Since its discovery in 2004 (Nobel prize in 2010), graphene -a single sheet of carbon atoms forming the thinnest free standing material to date- has attracted enormous interest due to its potentially tunable and exotic structural and electronic properties (Castro Neto et al., 2009; Geim & Novolselov, 2007; Katsnelson et al., 2006, 2007; Novoselov et al., 2004, 2007; Ohta et al., 2006; Y. Zhang et al., 2005). The pristine graphene is characterized as a zero-gap semiconductor with bonding π and antibonding π* bands touch in a single point at the Fermi level (EF) at the corner of the Brillouin zone, and close to this so-called Dirac point the bands display a linear dispersion, leading to extremely high charge carriers mobility at room temperature of approximately 15,000 cm2/V.s (Geim & Novolselov, 2007) which is significantly higher than that of the widely-used semiconductor, namely silicon (Si), of approximately 1400 cm2/V.s. Like carbon nanotubes, measurements (Lee et al., 2008) have shown that graphene is extremely strong and rigid compared to Si-based materials. These incredibly fascinating properties alongside the high thermal conductivity suggest that graphene is an excellent candidate for the applications in the circuits beyond the conventional complementary metal-oxide semiconductor technology and many other potential applications. Moreover and recently, the possibility of using graphene as a highly-sensitive gas sensor has been reported as the good sensor properties of carbon nanotubes are already known. It was shown that the increase of the concentration of graphene charge carrier induced by adsorbed gas molecules can be used to make highly sensitive sensors. These highly-sensitive properties of graphene can be attributed to the fact that graphene is a low-dimensional structure with only a surface but no volume which increase the chemical reaction of adsorbates and the surface atoms. Additionally, the high conductivity of graphene even in low charge density is another reason for being a highly-sensitive sensor.
Having established the importance of pristine graphene in many potential applications, the adsorption of single atoms (Chan et al., 2008; Farjam & Rafii-Tabar, 2009; Han et al., 2007; Hao et al., 2006; Li et al., 2008; Mao et al., 2008; Medeiros, 2010; Yang, 2009) and molecules (Duplock et al., 2004; Elias et al., 2009; Giannozzi et al., 2003; Ito et al., 2008; Leenaerts et al., 2008, 2009; Nakamura et al., 2008; Novoselov et al., 2004; Pinto et al., 2009; Sanyal et al., 2009; Schedin et al., 2007; Wehling et al., 2008; Y.-H. Zhang, 2010) on the bare graphene surface has been the subject for different theoretical and experimental investigations due to their promising applications in nanoscale electronics, bioelectronics, gas sensors, and hydrogen storage devices. Among these adsorbates, hydrogen has been considered as one of the most interesting and fantastic candidates. Recently, it has been experimentally reported, using the transmission electron microscopy, that a graphene sheet can be chemically converted into graphane through a hydrogenation process by reacting with atomic hydrogen (Elias et al., 2009). This process, however, transforms the zero-gap semiconductor graphene into a wide-gap semiconductor (insulator) graphane. Theoretically reported studies (Boukhvalov et al., 2008; Sofo et al., 2007) using the density functional scheme, have revealed that the chairlike configuration, with hydrogen atoms attached to the carbon atoms in alternative manner, is the energetically most preferable structure for graphane. Sofo et al. (Sofo et al., 2007) have found that the chairlike and boatlike conformers are semiconducting with 3.5 eV and 3.7 eV, respectively. As has been claimed in many literatures (H. Ohno, 1998; Y. Ohno et al., 1999; Savchenko, 2009), future hydrogen-fuel technologies should make use of graphane as hydrogen storage due to its very high hydrogen density. Moreover, this extremely thin material with a finite band gap is also likely to find its use in many technological and industrial applications. Overall, graphene surface could be successfully used as a base for creating new promising and useful materials, and it would be of quite interest to theoretically investigate the effects of incorporating various molecules into its structure for different technological and industrial applications.
The adsorption of various molecules onto graphene has also been investigated. The structural and electronic properties of oxygen-adsorbed graphene have been theoretically studied by Nakamura et al. (Nakamura et al., 2008) and Ito et al (Ito et al., 2008). Their results have indicated that the adsorption of oxygen molecules onto graphene produces epoxy and ether group phases which are almost bistable. Moreover, they have concluded that the ether structure is the most energetically preferable for adsorption involving both sides of the sheet, while the one-side adsorption structure appears only as a meta-stable phase, with a finite energy gap at the K point emerges and its value increases as the number of oxygen increases with respect to the number of carbon atoms. The key charge transfer mechanisms upon adsorption of NH3, NO, and NO2 onto graphene have been reported by Leenaerts et al. (Leenaerts et al., 2008, 2009). Their theoretical results indicate that the NO2 adsorbates induce a relatively strong doping comparing to the NO molecule. Within the framework of the local density approximation of the density functional theory, Pinto et al. (Pinto et al., 2009) have investigated the chemisorption of tetrafluoro-tetracyanoquinodimethane (F4-TCNQ) molecule on pristine graphene by means of the electronic properties. It was reported that the F4-TCNQ molecule acts like a p-type dopant for graphene with an approximately charge of 0.3 e/molecule being transferred from the highest occupied molecular orbital (HOMO) of graphene to the lowest unoccupied molecular orbital (LUMO) of the molecule. Zhang et al. (Y.-H. Zhang et al., 2010) have recently investigated the binding of organic electron donor and acceptor molecules on graphene sheets within the framework of the density functional theory. They found that the adsorption of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) and tetrathiafulvalene (TTF) cause hybridizations between the molecular levels and the graphene valence bands. These hybridizations transform the zero-gap semiconductor graphene into a metallic graphene. Despite the available studies, there are no enough theoretical comparative study on the physics and chemistry of the adsorption of small molecules onto the surface of pristine graphene.
In the present chapter, we aim to theoretically investigate the fundamental changes of the structural and electronic properties of graphene upon the incorporation of hydrogen, benzene, and naphthalene molecules. The first-principles calculations will be performed using the density functional theory in its local density approximation scheme and the pseudopotential method.
2. Calculation methodology
The present ab initio calculations have been performed using the density functional theory (DFT) (Hohenberg & Kohn, 1964) with a plane wave basis set as implemented in the QUANTUM ESPRESSO simulation package (Giannozzi et al., 2009). The electron–electron interactions were expressed within the local density approximation (LDA) as parameterized by Perdew and Zunger (Perdew & Zunger, 1981). The electron–ion interaction was treated by using the ultrasoft pseudopotential for carbon and hydrogen (Vanderbilt, 1990). We expanded the single-particle Kohn–Sham (Kohn & Sham, 1965) wave functions using a linear combination of plane-wave basis sets with a kinetic energy cutoff of 45 Ry. The Kohn–Sham equations were Self consistently solved by employing a 14×14×1 k points Monkhorst–Pack set (Monkhorst & Pack, 1976) within the hexagonal Brillouin zone. The repeated supercell technique was used to model the studied graphene-based structures. In each surface structure of pristine and molecule-adsorbed graphene we considered a 6×6×1 unit cell containing 72 carbon atoms. We have used our calculated in-plane lattice parameter for graphene of 2.45 Å which is in good agreement with the previously reported theoretical (Ito et al., 2008; Schabel & Martins, 1992; Yin & Cohen, 1984) and experimental values for bulk graphite (D. Mckie & C. Mckie, 1986). To minimize the interactions between the graphene sheet and its periodic image, we considered a vertical separation of 14.65 Å (six times the lattice parameter) along the surface normal direction. These parameters have been carefully chosen after several calculations to obtain well-converged results. Relaxed atomic positions for carbon and hydrogen atoms were obtained by using the total-energy and force minimization methods following the Hellmann–Feynman approach. The equilibrium atomic positions were determined by relaxing all atoms in the cell except the carbon atom at the origin which was kept in its bulk position.
3. Results and discussion
In the following subsections we will present, based on ab initio calculations, a comparative study of the structural and electronic properties of pristine graphene, hydrogen-adsorbed graphene (graphane), benzene-adsorbed graphene, and naphthalene-adsorbed graphene. To establish well-defined comparative study we have performed the calculations using unit cells of similar sizes and parameters.
3.1. Pristine graphene
It is rather important for our present comparative study to start with the structural and electronic properties of the pristine graphene. Figure 1 shows a schematic view of the fully-relaxed structure of the pristine graphene, indicating the basic structural parameters. It is well-known that each carbon atom has two 2s and two 2p electrons in its valence state. These four electrons lead to various sp-hybridized orbitals. For graphene, each carbon atom is bonded to three other carbon atoms according to an sp 2 hybridization. In the present calculations the C-C bonds are found to be 1.41 Å which are smaller than the C-C bond lengths of diamond of 1.52 Å. The C-C-C angle is measured to be 120° which is slightly larger than the prospective value of 109.5° in its diamond structure. These values suggest that, unlike the ideal sp 3 diamond structural phase, graphene has a significant sp 2 nature as stated above. This feature, therefore, leads to the considerable rigidity of graphene materials comparing with the normal semiconducting materials, such as Si.
The electronic band structure of the clean graphene sheet is plotted in Fig. 2 along the principal directions of the hexagonal Brillouin zone. It is clearly shown that the band structure of pristine graphene has a zero-gap semiconducting nature. It is important to note the folding of the bands due to the used supercell. In this plot, the top of the valence state and the bottom of the conduction state degenerate at the Γ point (Dirac point) instead of the K point of the hexagonal Brillouin zone. These two bands obey a linear in-plane dispersion relation near the Fermi energy at the Γ point of the Brillouin zone resulting in zero effective mass for electrons and holes and high mobility of charge carriers.
In a previous report (AlZahrani & Srivastava, 2009) we have studied the in-plane dispersion curves, at the Γ point, slightly above and slightly below the Fermi energy to extract the velocities of electron and hole carriers. These velocities were estimated to be 1.11×106 m/s and 1.04×106 m/s. The partial charge density plots of these two states at the K point confirm the bonding π and antibonding π* orbital nature of the HOMO and LUMO states of pristine graphene, as clearly shown in Fig. 3.
3.2. Hydrogen-adsorbed graphene
The chemical adsorption of hydrogen atoms on pristine graphene has gained great interest due to the immense changes in the electronic properties of graphene. These changes lead to a new wide-gap semiconducting material which has the name of graphane. Subsequently, graphane has been experimentally synthesized and reported that it obeys a reversible hydrogenation-dehydrogenation process (Elias et al., 2009). This material, therefore, could open the gate for enormous technological and industrial applications, such as hydrogenstorage and two-dimensional nanoelectronics. Our purpose in this section is to find the energetically most stable geometry of graphane and then to compare its structural and electronic properties with those of pristine graphene. To model such a material, we have initially considered four different preliminary configurations depending on the adsorption sites of hydrogen atoms above and/or below the graphene sheet. These structures are chairlike, boatlike (Sofo et al., 2007), tablelike, and stirrup configurations as schematically shown in Fig. 4. The key building block of these structures is the number and orientation (up or down) of the attached hydrogen atoms in each hexagonal cell of graphene. The chairlike conformer consists of hydrogen atoms which are alternatively attached to the carbon atoms on both sides of the sheet. The hydrogen atoms in the boatlike conformer are alternatively attached in pairs to the carbon atoms on both sides. In the tablelike configuration the hydrogen atoms are attached to every carbon atom from one side of the sheet. Finally, the stirrup structure has three hydrogen atoms attached to the carbon atoms from the upper side of the sheet and also three others attached to the carbon atoms from the bottom side. Our self-consistent calculations indicate that the chairlike configuration is the energetically most stable structure (minimum energy structure) with an energy gain of approximately 0.129 eV, 0.131 eV, and 0.655 eV comparing with the boatlike, stirrup, and tablelike configurations,
respectively. These findings for chair and boatlike structures are very comparable with the previously reported results obtained by Sofo et al. (Sofo et al., 2007). We note that boatlike and stirrup configurations are almost meta-stable structures and can be found in H-rich environment. In the following lines, we will focus our discussion on the structural and electronic properties of the ground state structure of graphane (chairlike conformer).
We have started our calculations for chairlike geometry of graphane with a flat sheet of graphene and hydrogen atoms at 1.0 Å above carbon species. Minimization of this structure leads to a fully-relaxed configuration as schematically depicted in Fig. 5. From this figure we have found that the C–C bond length is approximately 1.49 Å, which is larger than the C–C bond length in the ideal graphene (1.42 Å). However, this value is almost comparable with the C–C bond length obtained for graphite (1.47 Å) and diamond (1.52 Å) using similar computational parameters. Moreover, the calculated graphane C–C bond length is in excellent agreement with the bond length of 1.48 Å obtained by Igami et al. (Igami et al. 2001). Upon the H adsorption, the basis carbon atoms in the cell are found to experience a vertical buckling (perpendicular distance between the two carbon sublattices) of approximately 0.46 Å, which is in excellent agreement with the theoretical values obtained by Boukhvalov et al. (Boukhvalov et al., 2008) and Sahin et al. (Sahin et al., 2010) and the experimental value extracted by Elias et al (Elias et al., 2009). Having this amount of buckling, the lattice constant of graphene increases from 2.45 Å to 2.50 Å. This amount of buckling leads not only to a structural variation but also to a significant change in the electronic properties of graphene.
Consistent with previously reported results (Boukhvalov et al., 2008; Sahin et al., 2010; Sofo et al., 2007), the C–H bond length is measured to be 1.12 Å, which is identical to the typical bond length of the hydrocarbon compounds. While the angle between two adjacent C-C bonds (C-C-C angle) is found to be 102°, the angle between C-H and C-C bonds (C-C-H angle) is determined to be 108°. The average value of these angles is slightly smaller than the tetrahedral angle of diamond of 109.5°. These values are in mild agreement with the previous theoretical results (Boukhvalov et al., 2008; Sahin et al., 2010). However, this suggests that the nature of C–C and C–H bonds is not entirely sp 3 but sp 3 -like. Overall, these findings for calculated bond lengths and angles clearly indicate that the bonding in graphane is sp 3 -like.
The electronic band structure of chairlike graphane is calculated along the principal directions of the hexagonal Brillouin zone as shown in Fig. 6. It is clearly noted that the bonding π and antibonding π* states of clean graphene are now removed. Since graphane is an sp 3-like saturated structure with every C atoms being bounded to three adjacent C atoms and a single H atom, the system is found to be non-magnetic semiconducting with a direct LDA band gap of 3.9 eV, with HOMO at EF -3.4 eV and LUMO at EF +2.5 eV.
This value of band gap is slightly larger than the reported value of 3.5 eV (Sofo et al., 2007). It is rather important to indicate that due to the well-known deficiency of the LDA in dealing with semiconducting systems, the underestimated band gap of 3.9 eV is corrected by GW0 approximation to become 5.97 eV (Lebèrgue et al., 2009). From Fig. 6, we clearly note that the uppermost occupied band is doubly degenerate at approximately 7 eV below the Fermi level at the zone edge, namely K point. This degeneracy has also been observed for pristine graphene but with energetic shift due to the charge transfer from H atoms towards the graphene. We also find a double degeneracy of the top of valence band at about 3 eV below the Fermi level. Such degeneracy suggests that these bands have a symmetrical orbital nature but with different effective masses. Above the Fermi level, we can identify band degeneracy at the zone edges K and M with eigenvalues of 8 eV and 5 eV, respectively. These features can be directly related to the graphene sheet as we have noted in Fig. 2 but with significant change in their energies. Inspection of the partial charge density, at the K point, of both HOMO and LUMO states reveals that the π bonding orbital in C-C bonds of graphene is broken and a new sp z orbital is created between H and the upper C atom (i.e. the carbon atom that was tilted upwards) upon hydrogenation process. Moreover, the antibonding π* orbital in graphene is removed and replaced by the antibonding state which is a hybridization of the H s and C p orbitals. These plots are shown in Fig. 7.
It is quite important for the device engineering and manufacturing to figure out the bonding nature of C-C and C-H bonds. To perform such an examination, we performed total charge density calculations in a plane and along the C–C and C–H bonds. Figure 8(a) shows a contour map of the total charge density in / plane. It clearly indicates that the charge distribution around the C-C bond is supportive of that in tetrahedrally coordinated diamond as shown in Fig. 8(b). Our results indicate that the C–C and C–H bonds have a noticeable degree of covalency, as shown in panels (c) and (d) of Fig. 8. A considerable amount of charge is uniformly localized around the carbon atoms. It is interesting to note that the double-hump feature of the charge density along the neighboring C atoms (Fig. 8(c)) is typical of the diamond structure, which is not an artifact of the pseudopotential method. Moreover, we have clearly observed that a little amount of charge being transferred from the hydrogen towards the carbon atoms. Quantitatively, we have used the Löwdin population analysis scheme (Lowdin, 1950) to obtain numeral information about the atomic charges. Employing this scheme, the wave functions are projected onto linear combinations of atomic orbitals; we find that a charge of 0.2e has been transferred from the hydrogen atoms to the carbon atoms for each unit cell. Our calculated value is in good match with the result obtained by Sofo et al (Sofo et al., 2007).
3.3. Benzene-adsorbed graphene
Rather than hydrogen, it has been reported that the adsorption of organic molecules on graphene leads to significant changes in the fundamental atomic and electronic properties of the substrate. To examine the reliability of these changes we will study the mechanism of the chemisorption of small molecules (benzene and naphthalene) on a clean sheet of graphene. This subsection will be designed to study the benzene-adsorbed graphene structure whereas the next subsection will detail the naphthalene-adsorbed graphene system. To investigate the basic properties of graphene upon the adsorption of benzene, we firstly check different possible adsorption sites of the molecule onto the substrate.
Neglecting the unfavorable substitutional sites, we have considered two configurations for the adsorption of benzene on pristine graphene. In these we have attempted a hollow and a stack adsorption sites, as schematically shown in Fig. 9. Therefore, to evaluate the energetically most preferable configuration between them, we compare their surface formation energies according to the formula:
The symbols,and indicate the total energies of the optimized structures of the benzene-adsorbed graphene, pristine graphene, and isolated benzene molecule, respectively. It is important to state that these total energies are calculated within similar unit cells and computational parameters. Using the above equation we find that the adsorption energies of hollow and stack structures are approximately -0.25 eV and -0.30 eV, respectively. These values suggest that the stack configuration represent the ground-state structure of the benzene-graphene system with energy gain of about 0.05 eV comparing with the hollow phase. Therefore we will focus our theoretical investigation on the stack configuration to determine the structural and electronic properties of benzene/graphene structure. The starting point towards the structural optimization of the present system is the initial position of benzene molecule above the graphene sheet. The molecular atoms (benzene molecule) are initially placed at 1.5 Å above the carbon atoms of the graphene. After several iterations of relaxation process, the benzene molecule adopts a planar geometry at 3.52 Å above the graphene sheet. While this value is consistent with the experimental value of 3.6 Å that is estimated from binding energy curves performed by Chakarova-Kack et al. (Chakarova-Kack et al., 2006), it is slightly larger than the value of 3.17 Å obtained by Zhang et al (Y.-H. Zhang et al., 2010). This inconsistency is due to the quite low energy cutoff used in their calculations. Subsequently we have found that the C–C and C–H bond lengths of benzene on the top of graphene are measured to be 1.39 Å and 1.10 Å, respectively. These values are identical to those of the hydrocarbons compounds of 1.40 Å and 1.10 Å for C-C and C-H bonds, respectively. Since the calculated C–C–C and C–C–H angles of the molecule are identical and equal to 120°, we conclude that benzene reorients itself in a planar manner above the graphene. This orientation has also been noted for F4-TCNQ (Pinto et al., 2009) which indicates similar adsorption mechanism for organic molecules on graphene. Adsorbed-graphene sheet, on the other side, has been found to have a C–C bond length of 1.41 Å and a C–C–C angle of 120°. These suggest that, even though benzene is being adsorbed, graphene preserves its basic structural behaviour.
Further, we have performed surface electronic band structure for the benzene-adsorbed graphene configuration along the high-symmetry directions, K→Γ and Γ→M, as shown in Fig. 10. Setting the Fermi level at the zero-energetic position, we clearly note that the Dirac point of the systems is coincided with the Fermi level, indicating a zero-gap nature. This indicates that, for low-energy states, the adsorption of benzene leads to unchanged electronic structure regarding to pristine graphene. Accordingly, this suggests that charge transfer is not expected to occur between the graphene and the molecule. Such an observation can be understood if we believe that only the states very far below/above the Dirac point of graphene are perturbed by the molecular adsorption. However, this conclusion is supportive of the result obtained by Zhang et al. (Y.-H. Zhang et al., 2010). In their study they found that the adsorption of benzene on pristine graphene results in insignificant amount of electronic charge being transferred from the molecule to the graphene sheet.
3.4. Naphthalene-adsorbed graphene
As has been performed for benzene-adsorbed graphene structure, we have tested at least two adsorption sites for naphthalene molecule onto graphene. Between hollow and stack configurations we have found that the latter represents the minimum-energy structure of naphthalene-adsorbed graphene, as shown in Fig. 11. Our calculations indicates that the adsorption energy of stack and hollow phases are approximately −0.47 eV and −0.39 eV, respectively. The molecule is found to be relaxed 3.15 Å above the sheet suggesting no bond formation between the molecule fragments and the carbon atoms of the graphene. Looking at the C–H bond length of the molecule we have identified no appreciable change and its typical value of 1.10 Å. Comparing the naphthalene-adsorbed system with the benzene-adsorbed system, we have clearly noted considerable alterations in the C–C bond lengths of the molecule. These bond lengths are categorized into three groups: 1.37 Å, 1.40 Å, and 1.43 Å. These values are in the acceptable range of the typical bond lengths of an isolated naphthalene molecule (1.36–1.42 Å). The C–C–C and C–C–H angles vary in the interval 121–122° and 118–120°, respectively. These results suggest a very tiny amount of vertical tilt in the carbon planes. However, the substrate keeps its original structure as also seen for benzene-adsorbed structure.
In Fig. 12, we have depicted the electronic band structure of the naphthalene/graphene system. Despite that the band structure for the benzene/graphene system looks very similar to the pristine graphene in the low-energy region (±2.0 eV with respect to Fermi level EF), the energy bands for the naphthalene/graphene system performs little changes below the Fermi level. From the figure we clearly identify a new flat (non-dispersive) band at energy of EF −1.3 eV. This band is believed to be originated from the molecule states. Overall, the system has an entire zero-gap behaviour with indication that no charge being transferred from/to the graphene substrate.
Within the framework of local density approximation of the density functional theory and pseudopotential theory we have presented a comparative ab initio study for the adsorption of molecules on a pristine graphene. The sp 2 structure and zero-gap behaviour are found to the fundamental characteristics of clean graphene with degenerate bonding π and antibonding π* states at the K point. Upon the adsorption of hydrogen atoms on pristine graphene, a chairlike configuration is found to be the energetically most stable structure for the system (graphane). As the four valence electrons of carbon atoms participate in the formation of the covalent bonzds with hydrogen atoms the π bands are removed from the band structure of graphane. The absence of these bands leads graphane to be a semiconducting with wide direct gap at the Γ point. Moreover, the structural transformation of carbon bonds from sp 2 to sp 3 -like hybridization results in an increase in the bond length from 1.41 Å to 1.49 Å. Unlike the hydrogen-adsorbed graphene, benzene and naphthalene-adsorbed structures are found to only stabilize the graphene sheet with no significant change in its low-energy electronic properties.