ARTICLE pubs.acs.org/JPCC
Favorable Zigzag Configuration at Etched Graphene Edges Yufeng Guo* and Wanlin Guo† Institute of Nanoscience and Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China ABSTRACT: To control and improve edge quality during etching process is a desired goal for fabricating graphene nanostructure. The preferred edge atomic configurations and shapes when etching pure armchair and zigzag graphene edges have been extensively studied by first-principles calculations. In the beginning stage of etching, it is energetically favorable to remove a specific four-atom carbon segment from flat armchair edge and a three-atom segment from zigzag edge. The subsequent etching on armchair edge shows strong tendency to start from the etched site because of higher chemical reactivity, and a triangle pit with an angle of 120° and zigzag boundary configuration is expected to form on armchair edge. In contrast, the initial etched site on zigzag edge exhibits similar chemical reactivity to other unetched edge atoms. Nevertheless, all created configurations at the etched boundaries are zigzag-edged despite the fact that armchair or zigzag edge could be etched into several shapes. Our results promise that the zigzag chirality be dominating on the edges of graphene nanostructure after patterned under proper etching condition.
1. INTRODUCTION Graphene has attracted great scientific interests in fundamental research because of its intriguing properties and potential applications in future electronics and spintronics.1 3 A remarkable feature of graphene is that its electronic and magnetic properties are dependent on its size and edge structures.4 9 Controlled fabrication of graphene structure with desired sizes, morphology, and edges is the foundation of actual application in nanoelectronic devices. To this end, graphene nanostructure and nanoribbons with different levels of edge quality can now be fabricated by miscellaneous methods, including electron beam lithography,10 isotropic plasma etching,11 scanning tunneling microscopy lithography,12 sonication of graphene sheets,13 unzipping carbon nanotubes,14 20 and chemical oxidation.21,22 In particular, anisotropic etching procedures such as catalytic hydrogenation with catalyst particles,23,24 carbon-thermal reduction,25,26 and hydrogen plasma etching,27,28 have recently been proved to be effective ways to fabricate graphene nanostructure of welldefined crystallographic edges because the zigzag and armchair graphene edges have quite different chemical activity and stability.29,30 Under proper condition, anisotropic etching may start from graphene edge and selectively react with the edge carbon atoms without introducing any damage in the basal plane.27,28 The graphene nanostructures obtained from anisotropic etching methods exhibit hexagonal shape and zigzag-type edge configurations.25,26,28 However, in those experiments, the physical mechanism for realizing zigzag configuration on graphene edge has so far not been well understood. Etching process actually can be considered as breaking C C bonds and removing the broken C atoms. The etching tendency and chemical reactivity on r 2011 American Chemical Society
graphene edges are directly related to the final edge shape and atomic configuration. Graphene edges are composed of carbon atoms arranged in zigzag or armchair configuration. Further study on the etching-induced structural difference between armchair and zigzag edges is paramount for realizing better control on graphene edge in anisotropic etching. In this work, we have extensively investigated the favorable edge atomic configurations when etching armchair and zigzag graphene edges by using density functional theory (DFT) calculations. We find that it is energetically favorable to remove a specific four-atom carbon segment on armchair edge and a three-atom segment on zigzag edge in the initial etching stage. The etched site on the armchair edge is highly reactive, from which the subsequent etching is inclinable to start. This trend leads to a triangle pit with zigzag boundary configuration forming on the armchair edge. On the contrary, there is no such strong trend on zigzag edge because the initial etched site has similar reactivity to other edge atoms, but the probable edge structures after etching still remain the zigzag configuration. This may provide some insight into the underlying mechanism for achieving zigzag edge chirality when using anisotropic etching methods.
2. MODEL AND METHOD We choose two rectangle unit cells of graphene structures with armchair and zigzag edges. The lengths of periodic unit cells along the edge direction for zigzag and armchair edges are 1.94 and 2.1 nm, respectively. A vacuum layer of 1.6 nm is kept along Received: June 17, 2011 Revised: August 29, 2011 Published: September 20, 2011 20546
dx.doi.org/10.1021/jp205671r | J. Phys. Chem. C 2011, 115, 20546–20549
The Journal of Physical Chemistry C
ARTICLE
Figure 1. Contour plots of 2D projection of the charge density of the bands ( 0.2, 0.2 eV around the Fermi energy) in the vicinity of the Fermi level for (a) optimized armchair and (b) zigzag graphene edges. The black dots are carbon atoms. Only the outmost atoms and the nearest second layer atoms are considered to be removed at the beginning stage of etching.
Figure 2. (a) Number of broken C C bonds and the binding energies for removing 1 C atom on the armchair edges. (b) Four-atom C segments with the same number of broken C C bonds on the armchair edge. The red color dots represent the C atoms that will be removed.
the direction perpendicular to the edge to avoid any slab interaction, and the other side of the graphene structure is terminated by hydrogen atoms. The computations were performed using the VASP code with the ultrasoft pseudopotential and local density approximation (LDA) for the exchange-correlation potential.31 33 First, each graphene including etched structure is relaxed by using a conjugate-gradient algorithm until the force on each atom is 2, whereas the total trend of the corresponding number M is to increase with increasing atom number. The increase in the magnitude of binding energy indicates that removing more atoms needs more energetic input. For some C segments of different atom number N, the number of the bonds needed to be ruptured is the same, as shown by Figure 3a. Etching process is attributed to rupturing C C bonds and volatilization of carbon atoms. To unveil the intrinsic relation 20547
dx.doi.org/10.1021/jp205671r |J. Phys. Chem. C 2011, 115, 20546–20549
The Journal of Physical Chemistry C
ARTICLE
Figure 4. (a) Contour plot of the charge density ( 0.2, 0.2 eV around the Fermi energy) in the vicinity of the Fermi level for the four-atom etched armchair edge after structural relaxation and the optimized structure after the removal of the boundary C atoms at the etching location. (b) Corresponding distribution of the charge density around the Fermi level for the right structure in panel a and the predicted 120° triangle pit with zigzag boundary configuration on the armchair edge. The removed boundary C atoms are highlighted by red color lines and the black dots are carbon atoms.
between the binding energy of the C segment and its local bonding state, we have calculated the ratio Er of the minimum binding energy E bm to the corresponding number M by Er = Ebm/M. This ratio is an indicator measuring the hierarchy in probability of breaking C C bonds when supplying the same energetic input. The lower Er suggests higher energetic efficiency in rupturing C C bonds and preferred etching on the segment. Figure 3b shows the variation of the ratio Er with the atom number N. The minimum Er of 4.68 eV/bond is obtained at N = 4, whereas the second and third minimum values are at N = 8 and 12, respectively. The corresponding segment structure of N = 4 is shown by the inset of Figure 3b. As a consequence, on the armchair edge, it is energetically favorable to remove this kind of four-atom segment in the initial etching stage. The relaxed edge after removing the four-atom segment is given in Figure 3b as well. The energy difference between the minimum and second minimum values in Figure 3b is 0.14 eV/bond. The temperature change for overcoming this energy difference35 is estimated to be ∼540 K. This means that the energetically favorable etching be dominating over a large range of temperature. After the four-atom segment is removed, the atomic configuration of the etched site becomes different from the original armchair edge (the inset in Figure 3b), and the isotropic tendency for etching no longer exists along such modified edge. As shown in Figure 4a, the charge densities of the bands in vicinity of the Fermi level mainly distribute and locate on the boundary carbon atoms of the etched site and few on other armchair edge atoms. The carbon atoms of the etched site are more chemically reactive so that the next etching is strongly favored to occur at such site. On the basis of this trend, a 120° triangle pit with zigzag configuration will be formed on the armchair edge with removing or etching the boundary atoms, as shown in Figure 4a. For the subsequent etching trend after the formation of the zigzag-type pit, the corresponding distribution of the charge density around the Fermi level at the etched edge has been given in Figure 4b. It is clearly shown that the charges still locate at the zigzag sites of the pit, suggesting that the zigzag configuration possesses higher tendency and activity for etching than that of armchair configuration. With further removing the boundary C atoms, the edge of the triangle pit will be enlarged but will still remain the zigzag chirality (Figure 4b). According to
Figure 5. (a) Variations of (a) the minimum binding energy Ebm and the corresponding broken C C bond number M and (b) the ratio Er with the atom number N on the zigzag edge. The insets show the relaxed structure after removing the three-atom segment of the minimum Er.
this trend, it can be concluded that the triangle pit with an angle of 120° and zigzag boundary configuration is favorable to form when etching pure armchair edge. Moreover, the theoretical predicted pit is consistent with the structures with an angle of 120° observed in anisotropic etching experiments.24 26,28 The same procedure has been used to study the favorable etching tendency on the zigzag edge. Figure 5 shows the variations of the minimum binding energy Ebm and the corresponding broken C C bond number M and the ratio Er with the atom number N. The minimum binding energy of even-number N is lower than that of number N-1, but the total trend of Ebm is still to decrease with increasing atom number. The minimum Er is 3.58 eV/bond at N = 3, and the second and third minimum values appear at N = 5 and 7, respectively. It is energetically favorable to remove the three-atom segment from the zigzag edge in the initial etching stage (the inset of Figure 5b). The difference between the minimum and second minimum values is 0.22 eV/bond, approximately equivalent to a temperature of 850 K, so the temperature effect on the initial etching trend is weaker than that of armchair edge. For the relaxed structure of the three-atom etched zigzag edge, the zigzag configuration at the etched site is similar to that of other unetched edge (the inset of Figure 5b). Furthermore, the charge density in vicinity of the Fermi level mainly distributes on the outmost two-carbon layer of the unetched edge and the zigzag site of the etched location, as shown in Figure 6a,b. The etched site therefore has similar reactivity to other edge atoms due to the same atomic arrangement. The subsequent etching may occur at different locations of the edge. This provides us a possible tendency that the zigzag edge will be etched layer-bylayer if the following etching starts from the outside part. From this layer-by-layer mechanism, the zigzag edge will be etched into smooth zigzag configuration, as shown by the left structure in Figure 6c. Nevertheless, the subsequent etching may still occur on the etched location due to the charge distribution at the zigzag site. A predicted pit, which is formed by removing the boundary atoms of the etched site, is plotted in the right of Figure 6c. Compared with the armchair edge, there is no obvious etching trend on the zigzag edge after the three-atom segment is removed. 20548
dx.doi.org/10.1021/jp205671r |J. Phys. Chem. C 2011, 115, 20546–20549
The Journal of Physical Chemistry C
ARTICLE
’ REFERENCES
Figure 6. (a) Contour plot and (b) the corresponding isovalue surface (in unit of 0.03 e/(Å)3) of the charge density ( 0.2, 0.2 eV around the Fermi energy) in the vicinity of the Fermi level for the three-atom etched zigzag edge after structural relaxation. The active boundary atoms are highlighted by red color lines, and the black dots are carbon atoms. (c) Possible etched structures at the zigzag edge.
Although the pure zigzag edge could be etched into different shapes, the boundary carbon atoms are always locally arranged in the zigzag configuration. According to the energy difference in the initial stage, the effect of temperature on the favorable tendency is slight, but both armchair and zigzag edges may have different initial shapes if the etching intensity becomes strong enough. This will result in diversified final etched structure, and the edge chirality becomes less controllable. Consequently, proper temperature and moderate etching intensity are necessary for achieving the desired graphene edge.
4. CONCLUSIONS In summary, our first-principles calculations show that there is an energetically favorable rule in the initial stage of etching pure armchair and zigzag graphene edges. The difference in chemical reactivity and etching tendency will result in various shapes when etching graphene edges. Nevertheless, the final boundaries of the etched sites are favorable to be arranged in zigzag configuration for both armchair and zigzag edges. Our study promises that the preferred edge chirality for graphene nanostructure after etched under proper conditions is to be zigzag configuration. This also provides some insight into fundamental understanding of structural change in anisotropic etching on graphene edges and a possible route for controlling the edge atomic configuration of graphene nanostructure. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: 86-25-84890513. Fax: 8625-84895827. Notes †
E-mail:
[email protected] (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) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (3) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109. (4) Son, Y. W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (5) Novoselov, K. Nat. Mater. 2007, 6, 720. (6) Yang, L.; Park, C. H.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2007, 99, 186801. (7) Wang, X.; Ouyang, Y.; Li, X.; Wang, H.; Guo, J.; Dai, H. J. Phys. Rev. Lett. 2008, 100, 206803. (8) Zhang, Z. H.; Chen, C. F.; Guo, W. L. Phys. Rev. Lett. 2009, 103, 187204. (9) Qian, H.; Negri, F.; Wang, C.; Wang, Z. J. Am. Chem. Soc. 2008, 130, 17970. (10) Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805. (11) Stampfer, C.; G€uttinger, J.; Hellm€uller, S.; Molitor, F.; Ensslin, K.; Ihn, T. Phys. Rev. Lett. 2009, 102, 056403. (12) Tapaszt o, L.; Dobrik, G.; Lambin, P.; Biro, L. P. Nat. Nanotechnol. 2008, 3, 397. (13) Wu, Z. S.; Ren, W. C.; Gao, L. B.; Liu, B. L.; Zhao, J. P.; Cheng, H. M. Nano Res. 2010, 3, 16. (14) Kosynkin, D. V.; Higginbotham, A. L.; Sinitskii, A.; Lomeda, J. R.; Dimiev, A.; Price, B. K.; Tour, J. M. Nature 2009, 458, 872. (15) Cano-Ma’rquez, A. G.; Rodríguez-Macias, F. J.; Delgado, J. C.; Espinosa-Gonzalez, C. G.; Lopez, F. T.; Gonzalez, D. R.; Cullen, D. A.; Smith, D. J.; Terrones, M.; Vega-Cantu, Y. I. Nano Lett. 2009, 9, 1527. (16) Jiao, L. Y.; Zhang, L.; Wang, X. R.; Diankov, G.; Dai, H. J. Nature 2009, 458, 877. (17) Guo, Y. F.; Jiang, L.; Guo, W. L. Phys. Rev. B 2010, 82, 115440. (18) Guo, Y. F.; Zhang, Z. H.; Guo, W. L. J. Phys. Chem. C 2010, 114, 14729. (19) Higginbotham, A. L.; Kosynkin, D. V.; Sinitskii, A.; Sun, Z. Z.; Tour, J. M. ACS Nano 2010, 4, 2059. (20) Kim, K.; Sussman, A.; Zettl, A. ACS Nano 2010, 4, 1362. (21) Masubuchi, S.; Ono, M.; Yoshida, K.; Hirakawa, K.; Machida, T. Appl. Phys. Lett. 2009, 94, 082107. (22) Wang, X. R.; Dai., H. J. Nat. Chem. 2010, 2, 661. (23) Campos, L. C.; Manfrinato, V. R.; Sanchez-Yamagishi, J. D.; Kong, J.; Jarillo-Herrero, P. Nano Lett. 2009, 9, 2600. (24) Sch€affe, F.; Warner, J. H.; Bachmatiuk, A.; Rellinghaus, B.; B€uchner, B.; Schultz, L.; R€ummeli, M. H. Nano Res 2009, 2, 695. (25) Incze, P. N.; Magda, G.; Kamaras, K.; Biro, L. P. Nano Res 2010, 3, 110. (26) Krauss, B.; Incze, P. N.; Skakalova, V.; Biro, L. P.; von Klitzing, K.; Smet, J. H. Nano Lett. 2010, 10, 4544. (27) Xie, L. M.; Jiao, L. Y.; Dai, H. J. J. Am. Chem. Soc. 2010, 132, 14751. (28) Yang, R.; Zhang, L.; Wang, Y.; Shi, Z.; Shi, D.; Gao, H. J.; Wang, E. G.; Zhang, G. Y. Adv. Mater. 2010, 22, 4014. (29) Radovic, L. R.; Bockrath, B. J. Am. Chem. Soc. 2005, 127, 5917. (30) Jiang, D. E.; Sumpter, B. G.; Dai, S. J. Chem. Phys. 2007, 126, 134701. (31) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (32) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251. (33) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892. (34) Liu, Y. Y.; Dobrinsky, A.; Yakobson, B. I. Phys. Rev. Lett. 2010, 105, 235502. (35) Guo, W. L.; Guo, Y. F. J. Am. Chem. Soc. 2007, 129, 2730.
’ ACKNOWLEDGMENT This work is supported by the 973 Program (2007CB936204), NSF (10732040, 11072109), and Jiangsu NSF (BK2009365) of China. 20549
dx.doi.org/10.1021/jp205671r |J. Phys. Chem. C 2011, 115, 20546–20549
