Band Gap Tuning of Hydrogenated Graphene: H Coverage and

Feb 10, 2011 - Institute of Textile and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong, P. R. China ... graphene from 0 to 4.66 eV by ...
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Band Gap Tuning of Hydrogenated Graphene: H Coverage and Configuration Dependence Haili Gao,†,‡ Lu Wang,†,‡ Jijun Zhao,†,‡,* Feng Ding,§ and Jianping Lu^ †

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, P. R. China ‡ College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, P. R. China § Institute of Textile and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong, P. R. China ^ Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States ABSTRACT: The electronic states of partially hydrogenated graphene (HG) structures are studied by the density functional theory calculations. Several types of HG configurations, including randomly removing of H pair, randomly removing individual H atoms, and ordered H pairs removal, are investigated. We find that the configurations with randomly removing H pairs are most energetically favorable. More interestingly, the band gap for such configurations decrease with H concentration and approaches zero around 67% H coverage. The ability to continuously tune the band gap of hydrogenated graphene from 0 to 4.66 eV by different H coverage provides a new pathway for engineering the electronic structure of graphene materials and enhances their applications in electronics and photonics.

1. INTRODUCTION Graphene, a single atomic layer of carbon atoms materials, has the potential to become a platform for engineering electronic devices of truly atomic thickness.1-3 The pristine graphene, with band crossing at the Dirac points of the Brillouin zone, is a semimetal with remarkable conducting properties.4,5 However, the gapless feature of graphene limits its applications in electronics and photonics;6 thus, a tunable band gap in the intermediate energy range (e.g., 1-3 eV) is highly desirable. There have been considerable efforts to open (and tailor) the band gap of graphene.7-30 So far, these gap-opening strategies can be cataloged into two basic mechanisms, either to disturb the band crossing at Dirac points via breaking the equivalence of the two sublattices of graphene, or to transform the carbon hybridization from sp2 into sp3 via chemical functionalization. The first mechanism can be realized by the substrate-graphene interaction,7,8 applying external electric field9,10 or uniaxial strain,11,12 cutting graphene into nanoribbons,12-14 and adsorption of molecules (e.g., H2SO4, H2O, NH3, and CrO3) on the graphene surface.15-17 Because the band crossing in graphene is very robust, the effectivity of this approach is limited and only relatively small band gaps of less than ∼0.3 eV (mid-infrared energy) have been achieved.6,8-10 In contrast, chemical functionalization of graphene can efficiently transform the hybridization state of carbon atoms from sp2 into sp3 and thus open a large gap up to several electron volts. Chemisorption of a variety of functional groups (including H, F, OH, COOH, O, etc.) on either one side or both sides of the graphene was theoretically explored via first-principles r 2011 American Chemical Society

calculations.18-24 The predictions of large gap opening were confirmed by recent experiments on oxidation25-28 or hydrogenation of graphene.29,30 For example, a tunable gap as function of oxidation level was reported in the experiments of graphene oxide (GO) or reduced GO,27 which was also demonstrated by first-principles calculations.24 Elias et al. reported reversible hydrogenation of graphene and showed that the electronic properties could be controlled by H adsorption and desorption.29 After reacting with plasma-oriented atomic hydrogen, graphene was transformed from a semimetal into an insulating graphane, which was theoretically predicted by Sofo and co-workers.19 Recently, Balog et al. observed that patterned H adsorption on the Moire superlattice positions of graphene can open a band gap of ∼0.45 eV.30 In addition, the electronic properties of fully hydrogenated graphene (namely, graphane) can be tailored in different ways; for examples, cutting the graphane sheet into nanoribbons can tune the band gap of graphane from 3.58 to 3.82 eV,31 creating a vacancy H cluster in graphane can reduce the band gap as the vacancy size increases,32 removing half of the H atoms on graphane even results in a small indirect gap and ferromagnetism.33 The zero band gap of graphene and the large band gap of graphane (5.4 eV from accurate GW calculations20) suggest that it is possible to tailor the band gap in a wide range by controlling the hydrogen coverage. It was known that structural defect or chemical Received: October 1, 2010 Revised: December 22, 2010 Published: February 10, 2011 3236

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Figure 1. (a) Top view (upper) and side view (lower) of partially hydrogenated graphane with 87.5% H coverage (C240H210 in supercell), (b) top view (upper) and side view (lower) of partially hydrogenated graphane with 75% H coverage (C240H160 in supercell). The gray balls stand for sp3 C atoms saturated with H atom, red balls highlight unsaturated sp2 C atoms, and light-blue balls represent H atoms.

impurity (like H vacancy) on graphene (ribbon) or graphane may induce impurity states in middle of the gap region (so-called midstates).3,20,34,35 For example, removal of one H atom from graphane introduces a sp2 hybridized C atom into the sp3 carbon network. Each sp2 C atom creates one unpaired local π electron (or radical), resulting in the midstates in the band structure. However, how to tune the band gap and the electronic structure of graphanebased materials systematically remains to be discovered. In this letter, we present the results of systematic investigation on the electronic structures of hydrogenated graphene (HG) with different configurations using DFT calculations. We found that removal of two neighboring H atoms from HG (namely, creating a H vacancy pair) leads to a simultaneous pairing of local π electrons from two sp2 hybridized C atoms and pushes the impurity states away from the midgap region. Thus, comparing with removing individual H atoms, removing H pairs is energetically more favorable and its impact on the electronic structure in the band gap region is less severe. For large H coverage HG (g66.7%) made by random removal of paired H atoms from graphane, our DFT calculations predicted a tunable band gap between zero and 4.66 eV, which is desirable for many electronic and photonic applications.

2. STRUCTURAL MODELS AND COMPUTATIONAL METHODS We started from the fully hydrogenated graphene (graphane) on two sides in the chairlike configuration.19 Here, we only considered the chairlike configuration of graphane because of the following two reasons: (1) the chairlike conformation is more stable than the boatlike configuration,19 (2) the chairlike graphane possesses higher symmetry than the boatlike configuration and is able to remove adjacent H atoms in pair on two side of the sheet. To account for the nature of random distribution of H vacancies in graphane, a large orthogonal supercell (12  10 rectangular unit cells) containing 240 carbon atoms and 240 hydrogen atoms (C240H240) was used in this study. The optimized lattice parameters are 26.417 and 25.420 Å, respectively. The supercell dimension for the direction perpendicular to the graphane sheet is chosen as 20 Å, leaving a ∼15 Å vacuum region to separate the graphane layer from its adjacent images. Partially HG (or dehydrogenated graphane) configurations were constructed by removing hydrogen atoms from a perfect

graphane. A previous calculation by Sofo et al. showed that the perfect graphane is very stable with negative formation energy (-0.15 eV/atom) close to the cyclohexene.19 Thus, removing a hydrogen atom from perfect graphane (i.e., introducing a single H vacancy) is energetically unfavorable (∼4.83 eV/vacancy from our DFT calculations). Because individual H vacancies correspond to a high-energy state in graphane, they tend to aggregate into multifold vacancies to reduce the formation energy.32 With sufficient thermal annealing, a phase separation between graphene and graphane would inevitably occur, which would break the homogeneity of the material. Thus, a practical way of creating a homogeneous partial HG from graphane is through a kinetic process at low temperature (e.g., by electron/ion irradiation36). Although the detailed atomic configuration of the partial HG or the dehydrogenated graphane with high H coverage is unclear yet, previous studies revealed that hydrogen distribution on the HGs with relatively low H coverage is usually random rather than forming some ordered structures with periodic patterns (as discussed in following text).37-40 Hence, we adopted large supercell models with random or patterned distributions of H vacancies, which are different from most previous studies using ordered structures and smaller supercells.18-24 With the presence of multifold vacancies, the H vacancies may either randomly distribute on the graphane host or form some patterned configurations. In this work, three types of HG configurations are considered: I, randomly removing H pairs from fully HG; II, randomly removing individual H atoms from fully HG; III, creating paired H vacancies according to some ordered pattern. Besides the above three types, there are other ways of generating partially HG configurations, for example, patterned H atoms adsorption on the surface of a perfect graphene,30 creating a vacancy H cluster (island) in a graphane sheet,32 or removing half of H atoms on a graphane.33 For configurations I with randomly paired H vacancies, we considered a series of H coverage of 95.8%, 91.7%, 87.5%, 83.3%, 79.2%, 75%, 70.8%, and 66.7%, corresponding to C240H230, C240H220, C240H210, C240H200, C240H190, C240H180, C240H170, and C240H160 in our supercell model, respectively. For each H coverage, we generated one hundred random configurations and selected four energetically favorable ones to further investigate their electronic properties. Figure 1 presents two examples of C240H210 and C240H160 supercells with randomly distribution of paired H vacancies. 3237

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H vacancy on graphane can be calculated from the difference of total energies for perfect graphane and the summation of the total energies for dehydrogenated graphane with two vacancies (paired or unpaired) plus those for two single H atoms. By definition, positive formation energy represents endothermic process of dehydrogenation. The computed formation energy of two SVs is 9.66 eV, whereas it is only 6.28 eV for a DV. In other words, formation of two adjacent SVs (namely, a DV) costs 3.38 eV less than that for two unpaired SVs. The energetic preference of paired vacancies over unpaired vacancies also plays critical role in the hydrogenated graphene with different H concentrations, as we will show in the following. Stability of Dehydrogenated Graphane as Function of H Coverage. The stability of hydrogenated graphene as function of H coverage can be described by the binding energy Eb of hydrogen atoms defined as:37 Eb ðnÞ ¼ ðEGR þ nEH - EPHG Þ=n ð1Þ

Figure 2. Structures (top-view) of partially dehydrogenated graphane with patterned distribution of H pair vacancies: (a) 87.5% H coverage or C240H210 in supercell, (b) 62.5% H coverage or C240H150 in supercell, (c) 37.5% H coverage or C240H90 in supercell, (d) 12.5% H coverage or C240H30 in supercell. The gray balls stand for sp3 C atoms saturated with H atom, red balls highlight unsaturated sp2 C atoms, and light-blue balls represent H atoms.

For comparison, we also considered a series of patterned H pair removal configurations (type III) with H coverage of 87.5% (C240H210), 75% (C240H180), 62.5% (C240H150), 50% (C240H120), 37.5% (C240H90), 25% (C240H60), and 12.5% (C240H30). Four representative structures are shown in Figure 2. Spin-polarized self-consistent field electronic structure calculations were performed using density functional theory implemented in the DMol3 program.41,42 No magnetization was observed in the present hydrogenated graphene systems with paired H vacancies, which can be interpreted as a consequence of pairing of all π electrons. The exchange-correlation functional was treated by the generalized gradient approximation (GGA) with the PW91 parametrization.43 All systems were fully relaxed without any symmetry constraint. All-electron treatment and double numerical basis including d- and p-polarization function (DNP)41 were used. During the geometry optimizations, the Γ point was used to sample the k space. For the calculations of electronic properties, the Brillouin zone was sampled by a 5  5  1 Monkhorst-Pack mesh44 of k points. The relaxation of atomic positions was considered to be converged when the change in total energy is less than 1.0  10-5 Ha/Å, and the force on each atom less than 0.004 Ha/Å.

3. RESULTS AND DISCUSSION Stabilities of Paired and Unpaired Vacancies. We first discuss the relative stability of paired and unpaired H vacancies by comparing the formation energies of two well separated single vacancies (SVs) and one double vacancy (DV) with two adjacent unsaturated sp2 C atoms, both having the same formula of C240H238 in our simulation supercell. The formation energy for

where EGR and EPHG are the total energies of the pristine graphene and the partially HG adsorbed with n hydrogen atoms respectively, and EH is the total energy of an isolated H atom (-13.56 eV from the present PW91/DNP calculation). The computed binding energy of the perfect graphane is 2.59 eV/H, which is close to a previous theoretical value of 2.54 eV/H at PBE/6-31G** level using the Gaussian 03 program.37 Part a of Figure 3 plots the hydrogen binding energies as functions of H coverage for the dehydrogenated graphane configurations with both paired (type I) and unpaired (type II) H vacancies. At each H coverage, the Eb values averaged over four random configurations were used. We found that the binding energy is insensitive to the detailed location of H vacancies, with energy difference of less than 0.003 eV/H for the four different random configurations. At the same H coverage, the partially HG configurations with paired H vacancies possess notably higher binding energies than those with unpaired H vacancies, indicating that the paired vacancies are more energetically favorable. The energetic preference of the paired H vacancies can be understood by the following picture. On a perfect graphane of sp3 bonding network, a single H vacancy creates a dangling bond (namely, a radical) and results in some local strain as well, each of which raises the total energy. In the condition of paired dehydrogenation, both unsaturated C atoms are turned to sp2 hybridized state and thus these two adjacent C atoms form a CdC double bond, through which the two π electrons pair together and the vacancy-induced local strain can be partially released.32 In contrast, each SV site possesses an unpaired π electron (radical) and the strain accumulated around cannot be relieved efficiently. The removal of radicals by CdC double bond has significant effect on the electronic structures of the dehydrogenated graphane, as we will discuss later. As illustrated in part a of Figure 3, the hydrogen binding energies for partially HG with both kinds of H vacancies decrease as the H coverage decreases. For the configurations with paired H vacancies, the binding energy is about 2.4 eV/H at the H coverage of 70.8%. This is still 0.07 eV/H higher than that for a H2 molecule. Thus, the formation of these partially hydrogenated graphene with sufficiently high H coverage from gaseous H2 molecules and graphene is exothermic, as it was found before.18,19 It is interesting to note that the configurations with randomly distributed double vacancies (type I) are more stable than those 3238

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Figure 3. (a) Hydrogen binding energies of partial hydrogenated graphene with paired (squares) and unpaired (circles) H vacancies as the functions of H coverage. The dot line denotes the binding energy of H2 of 2.33 eV/H (experimental value: 2.24 eV/H45). (b) Local atomic structures of paired (upper) and unpaired (lower) vacancies. The gray balls stand for sp3 C atoms saturated with H atom, red balls highlight unsaturated sp2 C atoms, and light-blue balls represent H atoms.

Figure 4. Density of states of (a) C240H240, i.e., graphane, (b) one representative C240H210 configuration with double vacancies (C240H210-DV), (c) one representative C240H210 configuration with single vacancies (C240H210-SV), (d) one representative C240H160 configuration with double vacancies (C240H160-DV). Fermi level is set to zero as marked by the red dot line. A Gaussian broadening of 0.1 eV was used.

with patterned distribution (type III) considered here. For instance, the H binding energies of C240H210 and C240H180 in type III configurations are 2.51 eV/H and 2.41 eV/H, which are about 0.01 eV/H and 0.03 eV/H lower than those of type I at the same H coverage, respectively. This suggests attractive interaction between paired H vacancies. Thus, phase separation may occur at high temperature when H vacancy pairs start to diffuse. Band-Gap Tuning. We now turn to the electronic structures of the hydrogenated graphene with different H coverage. For graphane with 100% H coverage, an accurate GW calculation20 predicted an insulating gap of 5.4 eV, comparable

to that of diamond crystal with full sp3 hybridization (5.48 eV). From our GGA calculations, the band gap of the perfect graphane is 4.66 eV (part a of Figure 4), lower than the GW value by ∼13.7%. Figure 4 compares the electron density of states of C240H240 (perfect graphane), C240H210 (dehydrogenated graphane with paired and unpaired H vacancies), and C240H160 (dehydrogenated graphane with paired H vacancies). One can see a clean band gap of ∼1.91 eV for C240H210 with paired vacancies (part b of Figure 4). In other words, the insulating graphane with a wide band gap of 4.66 eV becomes a semiconductor via appropriate pairwise dehydrogenation. The effect of band gap narrowing can 3239

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Figure 5. Energy gap of hydrogenated graphene as a function of H coverage. The rhombus symbols denote the gap values of different random HG configurations (type I) from GGA calculations, and the blue line is a linear fitting of the computational results (text). A thirdorder polynomial fitting of the gap-coverage relationship is given as the dashed line.

be attributed to the edge states in the gap region of the original graphane that are associated with the paired H vacancies. Further reducing H coverage to 66.7% (C240H160) eventually brings some impurity states into the middle of gap region and then diminishes the band gap (part d of Figure 4). In contrast, HG with single H vacancies always present some midstates in the gap region due to the unsaturated dangling bonds (part c of Figure 4 for C240H210 as an example). Our isosurface analysis shows that electron densities of the midstates mainly distribute around the unsaturated carbon atoms, whereas removal of nearest neighbor H atoms lead to the CdC double bonds, which induce impurity states near the band edges. Previously, Lebegue et al. also found that introducing a single H vacancy in graphane results in an impurity state within the gap region (about 2 eV above the valence band maximum).20 Therefore, to achieve a clean gap without midstates in the partially HG (or dehydrogenated graphane), paired H vacancies is essential. Figure 5 displays the theoretical band gap of HG with paired H vacancies (type I) as a function of H coverage. For each H/C ratio, band gaps for four energetically preferred random configurations are shown. Although the exact gap values somewhat vary with the detailed vacancy configuration, the overall trend is clear, that is, band gap of partially HG reduces with decreasing H coverage. The theoretical GGA gap drops from 4.66 eV for a fully hydrogenated graphene to zero for partially HG with 66.7% coverage. In the H coverage range between 66.7% and 100.0%, one can fit a third-order polynomial relationship for the energy gap (Δ in eV) of the dehydrogenated graphane versus the H coverage (χ in %) as: Δ ¼ - 130:20877 þ 4:81977χ - 0:05961χ2 þ 0:000249χ3 ð2Þ Considering that the GGA underestimate the band gap of graphane by about 13.7% with regard to the more accurate GW values, the true gaps of these hydrogenated graphene systems might slightly higher. As discussed above, tunable gap in randomly dehydrogenated graphane (type I) is valid in the conditions of high H coverage

(above ca. 67%). For the HG with lower H coverage, it is still possible to achieve a finite band gap if the adsorbed hydrogen can form some structural patterns. For example, for the ordered HG configurations of type III shown in parts c and d of Figure 2, the GGA gaps are 1.69 eV for C240H90 (37.5%) and 1.58 eV for C240H30 (12.5%), respectively. This indicates that the details of electronic states of a partially HG depend on the spatial arrangement of the sp3 or sp2 sites. With random distribution of sp2 and sp3 bonding on a large supercell, the existence of band gap depends on the edge states induced from the pairwise H vacancies (or CdC double bonds). Starting from a prefect sp3 graphane with large band gap (4.66 eV from our DFT-GGA calculation), introducing double hydrogen vacancies (DV) as sp2 defects in the system would create edge states near the top of valence band or the bottom of conduction band. Our careful analysis revealed that the interaction between neighboring double vacancies would shift the edge states toward the middle of gap region, which is the essential mechanism of band gap tuning by H coverage in the HG. Up to an H coverage of about 67%, there are sufficient interacting nearby DVs that bring the edge states from the valence band and conduction band together and make them merging at the Fermi level. The tunable gaps between midultraviolet and near-infrared regions (ca. 0.5-5 eV) in the hydrogenated graphene may lead to potential applications in future electronics and photonics (e.g., solar cells). Controlling the hydrogen coverage on graphene is feasible in experiments. For example, annealing of hydrogenated graphene carefully monitored at different temperature/time would result in different amounts of H2 desorption.29,46,47 Electron/ion irradiation at low temperature is another practical way to remove hydrogen atoms from the graphane36 and prevent us from the possible phase separation of graphene and graphane due to the aggregation of hydrogen atoms or vacancies.32 Furthermore, the holes formed by the H vacancies on the graphane surface provide ideal doping sites, which may lead to novel graphene-based semiconductors with n-type doping (deposited with alkali metals or alkaline-earth metals) or spin injection (deposited with magnetic transition metals).

4. CONCLUSIONS Using first-principles methods, we have investigated the stability and electronic properties of hydrogenated graphene. Among the three types of configurations considered, the most stable configurations are those generated by randomly pairwise dehydrogenation of the perfect graphane (type I), suggesting that clustering of H vacancy pairs stabilizing the structure. Within the coverage range of 66.7 to 100%, the hydrogen binding energy of the hydrogenated graphene is higher than that of H2 molecule. The dehydrogenated graphane with paired H vacancies presents a clean energy gap (without midstates) due to the formation of CdC double bond (or removal of radicals). For randomly dehydrogenated graphane, the GGA band gap reduces from 4.66 to 0 eV as the H coverage varies from 100% to 66.7%. Though the current DMol3 based DFT-GGA calculations are not very accurate in terms of the absolute magnitude of band gap, we expect that our qualitative results on the dependence of band gap on the H coverage remain robust with more accurate calculations. The tunable gap in the middle-ultraviolet to near-infrared energy range provides a new perspective to the application of graphene-based materials in electronics and photonics. 3240

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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