Lithium Intercalation Induced Decoupling of Epitaxial Graphene on

ARTICLE pubs.acs.org/JPCC

Lithium Intercalation Induced Decoupling of Epitaxial Graphene on SiC(0001): Electronic Property and Dynamic Process Yuanchang Li,† Gang Zhou,*,† Jia Li,‡ Jian Wu,† Bing-Lin Gu,† and Wenhui Duan*,† †

Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, People’s Republic of China ‡ Institute of Advanced Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, People’s Republic of China ABSTRACT: This work presents first-principles investigation of the dynamic process of lithium (Li) penetration through the buffer layer on 6H-SiC(0001) surface as well as the Li-insertion-induced change of electronic structure. It is found that the penetration is kinetically forbidden for perfect buffer layer because of the size confinement of its honeycomb structure. From the analysis of rate coefficient under real experimental conditions, topological defects no smaller than 8-membered ring are predicted to be essential for Li intercalation. Along with the Li insertion, the electronic property of the buffer layer is changed from n-type doping (Li adsorption) to that of quasi-free-standing graphene (Li intercalation). It is the electron injection by Li that results in the dissociation of the Si
C bonds and the decoupling of Li-intercalated buffer layer from the substrate. Moreover, we demonstrate the influence of such topological defects on the electronic property of epitaxial graphene, which provides some useful hints for understanding the observed gap and midgap state behavior.

I. INTRODUCTION Because of its extremely high free-carrier mobility1 and long ballistic mean free path at room temperature,2 graphene holds the promise of a revolution in the electronic industry. To realize micro- and nanoelectronic devices, great efforts are being made to develop new methods or technologies for producing largescale graphene. Among the methods considered, epitaxial growth on silicon carbide (SiC) has attracted considerable attention because of two advantages of epitaxial graphene: large wafer size and direct growth on semiconducting substrate. However, a buffer layer is always first formed during graphitization of SiC(0001) and, consequently, sandwiched between the substrate and graphene layers.3,4 Bonding to the substrate, the buffer layer loses the linearly dispersive π bands of free-standing graphene.4
6 Recently, much research effort has been devoted to manipulating the structural and electronic properties of the buffer layer by atomic adsorption or intercalation both theoretically and experimentally.7
11 Using different dopants, Jayasekera et al. realized a fine-tuning of the Fermi level with respect to the Dirac point and even half-metallicity under a proper gating.7 Choi et al. observed the n-type doping of graphene by sodium (Na) intercalation between the buffer and top graphene layers.8 In addition, Gierz et al. showed a transition of n-type doping from p-type doping for graphene with the decrease of intercalated Au
graphene distance.9 Especially, H,10 Li,11 and Au9 intercalation will make the buffer layer decouple from the SiC substrate and thus recover the character of quasi-free-standing graphene. It is experimentally proposed that the decoupling phenomenon can be attributed to the saturation of topmost Si atoms of the SiC r 2011 American Chemical Society

substrate by the intercalated atoms.9,10 However, the detailed mechanism is still unclear. Besides the spatial expansion effect as suggested in H intercalation case,12 electron injection accompanying with the dopants (e.g., Li) intercalation may also play an important role in the decoupling. Furthermore, the dynamic process of the dopant intercalation has not been investigated so far, and little is known about how the dopants intercalate into the interface between the buffer layer and the SiC substrate. What is the key factor in the dynamic process? As is well-known, any atom, including the smallest H, cannot readily penetrate through the perfect honeycomb lattice.13
15 In reality, during graphitization epitaxial graphene on SiC(0001) always contains a few topological defects (e.g., pentagon or heptagon) apart from the basal hexagon16,17 because of the effect of synthetic conditions. These topological defects, especially the large ones, can not only provide real channels for atom intercalation but also affect the electronic properties of epitaxial graphene dramatically. In this article, we investigate the effect of topological defects on the Li penetration process through the buffer layer on SiC(0001) by first-principles calculations. We find that the size confinement effect (i.e., geometrical effect) is dominant in the dynamic process, and Li intercalation spontaneously decouples the buffer layer from the SiC, in agreement with the recent experimental observation.11 The decoupling of Li-intercalated buffer layer is mainly attributed to the breaking of the Si
C bond Received: September 9, 2011 Revised: October 24, 2011 Published: October 31, 2011 23992

dx.doi.org/10.1021/jp208747q | J. Phys. Chem. C 2011, 115, 23992–23997

The Journal of Physical Chemistry C

ARTICLE

and the “in situ” formation of Li
silicide, which is different from that of H intercalation.12 Our above findings not only reproduce the experimental observation but also resolve the confusion of Li diffusion into the interface. Furthermore, we also explore the effect of defects on the electronic property of epitaxial graphene. These results are of importance to understand the microstructure of epitaxial graphene and manipulate its electronic properties for practical device applications.

II. CALCULATION METHOD AND MODEL The calculations, including geometrical optimization, electronic structure, and dynamic simulation, were carried out within the framework of density functional theory as implemented in the Vienna ab initio simulation package (VASP).18 Projector augmented wave19 pseudopotentials and Ceperley
Alder (CA)20 local density approximation (LDA) were employed to describe the electron
ion interaction and exchange-correlation energy, respectively. The cutoff of the plane wave basis set was 400 eV. The minimum-energy path and energy barriers for the migration/penetration were calculated using climbing √ image nudged elastic band (CI-NEB) method.21 We adopted a 3  √ 3R30° supercell on 6H-SiC(0001), accommodating a 2  2 graphene cell (Figure 1). The substrate was modeled by six SiC bilayers with the bottom dangling bonds (DB) passivated by the H atoms. The bottom three SiC bilayers were fixed at their bulk configuration while the other atoms were relaxed without any symmetry constraint until the residual forces were less than 0.01 eV/Å. To probe the defect√ effect on √the electronic property of epitaxial graphene, a larger 2 3  2 3R30° cell was used. A Γ-centered k-meshes of 15  15 √ 1 and 7√ 7  1 were applied √ to√sample the Brillouin zone of 3  3R30° and 2 3  2 3R30° cells, respectively. In the calculations of defects, the heptagon and octagon were included by introducing Stone
Wales (SW) defects and 5
8
5 rings (d585), both of which commonly exist in graphene.22 Note that the binding or intercalation energy is defined as the energy difference between the reactants (the substrate and the Li atom) and the products (the Li-adsorbed or -intercalated complex). A positive value means an exothermic reaction or process. III. RESULTS AND DISCUSSION A. Atomic Configurations and Band Structures of Li Adsorption and Intercalation. For the buffer layer on the

SiC(0001) surface, a part of carbon atoms (denoted as Cb atoms) chemically bond with the underneath Si atoms (hereafter referred to as the Si
Cb bond).4
6 This results in atomic corrugation in the buffer layer, which is different from the intrinsic ripple in graphene (i.e., thermal fluctuations),23 and the absence of the linearly dispersive π bands in the electronic structure. According to the experiment of Li intercalation in epitaxial graphene on SiC,11 we start with Li adsorption on the buffer layer. Note that carbon atoms in the buffer layer can be divided into two groups: Cb atoms bonding with the underneath Si atoms and the others (denoted as Cf). We examine various adsorption configurations to search for the ground state of Li adsorption. As shown in Figure 1a, there are six high-symmetry adsorption sites: top sites of the Cf (T1) and Cb (T2) atoms, center sites of the Cf
Cf (B1) and Cf
Cb (B2) bonds, center sites of the flat (H1) and corrugated (H2) hexagons (note that the corrugated one contains Cb atoms). Our structural

Figure 1. (a) Top view and (b) side view of SiC(0001) with a carbon buffer layer. Yellow (large) and gray (small) balls represent Si and C atoms, respectively. Note that for clarity only topmost SiC bilayer and half of the SiC substrate are shown, and C atoms in the buffer layer are represented by a stick lattice to distinguish them from the ones in the substrate in (a). High-symmetry sites for Li adsorption are shown in (a). Herein, symbols H and B denote the center sites of the hexagon and C
C bond, while T indicates the top site of the C atom. The hexagons in the buffer layer can be divided into two types according to whether they contains C atom bonding with the underneath Si atom or not, as denoted by numbers 1 and 2, respectively. The dashed rhombus shows the supercell considered here. For intercalation, the initial positions are chosen according to the three types of atoms (Sib, Siu, and C) in the topmost SiC bilayer as denoted in (b).

relaxations reveal three low-energy adsorption sites: H1, H2, and T2. The most favorable adsorption configuration is the Li adsorption at the H1 site, i.e., on the center of a flat hexagon (see the left panel of Figure 2a), with the binding energy of 0.9 eV. The binding strength is very close to that of Li adsorption on graphene (0.86 eV).24 The binding energies of the Li at the H2 and T1 sites are nearly degenerate, 0.15 eV smaller than that at the H1 site. The band structure of Li-adsorbed system (H1 configuration) is shown in the right panel of Figure 2a. It can be seen that, as compared with the case without Li adsorption,4,5 some new bands (highlighted in cyan in Figure 2a) cross the Fermi level, causing the n-type doping, but the Fermi level is still pinned by the DB electrons of the unsaturated Si atoms below the buffer layer. Then we turn to study the Li-intercalation system. As shown in Figure 1b, the top SiC bilayer contains three types of atoms: fully coordinated Si atoms (Sib), three-coordinated (unsaturated) Si (Siu), and the C atoms (C). Correspondingly, we choose various initial positions of Li intercalation at the interface. After structural relaxation, we obtain two stable Li-intercalated configurations corresponding to the Li saturating the Sib and Siu, respectively (hereafter referred to as the Li
Sib and Li
Siu configurations), with the intercalation energies of
0.24 and
0.42 eV. 23993

dx.doi.org/10.1021/jp208747q |J. Phys. Chem. C 2011, 115, 23992–23997

The Journal of Physical Chemistry C

ARTICLE

Figure 2. The most stable atomic configurations and corresponding band structures for (a) Li adsorption on and (b) intercalation into the buffer layer on the SiC substrate. Yellow, gray, white, and pink balls represent Si, C, H, and Li atoms, respectively. In (a), for the sake of clarity, only topmost SiC bilayer is shown, and C atoms in the buffer layer are represented by a stick lattice to distinguish from the ones in the substrate, and the new bands across the Fermi level as compared with the case without Li adsorption are highlighted in cyan. The Fermi level (red horizontal) is set to zero in the band structures.

The negative value means Li intercalation is an endothermic process, which may occur only at elevated temperature. This is in accordance with the experimental observation that the annealing at 330 °C makes the deposited Li islands vanish, and once the Li is sandwiched by the buffer layer and the substrate, it is preserved in situ at room temperature.11 In the favorable Li
Sib configuration (Figure 2b), the two Si
Cb bonds are broken and the Li weakly bonds to the two Sib atoms. Consequently, the buffer layer is structurally decoupled from the SiC substrate (the average distance between them becomes 4.31 Å). In contrast, in the Li
Siu configuration (not shown in the figure), the Li only passivates the unsaturated Siu, which induces a further structural distortion of the top SiC bilayer, and the buffer layer is not decoupled although the Si
Cb increases by about 0.1 Å. In other words, the Li prefers to break the Si
Cb bond and then bonds with more Si atoms, rather than saturate the DB of Siu. This result is completely opposite to that observed in H-intercalated case, where the DB is preferentially passivated.12 The energy difference between the Li
Sib and Li
Siu configurations is rather small (0.18 eV), suggesting that both two configurations may appear under practical experimental conditions. The possible coexistence of a mixture of decoupled and nondecoupled regions in the buffer layer was proposed previously11 in order to explain the observed three π bands from only a single sheet of graphene plus a buffer layer. Our study provides a strong support for this picture. In addition, the finding that the decoupling only occurs in the Li
Sib case may also explain the observed lower efficiency of Li than H in the decoupling the buffer layer from the substrate.11 The difference in Li and H intercalations mainly arises from different interactions of the Li and H atoms with the terminal Si atoms of the SiC substrate. In principle, the H atom tends to form the covalent bond, so spontaneously approaches to the Siu under the attraction of the DB; while the lower electronegativity determines that Li always donates the electrons, so an ionic-like bond is preferable between the Li and the terminal Si atoms. In this regard, the Li atom prefers the Si
Cb bond to the DB. The different bonding characteristics (ionic or covalent) of Li and H were also observed in silicon electrodes of lithium-ion batteries very recently.25 The interaction mode between the intercalated Li and the terminal Si atom determines the final intercalation structures and electronic properties. Before Li intercalation, the electron is transferred to the Cb from the Si in the polar Si
Cb bonds because of the lower electronegativity of Si compared to C.

So when adsorbed on the Si
Cb bond, the Li prefers to stay close to the Si and then donates the electron. The accepted electron increases the anionicity of the Si, facilitating the breaking of the Si
Cb bond. As a result, the buffer layer is decoupled from the SiC substrate (left panel of Figure 2b), accompanying with the occupation of Li atoms at the interstitial sites just below the originally corrugated hexagon. Another important evidence for the ionic-like Li
Si bond is that the top Si layer gets more wrinkled (the largest height difference is 0.53 Å) than before (the largest height difference is 0.33 Å). The band structure of the Li
Sib intercalation configuration, as shown in the right panel of Figure 2b, further demonstrates the decoupling behavior. One can see that the linearly dispersive π bands are restored and the Dirac point lies 1 eV below the Fermi energy at the K point, implying that quasi-free-standing graphene is obtained. The above results from Li intercalation are in good agreement with the experimental observations.11 B. Dynamic Process of Li Penetration through Buffer Layer. It is important to explore the dynamic process of Li insertion for understanding doping effect, optimizing doping and annealing conditions, and choosing suitable doping materials for graphene-based electronic devices. Our calculations and analysis in section IIIA clearly indicate the process from Li adsorption to Li intercalation is endothermic. Moreover, the minimum and maximum distances between the buffer layer and the substrate are respectively 1.99 Å (corresponding to the Si
Cb bond length) and 2.60 Å, much smaller than the interlayer distance of graphite (∼3.35 Å26). Such a spatial confinement would greatly hinder lateral diffusion of Li into the system, unlike the case of Li-intercalated graphite. Therefore, in the following, we will concentrate entirely on the Li-penetration process through the buffer layer. Previous work showed that the diffusion barrier of the Li atom on graphene does not exceed 300 meV.27 It is obvious that typical experimental temperature (up to 330 °C) is high enough to drive the migration of Li atom on the buffer layer. So we will not consider the process of the Li migration on the buffer layer any more, but directly calculate the minimum-energy path of Li penetrating through the buffer layer. The minimum-energy path obtained is through the corrugated hexagon, with H2 as initial adsorption site and a transition state that the Li is embedded in the graphene sheet, as illustrated in Figure 3. We can see only one peak in the minimum-energy path, indicating that the decoupling of the buffer layer from the substrate is a natural consequence of the Li intercalation. The calculated energy barrier is as high as 23994

dx.doi.org/10.1021/jp208747q |J. Phys. Chem. C 2011, 115, 23992–23997

The Journal of Physical Chemistry C

ARTICLE

Table 1. Energy Barriers (ΔE) of Li Penetration through Different Kinds of Rings in Graphene ring

a

Figure 3. Calculated minimum energy√path of √ Li penetrating through the buffer layer on the SiC substrate. A 3  3R30° supercell is used in the calculations. The x-axis indicates reaction coordinate of the process. Yellow, gray, and pink balls represent Si, C, and Li atoms, respectively. The energy barrier is 3.98 eV. The inset shows the transition state configuration.

3.98 eV for Li penetrating through the perfect buffer layer composed of flat and corrugated carbon hexagons. In order to quantify the possibility of the Li penetration under real experimental conditions, we further calculate the corresponding rate coefficient k, defined by the van’t Hoff
Arrhenius formula within the harmonic approximation28 as 3N Q

k¼

j¼1

νIS j

3NQ
1 j¼1

e
ΔE=kB T

ð1Þ

νTS j

TS where νIS j and νj are respectively the frequencies of normal-mode at the initial and transition states. ΔE is the energy barrier for penetration at the transition state, and kB, T, and N are the Boltzmann constant, temperature, and the number of atoms, TS are obtained from respectively. The frequencies of νIS j and νj the phonon calculations at initial and transition state configurations. It is noted that similar thermodynamic analysis has been successfully used to demonstrate the defect migration in graphene.29 The obtained rate of Li penetration through the perfect buffer layer is 10
23 per second at experimental temperature of 330 °C. Even at elevated temperature of 600 °C, the rate coefficient k is only 10
13 per second. These low values indicate that the experimentally observed penetration is impossible through the perfect buffer layer. In fact, a simplified estimation based on eq 1 shows that in order to achieve a rate coefficient of ∼1 per second the energy barrier should not be higher than 1.2 eV. For the transition state (shown in the inset of Figure 3), the Li pushes away six carbon atoms of the hexagon on the way, and such a deformation of the lattice causes a large energy consumption (i.e., geometrical effect). Evidently, the energy barrier is dominantly determined by the size of channel (i.e., n-numbered ring) that Li atom penetrates through. This indicates that a single graphene sheet (SGS) model, in which no SiC substrate is introduced, should be applicable to estimate the penetration barrier. We first examine the accuracy of this approximate model. √ The √ effect of the mismatch between the SiC (0001)- 3  3R30° surface and graphene is taken into account by stretching the lattice of graphene by 8%5 in the SGS model. The calculated penetration barrier is 4.16 eV (see Table 1), only a little larger than the calculated value (3.98 eV) for the buffer layer with the

ΔE (eV)

hexagon

7.55

stretched hexagona heptagon

4.16 3.52

octagon

1.15

The honeycomb lattice of graphene is stretched by 8%.

SiC substrate. The small deviation likely arises from the atomic corrugation of the buffer layer which is omitted in the SGS model. Moreover, we also calculate the penetration barrier of the Li through the regular hexagon of ideal graphene (i.e., no stretch) and find it is 7.55 eV (Table 1), far larger than that through the stretched one. This is in agreement with the previous studies that the perfect honeycomb lattice may not be penetrated through by any atom, even the H.13
15 The above results indicate that the SGS model can yield a reasonable penetration barrier provided the “holes” in graphene honeycomb lattice have the same size as that on SiC substrate. It should be noted that epitaxial graphene was experimentally found to exhibit a small strain,30,31 rather than √ compressive √ √ a large tensile strain in a 3  3R30° model. In fact, by a 6 3 √ 6 3R30° reconstruction of SiC(0001) surface, the lattice mismatch between the buffer layer and the SiC substrate can be greatly reduced.6 To obtain the penetration barrier in real conditions, we should discard the 8% stretching. Moreover, Li penetrates not only the buffer layer but also the above graphene layer in experiment,11 whose lattice constant is also very close to the equilibrium one in free-standing graphene.30 Therefore, we adopt the SGS model with the equilibrium lattice constant to study the defect-mediated intercalation of Li in the system. The topological defects in epitaxial graphene are usually composed of n-membered rings.16,17,22 Generally speaking, the larger the rings are, the smaller should the penetration barrier be. We focus on the cases of the heptagon and octagon. They are just larger than the basal hexagon and, more importantly, are clearly identified in graphene by transmission electron microscopy.22 Here, we employ a large enough supercell of 8  8 to eliminate the interaction between neighboring defects. The calculated penetration barriers through the heptagon and octagon are 3.52 and 1.15 eV, respectively (see Table 1). At this rate, we can deduce that for Li penetration the size of the topological defect should be no smaller than the octagon, while a pentagon
heptagon pair that is frequently encountered in sp2 carbon systems is not large enough. It is worth noting that all the values in Table 1 are smaller than those of Li entering carbon nanotube through the side walls.13 This difference can be attributed to the curvature effect, especially for the small tubes. C. Defect Effect on the Electronic Properties. As discussed above, for Li penetration, the buffer layer should contain at least octagon. In what follows, we turn our attention to the effect of the d585 defect on the electronic property of epitaxial graphene on the SiC substrate. It is worth mentioning that two C atoms are missing in the d585 defect.22 It is substantially different from defects without missing atoms like SW defect32 and thus may have different physical properties. Because of the inequivalence of Cb and Cf, the d585 have two types of patterns dependent on the two missing atoms (one with two Cf atoms and the other with 23995

dx.doi.org/10.1021/jp208747q |J. Phys. Chem. C 2011, 115, 23992–23997

The Journal of Physical Chemistry C

ARTICLE

Figure 4. (a) Band structure of buffer layer with 5
8
5 defect on the SiC (0001) substrate. (b) Atomic configuration (side view) and band structure of the system with an additional perfect graphene on the defective buffer layer. Plot of decomposed charge density in the left panel corresponds to the midgap states labeled by α in the right panel, with the isosurface of 40 e/Å3. The Fermi level is always set to zero (red horizontal line).

Cb and Cf). Our binding energy calculations reveal that the d585 defect with two Cf atoms missing is more favorable by 1.26 eV. The band structures of the defective buffer layer and the one covered with an additional perfect graphene layer on the SiC substrate are shown in Figures 4a and 4b, respectively. Unlike the defect-free situation, where the Fermi level is pinned by the DB state of the Siu, the band structure exhibits a thoroughly gapped feature when only the buffer layer on the SiC is considered (see Figure 4a). There are still no linearly dispersive π bands. Whereas the situation is quite different when a perfect graphene layer is added on the buffer layer, the π bands recover, as shown in the right panel of Figure 4b. It can be seen that the Dirac cone is split accompanying with the appearance of the midgap states. The calculated gap is 0.23 eV, very close to the experimental value of 0.26 eV.33 In consideration of the systematical underestimation of the band gap by LDA calculations, the value can be viewed as a lower bound for the actual case. To trace the origin of midgap states, we plot the decomposed charge density of these two bands (labeled by α) in the left panel of Figure 4b. Clearly, they are mainly contributed by the buffer layer (especially the C atoms around the defect). The upper half of linear Dirac cone crosses the Fermi level, indicating that the system is slightly electrondoped. Bader analysis34 of the charge distribution shows an electron density of ∼3.5  1012 cm
2 in the topmost graphene layer. Such an interlayer electron transfer behavior between the graphene layers has been reported experimentally.35

IV. CONCLUSIONS We systematically investigate the Li adsorption on, penetration through, and intercalation into the buffer layer on the SiC (0001) substrate using first-principles calculations. We propose a defect-mediated mechanism for the Li intercalation observed in experiment.11 Along with the electron injection by Li intercalation, the Si
C bonds between the buffer layer and substrate are broken, and thus the buffer layer is decoupled from the substrate, leading to quasi-free-standing graphene. This finding sheds light on the dopant selection for the buffer layer decoupling. Moreover, we demonstrate that the missing-atom defects in the buffer layer may be responsible for the gap opening and midgap state observed in epitaxial graphene. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (G.Z.); dwh@phys. tsinghua.edu.cn (W.D.).

’ ACKNOWLEDGMENT We acknowledge the support of the Ministry of Science and Technology of China (Grants 2011CB921901 and 2011CB606405) and the National Natural Science Foundation of China (Grant 11074139). ’ REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Science 2006, 312, 1191. (3) Choi, J.; Lee, H.; Kim, S. J. Phys. Chem. C 2010, 114, 13344. (4) Varchon, F.; Feng, R.; Hass, J.; Li, X.; Nguyen, B. N.; Naud, C.; Mallet, P.; Veuillen, J.-Y.; Berger, C.; Conrad, E. H.; Magaud, L. Phys. Rev. Lett. 2007, 99, 126805. (5) Mattausch, A.; Pankratov, O. Phys. Rev. Lett. 2007, 99, 076802. (6) Kim, S.; Ihm, J.; Choi, H. J.; Son, Y.-W. Phys. Rev. Lett. 2008, 100, 176802. (7) Jayasekera, T.; Kong, B. D.; Kim, K. W.; Nardelli, M. B. Phys. Rev. Lett. 2010, 104, 146801. (8) Choi, S.-M.; Jhi, S.-H. Appl. Phys. Lett. 2009, 94, 153108. (9) Gierz, I.; Suzuki, T.; Weitz, R. T.; Lee, D. S.; Krauss, B.; Riedl, C.; Starke, U.; H€ochst, H.; Smet, J. H.; Ast, C. R.; Kern, K. Phys. Rev. B 2010, 81, 235408. (10) Riedl, C.; Coletti, C.; Iwasaki, T.; Zakharov, A. A.; Starke, U. Phys. Rev. Lett. 2009, 103, 246804. (11) Virojanadara, C.; Watcharinyanon, S.; Zakharov, A. A.; Johansson, L. I. Phys. Rev. B 2010, 82, 205402. (12) Lee, B.; Han, S.; Kim, Y.-S. Phys. Rev. B 2010, 81, 075432. (13) Meunier, V.; Kephart, J.; Roland, C.; Bernholc, J. Phys. Rev. Lett. 2002, 88, 075506. (14) Guisinger, N. P.; Rutter, G. M.; Crain, J. N.; First, P. N.; Stroscio, J. A. Nano Lett. 2009, 9, 1462. (15) Persson, K.; Sethuraman, V. A.; Hardwick, L. J.; Hinuma, Y.; Meng, Y. S.; van der Ven, A.; Srinivasan, V.; Kostecki, R.; Ceder, G. J. Phys. Chem. Lett. 2010, 1, 1176. (16) Qi, Y.; Rhim, S. H.; Sun, G. F.; Weinert, M.; Li, L. Phys. Rev. Lett. 2010, 105, 085502. (17) Rutter, G. M.; Crain, J. N.; Guisinger, N. P.; Li, T.; First, P. N.; Stroscio, J. A. Science 2007, 317, 219. (18) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169. Comput. Mater. Sci. 1996, 6, 15. (19) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (20) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (21) Henkelman, G.; Uberuaga, B. P.; Jonasson, H. J. Chem. Phys. 2000, 113, 9901. (22) Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. ACS Nano 2010, 5, 26 and references therein. 23996

dx.doi.org/10.1021/jp208747q |J. Phys. Chem. C 2011, 115, 23992–23997

The Journal of Physical Chemistry C

ARTICLE

(23) Fasolino, A.; Los, J. H.; Katsnelson, M. I. Nature Mater. 2007, 6, 858. Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S. Nature (London) 2007, 446, 60. (24) Ataca, C.; Akt€urk, E.; Ciraci, S.; Ustunel, H. Appl. Phys. Lett. 2008, 93, 043123. (25) Zhao, K.; Wang, W. L.; Gregoire, J.; Pharr, M.; Suo, Z.; Vlassak, J. J.; Kaxiras, E. Nano Lett. 2011, 11, 2962. (26) Takami, N.; Satoh, A.; Hara, M.; Ohsaki, I. J. Electrochem. Soc. 1995, 142, 371. (27) Persson, K.; Hinuma, Y.; Meng, Y. S.; Van der Ven, A.; Ceder, G. Phys. Rev. B 2010, 82, 125416. (28) Vineyard, G. H. J. Phys. Chem. Solids 1957, 3, 121. (29) Li, J.; Li, Z.; Zhou, G.; Liu, Z.; Wu, J.; Gu, B.-L.; Ihm, J.; Duan, W. Phys. Rev. B 2010, 82, 115410. (30) Ferralis, N.; Maboudian, R.; Carraro, C. Phys. Rev. Lett. 2008, 101, 156801. (31) Robinson, J. A.; Wetherington, M.; Tedesco, J. L.; Campbell, P. M.; Weng, X.; Stitt, J.; Fanton, M. A.; Frantz, E.; Snyder, D.; VanMil, B. L.; Jernigan, G. G.; Myers-Ward, R. L.; Eddy, C. R., Jr.; Gaskill, D. K. Nano Lett. 2009, 9, 2873. (32) Peng, X.; Ahuja, R. Nano Lett. 2008, 8, 4464. (33) Zhou, S. Y.; Gweon, G.-H.; Fedorov, A. V.; First, P. N.; de Heer, W. A.; Lee, D.-H.; Guinea, F.; Castro Neto, A. H.; Lanzara, A. Nature Mater. 2007, 6, 770. (34) Henkelman, G.; Arnaldsson, A.; Jonsson, H. Comput. Mater. Sci. 2006, 36, 254. (35) Ohta, T.; Bostwick, A.; McChesney, J. L.; Seyller, T.; Horn, K.; Rotenberg, E. Phys. Rev. Lett. 2007, 98, 206802.

23997

dx.doi.org/10.1021/jp208747q |J. Phys. Chem. C 2011, 115, 23992–23997