PHYSICAL REVIEW B 86, 045453 (2012)

First-principles study of hydrogen and fluorine intercalation into graphene-SiC(0001) interface

A. Markevich,1,* R. Jones,1 S. Öberg,2 M. J. Rayson,2 J. P. Goss,3 and P. R. Briddon31College of Engineering, Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter, EX4 4QL, United Kingdom

2Mathematical Sciences, Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden3School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

(Received 11 April 2012; published 30 July 2012)

The properties of epitaxial graphene on SiC substrates can be modified by intercalation of different atomicspecies. In this work, mechanisms of hydrogen intercalation into the graphene-SiC(0001) interface, and propertiesof hydrogen and fluorine intercalated structures have been studied with the use of density functional theory. Ourcalculations show that the intercalation of hydrogen and fluorine into the interface is energetically favorable.Energy barriers for diffusion of atomic and molecular hydrogen through the interface graphene layer withno defects and graphene layers containing Stone-Wales defect or two- and four-vacancy clusters have beencalculated. It is argued that diffusion of hydrogen towards the SiC surface occurs through the hollow defects inthe interface graphene layer. It is further shown that hydrogen easily migrates between the graphene layer and theSiC substrate and passivates the surface Si bonds, thus causing the graphene layer decoupling. According to theband structure calculations the graphene layer decoupled from the SiC(0001) surface by hydrogen intercalationis undoped, while that obtained by the fluorine intercalation is p-type doped.

DOI: 10.1103/PhysRevB.86.045453 PACS number(s): 73.20.At, 68.65.Pq, 71.15.Mb, 73.22.Pr

I. INTRODUCTION

Graphene has a potential for applications in area includingnanoelectronics, biophysics, gas detection, and hydrogenstorage. However, these applications are limited by the absenceof established methods for the production of high quality andlarge area graphene samples. At the moment, one of the mostpromising ways for the production of large-area homogeneousgraphene layers is epitaxial growth on SiC substrates.1–4

Annealing hexagonal SiC at elevated temperatures results inthe loss of Si atoms from the surface, while the remaining Catoms rearrange in a graphene honeycomb structure. Single-layer or few-layers graphene (SLG or FLG) can be grownon both Si- and C-terminated SiC surfaces [SiC(0001) andSiC(0001̄), respectively]. However, the graphene-substrateinterface, growth kinetics and properties of epitaxial graphenelayers are very different for the two SiC faces.

The growth of FLG on Si-terminated SiC surface occursthrough the formation of the (6

√3 × 6√3)R30◦ (6R3) surface

reconstruction. Experimental and theoretical studies haveshown that the 6R3 reconstruction corresponds to a single layerof carbon atoms with a graphene-like atomic arrangement witha fraction of the C atoms covalently bound to the substrateSi atoms.3,5–7 No linear dispersion of π bands typical forfree standing graphene is observed for this interfacial layer,which is often called a buffer layer (BL). However, the nextgraphene layer above the buffer layer behaves electronicallyas a graphene monolayer, which is electron doped with acarrier density of n ≈ 1013 cm−2 due to charge transfer fromthe substrate.3,7–9 In addition to electron doping, there is aconsiderable reduction in carrier mobility in the layer, whichwas found to be lower than 2000 cm2/Vs.4 Epitaxial graphenelayers grown on SiC(0001) maintain the 30◦ orientation of thebuffer layer relative to the SiC surface and are arranged in thegraphitic AB stacking sequence.

For the C face of SiC, it was shown that the typical grapheneelectronic band structure appears already in the first epitaxialcarbon layer and covalent bonds between this layer and the

substrate do not occur.3 Furthermore, it was shown that, incontrast to the SiC(0001) surface, where graphene layers growin AB stacking, on the C face graphene layers consist ofdomains oriented at angles around 0◦ and 30◦ relative to theSiC surface.10,11 During growth the majority of domains do notexhibit AB stacking. As a result, each carbon layer behaveselectronically as an isolated graphene sheet and has a highcarrier mobility close to the value of 250 000 cm2/Vs.12

Although graphene layers on SiC(0001̄) show a muchhigher carrier mobility compared with those on SiC(0001), thegrowth on the Si faced SiC has some advantages. The lowergrowth rate for graphene layers on the Si face of SiC comparedto the C face allows for better control of the growth process, soa defined number of graphene layers can be grown. This givesa possibility of creating n-layer (n = 1,2,3, . . .) graphenesystems with AB stacking, which have different properties.The growth on SiC(0001) also leads to epitaxial graphenelayers with improved structural quality than those grownon the C face, particularly, with better homogeneity, biggergrain sizes, and smaller concentration of defects. Moreover,it was shown that graphene-SiC interface can be significantlymodified by intercalation of several chemical species.

For the Si face, Riedl et al. have observed a transformationof the buffer layer to monolayer graphene following annealingof their graphitized SiC samples at temperatures higher than600 ◦C in molecular hydrogen at atmospheric pressure.13Similar results were obtained by Virojanadara et al. whoexposed graphene-SiC samples to atomic hydrogen fluxesat temperatures higher than 450 ◦C.14 It was suggested thathydrogen atoms penetrated between the BL and the SiCsubstrate, broke the interface C-Si bonds and saturated anySi dangling bonds. This resulted in decoupling of the BLfrom the substrate and the formation of a band structuretypical for monolayer graphene lying within the band gap ofpassivated SiC. This process was found to be reversible withthe inverse transformation starting at about 700 ◦C associatedwith hydrogen desorption from the SiC surface.13,14 Other

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A. MARKEVICH et al. PHYSICAL REVIEW B 86, 045453 (2012)

experimental groups have reported on the intercalation offluorine,15 oxygen,16 gold,17,18 lithium,19,20 and sodium21 intographene-SiC interface. While, in general, intercalation resultsin the decoupling of the buffer layer from the substrate, itcan also lead to a doping of the decoupled graphene layers.For example, the intercalation of fluorine results in the strongp-type doping, while intercalation of Li or Na results in n-typedoping. The intercalation of Au may lead to either n- or p-typedoping depending on the Au coverage.

Theoretical investigations, based on ab initio modeling,have shown that intercalation of hydrogen22 and sodium23 isenergetically favorable and the type and level of doping, ob-tained from the band structure calculations, are in a good agree-ment with experimental results.23,24 However, mechanisms ofintercalation of different atomic species into graphene-SiCinterface have not been investigated sufficiently and arenot understood. Furthermore, there are some experimentaland theoretical results that are seemingly contradictory. Forexample, in an experimental investigation of atomic hydrogenadsorption on epitaxial graphene on SiC(0001), no evidenceof hydrogen penetration below a graphene layer was observedeven at 800 ◦C.25 Based on the first-principles modeling, theenergy barrier for H2 diffusion through the BL was reportedto be 6.5 eV,22 that is higher than the experimental value of4.52 eV for the dissociation energy of the H2 molecule.26 Theenergy barrier for atomic hydrogen diffusion through graphenewas reported to be about 4 eV from ab initio calculations.27

Thus, direct hydrogen diffusion through the BL on SiC(0001)seems to be unrealistic in the temperature range 450–600 ◦C,in spite of experimental evidences that it occurs.

Under the model that the intercalating species cannotpass through pristine graphene, the most plausible route forthe various species to the graphene-SiC interface is throughopenings in the layers afforded by the presence of variousdefects or grain boundaries. In practice these may be screwdislocations with an open core, grain boundaries and sampleedges. It was reported from the ab initio modeling that anopen core screw with Burgers vector 2c has a core energyonly about 10% higher than that of a full core.28 Such adifference could easily be eliminated if the walls of the opencore were passivated by hydrogen. However, the perfect screwdislocation with Burgers vector 2c appropriate for AB stackingmight dissociate into partials lowering its energy. It is thenunclear whether the H decorated open core screw is morestable than the dissociated closed core screw. In this paper wepresent the results of ab initio simulations of the diffusion ofintercalating species through hollow sites.

II. METHOD

All calculations in this work were performed using theAIMPRO29 density functional theory (DFT) code with the lo-cal density approximation (LDA) for the exchange-correlationpotential. Core levels were treated within the Hartwigsen-Goedecker-Hutter (HGH) pseudopotentials scheme.30 Kohn-Sham valence orbitals were represented by a set of atom-centered s-, p-, and d-like Gaussian functions.31 Spin polar-ization of the valence states was taken into account. Matrixelements of the Hamiltonian are determined using a plane-wave expansion of the density and Kohn-Sham potential32

with a cutoff of 200 Ha. All structures were modeled withperiodic boundary conditions.

For modeling hexagonal SiC we used 4H-SiC polytypestructure. The calculated lattice parameters, a = 3.05 Å andc = 10.01 Å, are in a good agreement with experimental data,a = 3.07 Å and c = 10.05 Å.33 The substrate was representedwith four bilayers of SiC. A vacuum layer of 25 Å was includedabove the SiC surface to separate slabs in the [0001] direction.

A flat graphene layer was placed on top of the SiC(0001)surface. The dangling bonds on the (0001̄) surface werepassivated with hydrogen atoms. An optimization of atomicpositions resulted in a graphene layer covalently bound tothe substrate, thus representing the buffer layer (BL). It wasshown that this approach correctly reproduced the structureand electronic properties of the BL on SiC(0001) when a real6R3 surface reconstruction is modeled.5,6 However, a unit cellfor the 6R3 surface geometry consists of 1310 atoms and istoo big for realistic modeling of diffusion mechanisms, whena large number of structural optimizations are required. Asan approximation to the real structure we used two differentsurface reconstructions: namely the (

√3 × √3)R30◦ (R3)

and 4 × 4 SiC surface reconstructions. The R3 model wasadopted in other theoretical investigations of graphene-SiCinterfaces.8,9 In order to distinguish between the modeledstructures and the real 6R3 reconstruction, the term interfacialcarbon layer (ICL) will be used hereafter instead of the bufferlayer (BL) within R3 and 4 × 4 models.

Integration over the Brillouin zone (BZ) was carriedout within the Monkhrost-Pack sampling scheme34 using12 × 12 × 1 and 6 × 6 × 1 grids for the 4 × 4 and R3models, respectively. Optimization of the atomic positionswas performed using a conjugate-gradient algorithm untilthe change in total energy between two subsequent iterationswas less than 1×10−5 Ha. For modeling diffusion processesand obtaining corresponding energy barriers, we used theclimbing image nudged elastic band (cNEB) method.35,36 Atleast seven system images were used for discrete representationof diffusion paths. Structural optimizations along a diffusionpath were carried out until the highest force acting on any atomin all system images were less than 0.001 atomic units.

III. RESULTS AND ANALYSIS

A. Electronic and structural properties of the interfacial carbonlayer on SiC(0001) according to the R3 and 4 × 4 models

We have first studied the suitability of the two simplifiedmodels of epitaxial graphene on SiC(0001) for the investiga-tion of hydrogen diffusion through the interfacial carbon layer(ICL). Figure 1 shows schematic representations of the R3 and4 × 4 SiC surface reconstructions for the ICL on SiC(0001).The R3 reconstruction has been used previously in theoreticalinvestigations of the graphene/SiC(0001) interface.8,9 Theband structure calculations show the absence of Dirac conesfor the ICL and predict correctly the n-type doping of thenext graphene layer above the ICL with the Fermi level at0.4 eV above the Dirac point. It should be noted, however,that ab initio calculations for the R3 reconstruction predictthe metallic behavior of the ICL on SiC(0001), while it hasbeen argued on the basis of angle resolved photoemission

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FIG. 1. (Color online) Schematic representation and the band structure of the iterfacial carbon layer (ICL) on the (√

3 × √3)R30◦ (a) and(c), and the 4 × 4 (b) and (d) SiC(0001) surface reconstructions. The (√3 × √3)R30◦ unit cell is indicated in (a). Silicon atoms are representedby large (yellow) circles. Smaller dark gray and light gray circles represent carbon atoms in the ICL and in the SiC substrate, respectively.Solid (red) lines represent occupied states, while (blue) dashed lines represent empty states. The position of the Fermi level is set to zero. Theinset in (d) shows that graphene π and π∗ bands are separated by the energy gap of 30 meV at the K point in the Brillouin zone.

spectroscopy (ARPES) measurements that the interface issemiconducting.3 The metallic band in the ICL/SiC(0001)band structure arises from the Si dangling bonds of thesubstrate. Because of the lattice mismatch between SiC andgraphene, an 8.2% extension of the graphene lattice constantis required to accommodate a 2 × 2 graphene cell on theR3 reconstructed SiC surface. Such a large extension of thegraphene lattice will inevitably affect the barriers for diffusionof a hydrogen atom through the ICL. It has also been shownfrom ab initio calculations that stretching of the C-C bondresults in significant increase of the chemical reactivity ofgraphene.37 Thus, it can be expected that the binding energyof the ICL to the SiC substrate and the binding energy of theH atom to the ICL will be overestimated in calculations usingthe R3 model.

The smallest structure in which graphene and SiC cells arealmost commensurate corresponds to the 4 × 4 SiC surfacereconstruction which accommodates the 5 × 5 graphene cell.This model requires only −0.02% change of graphene latticeconstant to adjust the mismatch between the calculated latticeparameters of SiC and graphene. However, it should beemphasized that in this case the ICL orientation with respect

to the substrate is 0◦ in contrast to the 30◦ orientation observedexperimentally. Figure 1(d) shows the band structure for the4 × 4 reconstruction. Remarkably, the graphene like π bandsare preserved for the ICL, despite a fraction of carbon atomsin the layer being covalently bound with the substrate. Thereis also an energy gap of about 30 meV separating the π and π∗bands at the K point of the Brillouin zone [inset in Fig. 1(d)].The Fermi level is located well above the bottom of the π∗band indicating high n-type doping of the interfacial carbonlayer and the metallic nature of the interface. Such a largedifference between the band structures calculated with the useof the two models shows the importance of the orientation ofthe ICL relative to the SiC substrate.

Table I shows the structural parameters and the bindingenergy per C atom calculated for the ICL on SiC surfaceswith the R3 and 4 × 4 reconstructions. The values for the R3model are in a good agreement with those found in previoustheoretical investigations.8,9 The average distance between theICL and the SiC(0001) surface is nearly the same for bothmodels. However, corrugations of the layer and the bindingenergy, calculated per C atom, differ significantly. For the 4 ×4 model, the binding energy per C atom is less than half that

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TABLE I. Calculated values for the average distance between theICL and the SiC surface, h, maximum difference in the height of Catoms in the ICL, �h, and the binding energy per C atom, Eb, for theICL on the SiC(0001) surface.

Model h, Å �h, Å Eb, eVR3 2.26 0.28 0.414 × 4 2.22 0.52 0.18

for the R3 model. This is due to several factors: (i) stretchingthe graphene lattice in the R3 model increases the chemicalreactivity of the layer; (ii) in the R3 model the C atoms thatform covalent bonds with the substrate are located directlyabove the surface Si atoms, which is not the case for the 4 × 4model; and (iii) it is also very likely that the binding energydepends on the ICL/substrate orientation although it is difficultto estimate the contribution of this.

From the modeling of the actual reconstruction with 6R3periodicity the corrugation of the ICL was reported to beof the order of 1 Å.6 This value is much bigger than thoseobtained from our calculations for both the R3 and 4 × 4models. It should be noted, however, that in small cells,atomic displacements induce high lattice strains that resultin a significant increase in the total energy of the system. Inbigger cells, such lattice strains can be reduced because of thecorrelated motions of a large number of atoms. The particulardistribution of graphene C atoms, some of which are tightlybound to the substrate Si atoms and some are not, are differentfor the R3, 4 × 4 and 6R3 reconstructions, and this can alsoresult in different magnitude of the corrugation of a graphenelayer.

B. Effect of lattice strain on the binding energy and diffusionof hydrogen through a graphene layer

To investigate the effect of a graphene lattice extension onthe diffusion of atomic hydrogen through the layer, we firstperformed a set of calculations for single isolated graphenesheets with different lattice constants varying in the rangeof 0–10%. For these calculations, 6 × 6 graphene cells havebeen used. The 9 × 9 × 1 k-points greed has been used for theBrillouin zone integration.

The barrier for diffusion of a hydrogen atom through agraphene layer is defined as the energy difference between theinitial stable configuration and the saddle point configuration.The most stable position of a hydrogen atom on graphene is theH atom chemisorbed to a C atom. So, it is reasonable to takethis configuration as the initial one for the diffusion process.Thus the diffusion barrier can be calculated as

Q = ESP − Einit = ESP − (Egr + EH − Ebind), (1)where ESP is the energy of the saddle point configuration, Egris the energy of a separate graphene layer, EH is the energy ofa distant hydrogen atom, and Ebind is the binding energy of anH atom on graphene.

The dependence of Q on Ebind should be pointed out. Thebinding energy of the chemisorbed H atom on graphene withequilibrium lattice constant was calculated to be 1.18 eV. Thisvalue is larger than those in the range of 0.2–0.9 eV found inthe majority of previously published theoretical works. Such

FIG. 2. (Color online) The calculated values of the binding energyof an H atom on graphene (blue triangles) and diffusion barrier of an Hatom through a graphene sheet (red and black circles and squares) fordifferent values of the graphene lattice constant stretching. Circles andsquares distinguish two different dependencies of the diffusion barriervs strain that correspond to the change of H diffusion path throughthe graphene layer. Open circles and squares show the calculateddiffusion barriers if the binding energy term is excluded from theEq. (1). This corresponds to energy barriers for H diffusion througha graphene layer if the initial configuration is defined as an H atomremote from the layer. Lines represent linear fits to the data.

a large scattering in the data can be explained by the use ofdifferent exchange-correlation functionals. The calculationswith hybrid functionals give the lowest values of the bindingenergy, while the values of 0.6–0.9 eV are typical for GGA.37,38

Previous calculations with the use of LDA predict the bindingenergy in the range 1–1.4 eV, which is close to our result.37,39

The energy barrier for diffusion of an H atom through agraphene layer was calculated to be 3.73 eV. In agreement withthe results of Ito et al.,40 it is found that in the saddle pointconfiguration the hydrogen atom is not exactly in the centerof graphene hexagon but slightly shifted towards one of the Catoms. Figure 2 shows the dependence of the binding energyand diffusion barrier of an H atom on the extension of graphenelattice constant. In the vicinity of 10% isotropic expansion ofgraphene lattice, the change in the absolute value of the bindingenergy of H on graphene can be approximated by a lineardependence with a slope of 89 meV per 1% strain. This resultis in a good agreement with the investigation of Andres et al.37

and confirms the substantial increase of chemical reactivityof graphene upon the lattice stretching. It should be notedthat for small amounts of stretching, 0–3%, the dependenceof the binding energy of H on the graphene lattice dilationdeviates from linear. However, the detailed investigation ofthis dependence is beyond the scope of this work.

As can be seen from Fig. 2, there is a large decrease inthe energy barrier for H diffusion through a strained graphenelayer. The barrier to H penetration drops from 3.73 to 0.89 eVfor 0% and 10% stretching, respectively. There are two clearlydistinct regions in the plot of the diffusion barrier versus strain(shown with circles and squares in Fig. 2). An analysis showsthat the data can be approximated by two linear dependencies

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with different slopes. In the range from 0% to about 3.2%expansion, the diffusion barrier changes with a rate of 78 meVper 1% dilation. Above 3.2%, the slope becomes much greater,corresponding to the change of the diffusion barrier with therate of 380 meV per 1% dilation. The transition between tworegions corresponds to the change of H diffusion path throughthe graphene layer. For a small strain, the H atom in the saddlepoint configuration is close to the center of the hexagon formedby C atoms. When the extension of graphene lattice is largerthan 3.2% the saddle point configuration corresponds to theH atom in the middle of the C-C bond. Figure 2 also showsa plot of Q-Ebind versus graphene lattice constant expansion.This corresponds to energy barriers for H diffusion through agraphene layer if the initial configuration is defined as an Hatom remote from the layer.

To summarize, we note that (1) the permeability of grapheneto H and the graphene chemical reactivity can be changedsignificantly by tensile strain and (2) the use of the R3 modelfor the ICL on SiC(0001), which requires the extension ofgraphene lattice constant by 8.2%, will probably give incorrectvalues for the binding energy of H with the ICL and for the dif-fusion barrier of hydrogen through the layer. Thus we suggestthat the 4 × 4 reconstruction, although it has not been observedexperimentally, is a better approximation than the R3 modelin the cases when the actual energies of atomic interactionsare of more importance than the electronic properties.

C. Properties of a quasi-free-standing graphene layeron H- and F-passivated SiC(0001)

Figure 3(a) shows the band structure of graphene onthe H-passivated SiC(0001) surface calculated with the useof the 4 × 4 model. The band structure can be expressedas a sum of two components: the substrate component,consisting of the SiC slab and H-passivated SiC surface, andthe graphene component. The graphene related bands arealmost identical to those calculated for a separate graphenelayer, indicating the small interaction of graphene with thesubstrate. The quasi-free-standing nature of graphene onthe hydrogenated SiC(0001) has been also supported byexperimental investigations.13,41

The Fermi level crosses the Dirac point indicating thatthere is no doping of the graphene layer. However, a slightp-type doping of the decoupled graphene layer has beenobserved experimentally.13,41 This effect has vanished afterheating samples above 700 ◦C. Thus the p-type doping hasbeen proposed to arise from some surface adsorbates on thelayer.13 It should be noted that the key features of the bandstructure, namely, appearance of graphene Dirac cones in theSiC energy gap and the absence of doping, are identical forthe 4 × 4 and R3 reconstructions. This fact also supports theabove mentioned results on the independence of the substrateand graphene components, since the band structures for theICL strongly interacting with the substrate are very differentfor the 4 × 4 and R3 model.

Recently, it was shown that the buffer layer can also bedecoupled from SiC(0001) by the intercalation of fluorineatoms.15 However, in this case, the strong p-type doping ofthe quasi-free-standing graphene layer was observed with theFermi level at about 0.79 eV below the Dirac point. Figure 3(b)shows the calculated band structure of the graphene layer onF-passivated SiC(0001) surface. The position of the Fermilevel is 0.38 eV below the graphene Dirac-point, indicatingp-type doping of the layer in agreement with the experimentalresults. However, the magnitude of the doping obtained fromthe calculations is less than half that observed experimentally.Some extra doping of the layer in the experimental conditionsmight arise from surface contaminants. It should be noted thatthe discrepancy between the calculated and experimentallyobserved level of doping occurs for graphene layers on bothH- and F-passivated SiC(0001) surface. In the band structureshown in Fig. 3(b), an electron pocket can also be seen aroundthe � point in the Brillouin zone. An analysis of the wavefunction distribution shows that the electron pocket is localisedat the SiC substrate, while a hole pocket, around the K point, isentirely located on the graphene layer. This result indicates thatthe p-type doping of graphene on the F-passivated SiC(0001)is due to a transfer of electrons from the graphene layer to theSiC substrate.

Table II shows the calculated values of the formation energy,the binding energy per C atom and the average distancefrom the substrate, for the quasi-free-standing graphene layer

(a) (b)

FIG. 3. (Color online) The calculated band structures for a graphene layer on top of the (a) hydrogenated and (b) fluorinated SiC(0001)surface. Solid (red) lines represent occupied states, while (blue) dashed lines represent empty states. The position of the Fermi level is set tozero.

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TABLE II. Calculated values of the formation energy, Ef , thebinding energy per C atom, Eb, and the distance from the substrate, h,for the quasi-free-standing graphene layer obtained by intercalationof hydrogen and fluorine atoms. The distance h is calculated withrespect to H(F) atoms.

Ef , eV Eb, meV h, ÅH −2.9 29 2.59F −10.8 25 2.85

obtained by intercalation of fluorine and hydrogen atoms.The formation energy is calculated as Ef = EICL − [Eqfg +N/2 × EH2(F2)], where EICL is the energy of the SiC substratewith the ICL, Eqfg is the energy of the quasi-free-standinggraphene layer on hydrogen (fluorine) passivated SiC, EH2(F2)is the calculated energy of the separate H2 (F2) molecule,and N is the number of H(F) atoms required to passivate allSi dangling bonds on the SiC(0001) surface. For the 4 × 4reconstruction, N is equal 16.

The negative values of the formation energy indicate that theprocess of H(F) intercalation and the decoupling of the ICLis energetically favorable. The formation energy also givesthe qualitative evaluation of the stability of the structure. TheH-intercalated samples were shown to be stable up to 600 ◦C.13The very high absolute value of the formation energy forthe case of fluorine intercalation suggests the extremely highstability of this structure.

The binding energy per C atom of the quasi-free-standinggraphene layer to the substrate was calculated to be of theorder of 30 meV for both structures. This result confirms thesmall interaction between the graphene and SiC substrate. Itshould be noted that in the case of graphene on F-passivatedSiC surface the charge transfer should result in an increase inthe binding energy density. This, however, can be compensatedby the repulsion due to antibonding character between the Fatoms and the π states on the graphene.

D. Mechanisms of hydrogen penetration between the interfacialcarbon layer and SiC(0001)

It was shown in the previous section that the decoupling ofthe interfacial carbon layer from SiC(0001) by intercalation ofhydrogen or fluorine atoms is energetically favorable. In thissection, we examine different ways for hydrogen penetrationbelow the ICL. For this reason we have modelled diffusion ofatomic and molecular hydrogen through the ICL and defectivegraphene layers using the NEB method. The actual diffusionbarriers depend on the binding energy of hydrogen in theinitial configuration, Ebind, according to Eq. (1). For a flat freestanding graphene layer without defects, the binding energyof an H atom to any C atom in the layer is identical. However,for the ICL and for defective graphene layers, the symmetry ofgraphene lattice is broken and adsorption sites with differentbinding energies exist. To facilitate the comparison of theenergy barriers for hydrogen diffusion through a graphenelayer, a ICL, and different defects in a graphene lattice,we exclude the binding energy term in Eq. (1) in furthercalculations. Thus the initial configurations for the diffusionpaths are the configurations with H (H2) far enough from theslab for which interactions between H (H2) and the graphene

layers are negligible. This choice is also justified by the factthat during the exposure of the ICL on SiC to a hydrogenatmosphere, some of the hydrogen atoms or molecules areadsorbed directly onto the ICL, while some of them diffusethrough defective sites in the layer to the SiC surface. Itshould be noted that in the case of H2 the choice of the initialconfiguration does not affect much the value of the diffusionbarrier, since the binding energy of H2 on graphene is rathersmall, with a value of just 0.1 eV according to our calculations.

The energy barrier for migration of a hydrogen atomthrough the ICL was calculated to be 2.55 eV. This value is thesame to that for H diffusion through the free standing grapheneif a remote H atom is taken as the initial configuration. Thisresult suggests that there is no qualitative difference betweenhydrogen diffusion through the ICL and free standing graphenelayer. However, binding energies for a hydrogen atom on agraphene layer and on the ICL were found to be quite different.We have tested five different adsorption sites for the H atomon the ICL. For these sites the calculated binding energieswere 2.10, 2.35, 2.65, 2.90, and 3.56 eV. All these valuesare much higher than the binding energy of H on the freestanding graphene, which was calculated to be just 1.18 eV.The result for the ICL indicates that chemisorbed hydrogenis more stable in this environment than on a free standinggraphene. Adding a binding energy term to the calculateddiffusion barrier of a hydrogen atom through the interfaciallayer will give values in excess of 4.7 eV. Such barriers aretoo high to be overcome at 600 ◦C, the temperature at whichthe hydrogen intercalation has been achieved experimentally.Modeling H2 diffusion through the ICL and free standinggraphene showed that a hydrogen molecule became unstablewhen passing through the defect-free layers, dissociating intoatomic hydrogen. Thus direct diffusion of hydrogen atomsand molecules through a defect-free ICL can be excludedfrom possible ways of H intercalation into the graphene-SiCinterface.

Other possible mechanisms of hydrogen penetrationthrough the ICL to the interface with SiC involve extendeddefects such as holes, threading edge and screw dislocations,discontinuities of the layer, grain boundaries, sample edges,etc. Of these, a threading open core dislocation is attractiveas such a defect runs through the n-layer graphene, includingthe ICL as well as the SiC. However, modeling this defectrequires supercells that are too large for realistic calculations,so instead we have calculated the barriers for hydrogen atomsand molecules migration through a heptagon ring in theStone-Wales defect and open rings composed of a divacancy(V2) and tetravacancy (V4). The incorporation of these defectsinto a graphene layer is accompanied by long-range relaxationsof the surrounding lattice. The size of the ICL in the 4 × 4model that corresponds to the 5 × 5 graphene cell, is notenough to account for these relaxations. Thus the defectswere modeled in the free standing graphene layers with 8 × 8graphene unit cells.

The reasons for choosing the V2 and V4 defects are asfollows. Carbon atoms removed from the layer creates dan-gling bonds on the defect edges which are highly chemicallyreactive. For V2 and V4, the dangling bonds reconstruct suchthat all atoms are fully bonded [see Figs. 4(a)–4(d)]. Thusinfluence of the dangling bonds upon diffusion of hydrogen

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(a) (b)

(c) (d)

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FIG. 4. (Color online) (a)–(d) Schematic representations of V2and V4 defects. In (a) and (c), carbon atoms that are removed from agraphene layer are shown in red. (b) and (d) show the correspondingreconstructed V2 and V4 defects. (e) Saddle point configurationfor H2 diffusion through the Stone-Wales defect. (f) Saddle pointconfiguration for H2 diffusion through the V4 defect.

is minimized for the case of these vacancy clusters. Thecalculated energy barriers for atomic and molecular hydrogendiffusion through these defects are given in Table III.

The energy barriers for H diffusion through the defectsconsidered are low enough to be overcome at about 600 ◦C.However, if the binding energy of H to the graphene layeris taken into account the hydrogen diffusion through the SWdefect will be very slow up to this temperature. The lower valueof the energy barrier for H diffusion through the V2 defect than

TABLE III. Calculated values of energy barriers in eV for H andH2 diffusion through a heptagon in a Stone-Wales (SW) defect andfor V2 and V4 vacancy clusters in a free standing graphene layer. Theenergy barriers were calculated with respect to H and H2 remote fromthe graphene layers.

Pristine SW V2 V4H 2.55 1.52 0.13 0.23H2 . . . 6.89 3.64 0.69

that through V4 can be explained as follows. For V2, there isa trade-off between the energy gain due to reconstructionsof the C dangling bonds and the strain these reconstructionscause in the lattice. The incorporation of an H atom partiallysaturates the dangling bonds and releases the lattice strain,that results in lowering the total energy. In the case of the V4defect, the interaction between the H atom in the saddle pointconfiguration and C atoms at the defect edges is rather small.This is confirmed by the fact that the magnetic moment of thissystem is 1μB , which arises from an unpaired electron on thehydrogen atom.

For H2 diffusion, the energy barrier can be overcome at600 ◦C only in the case of the V4 defect. Figure 4(f) showsin perspective the saddle point configuration for H2 diffusionthrough the V4 defect. The average distance between H2 andthe C atoms at the defect edges in the saddle point configurationis 2.27 Å. Thus hollow defects with lateral dimensions of about4.5 Å and larger can provide a path for hydrogen molecules todiffuse through the ICL.

While we have shown that hydrogen can reach the SiCsurface by diffusing through the hollow defects in the ICL,it remains to show that hydrogen atoms (molecules) canmigrate between the ICL and the substrate in order to reachand passivate all Si sites at the SiC-graphene interface.We considered two mechanisms of hydrogen intrasurfacialmigration. We first calculated the energy barriers for an Hatom migration between four different chemisorption sites onthe Si-terminated SiC surface below the ICL [see Fig. 5(a)].These barriers are all low and are 0.56, 0.59, and 0.67 eV. Thenwe considered migration of a hydrogen molecule between theH-saturated SiC surface and the decoupled graphene layer [seeFig. 5(b)]. The total energy of the most favorable configurationwas calculated to be only 0.34 eV higher than that for theconfiguration with the H2 molecule remote from the slab, andthe energy variation along the migration path was found to bewithin 0.3 eV. Thus hydrogen molecules can easily intercalatebetween H-passivated SiC surface and a partially decoupledgraphene layer, and thus migrate to the regions where the ICLis still covalently bound to the substrate. The energy barriersfor both considered mechanisms of hydrogen intrasurfacialdiffusion are low enough to be overcome at 600 ◦C.

We can now present our model for the processes that occurwhen the buffer layer on SiC(0001) is exposed to molecularhydrogen gas. If there are no hollow defects in the BL,hydrogen molecules will be physisorbed on the BL. If hollowdefects are present, some hydrogen will be dissociated atthe defect edges, and chemically passivate them. Others willdiffuse through the defects and reach the SiC surface. On theSiC surface, H2 molecules will dissociate into hydrogen atoms,which will then migrate along the surface, break covalentbonds between the substrate and the BL and passivate thesurface Si atoms. Finally, when all SiC surface dangling bondsare passivated with hydrogen atoms the BL is transformed toa graphene layer that only weakly interacts with the substrate.In the case of the BL exposure to the atomic hydrogen gas, thepicture is qualitatively the same, excluding steps involving H2dissociation. It should be noted that experimentally decouplingof several graphene layers has also been observed. We suggestthat in this case, the diffusion of hydrogen towards the SiCsurface occur through the hollow defects penetrating several

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(a) (b)

FIG. 5. (Color online) Schematic representation (a) H and (b) H2 diffusions along the SiC surface below the interface graphene layer.Silicon atoms are represented by large yellow circles. Smaller dark gray and light gray circles represent carbon atoms in the graphene layer andin the SiC substrate, respectively. The arrows show the direction of hydrogen diffusion.

carbon layers. In practice, these can be open core screwdislocation, grain boundaries, or sample edges.

IV. SUMMARY

In this work, density functional theory has been used to in-vestigate mechanisms of hydrogen intercalation into graphene-SiC(0001) interfaces as well as the properties of grapheneon H- and F-passivated SiC(0001) surfaces. It is shown thatprovided the passivating species can access the interfacialregion, intercalation of hydrogen and fluorine atoms, whichresults in decoupling of the buffer layer from the SiC substrate,is energetically favorable. The decoupled graphene layer onlyweakly interacts with the substrate. The band structure calcula-tions suggests that a graphene layer on H-pasivated SiC(0001)is undoped, while in the case of F-passivated SiC(0001), thecharge transfer results in p-type doping of graphene.

Our calculations also show that hydrogen atoms andmolecules cannot diffuse through pristine graphene layers at600 ◦C, the temperature around which hydrogen intercalationhas been achieved experimentally. Considering vacancy clus-ters as prototypes of open regions in graphene, it is shown

that the hydrogen diffusion readily occurs through hollowdefects in graphene layers. We suggest that in practice thedefects, through which hydrogen diffusion occurs, may beopen core screw dislocations, grain boundaries and sampleedges, which can penetrate several carbon layers. It isfurther shown that hydrogen can easily migrate along thegraphene-SiC interface, break covalent bonds between thebuffer layer and the substrate, and thereby passivate the SiCsurface.

We have also studied effects of the lattice strain on thepermeability and chemical reactivity of graphene. Accordingto our calculations dilation of the graphene lattice by 10%results in an increased binding energy of a hydrogen atom,and a decrease in the energy barrier for a hydrogen atom todiffuse through the layer by as much as 75%.

ACKNOWLEDGMENTS

The authors would like to thank Vladimir Markevichand Derek Palmer for helpful discussions. Financial supportfrom the COST action MP0901 “NanoTP” is gratefullyacknowledged.

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