Nanoengineering Structures on Graphene with Adsorbed Hydrogen

J. Phys. Chem. C 2010, 114, 3225–3229

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Nanoengineering Structures on Graphene with Adsorbed Hydrogen “Lines” Leonid A. Chernozatonskii*,† and Pavel B. Sorokin†,‡,§ Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, 4 Kosigina Street, Moscow, 119334 Russia, Siberian Federal UniVersity, 79 SVobodny AVenue, Krasnoyarsk, 660041 Russia, and Department of Mechanical Engineering & Materials Science, Rice UniVersity, Houston, Texas 77005 ReceiVed: October 21, 2009; ReVised Manuscript ReceiVed: January 12, 2010

It is shown that the lines of adsorbed hydrogen pair atoms divide a graphene sheet into electronically independent strips and form an electron waveguide or 2H-line graphene-based superlattice (2HG-SL). We investigated the electronic properties of such structures in detail. The electronic spectra of a “zigzag” (n,0)2HG-SL are similar to those of armchair graphene ribbons and have similar oscillation of the band gap with the width between adjacent 2H-lines (number n). The induced strain with the direction perpendicular to the hydrogen pair “lines” significantly changes the electronic properties of the investigated structures. For example, in the case of the 2HG-SL (3n,0) (n > 2) we observed the semiconductor-metal transition. Superlattices of the (n,n) type with a “staircase” of adsorbed pairs of H atoms are semiconductors with nearly linear decreasing of the band gap with increasing n. We found that the configuration with the opposite spin (antiferromagnetic) orientation between ferromagnetically ordered edge states of the (n,n) 2HG-SL is energy favorable. We also suggested an experimental way of fabricating these superlattices. Finally, we discussed properties of possible hydrogen lined waveguide junctions. 1. Introduction The emergence of graphene as a stable pure two-dimensional system has been one of the most important events in electronic condensed matter physics over the last years.1,2 Until recently, the 2D paradigm was limited mostly to electrons confined to quantum wells or inversion layers in semiconductor heterostructures. The situation changed five years ago when it was found that individual atomic planes could be pulled from a graphite crystal. Despite being only one atom thick, the 2D crystals remained stable and proved to be almost perfectly crystalline and highly conductive.3 One of many interesting properties of graphene is the Dirac type of electronic band structure and the drastic changes of the conductivity of graphene-based structures with electron confinement. Two possibilities for the realization of this effect have been proposed: carbon nanotubes4 (periodic boundary conditions for the wave-vector of the electron) and graphene ribbons (finitewidth graphene strips, zero boundary conditions). The band gap oscillation depends on the transversal size, with either zero or nonzero minimal values for carbon nanonotubes4 or graphene nanoribbons (GNRs),5 respectively. The GNRs are very interesting graphene successors. They have attracted much attention because of their properties and their potential for applications.6,7 In recent years GNRs have been experimentally obtained8 and theoretically investigated in detail5,9,10 (and references therein). But it should be mentioned that the theoretical prediction of GNRs properties was made long before the experimental preparation of ribbons.11-13 The quasi-one-dimensional electronic structure of GNRs is similar to that of single-walled carbon nanotubes (SWNT). * To whom correspondence should be addressed. E-mail: cherno@ sky.chph.ras.ru. † Emanuel Institute of Biochemical Physics RAS. ‡ Siberian Federal University. § Rice University.

In refs 14-16 another possibility of electron confinement using chemical adsorption of H atom pairs on the surface of graphene was proposed. Hydrogen lines split the graphene sheet into “strips” (electronic waveguides) with the same or different electronic properties, forming two-dimensional superlattices (see Figure 1a). Such structures were called 2H-line graphene-based superlattices. It was shown14,15 that the superlattices display electronic properties similar to those of graphene ribbons. The “zigzag” superlattice structures are semiconductors. Changing the width strip, i.e., the period, of such superlattices leads to changing the energy gap of the structures. Thus, a set of 2D-semiconductors with different properties can be obtained. The investigation of graphene based superlattices is inspired by the recent experiments with free-standing graphene sheets17 and hydrogen dimer adsorption on graphite during annealing.18 The hydrogenated graphene19 (called “graphane”20) was obtained recently and electronic properties of semiconducting “roads” in the graphane21 were theoretically predicted. In this paper we examined a 2HG-SL with different periods (widths). We investigated the strained superlattices and found pronounced dependence of the band gap upon the strain value. Besides the zigzag 2HG-SL, we studied armchair-type superlattices with indexes (n,n). We found that these structures revealed semiconducting properties like zigzag graphene ribbons and had an interesting spin configuration that could be used in spintronics. Finally, we qualitatively studied the structures of the 2H-lined waveguide junctions. The junctions between 2H lined waveguides with different widths can be used in nanoelectronics as nonlinear elements like the carbon nanotubes or the graphene ribbons junction. 2. Method and Model Our calculations were performed using density functional theory22,23 within the local density approximation for the exchange-correlation functional,24 employing norm-conserving

10.1021/jp9100653  2010 American Chemical Society Published on Web 02/03/2010

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Figure 1. Atomic geometry of 2H-line superlattice models: (a) perspective and (b) top view of (10,0)-2HG-SL and comparison with (c) 11-AGR. Unit cells of 2HG-SL and AGR are marked by the dotted line.

Troullier-Martins pseudopotentials25 in the Kleinman-Bylander factorized form.26 Finite-range numerical pseudoatomic wave functions were used as an atomic-orbital basis set. Slabs were treated in a supercell scheme allowing enough empty space between them to make intermolecular interactions negligible. The geometry of the structures was optimized until residual forces became less than 0.04 eV/Å. The real-space mesh cutoff was set to at least 175 Ry. The Monkhorst-Pack27 special k-point scheme was used with 0.08 Å-1 k-point spacing. We used the SIESTA package28,29 in all calculations. All the values given above were carefully tested and found optimal. 3. Results and Discussion In previous papers14-16 we used the classification of 2H-line graphene-based superlattice similar to nanotube classification. But the properties of these structures are closer to planar graphene ribbons than to nanotubes upon a closer view (e.g., the existence of superlattices with fractional indexes, which is impossible for nanotubes16). Therefore, in this paper we defined the width of the zigzag 2HG-SL as n, where n stands for the number of dimer lines for the superlattice similar to graphene ribbons. The geometric scheme of a (10,0)-2H-line graphenebased superlattice is shown in Figure 1b. Hydrogen atoms, shown in blue (dark), are covalently bound to C atoms, shown in orange (bright), forming lines perpendicular to the (n,0) direction in graphene. The H-atoms form local sp3-hybridization between hydrogen and carbon atoms, which causes a local geometrical distortion of the graphene sheet, as if forming diamond-like lines. In panels b and c of Figure 1 the comparison between 2HG-SL and GNR indexes is presented. Like graphene ribbons 2HG-SL display similar oscillation of band gap with increasing superlattice width (index n) that vanishes in the infinite limit of pure, semimetallic graphene.14-16 There are three types of 2HG-SLs. The (3m,0)-2HG-SL (where m is a positive integer) displays the minimum gap, whereas

(3m+2,0)-2HG-SL displays the maximum one, similar to carbon nanotubes4 and graphene ribbons.5 3.1. Electronic Structure of Strained Hydrogen Superlattices. It is a well-known fact that the band gap of carbon nanotubes30,31 and graphene ribbons32,33 could be changed by unaxial strain. Therefore it can be assumed that electronic properties of the considered structures can be changed by stretching across the hydrogen “lines”, Figure 2a. We calculated the dependence of the (n,0)-2HG-SL band gap upon the index n in tensed and compressed cases shown in Figure 2b. We found that the band gap of 2HG-SL is quite sensitive to strain: the stretching (2%) changes the band gap of 2HG-SLs up to 30%. In the case of the 2HG-SL (3m,0) (m > 2) we observed the semiconductor-metal transition. The transition is caused by valence and conduction bands overlapping in Γ-point during atoms closing. It should be mentioned that the dependence of the band gap of 2HG-SL of different indexes upon the strain is different. The band gap (3m,0) and (3m+2,0) display the ordinary dependence (the decrease of band gap under compression and the increase under tension) but 2HG-SL (3m+1,0) display the opposite behavior. This is typical for graphene based nanostructures (carbon nanotubes and graphene ribbons) and connected with an finite number of allowed states in the Brillouin zone of the nanostructures and can be explained as the moving of the nearest corner allowed line away from the K point in the (3m+1,0) case and toward the K point in the (3m+2,0) and (3m,0) cases. For example, in Figure 2c the changing of the band structure of (12,0)-2HG-SL is shown. The high dependence of the band gap of 2HG-SL upon the strain can be useful for application in electronics. We mention that such transversal strain is practically impossible to apply to graphene ribbons and therefore to obtain similar properties in experiment. 3.2. Armchair Hydrogen H2-Line Superlattices. Let us now study the graphene structures with 2H atomic lines forming

Graphene with Adsorbed Hydrogen “Lines”

Figure 2. (a) The (12,0)-2HG-SL with marked direction of strain. (b) The variation of band gaps of strained (n,0)-2HG-SLs as a function of the index n. The band gap values of 2HG-SL with indexes (3m,0) are marked by the black line (brown online) with filled circles, with indexes (3m+1,0) by the gray line (orange online) with empty circles, and with indexes (3m+2,0) by the gray line (yellow online) with filled triangles. The tension is marked by a dashed line, compression by the chained line. The values of band gaps of unstrained 2HG-SL are marked by the solid line. (c) The band structures of compressed (+2%), unstrained, and tensed (-2%) (12,0)-2HG-SL. The Fermi level is set to zero and marked by a horizontal line. The Brillouin zone is shown in the inset.

periodically arranged (n,n) armchair “strips”. Their widths are defined as n, where n stands for the number of zigzag lines (see Figure 3a). We investigated a different type of arrangement of hydrogen atoms in the “lines” (see Figure 3a-c). The band structures of the same type of superlattices are similar to each other. The band structures of all types of 2HG-SL are presented in Figure 3d-f. For comparison, in Figure 3g the band structure of a zigzag nanoribbon with nearly the same unit cell width is presented. Comparison between the energies of all types of 2HG-SL (12,12) is shown in Figure 3h. The (12,12)-2HG-SL of type 2 displays the highest energy and the (12,12)-2HG-SL of type 1 possesses the lowest energy The 2HG-SL of type 2 can be considered as an intermediate state between type 1 and type 3 2HG-SLs. Let us give detailed consideration to the first type of (12,12)2HG superlattice. In the superlattice of such type, pairs of H atoms are located on neighboring C atoms, forming “staircase stairs”, see Figure 3a. Considering first the spin degree of freedom, we find that the configuration with the opposite spin (antiferromagnetic) orientation between ferromagnetically ordered spins is favored as the ground state over the configuration with the same spin orientation between the two sides of hydrogen “staircases” (Figure 3i). The present result of antiferromagnetic spin configuration on the honeycomb lattice is consistent with the theorem for electrons on a bipartite lattice.34

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Figure 3. Geometry (a-c) and band (d-f) structures of type 1, 2, and 3 (12,12)-2HG-SLs with three kinds of arrangement of atoms in the “lines”; the gray (orange online) dotted horizontal lines mark the band gap of the structures. (g) The band structure of graphene ribbon (12-ZGNR in conventional notation5). The Fermi level in all spectra (E ) 0) is shifted to zero. In panel e the black (red online) and gray (blue online) lines denote bands of different spin states. (h) The comparison of energy between three kinds of arrangement of atoms in the “lines” of (12,12)-2HG-SLs. (i) The spatial distribution of the charge difference between different spin states (Fv(r b) - FV(r b)) (isovalue 0.01) for type 1 (12,12)-2HG-SL; (j) the variation of band gaps of armchair 2HG-SL of type 1 as a function of the index n.

This result shows the full analogy of the 2HG-SL with the GNR in which the antiferromagnetic spin orientation is the most favorable configuration, too.5 In the direction parallel to the 2H“lines” (ΓX region), the character of the spectrum is similar to the band structure of zigzag nanoribbons5 (compare panels d and g in Figure 3). The molecular orbitals of electrons at EF are localized near the C-H “staircase” and this localization is similar to its localization on the dislocation line in graphene35 or at the edges of the graphene ribbon.5 The band gap width of the 2HG-SL varies from 0.25 (for (8,8)-2HG-SL, superlattice period 16.6 Å) to 0.13 eV (for (24,24)-2HG-SL, superlattice period 50.7 Å). In the X direction (XM region) perpendicular to 2H-“lines” all superlattices display nearly linear spectrum behavior because a high energy barrier created by pairs of sp3 hybridized C atoms prevents the motion of the current carriers along the X direction therefore 2H-“strips” can be considered as electronically independent waveguides. 3.3. A Possible Method of 2HG-SL Fabrication. We proposed a possible method of 2HG-SL fabrication. It has been shown both theoretically36 and experimentally37 that the probability of hydrogen chemisorption increases with increasing local curvature of the sp2 carbon network. Then, bending a graphene sheet should increase the probability of hydrogen adsorption on its surface. The curvature of the sheet can be changed by using the finite surface: the edge of the crystal or the step on its surface. We studied both cases. To describe such structures,

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Figure 4. The schemes of graphene superlattice fabrication: (a) the use of crystal edge for increasing graphene curvature: region 1 is flat, while region 2 has positive curvature; (b) the graphene sheet with adsorbed hydrogen “line” (armchair type). The small step of the crystal surface is used: (c) the use of the step on the graphite surface: regions 1 and 4 are flat, while regions 2 and 3 have positive and negative curvature, respectively; (d) the further increase of the graphene curvature by using the longitudinal strain; (e) the shifted sheet of graphene with a single adsorbed hydrogen “line” (zigzag type), ready for the next 2H adsorption procedure.

we have used the molecular mechanic method,38 which gives a good qualitative description of geometrical and elastic properties of large carbon structures (containing >1000 C-atoms).39 The geometry optimization was performed with use of the conjugated gradient algorithm. First we studied the changing of graphene curvature on the crystal edge (i.e., on the graphite edge) (Figure 4a). Region 1 is unfavorable for adsorption due to zero curvature and low chemical activity. The curvature of graphene in region 2 is positive; therefore this region can be treated like a fragment of a carbon nanotube. Thus, a hydrogen line should be formed only in the second region during the experiment. Longitudinal shifting of graphene should flatten this region and bend another part of the sheet, thus making it possible to form periodically arranged. The calculations give us the curvature radius in region 2, equal to 4 Å. This value corresponds to (6,6) armchair nanotubes. The projection of the graphene sheet on the edge with the adsorbed hydrogen “line” is shown in Figure 4b. The step on the surface of the crystal can also change the superposed graphene sheet curvature as shown in Figure 4c. Similar to the previous case there is a region with positive curvature (2), a region with zero curvature that is unfavorable for adsorption, and a region (3) with negative curvature that hinders the formation of sp3-hybridization.36 Thus, a hydrogen line should only form in the second region during the experiment. Again, the longitudinal shifting of graphene should flatten this region and bend another part of the sheet, thus making it possible to form periodically arranged hydrogen lines step by step. When a single graphite layer step is used, the curvature radius in region 2 is equal to 18 Å. This value corresponds to the (46,0) zigzag nanotube. A double footstep, shown in Figure 4c, increases the graphene curvature a little further;the radius of curvature decreases to 15 Å. This value corresponds to the (38,0) zigzag tube. The longitudinal compression of the upper sheet (Figure 4d) leads to further increase of the curvature even in the case of one graphite layer step. A strain value of 2% results

Chernozatonskii and Sorokin

Figure 5. Geometric arrangement of 2H-“lines” on graphene in the nanoelectronicelements:(a)Y-junctionofthezigzag2H(8,0)+(12,0)+(8,0) waveguides; (b) L-junction of the zigzag 2H (8,0)+(12,0)+(8,0) waveguide; (c) Y-junction of armchair 2H (8,8)+(8,8)+(8,8) waveguides; and (d) T-junction of armchair (8,8) and zigzag (8,0)+(12,0)+(8,0) waveguides. In the insets the schematic energy barrier scheme is shown (I, semimetallic graphene; II, wide energy gap barrier; III, waveguide of semiconductor with narrow gap).

in significant decreases of region 2 curvature radius up to 8 Å, which is close to the radius of the (20,0) tube.15 Such an experimental procedure allows the graphene superlattices to be produced with adsorbed hydrogen atoms on one side of the sheet. In other experiments (e.g., in ref 19 a single layer of graphene was hydrogenated by cold hydrogen plasma) hydrogen can be on both sides and can form different configurations of hydrogen “lines” which can be more stable than those proposed in this paper. The study of such structures is the point of our future work. 3.4. Multiterminal 2H-Lined Waveguides on Graphene. Composite 2HG-SLs consisting of 2H-bordered strips with different widths were studied in refs14 and 15. The difference of band gaps of connected strips forms regions with different conduction properties, as in 1D superlattices described earlier (e.g., carbon nanotubes with alternate adsorbed hydrogen40-43 or BN-C nanotube connection44,45). An electron waveguide can be created by decorating a “quasi-metallic” zigzag strip on graphene by two “dielectric” ones, with larger band gaps, strips by their sides. Also it was shown earlier46-48 that the threeterminal planar junctions of carbon nanotubes display nonlinear electronic transport properties and have perspective applications in nanoelectronics as devices likely functioning as a transistor or a rectification element. We suppose that similar two- or threeterminal junctions formed by 2H-“lines” on the surface of graphene display the same properties. In Figure 5 the models of a symmetrical junction Y-2HG-SL (8,0)+(12,0)+(8,0) waveguides (Figure 5a) and the L-junction of (8,0)+(12,0)+(8,0) waveguides (Figure 5b) are presented. In Figure 5c,d armchair type junctions are shown (the Y-2HG-SL (8,8)-(8,8)-(8,8), Figure 5c, and the T-2HG-SL (8,8)-(8,0)+(12,0)+(8,0), Figure 5d). In the inset of Figure 5a the schematic energy barrier

Graphene with Adsorbed Hydrogen “Lines” scheme is shown. Area I is a semiinfinite semimetallic, graphene with zero band gap; area II is a semiconductor with a wide band gap (∼1 eV, see Figure 2b) (“dielectric”) barrier; area III is a semiconductor with a narrow gap (∼0.1 eV), the area of localization of HOMO and LUMO electrons (see Figure 2 in ref 15). The two- or three-terminal junctions can serve as nanodiodes and nanotransistors or as units of logic networks similar to analogical systems of carbon nanotubes49 or graphene ribbons.50 Electronic nanowaveguides and nanoheterostructures15 and therefore nanoelectronic devices based on 2HG-SL can be obtained by creating lines of pairs of H atoms adsorbed on graphene. For example, it can be created by AFM where a single atom manipulation has been carried out. The nanoprint method will allow the production of quantum electronic chips on a single graphite sheet which are analogues to the chips of integrated optics (electron waveguide-optical waveguide). 4. Conclusions We examined 2H-line graphene-based superlattices which are perspective as an element of nanoelectronics. We investigated electronic properties of strained zigzag superlattices. The dependence of the energy gap upon the strain is mainly determined by the SL index. For zigzag superlattices with 3m index, the uniaxial strain drastically changes the energy gap and thus leads to the semiconductor-metal transition. Armchair type superlattices with indexes (n,n) reveal semiconducting properties with narrow energy gaps like zigzag graphene ribbons and display interesting spin configuration which can be used in spintronics. We described a possible method of fabrication of the 2HG-SL on the edge of a crystal or a step on a crystal surface. We found that the curvature radius of bent graphene sheets arranged on the crystal edge is about 4 Å. The longitudinal compression of the upper graphene sheet situated on the step of the substrate layer increased the curvature of the sheet up to the radius of 8 Å. The hydrogen line should be formed only in the bent region during the experiment. Longitudinal shifting of graphene should flatten this region and bend another part of the sheet, thus making it possible to form periodically arranged hydrogen lines step by step. We modeled the junction of 2H-line graphene-based waveguides with different electronic properties. The investigated structures can be used in nanoelectronics as nonlinear elements like multiterminal junctions of carbon nanotubes or graphene ribbons. Acknowledgment. We are grateful to the Joint Supercomputer Center of the Russian Academy of Sciences for the possibility of using a cluster computer for quantum-chemical calculations and to I. V. Stankevich and L. Birop J. Bru¨ning for fruitful discussions. Molecular orbitals were visualized with use of the Molekel 4.3 program. This work was supported by the Russian Foundation for Basic Research (project no. 08-0201096) and by the Office of Naval Research, MURI Program. References and Notes (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) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197. (3) Sarma, S. D.; Geim, A. K.; Kim, P.; MacDonald, A. H. Solid State Commun. 2007, 143, 1. (4) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical properties of Carbon Nanotubes; Imperial College Press: London, UK, 1999.

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