graphene has not changed the graphite industry much, mainly because the properties of graphite monolayers are not that different from those of the nanographitic materials already used.

The properties of graphene and graphite are very similar because the interlayer bonding between the graphene layers in a graphite stack ranks among the weakest in nature. [START_REF] Pauling | The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry[END_REF] In fact, the bonding between two graphene layers in graphite is weaker than the bonding of a graphene sheet to many surfaces. This is why, when a graphite rod is rubbed on a piece of paper, few-layer graphene flakes transfer from the graphite rod (e.g., a pencil) onto the paper. It is this property that gives graphite its name (from the root graph, to draw). Because the interlayer coupling is so weak, a graphene sheet in graphite is in many respects essentially freestanding, so many of graphene's properties have been, and still are, accurately predicted from the properties of graphite.

However, there is one important exception: The electronic band structures of graphene and graphite within a few tenths of an electron volt of the energy where the valence and conduction bands meet (which in graphene is called the Dirac point) are significantly different. 7 (Also see the introductory article in this issue.) The fundamental reason for this is that, at least for Bernal-(AB-) stacked graphite, the interlayer coupling breaks the symmetry between A and B atoms in the twoatom unit cell of the graphene layer. Whereas, in a graphene monolayer, the band structure consists of Dirac cones located at the K and K ′ points (the two distinct corners of the hexagonal Brillouin zone), in graphite, the tips of the cones become parabolic and shift to produce the pockets of electrons and holes of the graphite semimetal. Hence, in contrast to graphene with its massless-fermion-like linear dispersion, the electrons and holes in graphite acquire a small mass near charge neutrality. These graphene properties have been well-known since the late 1940s 8 and have been extensively studied because they are basic for an understanding of carbon nanotube electronics. In fact, graphene electronics is based on nanotube electronics. 9 From the outset of graphene electronics, 9 the most important lesson learned from nanotubes was that quantum-confined graphene has useful electronic properties.

Current trends indicate that graphene electronics research will evolve along two paths. One path involves growing large area graphene sheets on various metals using chemical vapor deposition 6 and related methods and then transferring the sheets to an insulating substrate. This scheme is currently considered for the production of conducting transparent electrodes for touch screens, displays, and solar panels as an alternative to indium tin oxide. It might ultimately be used for flexible and inexpensive electronics that can be integrated with organic electronics. This line of graphene research aims to compete with existing technology and produce even cheaper electronics. (See the article in this issue by Bartelt and McCarty for a detailed discussion of graphene growth on metal surfaces.) Epitaxial graphene on silicon carbide, on the other hand, is considered to be an ideal material for high-end electronics that might be able to surpass silicon in terms of key parameters such as speed, feature size, and power consumption. 10, 11 It is expected that epitaxial graphene electronics will achieve operating speeds in the terahertz range. 11 Feature sizes on the order of 10 nm have already been realized. 10 Furthermore, epitaxial graphene growth techniques are also an ideal platform for structured graphene, 12 which consists of graphene wires and dots that are directly grown on patterned silicon carbide substrates, as described in a later section of this article. It is hoped that epitaxial graphene electronics will outperform other electronics platforms in at least one key parameter. (See the article in this issue by Nyakiti et al. for further information on epitaxial graphene.)

Graphene electronics in context

The first report on epitaxial graphene as an enabling material for large-scale electronics appeared in 2004. 9 The same article also included the first transport measurements of monolayer graphene. 9, 13 Graphene was already known to be a gapless semiconductor, but its potential for electronics applications had not been recognized until then (see, for example, Wallace 8 ). In contrast, the electronic properties of carbon nanotubes (known to be rolled-up graphene strips) had been studied since the early 1990s. [START_REF] Thostenson | [END_REF] Earlier work had already demonstrated that there are striking theoretical similarities between graphene ribbons (i.e., narrow graphene strips) and carbon nanotubes. 14 Hence, the original concept of graphene electronics recognized that appropriately produced graphene ribbons on an insulating substrate could be used as "wires" or as "semiconductors" depending on the morphology of the ribbons (in particular, their edges). 9 With some modifications, this concept still remains a leading paradigm for graphene electronics.

The concept of graphene-based electronics is essentially based on carbon nanotube electronics research. 9 Carbon nanotubes are either semiconducting or metallic depending on their chirality (orientation of the nanotube axis relative to the graphene lattice).

3, 15 Semiconducting nanotubes have been used to produce remarkable transistors, with high gain, large current on/off ratios (>10 [START_REF] Boehm | [END_REF] ), and room-temperature operation. 16 However, interconnects and patterning have remained problematic for nanotubes. Patterning of graphene, where both wires and devices would be formed from a monolithic graphene sheet, was recognized as a method to overcome these key issues. It was theoretically predicted that, as for carbon nanotubes, the ribbon orientation relative to the graphene lattice determines its electronic structure. One-third of armchair configurations (with edges parallel to one side of the graphene hexagon) have an electronic bandgap, whereas the other armchair configurations and all zigzag ribbons are expected to be metallic. Moreover, the predicted bandgap is on the order of 1 eV nm/ W, where W is the ribbon width. 14 Therefore, from the outset, graphene electronics was considered to be useful primarily at the nanoscale. However, in contrast to carbon nanotubes, which are discrete objects that must be assembled for electronics applications, graphene electronics involves nanopatterning, which provides a clearer route toward wafer-scale patterning.

Two-dimensional epitaxial graphene: Structure

Because of the scalability of graphene nano structuring and the structural quality of graphene nanostructures on the insulating SiC substrate, epitaxial graphene is recognized as an ideal platform for electronics 9, 13, 17 -24 (see also the article in this issue by Nyakiti et al.). Epitaxial graphene sheets are produced by thermal decomposition of SiC at high temperature in a vacuum 25, 26 or in argon gas 20 or by the confinement controlled sublimation (CCS) growth method. 17 The highest-quality (single or multiple) graphene layers are grown in a near-equilibrium environment as in the CCS method. In the CCS growth technique (used in our graphene laboratories at Georgia Institute of Technology since 2003), a SiC chip is held in a graphite enclosure that is heated in a vacuum and supplied with a small leak (Figure 1 a-b). The rate of graphene growth is controlled by the rate at which sublimed silicon vapor escapes through the leak. The graphene produced by CCS is superior in homogeneity to that obtained using methods that are far from equilibrium (for example, sublimation in a vacuum). 25 For electronics, epitaxial graphene on SiC has clear advantages over graphene deposited on substrates.

21, 24, 27, 28 First, it is grown directly on an insulating substrate, so it does not need be patterned immediately. In addition, the interface between epitaxial graphene and the silicon carbide substrate is formed at temperatures in excess of 1500C, so that it is reproducible, ordered, and clean. Consequently, no water or impurities are trapped under the graphene. In contrast, transferred graphene produced by mechanical or chemical exfoliation or growth on metals is plagued by interface impurities. Moreover, graphene-SiC interfaces can be modified by passivation and intercalation. A further advantage is that the SiC substrate is a large-bandgap semiconductor already used in electronics applications. Monocrystalline wafers with diameters up to 100 mm and atomically smooth surfaces that are ready for epitaxial growth are readily available (at a price of about US$20/cm 2 ).

Beyond applications, epitaxial graphene is ready for interrogation by the vast array of surfacescience probes that are now available, most of which cannot be used on deposited graphene materials. A few examples are given in the remainder of this section. Other examples are included in the article in this issue by Conrad and Hicks.

Graphene can be epitaxially grown on either of the two polar faces of SiC 26 (see Figure 1c). On the (0001) silicon-terminated face of hexagonal 4H-or 6H-SiC, thin graphite composed of to be transferred to another dielectric substrate; hence, it can one or several graphene layers (ABA-or ABC-stacked) can be grown. A graphene-like nonconducting buffer layer sits next to the SiC substrate and forms a noninteracting interface with the graphene layer(s) on top of it.

25, 29 -31

Consequently, a Si-face monolayer is electronically essentially identical to a freestanding graphene layer.

Graphene grown on the (000-1) carbon-terminated face (the C face) of SiC is quite different from that grown on the (0001) Si face. 18, 19, 32 The CCS-grown layer stack on the C face is called multilayer epitaxial graphene (MEG) because it is azimuthally ordered in a particular way with alternating 0° and 30° rotations relative to the SiC(000 1) substrate (although defects in this order are still abundant). Because of this non-Bernal stacking, the symmetry between the atoms in the unit cell is not broken in multilayers of C-face graphene. 19, 33 Consequently, even though it is multilayered, MEG has the electronic band structure of isolated graphene layers, with only a small perturbation due to weak effective interlayer coupling. Specifically, angle-resolved photoemission spectroscopy (ARPES) measurements showed a set of nearly independent linearly dispersing bands (Dirac cones) at the graphene K point, each one originating from an individual rotated layer in the multilayer stack. 34 Experiments detected neither van Hove singularities at the K point, indicative of saddle points in the band structure, nor significant changes in the Fermi velocity, 35 both of which had been predicted for rotated layers (also see the article in this issue by Hicks and Conrad).

Consequently, MEG films are stacks of graphene layers with the electronic structure of electronically decoupled graphene layers. The properties of this material have been extensively studied. For example, ongoing ARPES studies are being used to interrogate the subtle interactions between the topmost layers. 34, 35 Infrared Landau-level spectroscopy, 36, 37 which probes transitions between Landau levels in a magnetic field, accesses interior layers in multilayer stacks, and Raman spectroscopy 38 provides information on electron-phonon coupling. Ultrafast optical-pump terahertz-probe spectroscopy monitors carrier relaxation processes.

-42

It is known that at least the topmost graphene layer on a C-face graphene stack is continuous over the entire wafer and atomically flat over hundreds of square micrometers. 43 This allows high-resolution scanning tunneling microscopy (STM) experiments to be performed that are virtually impossible with deposited graphene layers, which need to be precisely located and contacted to a metallic drain and are plagued with electron-hole puddles and ripples that blur the spectral resolution. STM experiments on epitaxial graphene at milli-Kelvin temperatures in high magnetic fields have provided, for instance, significant insight into the Landau-level distribution and a first-time direct mapping of the quantized states in graphene, with direct evidence of new many-body states in graphene.

-45

Epitaxial graphene films are well suited for chemical modification, by virtue of their large surface areas and unreactive and stable substrate. For example, MEG films have been successfully functionalized directly on the chip, to produce semiconducting graphene oxide films on the SiC substrate. 46 Aryl groups have been grafted onto MEG to modify its properties in attempts to produce high-mobility semiconducting graphene.

22, 47

Micropatterning by local thermal desorption of epoxy and hydroxyl groups has been proposed as a method to create conducting nanoribbons on a nonconducting epitaxial graphene oxide matrix. 48, 49 Noncovalent chemical modifications of epitaxial graphene that preserve the electronic band structure of graphene were also successfully achieved for protein immobilization.

50

Electronic transport and devices on the C face Quantum Hall effect on an epitaxial monolayer

One distinctive characteristic of graphene is an additional quantum number that represents the weight of the wave function for a particular momentum direction on each of the two triangular sublattices that compose the honeycomb atomic structure. This quantum number, called pseudospin, has the characteristics of a spin but is bound to the direction of momentum. Because the electronic wave character (pseudospin) cannot be changed by scattering in the perfect atomic structure, the dynamics of the electrons is modified compared to that of classical two-dimensional electron gases. In particular, the presence of a pseudospin causes two-dimensional graphene to be immune from back-scattering, increasing carrier mobility. 7 It also manifests in the appearance of quantum Hall effect (QHE) plateaus at conductance values that are half-integer multiples of 4e 2 /h . 51, 52 (Here, e is the electron charge, and h is Planck's constant. The factor of four multiplying e 2 /h is expected because of the twofold valley and twofold spin degeneracies in graphene.) The half-integer QHE, hallmark of monolayer graphene, is clearly observed in monolayer epitaxial graphene grown on the C face 10, 53, 54 (Figure 2).

The charge density in an epitaxial graphene monolayer can be adjusted by compensating the intrinsic n doping through exposure to the environment (water, light) or through resist coating, or it can be tuned by a top gate, as in Figure 2 c-d. 10 When graphene is environmentally doped, heating it in a vacuum restores its pristine condition. Mobilities up to 40,000 cm 2 V -1 s -1 can be achieved at a carrier density of 0.19 Å~ 10 12 cm -2 , which is low enough for observation of the extended R xy = h /2e

2 plateau (corresponding to a filling factor [the electron density relative to the number of states of a Landau level] of ν = 2) at a relatively low magnetic field (onset at B ≈ 3 T). 10 Note also that a well defined plateau is observed in Figure 2b at temperatures above 77 K, that is, well above the usual temperature for quantization in conventional two-dimensional electron gases. 54 This opens the way to QHE-based metrology applications (see the article in this issue by Schopfer and Poirier).

Ultrahigh-frequency field-effect transistors

At the time of this writing, graphene is not suited for digital electronics, because of its lack of a bandgap, which is absolutely required for digital switches. However, for the channel material of field-effect transistors (FETs) in amplifiers, a bandgap is not required, so graphene provides a unique opportunity for ultra high frequency electronics. These devices require (among other properties) a high-mobility channel material. Moreover, a silicon carbide substrate is compatible with these high frequencies. Several proof-of-concept experiments have demonstrated the feasibility of this technology.

19, 55, 56 A unity-current-gain cutoff frequency of f T > 200 GHz has been demonstrated with a Si-face epitaxial graphene channel device, thereby showing that this material can indeed be used for state-of-the-art electronic devices. 57 Rapid progress is also being made with C-face graphene FETs (see Figure 3), for which f T ≈ 100 GHz is routinely obtained. To achieve such performance, a double-gate structure covering a short and wide channel between the source and drain is used (Figure 3b inset). This transistor design has been optimized to minimize parasitic capacitances. The device is top-gated with an aluminum-capped Al 2 O 3 dielectric that preserves good electronic mobility of 8700 cm 2 V -1 s -1 . As usual for graphene devices, the desirable saturation of the current with increasing source-drain voltage is not reached (Figure 3a). 57 Nonetheless, the device exhibits promising characteristics (maximum current density greater than 1.5 mA µm -1 and transconductance greater than 0.4 mS µm -1 at a charge density of n = 1.6 Å~ 10 12 cm -2 ). (For further discussion of transistor characteristics, see the article in this issue by Avouris and Xia.)

To be competitive with current semiconductor technology, the f T value of graphene devices will need to be increased considerably, as half-terahertz operation of SiGe heterojunction bipolar transistor has already been demonstrated. 58 Terahertz operation is, in principle, possible for epitaxial graphene, based on the high carrier velocity in graphene and the high phonon frequency of SiC.

11, 59 One of the most significant limitations is the access resistance, which is the series resistance of the short, ungated portion of graphene between the source and drain leads seen in the inset of Figure 3b . Even though the resistivity of graphene at room temperature is comparable to that of copper (10 µΩ cm), the resistance of a graphene source lead with a lengthto-width aspect ratio of 10:1 is several kilo-Ohms. The minimum reported access resistance of 350 Ω per micrometer of channel width is still prohibitive for terahertz operation, but this problem is primarily technical and surmountable using C-face graphene, which has a high carrier mobility.

Spintronics

Epitaxial graphene has also recently demonstrated its utility for spintronics. Spintronic devices use spin rather than charge as the state variable for information processing. valve operates as follows: Spin-polarized electrons are injected into a graphene ribbon using a magnetically polarized contact. The spin polarization is detected by means of a second magnetically polarized contact, which preferentially admits electrons whose spin is aligned with it. The spin signal is the difference in the resistance between the cases of parallel and antiparallel magnetization of the electrodes.

Recently, highly efficient spin transport was measured in MEG with spin signals in the mega-Ohm range, efficiencies up to 75%, and spin propagation lengths exceeding 100 µ m. 61 The high efficiency (the difference in the measured resistance between two oppositely magnetically polarized contacts, relative to perfect transmission) and long spin diffusion length imply an exceptionally small degradation of spin information during the transport through the epitaxial graphene channel. The spin diffusion lengths in graphene are nearly two orders of magnitude higher than those reported in metals, semiconductor systems, and transferred graphene flakes. Such exceptional results are attributable not only to the high mobility of epitaxial graphene, but also to the flatness of the layers and the absence of ripples that can depolarize the spins. Further, these promising results indicate that epitaxial graphene could serve as a scalable platform for spintronics in more complex structures. Although much more development is still needed, the possibility of spintronic devices and networks might now be a little closer thanks to graphene. (See the article in this issue by Seneor et al. for a detailed discussion of graphene use for spintronics.)

Structured graphene

Since the advent of graphene-based electronics, 9 it has been clear that graphene's potential as a superior electronic material is most relevant at the nanoscale, where quantum interference effects manifest themselves in structures on the order of the Fermi wavelength, λ F . To gauge the relevant dimensions, note that, at a charge density of n s ≈ (2-5) Å~ 10 12 cm -2 (the natural charge of a pristine epitaxial graphene monolayer), that is, for a Fermi energy about 200 meV above the Dirac point, λ F is approximately 20 nm. It becomes greater than 300 nm for the quasi-neutral graphene layers (n s < 5 Å~ 10 9 cm -2 ) in the stack of MEG.

Whereas most schemes for fabricating nanoscale graphene structures start from extended graphene sheets and pattern them by lithographically defined etching, epitaxial graphene on SiC can be shaped directly at the nanoscale without such post-growth patterning.

10, 12

Lithographically patterned graphene nanoribbons have been extensively studied. As described previously, the original idea 9 was that graphene ribbons would be semiconductors with bandgaps on the order of 1 eV/ W, where W is the ribbon width in nanometers. Several studies in fact appeared to confirm bandgaps of this order in patterned graphene ribbons. 62 However, in most cases, the large response to the gate voltage in very narrow ribbons (with on/off current ratios up to 10 6 ) turned out to be caused by a mobility gap rather than a bandgap. 63 The edges of lithographically patterned ribbons are disordered (electronically resembling a series of quantum dots). This disorder causes strong localization of the charge carriers and a large reduction in the mobility in the energy region near the Dirac point, degrading the current at low charge densities. Because the localized states still must be charged and discharged by the device currents, devices that rely on mobility gaps are typically not suitable for high-speed digital electronics.

Remedying this problem requires methods to keep the ribbon edges intact. The following subsections describe three paths that avoid lithographic patterning of graphene itself and instead produce the desired shapes in the graphene growth phase. The first method promotes graphene growth by etching depressions or mesas on SiC 12 and is best suited for C-face graphene. The second approach, C-face patterning, uses a lithographically defined cap that prevents formation of graphene under it. 64 The third method is the most promising and consists of growing graphene on the faceted sidewalls of trenches that are etched into the SiC. 10, 12 This method takes advantage of the facet-dependent growth rate. Because Si-face graphene growth is particularly slow, the sidewalls of the trenches etched in SiC are the first to graphitize.

C-face pits and mesas

Monolayer graphene growth on the C face is complex 17, 65 and ultimately yields a uniform distribution of monolayer patches over the silicon carbide substrate. High-mobility monolayer patches as large as several hundred square micrometers in area can be grown continuously over the substrate steps. 10 The CCS growth method is used, and growth is arrested after a few minutes at 1550°C. Monolayer C-face films are identified by atomic force microscopy (AFM), ellipsometry, optical transmission and Raman spectroscopies, and ultimately by the characteristic half-integer QHE 53 (see Figure 2). Note that growth at screw dislocations (which are always present in current SiC crystal wafers) is difficult to control and typically causes deep crevices covered with multilayer graphene.

Structured growth of monolayers on the C face has routinely been achieved on etched mesas and trenches in 4H-SiC. 10 Following Reference 66 , a good starting point for graphene growth is a surface with step-free mesas. These form under certain conditions when the natural steps originating from the substrate miscut angle flow at high temperature and bunch at the edges of etched mesas. Graphene on the C face is recognized by its pleats, which result from a larger contraction of SiC relative to graphene upon cooling from the high temperature applied during growth. 10 In another approach, 10 monolayer graphene growth at specific locations can also be initiated at the edges of trenches etched in SiC prior to graphitization. Further work will reveal whether this method can lead to a viable process for growing nanoscale graphene patches at predetermined locations.

Local capping

Another route for growing graphene at specific locations is to prevent silicon sublimation from the SiC substrate by capping it with an aluminum nitride layer. 64 The AlN coating is patterned and etched away to open bare SiC windows for subsequent graphitization by the CCS method 17 (see Figure 4 a). This process relies on the ability of the cap to withstand graphitization temperatures up to 1420°C under 100 Pa of argon pressure. The Raman spectra in Figure 4 b-c clearly show that, under optimized growth conditions, the AlN coating efficiently prevents graphene growth under it. 64 Consequently, the resulting graphene structure does not need post-growth etching. Graphene Hall bars were fabricated with this method and characterized by scanning Raman spectroscopy, ellipsometry, and transport measurements. The Hall mobility for the Hall bar in Figure 4a was determined to be about 600 cm 2 V -1 s -1 , and the mobility can be further enhanced for such structures by fi ne tuning the growth conditions and improving the quality of the SiC surface prior to graphitization.

Sidewalls

The third, extremely promising, route for graphene growth is the structured growth method 10, 12 (also called the templated growth method), in which graphene growth is initiated on the sidewalls of pre-etched SiC trenches. This process relies on the observations that graphene growth is slowest on the (0001) face and that growth on this face proceeds from the steps to the terrace regions.

67

The general approach is schematically depicted in Figure 5 a-c; details can be found in References 12 and 17. The SiC surface (Si face) is first vertically plasma etched through a patterned mask to produce steps of well-defined height. When required, this procedure is repeated several times to produce structures with varying depths (as shown in Figure 5c). The etched SiC template is then annealed at a temperature of about 1550°C for about 10 min, and the etched steps crystallize at high temperature toward equilibrium (110n) or (112n) facets. For trenches on the order of 10 nm in depth, the normals to the facet surfaces have angles of 28-32° with respect to the (0001) direction.

Using the CCS growth process with controlled growth parameters (time and temperature), a monolayer graphene film can be produced on only these facets and not (or minimally) on the (0001) upper and lower surfaces. The facets, or sidewalls, can be shaped into narrow ribbons, rings, crosses, or essentially any shape. Notably, for transport measurements, graphene nanoribbons can be seamlessly connected to four wide ribbons for four-point transport measurements (Figure 5d-f). For this purpose, a shallow (∼ 10-nm) trench is etched, bridging two previously etched deep U-shaped trenches (>100 nm, see Figure 5d). 10 After CCS growth, the sidewalls of the U trenches form the broad graphene leads for the two narrow graphene sidewall ribbons between the U's (Figure 5e-f). Metal contacts are provided to the wide graphene leads for transport measurements of the narrow graphene ribbons. Gate structures can be subsequently patterned on top of the sidewall ribbon. Further examples of structured graphene are shown in Figure 6.

The structured growth method circumvents the damaging lithographic patterning process that causes large mobility reductions in lithographically patterned graphene ribbons. Instead of being chemically etched by oxygen plasma through a mask (which is far from gentle), the graphene edges of ribbons produced by structured growth are annealed at high temperature and anchored into the reconstructed SiC surface. Graphene nanostructures can be imaged by electrostatic force microscopy (EFM) at high resolution (about 10 nm according to modeling of the tipgraphene interaction). Raman spectroscopy (about 1-µm resolution) unambiguously shows the characteristic graphene spectrum (similar to that in Figure 4b). In particular, for graphene grown on the structure shown by AFM in Figure 7 a, spatial scans of the graphene Raman 2D peak (Figure 7b) reveal that, in well-prepared samples, graphene grows almost exclusively on the sidewalls, as confirmed by EFM (Figure 7c).

All graphene ribbons produced by this method have been found to be metallic with significant mean free paths. There is no evidence for a bandgap or a transport gap, in contrast to lithographically patterned graphene. 62, 63, 68 The absence of localization or a Coulomb blockade, which is observed when tunneling occurs between small decoupled graphene regions, 63 indicates much-reduced scattering compared to that of nanoribbons etched after growth, presumably due to smoother edges. In fact, early tight-binding calculations 14 predicted that all graphene ribbons should be metallic, with the exception of those with armchair edges. Even among armchair ribbons, only those for which the width is an integer multiple of three hexagons are semiconductors. Several calculations that go beyond the tight-binding approximation 69, 70 have predicted that ribbons will be semiconductors, but in all cases, the edge structure and chemistry play essential roles, and their control is important.

High-resolution transmission electron microscopy cross sections and scanning tunneling microscopy images of graphene grown on the sidewalls of steps indicate that graphene curves terminate perpendicular to the silicon carbide surface at the bottom of steps and that the graphene edges are mainly of the zigzag variety. 67 The sidewall graphitization method is also appropriate for large-scale production of patterned structures (see examples in Figure 6). Ribbons and interconnecting structures can be produced simultaneously, after the SiC substrate has been structured by plasma etching. Note that the graphene nanoribbon width is determined by the step height (and thus the SiC plasma etch time) and not by the feature size of the SiC etch mask. Hence, optical lithography can be used to produce nanometric wafer-scale graphene devices. An example of 10,000 interconnected transistors produced on a 4 mm ~ 6 mm SiC chip is shown in Figure 8, along with some transport characteristics. 12 Wide graphene ribbons (about 250 nm in width) were produced in this array on the C face, demonstrating the feasibility of sidewall growth on both faces. The weak gating is attributed to the metallic nature of the ribbons.

Conclusions

This overview of epitaxial graphene for electronics applications is meant to stimulate further attention to this field. Our perspective is that, for graphene to have an impact on electronics, the basic tenets of microelectronics should be respected. Modern microelectronics deals with structures that are a few tens of nanometers in size that are reliably patterned by the billions. The only reason that this can be achieved is that the silicon substrates being used are atomically welldefined: they are single crystals, which is obviously preferable over disordered substrates. Consequently, it is very likely that any new electronics technology will adopt this strategy from the outset.

Herein, we have shown that graphene on single-crystal silicon carbide offers a wide range of advantages. Beyond its potential for large scale patterning, epitaxial graphene on SiC can be studied using state-of-the-art surface-science probes, including angle-resolved photoemission spectroscopy, low-energy electron diffraction, scanning tunneling microscopy, atomic force microscopy, transmission electron microscopy, and many others, that cannot be used for materials produced on poorly defined substrates. It is clear that epitaxial graphene electronics has not yet realized its full potential. However, the first small steps have been made. Commercially viable ultrahigh-frequency epitaxial graphene analog devices are on the horizon. The most critical next step will be to open a bandgap in the material, and steady progress is being made to achieve this goal. Indeed, epitaxial graphene has few competitors in efforts to produce new electronics platforms.

Figure Captions

Figure 1. Graphene growth by the confinement controlled sublimation (CCS) method. (a) A SiC chip is placed in a graphite enclosure that is provided with a small leak and inductively heated using a molybdenum sleeve as the susceptor. A quasi-equilibrium is established at high temperatures to moderate the graphene growth. (b) Photograph of the furnace showing the evacuated glass tube, the water-cooled radio-frequency induction coil, and the white-hot susceptor. (c) Schematic of graphene on SiC (silicon, yellow; carbon, black). The SiC wafer is shown as unrealistically thin to allow comparison of the two nonequivalent faces. The bottom face (C face) is covered with two graphene layers, whereas the top face (Si face) schematically terminates in a covalently bonded buffer layer. In subsequent growth on this face, the buffer layer is converted into a graphene layer by the new buffer layer that grows under it. Adapted from Reference 17.

Figure 2 .

 2 Figure 2. The quantum Hall effect in C-face epitaxial monolayer graphene for micrometer wide Hall samples with CCS-produced graphene. Resistivity ρ xx (black) and Hall resistance ρ xy (red) versus magnetic field at 4 K for (a) the C-face Hall bar shown in the inset (mobility µ = 39,800 cm 2 V -1 s -1 , charge density n = 0.19 × 10 12 cm -2 ) and (b) the C-face Hall bar shown in the inset (µ = 21,100 cm 2 V -1 s -1 , n = 0.92 × 10 cm -2 ), also showing the persistence of the ν= 2 plateau in ρ xy at 200 K (where ν represents the filling factor). (c) Resistivity ρ xx and Hall conductivity σ xy = ρ xy /( ρ xx 2 + ρ xy 2 ) versus gate voltage V G for a top-gated C-face Hall bar (1 µm × 4.3 µm), showing plateaus in the n -and p -doped regimes. The mobility for n doping is 6200 cm V -1 s -1 , and that for p doping is 8500 cm V -1 s -1 . The application of the top gate significantly reduces the mobility compared with those of the bare samples in (a) and (b). (d) Resistivity ρ xx as a function of gate voltage at 4 K and zero magnetic field. The inset shows the Hall bar measured in (c) and (d). All scale bars are 2 µm. Adapted from References 10, 53, and 54.

Figure 3 .

 3 Figure3. Ultrahigh-frequency C-face epitaxial graphene field effect transistor (GFET). (a) Source-drain current density (I sd ) versus voltage (V sd ) on a 200-nm-long gate, 3-µm-wide device at gate voltages (V G ) from 0 V to 3 V in 0.5-V steps. A current density greater than 1.5 mA/ µ m can be applied to the device, and mild current saturation is observed at large drain-source biases. (b) ac current gain (H 21 ) versus frequency for the GFET in (a) after de-embedding. A cutoff frequency (f T ) of 90 GHz is extracted by extrapolating the measurement to unity gain. Inset: Atomic force microscopy (AFM) image of a dual-gate GFET similar to the one measured in (a) and (b). D, drain; G, gate; S, source. Scale bar = 5 µm. Adapted from Reference 10.

Figure 4 .

 4 Figure 4. Capping method for structured graphene growth using a patterned AlN cap. (a) AFM image of a completed graphene Hall bar structure fabricated by the CCS method. The light gray areas correspond to graphene, and the dark areas correspond to AlN-covered regions that prevent graphene growth. Metal contacts (gold/palladium) are applied for subsequent electrical measurements. This Hall bar has a Hall mobility of about 600 cm 2 V -1 s -1 , significantly less than that of pristine graphene. (b) Micro-Raman spectrum of the AlN-capped SiC substrate, which does not exhibit graphene features after CCS annealing. (c) Micro-Raman spectrum of the graphene areas, showing characteristic graphene features (D, G, and 2D bands). The relatively intense D band confirms that the graphene is significantly disordered, accounting for the observed low mobilities. Adapted from Reference 64.

Figure 5 .

 5 Figure 5. Illustrative example of structured growth patterning. (a)-(c) Schematic illustration of the production of structured graphene and devices: (a) A vertical step is etched in the SiC substrate. (b) After CCS growth, the sidewall has recrystallized into a stable SiC facet, on which graphene grows preferentially. (c) Repeated plasma etching produces structures with varying depths. (d-f) A graphene ribbon is seamlessly connected to wide graphene leads. (d) AFM image of a SiC surface patterned with two deep U-shaped etched trenches (dark lines) connected to a shallow trench for subsequent graphene nanoribbon growth. Four wide graphene leads form at the edges of the two deep trenches. These form electrical leads connected to two thin graphene ribbons that form on the upper and lower edges of the shallower trench (faint horizontal stripe). (e) AFM image, representing the topography, and (f) electrostatic force microscopy (EFM) image, whose contrast distinguishes graphene from silicon carbide, of the surface presented in (d) after CCS graphitization. The rounding comes from the SiC step fl ow to produce a stable crystalline SiC facet. Adapted from References 10 and 12.

Figure 6 .

 6 Figure 6. Examples of epitaxial graphene sidewall structures produced by the structured growth method, demonstrating its versatility: (a) an array of parallel ribbons grown on the step edges of a vicinal surface, (b) graphene grown in many orientations on the sidewalls of complex convoluted trenches, (c) a Hall bar with four transverse voltage probes, and (d) rings grown on the sidewalls of pillars. The top images in (a), (b), and (d) and the left image in (c) represent the AFM topography, and the corresponding bottom and right images are EFM images showing bright areas where graphene grows at the edges of the etched patterns. Adapted from Reference 10.

Figure 7 .

 7 Figure 7. (a) AFM image, (b) Raman 2D peak mapping, and (c) EFM image of a Si-face SiC surface with graphene selectively grown on the sidewalls, confirming that graphene growth is largely confined to the sidewalls.

Figure 8 .

 8 Figure 8. Example of large-scale patterning of epitaxial graphene devices using the structured growth method. (a) Illustration of 10,000 transistors fabricated within a 4 mm × 6 mm chip using the sidewall graphitization method, with a schematic of the transistor structure at the top right. (b) Typical gating characteristics between source S and drain D showing the conductance G (in millisiemen-squares) versus gate voltage V G . Inset: Plan view of the transistor structure. Scale bar, 20 µm; channel length, 7 µm. Adapted from Reference 12.

  Figure'1'

Figure' 2 '

 2 Figure'2'

  Figure'3'

  Figure'4'

  Figure'5'

Acknowledgments

We acknowledge funding from the National Science Foundation (DMR-0820382), the Keck Foundation, the Air Force Office of Scientific Research, and the Partner University Fund. We warmly thank P. S. Chakraborty, N. Lourenco, and J. Cressler for the ultrahigh-frequency FET measurements presented in Figure 3.


Suenne Kim

Si Zhou

Yike Hu

Muge Acik

Yves J Chabal

Claire Berger

Walt De Heer

Angelo Bongiorno

Elisa Riedo

Room Temperature Metastability of Multilayer Graphene Oxide Films

Graphene oxide has multiple potential applications. The chemistry of graphene oxide and its response to external stimuli such as temperature and light are not well understood and only approximately controlled. This understanding is crucial to enable future applications of this material. Here, a combined experimental and density functional theory study shows that multilayer graphene oxide produced by oxidizing epitaxial graphene via the Hummers method is a metastable material whose structure and chemistry evolve at room temperature with a characteristic relaxation time of about one month. At the quasi-equilibrium, graphene oxide reaches a nearly-stable reduced O/C ratio, and exhibits a structure intensively deprived of epoxide groups and enriched of hydroxyl groups. Our calculations show that the structural and chemical changes are driven by the availability of hydrogen in the oxidized graphitic sheets, which favors the reduction of epoxide groups and the formation of water molecules.

1 Graphene [START_REF] Berger | Electronic confinement and coherence in patterned epitaxial graphene[END_REF][START_REF] Geim | The rise of graphene[END_REF] and graphene-based materials hold great promises for next generation of nanodevices [START_REF] Medhekar | Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties[END_REF][START_REF] Wei | Nanoscale tunable reduction of graphene oxide for graphene electronics[END_REF][START_REF] Gao | Direct laser writing of micro-supercapacitors on hydrated graphite oxide films[END_REF][START_REF] Loh | Graphene oxide as a chemically tunable platform for optical applications[END_REF]. One of the most pressing issues for the technological use of graphene is the possibility to control physical and chemical properties via ad hoc functionalization [START_REF] Ruoff | Graphene: Calling all chemists[END_REF]. Thermal, chemical, and optical reduction of graphene oxide have been explored as a route to produce graphene-based materials with the desired electron transport [START_REF] Wei | Nanoscale tunable reduction of graphene oxide for graphene electronics[END_REF][START_REF] Wu | Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics[END_REF][START_REF] Mattevi | Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films[END_REF][START_REF] Yan | Structural and electronic properties of oxidized graphene[END_REF][START_REF] Yan | Oxidation functional groups on graphene: structural and electronic properties[END_REF], mechanical [START_REF] Medhekar | Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties[END_REF], and optical [START_REF] Loh | Graphene oxide as a chemically tunable platform for optical applications[END_REF] properties. Graphene oxide (GO) in itself is a material of great interest for its potential applications in nano-electronics [START_REF] Wei | Nanoscale tunable reduction of graphene oxide for graphene electronics[END_REF][START_REF] Wu | Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics[END_REF][START_REF] Eda | Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material[END_REF], nanoelectromechanical systems [START_REF] Medhekar | Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties[END_REF][START_REF] Robinson | Wafer-scale reduced graphene oxide films for nanomechanical devices[END_REF], sensors [START_REF] Robinson | Reduced graphene oxide molecular sensors[END_REF], polymer composites [START_REF] Potts | Graphene-based polymer nanocomposites[END_REF][START_REF] Putz | Highnanofiller-content graphene oxide-polymer nanocomposites via vacuum-assisted selfassembly[END_REF][START_REF] Dreyer | Graphite oxide as a dehydrative polymerization catalyst: a one-step synthesis of carbon-reinforced poly(phenylene methylene) composites[END_REF], catalysis [START_REF] Dreyer | Carbocatalysis: heterogeneous carbons finding utility in synthetic chemistry[END_REF][START_REF] Dreyer | Graphene oxide: a convenient carbocatalyst for facilitating oxidation and hydration reactions[END_REF][START_REF] Jia | Graphite oxide as an auto-tandem oxidation-hydration-aldol coupling catalyst[END_REF], energy storage devices [START_REF] Gao | Direct laser writing of micro-supercapacitors on hydrated graphite oxide films[END_REF][START_REF] Wang | Ternary self-assembly of ordered metal oxide-graphene nanocomposites for electrochemical energy storage[END_REF][START_REF] Kim | High-performance supercapacitors based on poly(ionic liquid)modified graphene electrodes[END_REF], and optics [START_REF] Loh | Graphene oxide as a chemically tunable platform for optical applications[END_REF]. Graphene does not have a native oxide and harsh chemical treatments are necessary to produce multilayer graphene oxide films [START_REF] Wu | Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics[END_REF][START_REF] Eda | Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material[END_REF][START_REF] Dikin | Preparation and characterization of graphene oxide paper[END_REF][START_REF] Dreyer | From conception to realization: an historial account of graphene and some perspectives for its future[END_REF]. Understanding the chemical transformations occurring in GO in response to external stimuli such as temperature and light remains a challenge [START_REF] Dreyer | The chemistry of graphene oxide[END_REF][START_REF] Gao | New insights into the structure and reduction of graphite oxide[END_REF][START_REF] Acik | The role of intercalated water in multilayered graphene oxide[END_REF][START_REF] Rourke | The real graphene oxide revealed: stripping the oxidative debris from the graphene-like sheets[END_REF][START_REF] Ekiz | Reversible electrical reduction and oxidation of graphene oxide[END_REF].

Theoretical studies so far have focused primarily on single-layer GO sheets [START_REF] Yan | Structural and electronic properties of oxidized graphene[END_REF][START_REF] Yan | Oxidation functional groups on graphene: structural and electronic properties[END_REF][START_REF] Bagri | Structural evolution during the reduction of chemically derived graphene oxide[END_REF][START_REF] Wang | Stability of graphene oxide phases from first-principles calculations[END_REF],

neglecting multilayer GO films.

The traditional route to produce GO films involves several steps: oxidation of graphite via the Hummers method, exfoliation of graphite oxide, dissolution of GO layers in aqueous solution, and deposition of these layers onto a surface from the aqueous dispersion of GO [START_REF] Eda | Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material[END_REF][START_REF] Dikin | Preparation and characterization of graphene oxide paper[END_REF]. Here, GO films are obtained by oxidation via the Hummers method of ultra-thin graphene films epitaxially grown on SiC [START_REF] Wei | Nanoscale tunable reduction of graphene oxide for graphene electronics[END_REF][START_REF] Wu | Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics[END_REF]. This method differs from the traditional approach because it does not require the exfoliation/dissolution of the GO layers in aqueous solution and the filtration/deposition on a substrate. A variety of experiments indicate that GO grown by oxidizing graphene films via the Hummers method presents properties equivalent to those of GO obtained by using the traditional approach, with improved film homogeneity and uniformity over extended areas [START_REF] Wei | Nanoscale tunable reduction of graphene oxide for graphene electronics[END_REF][START_REF] Wu | Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics[END_REF] (see Methods and Supplementary Information, Figs. S1-S4).

Here, we report on a combined experimental and density functional theory study of the structural and chemical stability of multilayer GO films. We show that at room temperature multilayer GO is a metastable material undergoing spontaneous chemical modifications and reduction with a relaxation time of ∼35 days. The self-limiting processes lead multilayer GO toward a longer-living quasi-equilibrium state, in which GO exhibits a structure deprived of epoxide groups and enriched of hydroxyl groups, with a final reduced O/C ratio of 0.38. DFT calculations also show that these structural and chemical changes are driven by the availability of H species in the oxidized graphitic sheets.

The excess H species contained in freshly prepared GO films are progressively consumed via reaction firstly with epoxide groups and secondly with hydroxyl groups to form water molecules which can be realesed. The overall structural and chemical evolution of the metastable GO films is shown to be controlled by diffusion processes.

Multilayer graphene oxide is here synthesized via the Hummers method [START_REF] Jr | Preparation of graphitic oxide[END_REF], by oxidation of graphene films grown epitaxially on the C-terminated surface of a SiC wafer [START_REF] Berger | Ultrathin expitaxial graphite: 2d electron gas properties and a route toward graphene-based nanoelectronics[END_REF] (for more details see the Methods part). X-ray photo-emission spectroscopy (XPS) is used to monitor changes of the structural and chemical composition of these GO films with aging time, defined as the time elapsed after oxidation of graphene films. Figure 1a shows a sequence of three C 1s core-level XPS spectra acquired at room temperature from a GO film 1, 40, and 70 days after its synthesis. In between the XPS measurements, the GO films are stored in controlled conditions (T=26±1 • C, dark environment, and relative humidity of 30±10%). More C 1s spectra acquired from different regions of the same sample and obtained from different GO films are reported in the Supplementary Information (Fig. S3); all curves display the same features and temporal evolution. In particular, they show that the GO films undergo significant chemical changes and spontaneous reduction uniformly across the surface. In this study, C 1s and O 1s core-level spectra are fitted with Gaussian-Lorentzian waveforms after performing a Shirley background subtraction. The C 1s spectra acquired from the GO films are fitted with three peaks. In accordance with previous XPS studies of GO flakes [START_REF] Mattevi | Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films[END_REF][START_REF] Yang | Chemical analysis of graphene oxide films after heat and chemical treatments by x-ray photoelectron and micro-raman spectroscopy[END_REF], we assign the first peak occurring at ∼284.7

eV to C-C, C-H and C vacancies [START_REF] Larciprete | Dual path mechanism in the thermal reduction of graphene oxide[END_REF]; the second peak at ∼286.7 eV is assigned to C-OH (hydroxyl) and C-O-C (epoxide) groups; and the third peak at ∼288.3 eV is assigned to C=O (carbonyl) species. The C=O peak in the various C 1s XPS spectra appears to be much smaller than the other two peaks (see Fig. 1a and Supplementary Fig. S3), indicating that carbonyl groups are present in limited number in these GO films. We also remark that differently from previous XPS spectra of GO flakes, the GO films prepared by oxidation of epitaxial graphene do not present carboxyl peaks, indicating that the GO films used in our study lack edges and holes, as also observed in the AFM and optical images reported in the Supplementary Information.

The C 1s XPS spectra of aging GO films show distinctively the increase of the C-C peak, whose area divided by the total C 1s spectral area will be denoted hereafter as P G , and the concurrent decrease of the hydroxyl/epoxide peak, whose area divided by the total C 1s spectral area will be designated as P GO . Figure 1b depicts the P GO /P G ratio obtained from XPS spectra of a GO film versus the time elapsed after GO synthesis. The same Figure 1b reports also the time evolution of the oxygen to carbon ratio, P oxygen , in the GO film. P oxygen is estimated from the O 1s/C 1s intensity ratio, corrected by a Scofield relative sensitivity factor of 2.93 (see Supplementary Fig. S4 for the O 1s spectra). Overall, these experimental data indicate that at room temperature GO undergoes significant chemical and structural changes after the sample preparation. The oxygen content and P GO /P G ratio decrease with time and stabilize after about 40 and 70 days, respectively. As shown in Fig. 1b, both P oxygen and P GO /P G are well-fitted by an exponentially decaying function. The fit parameters show that P oxygen starts out with a value of about 0.44, decays with a time constant of 20 days, and attains a steady state value of 0.38. In the case of P GO /P G , the corresponding quantities are 1.79, 35 days, and 0.67, respectively. In Fig. 1c, the table reports the values of P oxygen and P GO /P G obtained from XPS measurements of three different GO films prepared in similar conditions, at different stages of aging. One of these samples is about a year old. For this aged sample, we obtain values of P oxygen and P GO /P G equal to 0.37 and 0.64, in good agreement with the steady state values derived from the fitting analysis of Fig. 1b. This result corroborates the picture that the spontaneous structural and chemical modifications occurring in GO drive this material toward a longer-living quasi-equilibrium state. We remark that kinetics parameters deduced from a recent study [START_REF] Jung | Reduction kinetics of graphene oxide determined by electrical transport measurements and temperature programmed desorption[END_REF] of the thermal reduction process of GO flakes in solution cannot explain the here observed spontaneous changes of GO films at room temperature, indicating that we are observing a very distinctive mechanism.

To interpret our experimental results and, at the same time, gain atomistic insight, we have performed DFT calculations. To model multilayer GO, we disregard surface and interface effects, and we use periodic atomistic structures of bulk GO to represent the interior of the GO films. To generate the model structures of bulk GO, we consider an orthorhombic supercell of graphite consisting of 4 graphitic layers and 5×6 graphene unit cells per layer, and including a pseudo-random distribution of O, OH, H, and H 2 O species near and between the graphitic layers. The geometry of both the ions and the periodic cell are then optimized via a ∼4-ps long Car-Parrinello molecular dynamics simulation [START_REF] Giannozzi | Quantum espresso: a modular and open-source software project for quantum simulations of materials[END_REF]. To relieve the large stress and unfavorable ionic configurations present in the outset structure, the zero-pressure variable-cell molecular dynamics simulations are carried out by damping very gently both electronic and cell degrees of freedom. Similarly to the harsh treatments needed to produce GO films, we use this strategy to generate several realistic model structures of GO at 0 atm and 0 K with a O/C ratio of either 0.44 or 0.38, and a H/C ratio ranging between 0.1 and 0.24. In particular, for a fixed O/C ratio, we generate between 2 and 4 atomistic models including different relative amounts of epoxide, hydroxyl, chemisorbed hydrogen, and water molecules. The atomistic models include between 370 and 394 atoms.

The model structures of bulk GO generated from DFT exhibit the expected layered structure of an epitaxial film. Interlayer distances depend on both the composition and the amount of water molecules intercalated between the graphitic layers [START_REF] Medhekar | Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties[END_REF]. Due to the large number of chemisorbed species, the graphitic sheets exhibit significant out-ofplane distortions. Notwithstanding, the planar dimensions of the graphitic sheets increase by less than 1% with respect to those of ideal graphene. In addition to epoxide and hydroxyl groups, the model structures show that the oxidized graphene sheets in GO can accommodate both chemisorbed H and, in limited number, carbonyl groups. The atomistic models of GO show that epoxide, hydroxyl, and hydrogen species chemisorbed on the graphitic layers form together with the intercalated H 2 O molecules a complex hydrogen bond network (Fig. 2 and Supplementary Fig. S8).

To interpret the XPS measurements, we use DFT to calculate the C 1s XPS spectra of selected model structures of bulk GO. Individual core-level shifts are calculated by carrying out total-energy DFT calculations of the full model structure in which the pseudopotential for the selected C atom is replaced with one that simulates the presence of a screened 1s hole in the core [START_REF] Pehlke | Evidence for site-sensitive screening of core holes at the si and ge(001) surface[END_REF][START_REF] Haerle | sp 2 /sp 3 hybridization ratio in amorphous carbon from C 1s core-level shifts: X-ray photoelectron spectroscopy and first-principles calculation[END_REF]. The computed energy shifts account for the vertical photoexcitation transition and include core-hole relaxation effects [START_REF] Pehlke | Evidence for site-sensitive screening of core holes at the si and ge(001) surface[END_REF][START_REF] Haerle | sp 2 /sp 3 hybridization ratio in amorphous carbon from C 1s core-level shifts: X-ray photoelectron spectroscopy and first-principles calculation[END_REF]. The final spectra are obtained by broadening the individual core-level shifts with a Gaussian function of width 0.5 eV. Absolute binding energies cannot be determined with this approach. Therefore, calculated XPS spectra are compared individually to the experimental ones, and rigidly translated along the energy axis to obtain the best match. Figures 3a and3b show the experimental XPS spectra of a GO film acquired after an aging time of 1 day and 40 days, respectively, and with a corresponding P oxygen = 0.44 (Fig. 3a), and P oxygen = 0.38 (Fig. 3b). The same Figures show the calculated XPS spectra (filled circles) obtained from DFT by considering model structures of GO with O/C ratios of 0.44 (Fig. 3a) and 0.38 (Fig. 3b), respectively, and well-defined structural and chemical features (Fig. S8). In particular, the striking agreement between computed and experimental spectra is obtained by considering model structures of GO with a negligible amount of H 2 O molecules (1-2% of the total O-content) and carbonyl groups, and a well-defined relative amount of epoxide and hydroxyl species. At fixed C:O:H composition, our DFT calculations indeed show that increasing the amount of intercalated H 2 O molecules in multilayer GO leads inevitably to a loss of O species chemisorbed on the graphitic layers and, regardless of the relative amount of epoxide and hydroxyl groups, to deteriorating the agreement between experiments and theory, confirming the presence of a small amount of intercalated water in the GO films obtained by Hummers oxidation of epitaxial graphene films pre-grown on SiC.

For a more quantitative analysis of our data, we use the experimentally measured values of P G , P GO , and P oxygen to estimate the concentrations of epoxide and hydroxyl groups in multilayer GO. To this end, we assume that, consistently with the DFT results, the amount of intercalated water (or oxygen) molecules in GO is small and hence that the O 1s XPS spectrum results only from epoxide, hydroxyl, and carbonyl groups. By further considering only first next-neighbor effects on C 1s core-level shifts, we can write that:

P GO ∼ = 2P epoxide + P hydroxyl + P carbonyl (1)
P oxygen ∼ = P epoxide + P hydroxyl + P carbonyl ,

where P epoxide , P hydroxyl , and P carbonyl are the fractions of epoxide, hydroxyl, and carbonyl groups relative to the total number of carbon atoms in GO. By using P G , P GO , and P oxygen obtained from fitting the experimental XPS spectra, and by taking P carbonyl equal to the ratio of the spectral area of the peak at 288.3 eV (assigned to C=O species) and the total C 1s XPS area, Eqs. ( 1) and ( 2) can be solved to estimate P epoxide and P hydroxyl . The results of this analysis for GO films at various stages of aging are shown in Fig. 3c and in the Supplementary Information.

The physical reasonableness of the results and assumptions of the analysis shown in 2) and reported in Fig. 3c. Atomistic models including either a significant amount of intercalated water molecules or different relative number of epoxide and hydroxyl groups worsen considerably the agreement between experimental and DFT spectra. Therefore, although we expect deviations in P epoxide and P hydroxyl obtained from Eqs. ( 1) and ( 2) and the experimental XPS spectra due to the uncertainty in the actual content of hydrogen and water in GO, our study unambiguously shows that multilayer GO films aging at room temperature undergo significant chemical changes. In particular, we find that the fraction of epoxide groups of about 0.23 present in 1-day old films drops to 0.08 in aged (96 days old) films, while the fraction of hydroxyl groups increases from about 0.20 to 0.25. On the basis of DFT calculations, the fraction of water molecules intercalated between the graphitic layers remains at all aging stages negligible, smaller than 3% wt. and 7% wt. in freshly synthesized and aged GO films, respectively.

Infrared spectroscopy measurements (see Supplementary Information, Figs. S5-S6, and

Ref. [START_REF] Galande | Quasi molecular fluorescence from graphene oxide[END_REF]) highlight the presence in GO of C-H species, desorbing at mild temperatures (≤60 • C). These species may be at the origin of the room-temperature metastable character of GO. To gain more insight into the room-temperature chemical changes of multilayer GO, we carry out additional DFT calculations (Fig. 4). In particular, we compute the chemisorption energy and diffusion energy barrier of individual H, O, and OH species on a single graphene sheet, as well as the activation energy of the reactions {C-H}+{C-O-C}→{C-OH}+{C-C} and {C-H}+{C-OH}→{C-C}+H 2 O, involving species chemisorbed on the graphene sheet and leading to the formation of a physisorbed water molecule. Our DFT calculations show that in presence of chemisorbed H species on graphene, epoxide groups are energetically more costly than hydroxyl groups, which in turn are energetically unfavored with respect to free water (Fig. 4). The DFT calculations also show that both epoxide and hydroxyl groups react readily with the C-H species and that the kinetics of this two-step H-mediated reduction mechanism is controlled entirely by diffusion phenomena. In particular, we find reaction activation energies ≤0.15 eV and energy barriers of 0.55 eV, 0.81 eV, and 0.35 eV for the diffusion of a chemisorbed H, epoxide, and hydroxyl groups, respectively. These results indicate that epoxides are the slowest diffusing species and, although at high temperature their diffusion and encounter can lead to the formation of either carbonyl groups or free O 2 [START_REF] Bagri | Structural evolution during the reduction of chemically derived graphene oxide[END_REF][START_REF] Larciprete | Dual path mechanism in the thermal reduction of graphene oxide[END_REF], at room temperature the reaction of the more rapidly diffusing C-H species with epoxide groups is more likely.

Epoxide rings are strained and more reactive than hydroxyl groups, and the availability of H in freshly synthesized GO films ought to trigger epoxide disruption, strain relief, and the sequential formation of hydroxyl and water species. Our DFT calculations show that these processes may indeed be the mechanisms responsible for the observed structural and chemical changes of GO. According to this picture, the quasi-equilibrium state of GO is attained after consumption of the excess C-H species present in the freshly synthesized films, by means of the following two processes: firstly, reduction of epoxide and hydroxyl groups and subsequent formation and release of water molecules (within about 40 days as indicated by P oxygen in Fig 1b), and secondly, further reduction of epoxide groups and increase of hydroxyl species (between 40 and 100 days as shown in Fig. 3c).

In summary, in this combined experimental and DFT study we show that multilayer graphene oxide obtained by oxidation via the Hummers method of graphene films grown epitaxially on silicon carbide is structurally and chemically metastable at room temperature. In particular, multilayer GO films undergo spontaneous modifications and reduction with a relaxation time of ∼35 days. These self-limiting processes lead multilayer GO toward a longer-living quasi-equilibrium state, in which GO exhibits a structure deprived of epoxide groups, whereas it remains rich in hydroxyl groups, with a final reduced O/C ratio of 0.38. The presence C-H species in GO is found to favor the reduction of epoxides and less extensively hydroxyl groups, and the formation and release of intercalated water molecules. This study provides fundamental understanding of the structural and chemical stability of multilayer graphene oxide. This new understanding will be crucial for the use of this material in industrial applications. Furthermore, this study suggests that a possible route to control structure, chemistry, and properties of GO would be to gauge the hydrogen content in GO, as well as performing the thermal or chemical reduction process after the quasi-equilibrium is attained.

Methods

Sample Preparation.

Graphene films are epitaxially grown on the C-surface of a SiC wafer and the details are reported elsewhere [START_REF] Berger | Ultrathin expitaxial graphite: 2d electron gas properties and a route toward graphene-based nanoelectronics[END_REF]. The Hummers method [START_REF] Jr | Preparation of graphitic oxide[END_REF] is employed for the oxidation of the epitaxial graphene films. First, epitaxial graphene on SiC chips are dipped into a The thickness of the as formed multilayer GO films is deduced by the number of graphene layers present prior to the oxidation process and estimated by ellipsometry experiments.

The properties of GO films grown with this procedure are investigated by means of optical imaging, atomic force microscopy, and Raman spectroscopy (see Figs. S1 andS2). Kelvin gradient approximation parametrization for the exchange-correlation energy functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. Variable-cell Car-Parrinello molecular dynamics simulations [START_REF] Giannozzi | Quantum espresso: a modular and open-source software project for quantum simulations of materials[END_REF] are carried out to optimize the geometry of the ion positions and cell parameters of periodic structures of GO. Total-energy DFT calculations are performed to calculate C 1 core-level energy shifts [START_REF] Pehlke | Evidence for site-sensitive screening of core holes at the si and ge(001) surface[END_REF][START_REF] Haerle | sp 2 /sp 3 hybridization ratio in amorphous carbon from C 1s core-level shifts: X-ray photoelectron spectroscopy and first-principles calculation[END_REF]. Norm-conserving Troullier-Martins pseudopotentials are generated with the fhi98PP package [START_REF] Fuchs | Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory[END_REF]. This computation scheme reproduces excellently the structure, bond energies, and C 1s core-level energy shifts of small H, C, and O containing molecules.

Structure and electronic properties of graphene, diamond, and graphite are also reproduced at the expected level of accuracy [START_REF] Hasegawa | Energetics of interlayer binding in graphite: the semiempirical approach revisited[END_REF].

Fig. 3c is

  Fig. 3c is corroborated through the use of DFT calculations. Specifically, the model structures of GO yielding optimal agreement with the experiments as shown in Figs. 3a and 3b include fractions (relative to the amount of C) of epoxide, hydroxyl, intercalated water, chemisorbed hydrogen, and carbonyl groups equal to 0.246, 0.179, 0.004, 0.012, and 0.012, respectively, in the case of a film with O/C ratio (i.e. P oxygen ) of 0.44, and equal to 0.125, 0.235, 0, 0, and 0.016, respectively, in the case of a O/C ratio of 0.38. These values are in excellent agreement with those obtained from Eqs. (1) and (2) and reported

H 2 SO 4 /

 24 NaNO 3 solution placed in an iced water bath. Second, KMnO 4 is added to the solution. The mixture is then transferred to a 35 o C water bath for about 20 minutes. Deionized (DI) water (23 ml) is added slowly to the mixture. Finally, after 15 minutes, warm DI water (70 ml) and H 2 O 2 (1.5 ml) are added to terminate the reaction. The sample is then bought in air, rinsed with DI water, and dried in high purity nitrogen gas.

Figure 1 :

 1 Figure 1: Room temperature experimental XPS spectra of aged GO films. a, XPS C 1s spectra of a multilayer GO film at increasing aging times at room temperature: 1 (top), 40 (middle), and 70 (bottom) days after GO film synthesis. The spectra are fitted with three Gaussian-Lorentzian peaks. The P G (blue solid line) peaks is assigned to C-C bonds, and to a small fraction of possible C-H bonds and C vacancies; the P GO peak (orange solid line) is assigned to C species bound in epoxide and hydroxyl groups; the third peak (green solid line) is assigned to carbonyl species. b, P GO /P G in multilayer GO as a function of aging time (black circles), and corresponding oxygen content in the same sample (red triangles). Symbols show experimental values and statistical errors are derived by analyzing XPS spectra acquired from different regions of a given GO sample (see SI). The black and red solid lines show the fits with an exponential decaying function. c, Table reporting oxygen content and structural changes with time in three different GO films prepared in similar conditions.

Figure 2 :Figure 3 :

 23 Figure 2: Atomistic structures of multilayered GO generated from DFT. Left panel, ball-and-stick illustration of a model structure of GO showing the layered geometry and the complexity of the bonding network on the oxidized carbon basal planes. Right panel, a selected region of the model structure showing the predominant chemical species present in GO films obtained from graphene on SiC; clockwise from top and indicated by the coloured arrows: a hydrogen atom chemisorbed on the basal plane, an epoxide group, an intercalated water molecule, and a hydroxyl species. Gray, red, and white colours are used to represent C, O, and H atoms, respectively. The illustrations show regions of a 390-atom periodic model structure of GO presenting interlayer distances of about 4.22 Å and average intra-layer perpendicular buckling of 0.27 Å.

  Computational strategies for model structure generation and inverse problem solution have been inherited from Refs.[START_REF] Bongiorno | Oxygen diffusion through the disordered oxide network during silicon oxidation[END_REF][START_REF] Bongiorno | Transition structure at the Si(100)-SiO 2 interface[END_REF].

	∆t = 1 day					2.0			0.44
			P GO	P G		1.6			0.42
	∆t = 40 days			G GO / P P	1.2			0.38 0.40	P oxygen
	Intensity (arb.)					0.8	0	20	40 ∆t (days) 60	80	100	0.34 0.36
	∆t = 70 days
						Table 1		GO A	GO B	GO C
					∆t (days)	1	96	9	75	370
						P oxygen 0.44 0.38 0.46 0.41 0.37
	290	288	286	284	282	P GO / P G 1.79 0.76 1.26 0.86 0.64
		Binding Energy (eV)

Acknowledgements. S.K., S.Z., A.B., and E.R. acknowledge the support of the National Science Foundation (CMMI-1100290 and DMR-0820382). Y.H., C.B., and W.H. acknowledge the support of NSF grant DMR-0820382. E.R. acknowledges the support of the NSF grant DMR-0706031 and the Office of Basic Energy Sciences of the U.S. Department of Energy (DE-FG02-06ER46293). Y.J.C. and M.A. acknowledge the support of the Office of Basic Sciences of the U.S. Department of Energy (DE-SC001951). We thank D. Wang, P. Sheehan, and A. R. Laracuente of the U.S. Naval Research Laboratory for the 4-point electrical transport measurements.

probe force microscopy and UHV 4-point transport measurements are used for electrical characterization of the GO films (see Figs. S1 andS2). In general sheet resistances in the range 1-20 GΩ are measured. The data reported here are from three different GO samples, and the number of layers, L, of these samples is as follows: L = 11 for the GO film, called GO A , in Figs. 1a, 1b, 1c, 3, S3a, and S4; L = N/A for GO B in the table of Fig. 1c, and Supplementary Fig. S3b; and L = 11 for GO C in the table of Fig. 1c, and Supplementary Fig. S3c.

Analytical Measurements.

X-ray Photoelectron Spectroscopy measurements are carried out using a commercial Thermo Scientific K-Alpha XPS system with a focused-beam monochromated Al K-alpha source giving an incident X-ray photon energy of 1486.7 eV. The X-ray spot size is ∼40 µm. We use a 180 • double focusing hemispherical analyzer with a 50 eV pass energy. The scans are performed with a step size of 0.1 eV and a dwell time of 50 ms/step. We employ the software XPSPEAK41 for the spectral data analysis. After a Shirley background subtraction and correction for the different X-ray cross-sections using Scofield sensitivity factors, the C 1s spectra are fitted with three Gaussian-Lorentzian peaks with the constrain of equal Gaussian-Lorentzian pre-factors. The three peaks are named in the text as P G , P GO , and P carbonyl . The fits obtained by constraining the full-widths at half-maxima (FWHM) of the three peaks to be equal and the fits obtained by leaving these parameters as free, give results which are the same within the error bar presented in Figs. 1b and3c, and Table S1. These errors arise from variations in the XPS spectra when acquired from different regions of a given GO sample. We usually acquire XPS spectra from 2 to 5 regions, every single spectrum is shown in Fig. S3. The Doniach-Sunjic asymmetry coefficient is set to zero because the material investigated here, multilayer graphene oxide, is nonmetallic.

Infrared spectroscopy measurements and corresponding results are presented in the Supplementary Information.

Computational methods.

DFT calculations are performed by using the CP code of the QUANTUM-Expresso package [START_REF] Giannozzi | Quantum espresso: a modular and open-source software project for quantum simulations of materials[END_REF]. Periodic Γ-point DFT calculations are carried out by using an energy cutoff of 65 Ry for the plane wave basis set, norm-conserving pseudopotentials [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations[END_REF]

Correspondence.

Correspondence and requests pertaining to experiments and computations should be addressed respectively to E.R. (email: elisa.riedo@physics.gatech.edu) and A.B. (email: angelo.bongiorno@chemistry.gatech.edu).