Nano-Scale Corrugations in Graphene: A Density Functional TheoryStudy of Structure, Electronic Properties and HydrogenationAntonio Rossi,†,‡ Simone Piccinin,§,∥ Vittorio Pellegrini,‡,⊥ Stefano de Gironcoli,∥,§

and Valentina Tozzini*,⊥,#

†Dipartimento di Fisica ‘E. Fermi’, Universita di Pisa Largo B. Pontecorvo 3-56127 Pisa, Italy‡Graphene Laboratories, IIT Istituto Italiano di Tecnologia, Via Morego, 30 16163 Genova, Italy§CNR-IOM DEMOCRITOS c/o SISSA, Via Bonomea 265, 34136 Trieste, Italy∥SISSA, Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy⊥Istituto Nanoscienze, CNR, Piazza San Silvestro 12, 56127 Pisa, Italy#NEST-Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy

*S Supporting Information

ABSTRACT: Graphene rippled at the nanoscale level isgathering attention for advanced applications, especially in thefield of nanoelectronics and hydrogen storage. Convexityenhanced reactivity toward H was demonstrated on naturallycorrugated graphene grown by Si evaporation on SiC, whichmakes this system a platform for fundamental studies on theeffects of rippling. In this work, we report a density functionaltheory study on a model system specifically designed to mimicgraphene on SiC. We first study the supercell geometry andconfiguration that better reproduce the corrugated monolayer.The relatively low computational cost of this model system allowsa systematic study of the dependence of stability, structure, andelectronic properties of graphene subject to different levels ofstretching and corrugation. The most representative structure isthen progressively hydrogenated, imitating the exposure to atomic hydrogen, and stability, structural and electronic properties areevaluated as a function of hydrogenation. Our results quantitatively reproduce the measured evolution of electronic properties asa function of hydrogenation, offering the possibility of evaluating the coverage by means of STS measurements. The dependenceof hydrogen binding energy on coverage extends our previous results on reactivity of corrugated graphene, including the effect ofH clustering. This work reports quantitative results directly comparable with experimental measurements performed on epitaxialgraphene on SiC and reveals the quantitative interplay between local structure, electronic properties and reactivity to hydrogen,which could be used to design devices for flexible nanoelectronics and for H storage.

1. INTRODUCTIONThe interaction between hydrogen and graphene has recentlyreceived much attention, due to its potential interest fordifferent technological applications. While graphene is a highmobility conductor,1 its alkane counterpart, graphane,2

obtained covalently bonding one hydrogen atom to eachcarbon site, is a wide band gap insulator.3 Partially hydro-genated graphene displays intermediate properties:4 strippedgraphane/graphene hybrids are semiconductors with tunableband gaps;5−9 different hydrogen decorations, such as graphaneislands,10 have potentially interesting transport properties andpossible applications in nanoelectronics. Clearly, exploitingthese properties requires a control of the hydrogenation at thenanoscale.Graphene hydrogen interaction is clearly also interesting for

H storage applications. Because of its low molecular weight,graphene is potentially a storage mean with high gravimetric

capacity.11 However, molecular hydrogen is very weaklyphysisorbed by means of van der Waals interactions,12 andalthough these are stronger in nanostructured13,14 or multi-layered graphene,15 low temperatures are necessary for stablestorage.16,17 Chemisorption was alternatively considered: thecovalent bond of hydrogen to graphene is robust, leading tostable storage up to high temperature. But chemi(de)sorptionof H2 are high barrier processes (∼1−1.5 eV/atom18) implyingslow loading/release kinetics. Chemical (e.g., with Pd19) or“alternative” catalysis (e.g., electric fields20 or N-substitutionaldoping21) were also suggested.We recently proposed that the two-dimensionality and

structural/mechanical properties of graphene could be also

Received: November 14, 2014Revised: March 18, 2015Published: March 18, 2015

Article

pubs.acs.org/JPCC

© 2015 American Chemical Society 7900 DOI: 10.1021/jp511409bJ. Phys. Chem. C 2015, 119, 7900−7910

exploited to control chemisorption: the local curvatureenhances carbon reactivity,22 specifically to hydrogen,23 dueto the “pyramidalization” of the carbon sites on convexities, andconsequent extrusion of an unpaired sp3-like orbitals. Thissuggests the possibility of (de)hydrogenating graphene bycontrolling the local curvature. The proof of this concept wasgiven in ref 24, where the dependence of hydrogen bindingenergy on local curvature was quantified, and its preferentialbinding on convex sites and spontaneous release by curvatureinversion demonstrated by means of density functional theory(DFT) calculations and Car−Parrinello (CP) simulations. Thisstudy also suggested the possibility of using this effect as thebasis for a hydrogen storage device. Curvature control was alsoproposed to create specific hydrogen decorations for nano-electronic devices.25,26 The effect was experimentally confirmedon the naturally corrugated graphene monolayer grown by Sievaporation from 6H-SiC(0001).27

A number of computational studies, mainly DFT-based, haveaddressed hydrogen chemisorption and clustering on flatgraphene,28−31 while the effect of curvature was considered infullerenes32 and nanotubes33 and in tightly and artificiallyrippled graphene.24,22 Naturally rippled graphene grown by Sievaporation on SiC is a natural platform to experimentallystudy the effects of curvature on the physico-chemicalproperties of graphene. On SiC, however, graphene curvaturefollows a moire pattern with a specific supercell periodicity dueto the mismatch with the substrate lattice parameters. Anotherset of DFT studies analyzes specific aspects of the structuraland electronic properties of this system, either including theexact34 or approximate35 supercell periodicity, portion of thesubstrate,36,37 intercalants,38 or dopants.39 Though the interplaybetween curvature and hydrogen adhesion is proven, the routetoward its exploitation requires further, more specific andquantitative investigations.This study addresses the interplay between curvature,

electronic properties, and hydrogen binding on curved

graphene, on a model system optimized for reproducing thefeatures of graphene on SiC. The specific aim is to provide anaccurate, yet the simplest possible, computational representa-tion of the real system, for direct comparison with experimentand interpretation of measurements. In addition, the relativesimplicity of the model allows extensive and systematiccalculations. Models with different levels of curvature areevaluated, and their structural and electronic propertiesinvestigated. Subsequently, those better corresponding to theexperimental ones are selected and hydrogenated in stages,mimicking the process occurring upon exposure to hydrogen.Increasingly hydrogenated systems are analyzed, and theirstructural and electronic properties related to H-coverage. Afterthe discussion of results, conclusions and future developmentsare illustrated, with focus on the applications in hydrogenstorage and nanoelectronics, respectively.

2. MODELS AND METHODS

2.1. Model Systems. Si evaporation from the (0001) faceof SiC produces first a honeycomb carbon lattice, covalentlybonded to the substrate. If the process is prolonged, the firstcompletely detached sheet (“free standing”,27 or monolayer) isproduced, which displays the graphene electronic properties. Asa consequence of the small mismatch between SiC andgraphene parameter lattices, the monolayer displays a moire pattern of corrugation, whose exact periodicity is 6√3 ×6√3R30 referred to SiC, or 13 × 13 referred to graphene40

(red boundaries in Figure 1(a,c)). The periodicity of ripplingcan also be approximately described by a 6 × 6 supercell(referred to SiC, or 4√3 × 4√3R30, if referred to graphene,green boundaries in Figure 1a,c); thus, both supercells areconsidered in this study. Smaller supercells (specifically thestandard unit cell, the minimal rotated by 30 deg, √3 ×√3R30, and an intermediate one, the 3√3 × 3√3R30) areconsidered for comparison. All supercells and their Brillouin

Figure 1. (a) Supercells considered in this study (in colors), superimposed to the graphene lattice (in black). (b) Cell periodicity (with respect tographene and SiC lattice) and the number of atoms included (corresponding colors to part a). (c) Two supercells with the periodicity of the moire lattice (exact in red and approximate in green). In the background a representation of the corrugation is reported: light gray areas are protrudingareas. (d) Brillouin zones of the main cells (corresponding colors to part a). The main symmetry points of the unit and of the 6 × 6 cell are reportedin blue and green, respectively.

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zone (BZ) are reported in Figure 1, parts a, b, and d. It is to beobserved that the Dirac point (“blue” K in Figure 1d) isremapped in different special points upon BZ refolding whendifferent supercells are considered.The periodicity along z axis is set at 15.00 Å, thus the model

systems is a periodic multilayer with negligible intersheetinteraction. The sheets were increasingly rippled and stretchedby uniformly reducing or increasing the lateral cell size (by stepof 1%), and subsequently relaxing atomic position. For the 13 ×13 cell, the formation of ripples was guided by superimposedstarting small corrugations, as described in section 4. The localcurvature is measured by the average value of thepyramidalization pseudodihedral φ related to a single C site.41

Selected systems are then hydrogenated with a protocolemulating the kinetics of adsorption occurring upon exposureto low concentration atomic hydrogen,27 and in agreement withbinding energy enhancement with curvature:24 couples of Hatoms are added onto the sites with highest local curvature indimers or tetramers, on a single side of the sheet. The system isthen relaxed and the procedure repeated. The stability ofselected hydrogenated systems is then tested by means ofsimulated annealing with CP dynamics. Selected cases ofdouble side hydrogenations are also considered, for compar-ison.2.2. Density Functional Theory Calculations and

Simulations Setup. DFT calculations were performedexpanding the Kohn−Sham orbitals in plane waves and usingVanderbilt ultrasoft pseudopotentials42 with energy cutoff set at25 Ry (see Supporting Information, part S1 for convergencecheck). van der Waals (vdW) corrections were added,according to the scheme by Grimme.43 Perdew−Burke−Ernzerhof (PBE) exchange and correlation functional44 was

used for production calculations, but preliminary ones were alsoperformed in local density approximation (LDA)45 forcomparison (see Supporting Information, part S2.1). Forelectronic structure calculations the Brillouin zone was sampledwith Monkhorst−Pack grids with sufficiently dense sampling.46

For force and energy calculations, converge checks wereperformed in different compression conditions with respect tothe grid sampling (see Supporting Information, part S1, fordetails). After noting that cohesive energies changes less orabout 1%, we finally chose the Γ point scheme for structurecalculations. Gaussian smearing with 0.01 Ry spread was used.Local structural minima were searched using the Broyden−Fletcher−Goldfarb−Shanno algorithm,47 preceded by coordi-nated randomization in a few cases, and using standardconvergence criteria for electronic self-consistency (10−8 au)and forces (10−3 au).Molecular dynamics was performed within the CP48 scheme,

with the preconditioning scheme for the orbital mass,49 and atime step of 0.1205 fs. Equation integration was performed withVerlet algorithm, and a Nose thermostat50 is used to controlthe temperature. Annealing procedures are applied to selectedsystems. The temperature is increased by a combination ofcoordinate randomization and velocity rescaling. Calculationsand simulations are performed with Quantum Espresso(QE5.0.151). Inputs creation and postprocessing analysis wasperformed using in-house made software.

3. RESULTS

3.1. Structure and Stability of Rippled and StretchedGraphene. A model system with a few layers of SiC substrateand hydrogen includes ∼2000 atoms. While the simulations ofsuch a large model system is currently in progress for selected

Figure 2. (a) Coesive energies per C atom as a function of the strain, measured by the “effective” C−C bond length (i.e., the bond C−C bond lengthone would have if the graphene remained flat and regular): magenta, 3√3 × 3√3R30 cell; green, 4√3 × 4√3R30; red = 13 × 13. Filled dots = PBE+ vdW, empty dots = LDA + vdW, empty squares = LDA. (b and c) top and perspective view of the 2% contracted 4√3 × 4√3R30° supercell (3 ×3 repeated cells). In part b, the unit cell boundaries (in green) and the 13 × 13 cell boundaries (red) are superimposed. Structures colored accordingto the z coordinate: blue = protruding; red= intruding.

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cases on high performance computational facilities, here we areinterested in optimizing simpler model systems (withoutincluding explicitly the SiC substrate), equivalent in terms ofstructural and electronic properties of the graphene layers, to beused for extensive calculations. To this aim, the 13 × 13 and4√3 × 4√3R30 cells were considered, as they match (exactlyor approximately) the moire symmetry. These were laterallycompressed (stretched) in the range +(−)10% with respect totheir relaxed size. The same calculation was also performed onthe 3√3 × 3√3R30 cell, to obtain a rippling with a smallerwavelength and higher level of curvature.Two different functionals (LDA and PBE) with and without

vdW interactions were compared for the smaller supercells. Theenergies of optimized structures are reported in Table S3−S5 inthe Supporting Information and in Figure 2a, for the 4√3 ×4√3R30 (green dots), the 3√3 × 3√3R30 (magenta dots),and the 13 × 13 cells (red dots). The general behavior of theenergy as a function of the contraction/expansion (heremeasured in terms of CC distance of the flat structure inthe corresponding cell size) displays a minimum at zerocontraction (CC = 1.424 Å), with a harmonic-like behavioraround it (irregularities are discussed below). Figure 2a alsoshows that PBE (filled symbols) returns a value of the cohesiveenergy ∼1 eV smaller than the LDA (empty symbols) andnearer to the experimental one.52 vdW interactions bring littlechange in the cohesive energy (squares vs circles), howeverthey were included in all subsequent calculations because theyare likely to play a role in the interaction with hydrogen.24 For

the smaller cells, and for selected structures, convergencechecks on the cohesive energy and on the structure wasperformed with the respect to the increasing sampling of theBZ (see Supporting Information, section S1). A stabilization of∼0.6% is observed, with negligible changes in the structure,which justify the use of Γ point only to sample the BZ forstructure and forces calculations.We now comment on the structural/energetic features of

each kind of supercell. The 13 × 13 has the periodicity of thegraphene grown on SiC. The lattice parameter mismatchbetween SiC and graphene is such that the freestanding layer is∼0.1−0.2% contracted. We then first performed structurerelaxation on a 0.2% contracted cell, starting from differentconfigurations with randomly displaced atoms or with regulardisplacements with different periodicity (see SupportingInformation, part S2.4, for details). The final configurationsdisplay average out-of-plane C atoms displacements of ∼0.04 Å,which is approximately 1 order of magnitude smaller than theexperimental one measured for the first free-standing layer onSiC.27 In addition, none of the optimized structures is stabilizedin the correct symmetry of the moire pattern of graphene onSiC. Increasing the contraction level at ∼2% (Figure 2a, CC= 1.38 Å) an out of plane displacement of ∼1 Å is reached,which is similar to the experimental one, but the pattern ofdisplacement is still dissimilar. No improvement is obtained athigher contraction (∼10%). Our conclusion are (i) a simplecontraction of the 13 × 13 supercell cannot reproduce theexperimental corrugation, indicating that the substrate has a

Figure 3. Structural properties of stretched and compressed graphene of the 4√3 × 4√3R30 (a, c) and 3√3 × 3√3R30 (b, d) cell. The histogramsreport the CC distance distributions (a, b), and dihedral angle distribution (c,d) at the different cell compression/strain, from −10% to +10% ofthe relaxed cell size (for dihedrals, the distributions of strained structures are not reported, since they are flat). The insets report selected strained(one unit supercell) and contracted (3 × 3 supercells) structures (the level of strain/compression is indicated). In the strained structures the bondsare colored according to their length (shorter in red, longer in blue). In the contracted structures the colors represent the displacement in z direction(out of plane): blue = up; red= down. Dots and error bars in color (green = 4√3 × 4√3R30, magenta =3√3 × 3√3R30) report the mean of thedistribution and its variance.

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major role in determining the moire pattern and (ii) averageout of plane displacements corresponding to experimental onesare obtained with larger levels of compression with respect tothe real one, probably to compensate for the absence of theeffect of the highly corrugated buffer layer.In light of this, we considered the 4√3 × 4√3R30

supercells, whose symmetry corresponds approximately tothat of the ripples. For values of the contraction up to ∼5%, weobtain a pattern very similar to the experimental one (seeFigure 2, parts b and c, for 2% contraction and inset to Figure 3for 1%), consisting of hills (colored in blue) separated byinterconnected valleys (in red). Noticeably, this pattern is notsymmetric with respect to the plane: while this asymmetry isexpected in the experiment due to the substrate, it seems tospontaneously persist even without it. The inverted pattern(wells separated by interconnected ripples) also exists with thesame energy, in absence of the substrate. By an analysis of thecontracted supercells (see Supporting Information, part S2.3),it turns out that the experimental out of plane displacement isobtained for contraction of ∼2%. The larger value of thecontraction to reproduce the experimental corrugation isnecessary to compensate for the absence of the effect of thebuffer layer. We conclude that the 4√3 × 4√3R30 supercellwith ∼2% contraction is the optimal choice when one wants toreproduce the corrugated structure of a monolayer of grapheneon SiC without explicitly including the substrate.The cohesive energy minimum is achieved at a C−C distance

of 1.424 Å. The behavior, however, soon deviates fromharmonicity especially in the contraction region, wheredeviations appear around 2−3% and at 7−8% contraction.The analysis of the structural properties reveals interestingfeatures. We first consider the strained structures, which displaya simpler behavior. Upon stretching, the cell remains flat, butthe bond length distribution becomes bimodal. Bimodalitystarts around 5% in the case of 4√3 × 4√3R30 cell (Figure3a) and around 1−2% strain in the case of 3√3 × 3√3R30(Figure 3b) and is due to the formation of a pattern ofbenzene-like structures (hexagon with “small” bond lengths)separated by longer bonds (insets to Figure 3a,b). This“benzenization” is preceded, at intermediate stretching, bystates in which larger hexagons are separated by smaller bonds(6% stretching level in the 4√3 × 4√3R30 cell, inset of Figure3a). At 10% strain bonds break in the 3√3 × 3√3R30 andlarge vacancies form with no defined symmetry.In the contraction region, the structural analysis reveals

substantially different behavior comparing the 4√3 × 4√3R30

and 3√3 × 3√3R30 cells. This is somehow expected, since thedifferent cell size imposes a wavelength of ripples differing by25%. In the 4√3 × 4√3R30 cell (Figure 3a,c) the bondlengths contracts regularly up to −5%, and their distributionwidth increases. So does the φ dihedrals distributions,coherently with an increase of the average level of curvature.The inspection of structures (insets to Figure 3a, the completeseries reported in the Supporting Information, part S2.2)reveals the formation of “hills” of the expected symmetry, whichincrease in amplitude as the contraction increases. Around −5%however, a transition occurs: the form of the hills changes fromround to approximately triangular, with more net boundaries.Some of the sites tend to pyramidalize, as shown by theincreasing of two peaks at the positive and negative wings of theφ distribution. Correspondingly longer bonds appear, alsomoving the center of bond length distribution to larger values.Overall these features are the signature of the sp2 to sp3

transition.As an effect of the smaller periodicity, in the 3√3 ×

3√3R30 cell the transition features appear earlier (at 2−3%contraction) in the bond length and dihedrals distributions(Figure 3, parts b and d). There are additional differences: aninspection of the structures reveals at least four different ripplesgeometries explored by the system (insets of Figure 3b;Supporting Information, part S2.2, reports the whole series):ripples separated by wells at small contraction (up to −2%),linear wave-like ripples up to −6−7%, which then become wellsseparated by ripples (−8%), and then hills separated by valleys(−10%) passing again from a wavelike structure (−9%).Correspondingly the bond lengths and dihedral distributionsassume variegate shapes, depending on the contraction.The system clearly displays multistability, manifesting in the

change of ripples conformation and geometry. As alreadyobserved, multi stabilities are always present in the presence ofripples on isolated graphene, since the structures obtained byexchanging convexities with concavities are degenerate inenergy. Because these effects are less pronounced in the largercell, one can infer that they are generated by the interplaybetween periodicity and compression level. In fact, it isreasonable that, if convexities and concavities are spatiallyseparate enough (i.e., for ripples with long wavelength) and/orsmall in amplitude, the two degenerate structures can coexist.Otherwise they mix and tend to become unstable. In support ofthis picture, a recent work,53 shows that at given uniaxialcompression, the number of ripples formed increases as the sizeof the system increase. This indicates the existence of a critical

Figure 4. (a) Band gap as a function of the strain (positive values of the abscissa) and compression (negative values) for the 3√3 × 3√3R30(magenta) and 4√3 × 4√3R30 (green) cells. (b) Gap vs the squared root variance of the bond lengths for extended structures (same color code).(c) Squared root variance (bottom) and squared root of the average squared dihedrals (upper) vs the gap for contracted structures (same colorcode).

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periodicity, and a corresponding critical ripple wavelength,under which the system becomes unstable. A rough estimatefrom ref 52 would indicate a value between 1 and 2 nm at 5%uniaxial compression. In our systems compression is biaxial,thus it is reasonable that such instability could appear at smallerwavelength and/or lower compression levels. Indeed, what weobserve is that 4√3 × 4√3R30 cell (∼1.6 nm cell vector size)has a regular behavior with stable hills and valleys up to 5%,while in the 3√3 × 3√3R30 cell (∼1.2 cell vector size) thoseinstabilities already appear at 1−2% contraction. This indicatesa critical ripple wavelength between 1.1 and 1.5 nm for oursystems.In summary, the systematic analysis of graphene in the ±10%

deformation range reveals a “benzeinzation” transition in thestretching region and a “pyramidalization” transition in thecontraction region. The latter is preceded, at smallercontractions, by the formation of ripples with differentgeometries and amplitudes, which reveals instabilities as thecontraction increases and/or the wavelength (i.e., cell size)decrease, coherently with previous literature on the stability ofripples in graphene.53,54

3.2. Electronic Properties of Rippled and StretchedGraphene. The band structures of the optimized contracted/strained structures of the 4√3 × 4√3R30 and 3√3 ×3√3R30 cells were evaluated. The whole set of data is reportedin the Supporting Information (section S2.2) and the gapvalues as a function of the strain/contraction are plotted inFigure 4a. The plot shows an irregular behavior, which isrelated to the high variety of geometry and symmetries of thesystem.In the stretched structures of the 3√3 × 3√3R30 cell

(magenta dots), the gap is seen to increase quite regularly withthe strain, except for the 10% stretching, which correspond to ahighly defective one (with broken bonds). In the case of 4√3× 4√3R30 cell (green dots), it is null up to ∼5% and then itstarts increasing. An inspection of the global band structures(see Supporting Information) indicates that empty bands areelongated toward the higher energies and the filled ones towardthe lower energies, which produces an immediate gap openingfor the small cell; conversely, this happens later for the largerone. It is quite natural to relate the gap opening with the“benzenization” observed in the stretched structures, since thisproduces a symmetry breaking. Therefore, we plotted the gapvalue vs the squared root variance of the bond lengths σ, whichis a measure of the splitting of the bond lengths (Figure 4b).The plot shows a clear correlation for both the cells, indicatingthat the gap opening is related to the “benzenization” of thesystem.The analysis of the contracted structures is more difficult,

due to the large variety of geometries and symmetries of theripples. We first observe that in the 3√3 × 3√3R30 cell thegap is null up to 7% compression. The inspection of the ripplesand band structure in this region reveals very peculiarsymmetries: first a regular alternation of wells and hills (upto 2%) and then wavy-like ripples in a one of the basis vectordirections. The first symmetry produces only a slight verticaltranslation in the high energy empty and low energy occupiedbands leaving the Dirac point unaltered, while the secondproduces the horizontal translation of the Dirac point, with,however, quite unaltered band slopes. At ∼5% compression, n-type doping is also observed. The gap finally opens at around8% when the symmetry of ripples changes, forming wells andhills. At larger compressions, n-type doping and rippling

combine producing an alternating behavior (see SupportingInformation, part S2.2, for details of the band structures).As said, in the 4√3 × 4√3R30 cell, the wavy ripples are

never observed, and the hills/wells appear already at smallcontractions. Consequently the gap opening due to thissymmetry is immediately visible although initially small,reasonably proportional to the curvature level. In order toquantify this gap-structure relation, we plotted the gap in thecontraction region against the variance of the bond length σand against the squared root of the average squared dihedral φ,related to a global measurement of the curvature. Since in thecurved areas the bonds are also stretched, the two quantities arerelated. In fact, they show similar behavior as a function of thegap (Figure 4c). Data for 4√3 × 4√3R30 cell (green) clearlyshow two regimes: at small curvature the gap increases slowly,at larger curvature, more rapidly. The transition occurs at about5% compression, and is related to the already noted appearingof pyramidalization (see previous section). In the smaller cell(magenta dots), the transition appears to be directly from thegapless regime (with wavy ripples) to the sharp-pyramidalizedone, which is also confirmed by the inspection of the structures(see the Supporting Information, part S2.2.2.).In summary, also in compressed structures, one can

distinguish different structural/electronic regimes, which welabel “wavy”, “smooth”, and “sharp” regimes. The wavy regimeis characterized by wavy smooth ripples and null gap, thesmooth by the slowly increasing gap with no change in thebond hybridization, the sharp by the appearance of thepyramidalization toward the sp3 hybridization and rapidlyincreasing gaps. The appearance of the different regimesdepends also on the cell size, which introduces a substantiallydifferent periodicity of the ripples in the system, namely ∼1.2nm for the small cell and ∼1.7 nm for the larger one.

3.3. Hydrogen Reactivity and Stability on RippledGraphene. Selected rippled structures were then hydro-genated. These are the 4√3 × 4√3R30 cell with 2%contraction, chosen as the model system better mimickinggraphene on SiC, and the 3√3 × 3√3R30 cells with 7%contraction, chosen as a model for highly rippled graphene,because it is the undefected model with the largest curvaturelevel among those studied. Hydrogen atoms were progressivelyadded on the most convex sites of a single side, and the systemsubsequently fully relaxed at fixed cell. In the case of 3√3 ×3√3R30 cell a few cases of double side hydrogenation werealso considered. The full series of hydrogenated structures isreported in the Supporting Information, section S3.The hydrogen binding energies were evaluated as a function

of the H coverage in two different ways: (i) the average bindingenergy per atom (filled dots in Figure 5) and (ii) theincremental binding energy per atom, namely the bindingenergy of the newly added hydrogen at each step, with respectto previously partially hydrogenated structure (empty dots inFigure 5; see also Supporting Information, section S3, fornumerical values). From inspection of Figure 5, it isimmediately clear that hydrogen on the 7% compressed 3√3× 3√3R30 cells (magenta dots) is more stable than on 2%compressed 4√3 × 4√3R30 cell (green dots) by 1−2 eV,depending on the coverage. This is most likely an effect ofcompression that increases the average local curvature, and is inagreement with our previous findings, indicating a linearincrease of the binding energy with curvature for isolated atomhydrogen adhesion.24 Indeed, this result could be consideredthe extension to the case in which other hydrogen atoms are

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present in the structure. In particular, Figure 5 shows that in thecase of very high compression and corrugation, thechemisorbed hydrogen can also be more stable than molecularhydrogen, as previously suggested.24

The behavior of the binding energy as a function of thecoverage indicates that, on average, bound hydrogendestabilizes as the coverage increases. This might seem incontrast with the previously reported cooperative effect,30

which would rather produce stabilization in the presence ofalready bound hydrogen. This discrepancy is most likely due tothe fact that we relax structures but not the cell. It is true thatalready present hydrogen increases the local convexity becauseof the pyramidalization, and consequently the bound hydrogenstability. But hydrogen binding has also the effect of increasingthe C−C bond length, and consequently the average level ofcompressionif cell is kept fixedand consequently, theaverage energy of the system. Thus, the result plotted in Figure5 is the combined effect of hydrogen stabilization due toincreased convexity and global destabilization due to increasedeffective compression.The incremental energy behavior (empty symbols) more

difficult to interpret because it strongly depends on thedecoration of the partially hydrogenate structure at the previousstep (see the Supporting Information for representation of thestructures). Some of the intermediate configuration displayempty sites in the hydrogenated clusters, creating a graphane-like local structures, which turns out more stable and withevenly distributed stress; in the case of 3√3 × 3√3R30 cells,we also tried a double side hydrogenation. Thus, overall thebehavior of the incremental energy is roughly alternatingaround the average level, which is, at least in the case of thelarger cell, not too far from the average one at large coverage. Inagreement with previous literature, this analysis indicates, thatlocal curvature, and specifically the pyramidalization, is the keyfeature in the process of hydrogenation. However, in addition,

our results highlight the interplay between pyramidalization andclusterization of hydrogen on the graphene surface.

3.4. Electronic Properties of Hydrogenated RippledGraphene. The electronic bands of hydrogenated structureswere evaluated (see Supporting Information, section S3). Aninteresting property to consider is the value of the band gap as afunction of the hydrogen coverage. Unfortunately, this task isnot as straightforward as it might seem: the band structureturns out very complex and hydrogen-decoration dependent, sothat, at a given coverage, the band gap value displayed bydifferent H decoration spans a wide range, as it can be seenfrom Figure 6. Though a gap increasing trend seems to emergewith increasing coverage, in most cases, very small values of thegap persist even in the presence of a large coverage.

A closer inspection of the bands (see SupportingInformation, Tables S7 and S8) reveals that small or zerogaps appear in two distinct cases. The first is at low levels ofhydrogenation (e.g., in the case of dimers bound in ortho orpara conformation, see red inset to Figure 6). In that case theelectronic density of states near the Fermi level is inquantitative agreement with results previously obtained

Figure 5. Binding energies vs the hydrogen coverage in the 4√3 ×4√3R30 cell at 2% compression (green dots) and 3√3 × 3√3R30cell at 7% compression (magenta dots) and at 2% compression(magenta squares, the two values correspond to two differentdecoration, before and after a H site hopping, described in section3.5). Filled symbols are the average binding energies per H atom at agiven coverage (measured as % of hydrogenated sites). Empty dots areincremental binding energies per atom, i.e., measured with respect tothe partially hydrogenated structure of the previous step, instead thanto naked graphene. Both sets of energies are evaluated with respect toatomic hydrogen (left vertical axis) and to molecular hydrogen (rightvertical axis), the two differing by an offset of ∼2.23 eV/H atom.Dotted lines are guides for the eye.

Figure 6. Electronic band gaps as a function of coverage for 4√3 ×4√3R30 cell at 2% compression (green large dots) and 3√3 ×3√3R30 cell at 7% compression (magenta large dots). If localizedmidgap states are present, the gap is evaluated both including (smalldots) and excluding (large dots) them. The black dots areexperimental data from ref 27. The eye-guiding line in black is apolynomial fit Egap [eV] = 3.8 (cov/100)0.6. For 100% coverage theline passes through Egap = 3.8 eV, which is approximately the value ofthe graphane gap. Insets include the band gap plot around the Fermilevel (red lines = empty states; blue lines = filled states) and the STM-like representation of the electron density of states in selected energyintervals for selected cases. Namely: enclosed in red, the 4√3 ×4√3R30 hydrogenated with the para-dimer, DOS integrated ±0.5 eVwith respect to Fermi level; enclosed in blue: the 4√3 × 4√3R30hydrogenated with eight atoms, DOS integrated ±0.6 eV around theFermi level (upper part in orange) and integrated between Fermi leveland −1.6 eV (lower part, in red); enclosed in orange, the 4√3 ×4√3R30 hydrogenated with 10 atoms, DOS integrated between Fermilevel and −1.6 eV. The arrows connect the insets to the correspondingnumerical data for gap/coverage.

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theoretically or by scanning tunneling microscopy (STM)experiments.27 High electronic density is visible on thehydrogenated sites, but residual graphene-like delocalizedareas are present. In this case, the bands show a small gapand a quasi-graphene like linear dispersion near the Fermi level.The second case of vanishingly small gap is due to theappearance of nearly flat midgap states, as in the case of ∼8%coverage of 4√3 × 4√3R30 cell (blue insets to Figure 6). Theanalysis of the electronic density of the states around the Fermilevel reveals that these are very localized on the hydrogenatedsites, with very little density around the hydrogenated islands.Conversely, the deeper states at −0.3 to −1.5 eV include alsosome electronic density in the graphene part, but they areseparated by a gap of at least 0.5−0.6 eV from thecorresponding in the conduction band. Given the presence ofthose localized mid gap state in several of our structures, inthose cases we also evaluated the band gaps excluding them (inthese cases the bare gap is reported as small dots in Figure 6).In fact, these are not likely to contribute to the STMmeasurement, because localized and therefore nonconductive.Nondispersive states are always present, but in some case theyare mixed with dispersive ones. This is the case, for instance, of4√3 × 4√3R30 cell with 10 H atoms (orange inset), in whichone has a real gap of ∼0.4 eV formed by localized states mixedup with the dispersive ones. Coherently the correspondingelectronic density (only filled bands) shows both localizationand residual density in the conducting graphene-like areas.Figure 6 also reports (in black) experimental data taken from

the experimental measurement of the gap at two differenthydrogen coverages.27 As it can be seen, they are in agreementwith the trend of the gap evaluated excluding the nondispersivemidgap states, when present, confirming our analysis. On thebasis of these data, the increase of band gap as a function ofcoverage can be estimated ∼0.1 eV per 1% site occupation, inthe intermediate region, although it is better represented by apolynomial with exponent 0.6 (see caption of Figure 6), whichalso accounts for the saturation toward the 100% coverage(graphane has a theoretically estimated band gap of ∼3.7 eV3).The large fluctuations around the fitting line, as well as theemergence of the localized midgap states, might be explainedby the fact that in most cases here we are considering onlydecoration with specific symmetries, while the real hydro-genation process is likely to have a higher degree of disorder inthe hydrogenated sited distribution, being performed at hightemperatures. Nevertheless, a correlation between the gap valueand the coverage seems to emerge, which could be used toevaluate the chemisorbed H amount by STS measurements.3.5. Dynamical Stability of Hydrogenated Rippled

Graphene. We evaluated the dynamical stability of chem-isorbed hydrogen at room temperature in one of the mostunfavorable cases, namely the 3√3 × 3√3R30 cell withhighest coverage. To this end we performed a CP moleculardynamics simulation, where, after a gradual temperatureincrease (∼1.5 ps long, data not shown), the system is coupledto the thermostat at 300 K (see Figure 7a). A hopping event isobserved in 0.5 ps on sites highlighted with the blue oval inFigure7, parts b and c, as shown by the abrupt change in theinvolved C−H bond length (red and green lines in Figure 7).This event produces a stabilization of about ∼1 eV in thesystem which can be seen as corresponding decrease in the EKSenergy (dotted line in the central plot) and triggers amacroscopic oscillation in the temperature and energy (seecentral plot), whose period is 1.41 ps, meaning frequency in the

THz range. Considering that the characteristic wavelength ofthis system is ∼1−2 nm, and the dispersion relations of thegraphene phonons, these frequencies might correspond to ZAphonons, i.e., transverse out of plane displacements.55 In fact,the analysis of the oscillations of the z coordinate of selectedatoms near the hopping site (highlighted in yellow in Figure7c) show a beat at that frequency superimposed to fasteroscillations (dotted lines in the top graph). We remark that ZAphonons are precisely the modes that describe the deformationcorresponding to rippling in these systems. The macroscopicenergy oscillations have certainly a large component due to theexchange with the thermostat, and are not entirely due to thesheet deformation. However, the fact that they are triggered bya hopping event and that they are resonant with ZA phonons isan indication of the strong interplay between rippling,hydrogenation/hopping events and mechanical properties.This relationship could be a possible way for detecting singlehydrogen hopping by mean of vibrational analysis.

4. CONCLUSIONSIn this work, we have reported the structural and electronicproperties of corrugated graphene, pristine, and hydrogenated.The corrugation was created with the specific intention ofmimicking the natural corrugation of graphene grown on SiC.For this reason the 4√3 × 4√3R30 supercell was used, whoseperiodicity and symmetry correspond to the pseudoperiodicityof epitaxial monolayer graphene on SiC. This allows to recreatethe natural corrugation by slightly compressing the cellbiaxially. (We also verified that the same strategy did notwork on the cell with the exact symmetry of graphene on SiC.)The 3√3 × 3√3R30 cell was also considered, to recreate asimilar condition but with smaller wavelength and larger localcurvature, in order to enhance the effects. Stability, structuraland electronic properties of these two model systems subject toa wide range of levels of strain and compression were analyzed.This systematic study lead to a number of side results, inaddition to the main ones, regarding the interplay betweenstructural and electronic properties. A “benzenization” tran-sition is observed for large stretching, which changessubstantially the conductive properties of graphene. In the

Figure 7. CP molecular dynamics simulation of the hydrogenatedsystem. (a) Plot of different observables as a function of time. Frombottom to top: bond distance corresponding to the two sites involvedin the hopping of the proton (highlighted with the blue oval in parts band c): Temperature (solid line scale on the left) and KS energy(dotted line, scale on the right) during simulation; z displacement of aselected C atom (highlighted in yellow in part c); the dotted lines inthe top plot highlight the beat oscillations.

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compression region, a variety of different symmetries andgeometries of ripples are observed, depending on the strain andwavelength of compression, corresponding, in turn, to differentelectronic properties. These, however, can be rationalizedrelating them to structural order parameters, namely the bondlength variance or the average of the pyramidalization angle,both related to the sp2 → sp3 transition. The conclusion is that,while at low level of contraction graphene preserves itsconductive properties, at high level of contractions pyramidal-ization appears inducing a transition toward a corrugationinduced insulating state.Selected structures, namely those more similar to the

naturally corrugated graphene grown on SiC, were hydro-genated following a protocol which mimics the exposure toatomic H: atoms were added progressively to the more reactivesites, namely those more pyramidalized. The binding energy ofhydrogen on the surface was seen to decrease to a stable valueup to almost half coverage of graphene surface, which isreasonably the largest value reachable with single-side hydro-genation. The system is seen to accept spontaneously atomichydrogen up to this level. At high compression, the boundhydrogen turns out to be stable also with respect to molecularhydrogen. This is in agreement with our previous resultsobtained for isolated H atoms added on the corrugatedgraphene surface, extending them to the case of larger coverage.In addition, the analysis of the binding energy as a function ofthe coverage indicates a relation between the reactivity ofpyramidal sites, the increase of pyramidalization induced byhydrogenation, and the consequent increased mechanical stress.As expected, the electronic band gap increases with the

hydrogen coverage. The increase was quantified with a simplepolynomial fit, which also superimposes to experimental data.Therefore, this quantitative rule could be used to indirectlyevaluate the H coverage by STS measurements. However, thistrend emerges only when localized midgap states sporadicallyappearing in calculations are excluded from the gap calculation.We interpreted the emergence of those states, elusive withrespect to direct STM measurements because non conductive,as due to specific hydrogen decoration with specificsymmetries, whose statistical weight is low in real hydro-genation experiments at room temperature.27

Finally, we evaluated the dynamical stability of chemisorbedhydrogen at room temperature, choosing a system withparticularly unfavorable hydrogenation, by means of CPmolecular dynamics simulations. We observe, a spontaneoushopping event occurring in the ps time scale, by which thepotential energy of the system is decreased of ∼1 eV. As aconsequence, energy oscillations in the THz range are excited,with a component of out-of-plane related to ZA flexuralphonons (traveling ripples of nm wavelength). This unexpectedresult is, however, coherent with our previous findings,24

because it shows the interplay between the curvature dynamicalchange related to ZA phonons and the hydrogen destabiliza-tion. In addition, this opens the possibility of measuringhydrogen hopping on graphene surface by means of vibrationalmeasurements in the THz range. Overall, therefore, this workclarifies several aspects of the interplay between corrugation,electronic properties, vibro-mechanical properties and hydro-genation. These were obtained as “side results” as an effect ofthe systematic study of pristine and hydrogenated graphenewith different levels of average local curvature.Besides this, we optimized a modeling platform for a number

of possible developments. We verified that 4√3 × 4√3R30

supercell can reproduce the main characteristics of the naturallyrippled graphene on SiC. Thus, this model system can be usedfor further studies, and with the aim to compare withexperimental measurement of graphene on SiC. Thequantitative agreement between measured and calculatedtrend of the band gap vs hydrogen coverage is a validationtest for this model system. In addition, we have also reportedother “measurable” relations, such as the variation of bindingenergy vs coverage, or the possibility of detecting hydrogenhopping by means of measurements vibrations in the THzrange. We hope that this study will trigger experimentalinvestigation in the same directions.

■ ASSOCIATED CONTENT*S Supporting Information(i) Convergence checks, (ii) energy data in tabular form, and(iii) graphical representation of selected structures and theirelectronic bands, for pristine and hydrogenated graphene. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*(V.T.) Telephone: +39 050 509433. Fax: +39 050 509 417. E-mail: valentina.tozzini@nano.cnr.it.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Dr Chandramathy Surendrean Praveen for precioustechnical support for the QE code, and Dr Walter Rocchia andDr Stefan Heun for useful discussions. We gratefully acknowl-edge financial support by the EU, 7th FP, Graphene Flagship(Contract No. NECT-ICT-604391), the CINECA Award“ISCRA C” IsC10_HBG, 2013 and PRACE “Tier0” AwardPra07_1544 for resources on FERMI (IBM Blue Gene/Q@CINECA, Bologna Italy), IIT “Compunet platform” forproviding computational resources, and CINECA staff fortechnical support.

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