Abstract

Direct deposition of graphene on substrates would avoid costly, time consuming and defect inducing transfer techniques. In this paper we used ultrathin films of Ni, with thickness ranging from 5 to 50 nm, as a catalytic surface on glass to seed and promote chemical vapor deposition (CVD) of graphene. Different regimes and dynamics were studied for various parameters including temperature and reaction time. When a critical temperature (700 °C) was reached, Ni films retracted and holes formed that are open to the glass surface, where graphene deposited. After CVD, the residual Ni could be etched away and the glass substrate with graphene regained maximum transparency (>90%). The fact that we could achieve low growth temperatures indicates the potential of the technique to widen the range of substrate materials over which graphene can be directly deposited. We demonstrated this by depositing graphene patterns on ultrathin, 100 μm thick, sheet of glass with low strain point (670 °C), particularly suitable for flexible electronic and optoelectronic devices.

© 2016 Optical Society of America

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References

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2015 (4)

T. L. Chen, D. S. Ghosh, M. Marchena, J. Osmond, and V. Pruneri, “Nanopatterned Graphene on a Polymer Substrate by a Direct Peel-off Technique,” ACS Appl. Mater. Interfaces 7(10), 5938–5943 (2015).
[Crossref] [PubMed]

M. Kosaka, S. Takano, K. Hasegawa, and S. Noda, “Direct synthesis of few- and multi-layer graphene films on dielectric substrates by “etching-precipitation” method,” Carbon 82, 254–263 (2015).
[Crossref]

J. Sun, Y. Chen, M. K. Priydarshi, Z. Chen, A. Bachmatiuk, Z. Zou, Z. Chen, X. Song, Y. Gao, M. H. Rümmeli, Y. Zhang, and Z. Liu, “Direct Chemical Vapor Deposition-Derived Graphene Glasses Targeting Wide Ranged Applications,” Nano Lett. 15(9), 5846–5854 (2015).
[Crossref] [PubMed]

J. Sun, Y. Chen, X. Cai, B. Ma, Z. Chen, M. K. Priydarshi, K. Chen, T. Gao, X. Song, Q. Ji, X. Guo, D. Zou, Y. Zhang, and Z. Liu, “Direct low-temperature synthesis of graphene on various glasses by plasma-enhanced chemical vapor deposition for versatile, cost-effective electrodes,” Nano Res. 8(11), 3496–3504 (2015).
[Crossref]

2014 (6)

A. Dahal and M. Batzill, “Graphene-nickel interfaces: a review,” Nanoscale 6(5), 2548–2562 (2014).
[Crossref] [PubMed]

T. Hallam, N. C. Berner, C. Yim, and G. S. Duesberg, “Strain, bubbles, dirt, and folds: a study of graphene polymer-assisted transfer,” Adv. Mater. Interfaces 1(6), 1400115 (2014).
[Crossref]

C.-M. Seah, S.-P. Chai, and A. R. Mohamed, “Mechanisms of graphene growth by chemical vapour deposition on transition metals,” Carbon 70, 1–21 (2014).
[Crossref]

D. Q. McNerny, B. Viswanath, D. Copic, F. R. Laye, C. Prohoda, A. C. Brieland-Shoultz, E. S. Polsen, N. T. Dee, V. S. Veerasamy, and A. J. Hart, “Direct fabrication of graphene on SiO2 enabled by thin film stress engineering,” Sci. Rep. 4, 5049 (2014).
[Crossref] [PubMed]

A. Delamoreanu, C. Rabot, C. Vallee, and A. Zenasni, “Wafer scale catalytic growth of graphene on nickel by solid carbon source,” Carbon 66, 48–56 (2014).
[Crossref]

S. Garner, S. Glaesemann, and X. Li, “Ultra-slim flexible glass for roll-to-roll electronic device fabrication,” Appl. Phys., A Mater. Sci. Process. 116(2), 403–407 (2014).
[Crossref]

2013 (9)

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8(4), 235–246 (2013).
[Crossref] [PubMed]

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
[Crossref] [PubMed]

I. I. Kondrashov, P. S. Rusakov, M. G. Rybin, A. S. Pozharov, and E. D. Obraztsova, “Chemical Vapor Deposition of Graphene on Nickel from Different Gaseous Atmospheres,” J. Nanoelectron. Optoelectron. 8(1), 83–86 (2013).
[Crossref]

R. S. Edwards and K. S. Coleman, “Graphene film growth on polycrystalline metals,” Acc. Chem. Res. 46(1), 23–30 (2013).
[Crossref] [PubMed]

K.-J. Peng, C.-L. Wu, Y.-H. Lin, Y.-J. Liu, D.-P. Tsai, Y.-H. Pai, and G.-R. Lin, “Hydrogen-free PECVD growth of few-layer graphene on an ultra-thin nickel film at the threshold dissolution temperature,” J. Mater. Chem. C Mater. Opt. Electron. Devices 1(24), 3862–3870 (2013).
[Crossref]

Y. Zhang, L. Zhang, and C. Zhou, “Review of chemical vapor deposition of graphene and related applications,” Acc. Chem. Res. 46(10), 2329–2339 (2013).
[Crossref] [PubMed]

H. Kim, I. Song, C. Park, M. Son, M. Hong, Y. Kim, J. S. Kim, H. J. Shin, J. Baik, and H. C. Choi, “Copper-vapor-assisted chemical vapor deposition for high-quality and metal-free single-layer graphene on amorphous SiO2 substrate,” ACS Nano 7(8), 6575–6582 (2013).
[Crossref] [PubMed]

P. S. Rusakov, I. I. Kondrashov, M. G. Rybin, A. S. Pozharov, and E. D. Obraztsova, “Chemical Vapor Deposition of graphene on copper foils,” J. Nanoelectron. Optoelectron. 8(1), 79–82 (2013).
[Crossref]

I. Vlassiouk, P. Fulvio, H. Meyer, N. Lavrik, S. Dai, P. Datskos, and S. Smirnov, “Large scale atmospheric pressure chemical vapor deposition of graphene,” Carbon 54, 58–67 (2013).
[Crossref]

2012 (4)

R. Addou, A. Dahal, P. Sutter, and M. Batzill, “Monolayer graphene growth on Ni(111) by low temperature chemical vapor deposition,” Appl. Phys. Lett. 100(2), 021601 (2012).
[Crossref]

T. Kaplas, D. Sharma, and Y. Svirko, “Few-layer graphene synthesis on a dielectric substrate,” Carbon N. Y. 50(4), 1503–1509 (2012).
[Crossref]

J. Kwak, J. H. Chu, J.-K. Choi, S.-D. Park, H. Go, S. Y. Kim, K. Park, S.-D. Kim, Y.-W. Kim, E. Yoon, S. Kodambaka, and S.-Y. Kwon, “Near room-temperature synthesis of transfer-free graphene films,” Nat. Commun. 3, 645 (2012).
[Crossref] [PubMed]

C. V. Thompson, “Solid-state dewetting of thin films,” Annu. Rev. Mater. Res. 42(1), 399–434 (2012).
[Crossref]

2011 (4)

L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
[Crossref]

C.-Y. Su, A.-Y. Lu, C.-Y. Wu, Y. T. Li, K.-K. Liu, W. Zhang, S.-Y. Lin, Z.-Y. Juang, Y.-L. Zhong, F.-R. Chen, and L.-J. Li, “Direct formation of wafer scale graphene thin layers on insulating substrates by chemical vapor deposition,” Nano Lett. 11(9), 3612–3616 (2011).
[Crossref] [PubMed]

J. Lahiri, T. S. Miller, A. J. Ross, L. Adamska, I. I. Oleynik, and M. Batzill, “Graphene growth and stability at nickel surfaces,” New J. Phys. 13(2), 025001 (2011).
[Crossref]

C. Mattevi, H. Kim, and M. Chhowalla, “A review of chemical vapour deposition of graphene on copper,” J. Mater. Chem. 21(10), 3324–3334 (2011).
[Crossref]

2010 (3)

Y. Zhang, L. Gomez, F. N. Ishikawa, A. Madaria, K. Ryu, C. Wang, A. Badmaev, and C. Zhou, “Comparison of Graphene Growth on Single-Crystalline and Polycrystalline Ni by Chemical Vapor Deposition,” J. Phys. Chem. Lett. 1(20), 3101–3107 (2010).
[Crossref]

A. Ismach, C. Druzgalski, S. Penwell, A. Schwartzberg, M. Zheng, A. Javey, J. Bokor, and Y. Zhang, “Direct chemical vapor deposition of graphene on dielectric surfaces,” Nano Lett. 10(5), 1542–1548 (2010).
[Crossref] [PubMed]

S. Bae, H. Kim, Y. Lee, X. Xu, J. S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y. J. Kim, K. S. Kim, B. Özyilmaz, J. H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

2009 (7)

L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5–6), 51–87 (2009).
[Crossref]

S. J. Chae, F. Güneş, K. K. Kim, E. S. Kim, G. H. Han, S. M. Kim, H.-J. Shin, S.-M. Yoon, J.-Y. Choi, M. H. Park, C. W. Yang, D. Pribat, and Y. H. Lee, “Synthesis of large-area graphene layers on poly-nickel substrate by chemical vapor deposition: wrinkle formation,” Adv. Mater. 21(22), 2328–2333 (2009).
[Crossref]

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

A. B. Bourlinos, V. Georgakilas, R. Zboril, T. A. Steriotis, and A. K. Stubos, “Liquid-phase exfoliation of graphite towards solubilized graphenes,” Small 5(16), 1841–1845 (2009).
[Crossref] [PubMed]

V. C. Tung, M. J. Allen, Y. Yang, and R. B. Kaner, “High-throughput solution processing of large-scale graphene,” Nat. Nanotechnol. 4(1), 25–29 (2009).
[Crossref] [PubMed]

S. Giurgola, A. Rodriguez, L. Martinez, P. Vergani, F. Lucchi, S. Benchabane, and V. Pruneri, “Ultra thin nickel transparent electrodes,” J. Mater. Sci. Mater. Electron. 20(1), 181–184 (2009).
[Crossref]

L. Martínez, D. S. Ghosh, S. Giurgola, P. Vergani, and V. Pruneri, “Stable transparent Ni electrodes,” Opt. Mater. 31(8), 1115–1117 (2009).
[Crossref]

2008 (5)

B. O’Connor, C. Haughn, K.-H. An, K. P. Pipe, and M. Shtein, “Transparent and conductive electrodes based on unpatterned, thin metal films,” Appl. Phys. Lett. 93(22), 223304 (2008).
[Crossref]

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
[Crossref] [PubMed]

X. Li, G. Zhang, X. Bai, X. Sun, X. Wang, E. Wang, and H. Dai, “Highly conducting graphene sheets and Langmuir-Blodgett films,” Nat. Nanotechnol. 3(9), 538–542 (2008).
[Crossref] [PubMed]

D. Li, M. B. Müller, S. Gilje, R. B. Kaner, and G. G. Wallace, “Processable aqueous dispersions of graphene nanosheets,” Nat. Nanotechnol. 3(2), 101–105 (2008).
[Crossref] [PubMed]

Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei, “Graphene segregated on Ni surfaces and transferred to insulators,” Appl. Phys. Lett. 93(11), 113103 (2008).
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2007 (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
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S. Stankovich, D. A. Dikin, R. D. Piner, K. A. Kohlhaas, A. Kleinhammes, Y. Jia, Y. Wu, S. T. Nguyen, and R. S. Ruoff, “Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide,” Carbon 45(7), 1558–1565 (2007).
[Crossref]

2006 (2)

S. Stankovich, R. D. Piner, X. Chen, N. Wu, S. T. Nguyen, and R. S. Ruoff, “Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly(sodium 4-styrenesulfonate),” J. Mater. Chem. 16(2), 155–158 (2006).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
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2005 (1)

P. R. Gadkari, P. Warren, R. M. Todi, R. V. Petrova, and K. R. Coffey, “Comparison of the agglomeration behavior of thin metallic films on SiO2,” J. Vac. Sci. Technol. A 23(4), 1152 (2005).
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Adamska, L.

J. Lahiri, T. S. Miller, A. J. Ross, L. Adamska, I. I. Oleynik, and M. Batzill, “Graphene growth and stability at nickel surfaces,” New J. Phys. 13(2), 025001 (2011).
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Addou, R.

R. Addou, A. Dahal, P. Sutter, and M. Batzill, “Monolayer graphene growth on Ni(111) by low temperature chemical vapor deposition,” Appl. Phys. Lett. 100(2), 021601 (2012).
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Africh, C.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
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Ahn, J. H.

S. Bae, H. Kim, Y. Lee, X. Xu, J. S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y. J. Kim, K. S. Kim, B. Özyilmaz, J. H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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Allen, M. J.

V. C. Tung, M. J. Allen, Y. Yang, and R. B. Kaner, “High-throughput solution processing of large-scale graphene,” Nat. Nanotechnol. 4(1), 25–29 (2009).
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An, K.-H.

B. O’Connor, C. Haughn, K.-H. An, K. P. Pipe, and M. Shtein, “Transparent and conductive electrodes based on unpatterned, thin metal films,” Appl. Phys. Lett. 93(22), 223304 (2008).
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Bachmatiuk, A.

J. Sun, Y. Chen, M. K. Priydarshi, Z. Chen, A. Bachmatiuk, Z. Zou, Z. Chen, X. Song, Y. Gao, M. H. Rümmeli, Y. Zhang, and Z. Liu, “Direct Chemical Vapor Deposition-Derived Graphene Glasses Targeting Wide Ranged Applications,” Nano Lett. 15(9), 5846–5854 (2015).
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Badmaev, A.

Y. Zhang, L. Gomez, F. N. Ishikawa, A. Madaria, K. Ryu, C. Wang, A. Badmaev, and C. Zhou, “Comparison of Graphene Growth on Single-Crystalline and Polycrystalline Ni by Chemical Vapor Deposition,” J. Phys. Chem. Lett. 1(20), 3101–3107 (2010).
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Bae, S.

S. Bae, H. Kim, Y. Lee, X. Xu, J. S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y. J. Kim, K. S. Kim, B. Özyilmaz, J. H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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Bai, X.

X. Li, G. Zhang, X. Bai, X. Sun, X. Wang, E. Wang, and H. Dai, “Highly conducting graphene sheets and Langmuir-Blodgett films,” Nat. Nanotechnol. 3(9), 538–542 (2008).
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Baik, J.

H. Kim, I. Song, C. Park, M. Son, M. Hong, Y. Kim, J. S. Kim, H. J. Shin, J. Baik, and H. C. Choi, “Copper-vapor-assisted chemical vapor deposition for high-quality and metal-free single-layer graphene on amorphous SiO2 substrate,” ACS Nano 7(8), 6575–6582 (2013).
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Balakrishnan, J.

S. Bae, H. Kim, Y. Lee, X. Xu, J. S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y. J. Kim, K. S. Kim, B. Özyilmaz, J. H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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Baraton, L.

L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
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Basko, D. M.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8(4), 235–246 (2013).
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Batzill, M.

A. Dahal and M. Batzill, “Graphene-nickel interfaces: a review,” Nanoscale 6(5), 2548–2562 (2014).
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R. Addou, A. Dahal, P. Sutter, and M. Batzill, “Monolayer graphene growth on Ni(111) by low temperature chemical vapor deposition,” Appl. Phys. Lett. 100(2), 021601 (2012).
[Crossref]

J. Lahiri, T. S. Miller, A. J. Ross, L. Adamska, I. I. Oleynik, and M. Batzill, “Graphene growth and stability at nickel surfaces,” New J. Phys. 13(2), 025001 (2011).
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Benchabane, S.

S. Giurgola, A. Rodriguez, L. Martinez, P. Vergani, F. Lucchi, S. Benchabane, and V. Pruneri, “Ultra thin nickel transparent electrodes,” J. Mater. Sci. Mater. Electron. 20(1), 181–184 (2009).
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Berner, N. C.

T. Hallam, N. C. Berner, C. Yim, and G. S. Duesberg, “Strain, bubbles, dirt, and folds: a study of graphene polymer-assisted transfer,” Adv. Mater. Interfaces 1(6), 1400115 (2014).
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Bhardwaj, S.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
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Blighe, F. M.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
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Blume, R.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
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Bokor, J.

A. Ismach, C. Druzgalski, S. Penwell, A. Schwartzberg, M. Zheng, A. Javey, J. Bokor, and Y. Zhang, “Direct chemical vapor deposition of graphene on dielectric surfaces,” Nano Lett. 10(5), 1542–1548 (2010).
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Boland, J. J.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
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Bourlinos, A. B.

A. B. Bourlinos, V. Georgakilas, R. Zboril, T. A. Steriotis, and A. K. Stubos, “Liquid-phase exfoliation of graphite towards solubilized graphenes,” Small 5(16), 1841–1845 (2009).
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Brieland-Shoultz, A. C.

D. Q. McNerny, B. Viswanath, D. Copic, F. R. Laye, C. Prohoda, A. C. Brieland-Shoultz, E. S. Polsen, N. T. Dee, V. S. Veerasamy, and A. J. Hart, “Direct fabrication of graphene on SiO2 enabled by thin film stress engineering,” Sci. Rep. 4, 5049 (2014).
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Bulovic, V.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Byrne, M.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
[Crossref] [PubMed]

Cai, X.

J. Sun, Y. Chen, X. Cai, B. Ma, Z. Chen, M. K. Priydarshi, K. Chen, T. Gao, X. Song, Q. Ji, X. Guo, D. Zou, Y. Zhang, and Z. Liu, “Direct low-temperature synthesis of graphene on various glasses by plasma-enhanced chemical vapor deposition for versatile, cost-effective electrodes,” Nano Res. 8(11), 3496–3504 (2015).
[Crossref]

Casiraghi, C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[Crossref] [PubMed]

Castellarin-Cudia, C.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
[Crossref] [PubMed]

Cepek, C.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
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Chae, S. J.

S. J. Chae, F. Güneş, K. K. Kim, E. S. Kim, G. H. Han, S. M. Kim, H.-J. Shin, S.-M. Yoon, J.-Y. Choi, M. H. Park, C. W. Yang, D. Pribat, and Y. H. Lee, “Synthesis of large-area graphene layers on poly-nickel substrate by chemical vapor deposition: wrinkle formation,” Adv. Mater. 21(22), 2328–2333 (2009).
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Chai, S.-P.

C.-M. Seah, S.-P. Chai, and A. R. Mohamed, “Mechanisms of graphene growth by chemical vapour deposition on transition metals,” Carbon 70, 1–21 (2014).
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Châtelet, M.

L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
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Chen, F.-R.

C.-Y. Su, A.-Y. Lu, C.-Y. Wu, Y. T. Li, K.-K. Liu, W. Zhang, S.-Y. Lin, Z.-Y. Juang, Y.-L. Zhong, F.-R. Chen, and L.-J. Li, “Direct formation of wafer scale graphene thin layers on insulating substrates by chemical vapor deposition,” Nano Lett. 11(9), 3612–3616 (2011).
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Chen, K.

J. Sun, Y. Chen, X. Cai, B. Ma, Z. Chen, M. K. Priydarshi, K. Chen, T. Gao, X. Song, Q. Ji, X. Guo, D. Zou, Y. Zhang, and Z. Liu, “Direct low-temperature synthesis of graphene on various glasses by plasma-enhanced chemical vapor deposition for versatile, cost-effective electrodes,” Nano Res. 8(11), 3496–3504 (2015).
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Chen, T. L.

T. L. Chen, D. S. Ghosh, M. Marchena, J. Osmond, and V. Pruneri, “Nanopatterned Graphene on a Polymer Substrate by a Direct Peel-off Technique,” ACS Appl. Mater. Interfaces 7(10), 5938–5943 (2015).
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Chen, X.

S. Stankovich, R. D. Piner, X. Chen, N. Wu, S. T. Nguyen, and R. S. Ruoff, “Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly(sodium 4-styrenesulfonate),” J. Mater. Chem. 16(2), 155–158 (2006).
[Crossref]

Chen, Y.

J. Sun, Y. Chen, M. K. Priydarshi, Z. Chen, A. Bachmatiuk, Z. Zou, Z. Chen, X. Song, Y. Gao, M. H. Rümmeli, Y. Zhang, and Z. Liu, “Direct Chemical Vapor Deposition-Derived Graphene Glasses Targeting Wide Ranged Applications,” Nano Lett. 15(9), 5846–5854 (2015).
[Crossref] [PubMed]

J. Sun, Y. Chen, X. Cai, B. Ma, Z. Chen, M. K. Priydarshi, K. Chen, T. Gao, X. Song, Q. Ji, X. Guo, D. Zou, Y. Zhang, and Z. Liu, “Direct low-temperature synthesis of graphene on various glasses by plasma-enhanced chemical vapor deposition for versatile, cost-effective electrodes,” Nano Res. 8(11), 3496–3504 (2015).
[Crossref]

Chen, Y. P.

Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei, “Graphene segregated on Ni surfaces and transferred to insulators,” Appl. Phys. Lett. 93(11), 113103 (2008).
[Crossref]

Chen, Z.

J. Sun, Y. Chen, M. K. Priydarshi, Z. Chen, A. Bachmatiuk, Z. Zou, Z. Chen, X. Song, Y. Gao, M. H. Rümmeli, Y. Zhang, and Z. Liu, “Direct Chemical Vapor Deposition-Derived Graphene Glasses Targeting Wide Ranged Applications,” Nano Lett. 15(9), 5846–5854 (2015).
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J. Sun, Y. Chen, M. K. Priydarshi, Z. Chen, A. Bachmatiuk, Z. Zou, Z. Chen, X. Song, Y. Gao, M. H. Rümmeli, Y. Zhang, and Z. Liu, “Direct Chemical Vapor Deposition-Derived Graphene Glasses Targeting Wide Ranged Applications,” Nano Lett. 15(9), 5846–5854 (2015).
[Crossref] [PubMed]

J. Sun, Y. Chen, X. Cai, B. Ma, Z. Chen, M. K. Priydarshi, K. Chen, T. Gao, X. Song, Q. Ji, X. Guo, D. Zou, Y. Zhang, and Z. Liu, “Direct low-temperature synthesis of graphene on various glasses by plasma-enhanced chemical vapor deposition for versatile, cost-effective electrodes,” Nano Res. 8(11), 3496–3504 (2015).
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Chhowalla, M.

C. Mattevi, H. Kim, and M. Chhowalla, “A review of chemical vapour deposition of graphene on copper,” J. Mater. Chem. 21(10), 3324–3334 (2011).
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Choi, H. C.

H. Kim, I. Song, C. Park, M. Son, M. Hong, Y. Kim, J. S. Kim, H. J. Shin, J. Baik, and H. C. Choi, “Copper-vapor-assisted chemical vapor deposition for high-quality and metal-free single-layer graphene on amorphous SiO2 substrate,” ACS Nano 7(8), 6575–6582 (2013).
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Choi, J.-K.

J. Kwak, J. H. Chu, J.-K. Choi, S.-D. Park, H. Go, S. Y. Kim, K. Park, S.-D. Kim, Y.-W. Kim, E. Yoon, S. Kodambaka, and S.-Y. Kwon, “Near room-temperature synthesis of transfer-free graphene films,” Nat. Commun. 3, 645 (2012).
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Choi, J.-Y.

S. J. Chae, F. Güneş, K. K. Kim, E. S. Kim, G. H. Han, S. M. Kim, H.-J. Shin, S.-M. Yoon, J.-Y. Choi, M. H. Park, C. W. Yang, D. Pribat, and Y. H. Lee, “Synthesis of large-area graphene layers on poly-nickel substrate by chemical vapor deposition: wrinkle formation,” Adv. Mater. 21(22), 2328–2333 (2009).
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Chu, J. H.

J. Kwak, J. H. Chu, J.-K. Choi, S.-D. Park, H. Go, S. Y. Kim, K. Park, S.-D. Kim, Y.-W. Kim, E. Yoon, S. Kodambaka, and S.-Y. Kwon, “Near room-temperature synthesis of transfer-free graphene films,” Nat. Commun. 3, 645 (2012).
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Coffey, K. R.

P. R. Gadkari, P. Warren, R. M. Todi, R. V. Petrova, and K. R. Coffey, “Comparison of the agglomeration behavior of thin metallic films on SiO2,” J. Vac. Sci. Technol. A 23(4), 1152 (2005).
[Crossref]

Cojocaru, C. S.

L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
[Crossref]

Coleman, J. N.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
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Coleman, K. S.

R. S. Edwards and K. S. Coleman, “Graphene film growth on polycrystalline metals,” Acc. Chem. Res. 46(1), 23–30 (2013).
[Crossref] [PubMed]

Comelli, G.

L. L. Patera, C. Africh, R. S. Weatherup, R. Blume, S. Bhardwaj, C. Castellarin-Cudia, A. Knop-Gericke, R. Schloegl, G. Comelli, S. Hofmann, and C. Cepek, “In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth,” ACS Nano 7(9), 7901–7912 (2013).
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Copic, D.

D. Q. McNerny, B. Viswanath, D. Copic, F. R. Laye, C. Prohoda, A. C. Brieland-Shoultz, E. S. Polsen, N. T. Dee, V. S. Veerasamy, and A. J. Hart, “Direct fabrication of graphene on SiO2 enabled by thin film stress engineering,” Sci. Rep. 4, 5049 (2014).
[Crossref] [PubMed]

Dahal, A.

A. Dahal and M. Batzill, “Graphene-nickel interfaces: a review,” Nanoscale 6(5), 2548–2562 (2014).
[Crossref] [PubMed]

R. Addou, A. Dahal, P. Sutter, and M. Batzill, “Monolayer graphene growth on Ni(111) by low temperature chemical vapor deposition,” Appl. Phys. Lett. 100(2), 021601 (2012).
[Crossref]

Dai, H.

X. Li, G. Zhang, X. Bai, X. Sun, X. Wang, E. Wang, and H. Dai, “Highly conducting graphene sheets and Langmuir-Blodgett films,” Nat. Nanotechnol. 3(9), 538–542 (2008).
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Dai, S.

I. Vlassiouk, P. Fulvio, H. Meyer, N. Lavrik, S. Dai, P. Datskos, and S. Smirnov, “Large scale atmospheric pressure chemical vapor deposition of graphene,” Carbon 54, 58–67 (2013).
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Datskos, P.

I. Vlassiouk, P. Fulvio, H. Meyer, N. Lavrik, S. Dai, P. Datskos, and S. Smirnov, “Large scale atmospheric pressure chemical vapor deposition of graphene,” Carbon 54, 58–67 (2013).
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De, S.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
[Crossref] [PubMed]

Dee, N. T.

D. Q. McNerny, B. Viswanath, D. Copic, F. R. Laye, C. Prohoda, A. C. Brieland-Shoultz, E. S. Polsen, N. T. Dee, V. S. Veerasamy, and A. J. Hart, “Direct fabrication of graphene on SiO2 enabled by thin film stress engineering,” Sci. Rep. 4, 5049 (2014).
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A. Delamoreanu, C. Rabot, C. Vallee, and A. Zenasni, “Wafer scale catalytic growth of graphene on nickel by solid carbon source,” Carbon 66, 48–56 (2014).
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Dikin, D. A.

S. Stankovich, D. A. Dikin, R. D. Piner, K. A. Kohlhaas, A. Kleinhammes, Y. Jia, Y. Wu, S. T. Nguyen, and R. S. Ruoff, “Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide,” Carbon 45(7), 1558–1565 (2007).
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Dresselhaus, G.

L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5–6), 51–87 (2009).
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Dresselhaus, M. S.

L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5–6), 51–87 (2009).
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A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Druzgalski, C.

A. Ismach, C. Druzgalski, S. Penwell, A. Schwartzberg, M. Zheng, A. Javey, J. Bokor, and Y. Zhang, “Direct chemical vapor deposition of graphene on dielectric surfaces,” Nano Lett. 10(5), 1542–1548 (2010).
[Crossref] [PubMed]

Duesberg, G.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008).
[Crossref] [PubMed]

Duesberg, G. S.

T. Hallam, N. C. Berner, C. Yim, and G. S. Duesberg, “Strain, bubbles, dirt, and folds: a study of graphene polymer-assisted transfer,” Adv. Mater. Interfaces 1(6), 1400115 (2014).
[Crossref]

Edwards, R. S.

R. S. Edwards and K. S. Coleman, “Graphene film growth on polycrystalline metals,” Acc. Chem. Res. 46(1), 23–30 (2013).
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L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
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A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
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T. L. Chen, D. S. Ghosh, M. Marchena, J. Osmond, and V. Pruneri, “Nanopatterned Graphene on a Polymer Substrate by a Direct Peel-off Technique,” ACS Appl. Mater. Interfaces 7(10), 5938–5943 (2015).
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L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5–6), 51–87 (2009).
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S. Stankovich, D. A. Dikin, R. D. Piner, K. A. Kohlhaas, A. Kleinhammes, Y. Jia, Y. Wu, S. T. Nguyen, and R. S. Ruoff, “Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide,” Carbon 45(7), 1558–1565 (2007).
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S. Stankovich, R. D. Piner, X. Chen, N. Wu, S. T. Nguyen, and R. S. Ruoff, “Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly(sodium 4-styrenesulfonate),” J. Mater. Chem. 16(2), 155–158 (2006).
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B. O’Connor, C. Haughn, K.-H. An, K. P. Pipe, and M. Shtein, “Transparent and conductive electrodes based on unpatterned, thin metal films,” Appl. Phys. Lett. 93(22), 223304 (2008).
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A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
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I. I. Kondrashov, P. S. Rusakov, M. G. Rybin, A. S. Pozharov, and E. D. Obraztsova, “Chemical Vapor Deposition of Graphene on Nickel from Different Gaseous Atmospheres,” J. Nanoelectron. Optoelectron. 8(1), 83–86 (2013).
[Crossref]

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L. Baraton, Z. B. He, C. S. Lee, C. S. Cojocaru, M. Châtelet, J.-L. Maurice, Y. H. Lee, and D. Pribat, “On the mechanisms of precipitation of graphene on nickel thin films,” EPL 96(4), 46003 (2011).
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S. J. Chae, F. Güneş, K. K. Kim, E. S. Kim, G. H. Han, S. M. Kim, H.-J. Shin, S.-M. Yoon, J.-Y. Choi, M. H. Park, C. W. Yang, D. Pribat, and Y. H. Lee, “Synthesis of large-area graphene layers on poly-nickel substrate by chemical vapor deposition: wrinkle formation,” Adv. Mater. 21(22), 2328–2333 (2009).
[Crossref]

Priydarshi, M. K.

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Zheng, M.

A. Ismach, C. Druzgalski, S. Penwell, A. Schwartzberg, M. Zheng, A. Javey, J. Bokor, and Y. Zhang, “Direct chemical vapor deposition of graphene on dielectric surfaces,” Nano Lett. 10(5), 1542–1548 (2010).
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Figures (17)

Fig. 1
Fig. 1

GXRD spectra of 50 nm Ni UTMF at 1000°C (Sample C in Table 1) before and after CVD (grey and red lines, respectively), showing the crystallinity improvement after CVD treatment, as well as the appearance of a narrow peak at small angle associated to graphene growth.

Fig. 2
Fig. 2

Optical microscope images of 50 nm dewetted samples A, B and C after graphene growth at 700, 900 and 1000°C, respectively (for all 30 minutes reaction). Bright purple areas correspond to continuous/dewetted Ni while dark areas correspond to Ni-free regions where graphene is deposited directly on SiO2. Raman spectra was measured on dewetted areas (dark) demonstrating graphene deposition on SiO2. Scale bar: 10 μm.

Fig. 3
Fig. 3

Growth of suspended graphene on dewetted Ni holes (Sample A). (a) SEM image of a hole partially covered by suspended graphene, identifiable by the wrinkles; (b) AFM amplitude and (c) phase images of graphene suspended over a hole, different from that of the SEM image in (a). The green dotted line indicates the hole’s borders. (d) Cross sections of the AFM amplitude map corresponding to Ni continuous film only (red line) and suspended graphene (black line). In all figures the scale bar is 2 μm.

Fig. 4
Fig. 4

Raman maps of Sample B (50 nm/900°C) show (a) high I2D/IG ratio of SLG grown on the dewetted area, (b) ID/IG ratio map, and (c-d) FWHM of 2D peak and statistics for both areas (See original optical microscope image (Fig. 13(d)) and AFM measurement (Fig. 14), in Appendix. Scale bar: 5μm.

Fig. 5
Fig. 5

Percentage of graphene coverage versus quality, i.e. I2D/IG from Raman maps of: (a) Sample A, (b) Sample B, (c) Sample C and (d) Sample D. Note that the presence of Ni particle remains affect the Raman measurements, so the data are only indicative.

Fig. 6
Fig. 6

Schematic model of graphene growth on 50 nm Ni UTMF: (a) first step of annealing, where activation, reduction and crystallization take place, (b) nucleation of holes promoting Ni dewetting and deposition of graphene upon metal retraction starting at 700°C and (c) cooling down where graphene is already deposited on the silica substrate.

Fig. 7
Fig. 7

(a-b) Transmittance (including substrate contribution) and absorbance values at 550 nm of samples A-D before (in black) and after (in red) Ni removal. (c) Picture of Sample A and Sample C (Ni 50 nm at 700°C and Ni 50 nm at 1000°C, respectively) as deposited (first column), after graphene growth (second column) and after Ni removal (third column).

Fig. 8
Fig. 8

Flow chart on top shows different steps for graphene patterns fabrication (see more details in section 2.1). Optical images of Ni 50 nm UTMF patterned on Si/SiO2 and Corning® Willow® Glass substrates in square shapes of different size (a,e) as deposited via sputtering and (b,f) after Ni removal when graphene is deposited at the same condition than Sample A. SEM images in (c, g-h) show high quality graphene squares after Ni removal with absence of any metal residues and holes (also EDX results in Table 5 in Appendix) for both substrates. Au electrodes for 4-point probe measurements are shown in (d).

Fig. 9
Fig. 9

Tdewetting as a function of different UTMF thicknesses for Ni (our work) and Cu [41,42], dashed and solid line, respectively.

Fig. 10
Fig. 10

Reaction time effect on graphene quality evaluating (a) I2D/IG and (b) FWHM 2D peak, at 15, 30 and 60 minutes, respectively. Shaded area corresponds to values for theoretical SLG.

Fig. 11
Fig. 11

SEM pictures of Ni 50nm at 700°C, 800°C, 900°C, 1000°C (sample A, S8, sample B and sample C) showing the dewetting evolution when the process temperature is raised: (a) nucleation step of holes, (b-c) holes propagation and (d) total dewetting of the Ni UTMF. Scale bar: 10μm

Fig. 12
Fig. 12

Sample A (700°C, nucleation step): (a-b) AFM and SEM pictures showing the holes formed at the beginning of the dewetting (b) corresponds to the yellow dashed area in (a), (c-e) Raman maps of the area in (a) demonstrating graphene coverage on the holes, as I2D/IG ratios are very high, and FWHM 2D values are within 25-30 cm−1, values assigned to SLG. Scale bar: 2 μm.

Fig. 13
Fig. 13

Optical microscope image and I2D and shift of the G peak. (a-b) gives Raman maps (10x10 μm2) for two different regions of Sample A (blue squares), (c) S9, (d) Sample B, (map of the region within the blue square), (e) Sample D and (f) Sample C (map of the region within the blue square). Scale bar: 10μm.

Fig. 14
Fig. 14

AFM measurements of Sample B: (a) height map, (b) zoomed area from (a) (blue dashed square) showing the graphene domains, (c) height map with increased contrast to enhance the ripple and domain structures of graphene grown on SiO2 after metal retraction, and (d) phase map. (Map: 15x15 μm2).

Fig. 15
Fig. 15

SEM images and Raman maps of I2D/IG of graphene grown on different Ni thicknesses and at different temperatures (all 30 minutes reaction time): (a) S9 (5 nm, 900°C), (b) Sample D (15 nm, 1000°C) and (c) Sample C (50 nm, 1000°C). Scale bar: 2μm.

Fig. 16
Fig. 16

Transmittance spectra of highest quality UTMF Ni samples: (a) after CVD processing and (b) after etching process of 15 minutes.

Fig. 17
Fig. 17

Raman mapping of graphene square patterned on willow glass: (a) I2D peak, (b) I2D/IG ratio and (c) Raman spectra when measuring inside and outside of the pattern region.

Tables (5)

Tables Icon

Table 1 Process conditions and Raman signals for graphene grown on Ni UTMF (fused silica substrate) of different thickness (Raman measurements include the ratios between graphene peaks: I2D/IG, ID/IG and the FWHM of 2D peak. All measurements were performed on the dewetted areas, where the metal is retracted). (Results at different conditions for same thickness are collected in Table 2 of Appendix).

Tables Icon

Table 2 Process conditions and Raman/electrical results for graphene deposited on Ni UTMF

Tables Icon

Table 3 Raman measurement results on UTMF Ni of different thickness. (Raman measured on the non-dewetted areas).

Tables Icon

Table 4 Graphene layers calculation of different Ni films treated at different temperatures

Tables Icon

Table 5 EDX measurements on graphene after Ni removal from Sample A

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

S(GLs)= S( atoms·c m 3 )· L NiUTMF ρ GrapheneAtomicLayer
S= S O ·exp( H P k·T )
L D 2 (n m 2 )=5.4· 10 2 · E L 4 (e V 4 )·( I D / I G )

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