Abstract

Optical reflection microscopy is one of the main imaging tools to visualize graphene microstructures. Here is reported a novel method that employs refractive index optimization in an optical reflection microscope, which greatly improves the visibility of graphene flakes. To this end, an immersion liquid with a refractive index that is close to that of the glass support is used in-between the microscope lens and the support improving the contrast and resolution of the sample image. Results show that the contrast of single and few layer graphene crystals and structures can be enhanced by a factor of 4 compared to values commonly achieved with transparent substrates using optical reflection microscopy lacking refractive index optimization.

© 2013 OSA

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    [CrossRef] [PubMed]
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  15. Z. Q. Luo, M. Zhou, D. D. Wu, C. C. Ye, J. Weng, J. Dong, H. Y. Xu, Z. P. Cai, and L. J. Chen, “Graphene-induced nonlinear four-wave-mixing and its application to multiwavelength Q-switched rare-earth-doped fiber lasers,” J. Lightwave Technol.29(18), 2732–2739 (2011).
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    [CrossRef] [PubMed]
  26. C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
    [CrossRef] [PubMed]
  27. D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
    [CrossRef] [PubMed]
  28. R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
    [CrossRef] [PubMed]
  29. Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
    [CrossRef]
  30. H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
    [CrossRef]
  31. J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
    [CrossRef] [PubMed]
  32. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
    [CrossRef]
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    [CrossRef]
  34. M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
    [CrossRef]
  35. A. K. Geim, “Graphene: status and prospects,” Science324(5934), 1530–1534 (2009).
    [CrossRef] [PubMed]
  36. H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
    [CrossRef] [PubMed]
  37. 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]
  38. 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]

2012 (7)

P. Avouris and C. Dimitrakopoulos, “Graphene: synthesis and applications,” Mater. Today15(3), 86–97 (2012).
[CrossRef]

T. Premkumar and K. E. Geckeler, “Graphene-DNA hybrid materials: assembly, applications, and prospects,” Prog. Polym. Sci.37(4), 515–529 (2012).
[CrossRef]

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

S. Cheon, K. D. Kihm, J. S. Park, J. S. Lee, B. J. Lee, H. Kim, and B. H. Hong, “How to optically count graphene layers,” Opt. Lett.37(18), 3765–3767 (2012).
[CrossRef] [PubMed]

2011 (7)

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

D. K. Venkatachalam, P. Parkinson, S. Ruffell, and R. G. Elliman, “Rapid, substrate-independent thickness determination of large area graphene layers,” Appl. Phys. Lett.99(23), 234106 (2011).
[CrossRef]

Z. Q. Luo, M. Zhou, D. D. Wu, C. C. Ye, J. Weng, J. Dong, H. Y. Xu, Z. P. Cai, and L. J. Chen, “Graphene-induced nonlinear four-wave-mixing and its application to multiwavelength Q-switched rare-earth-doped fiber lasers,” J. Lightwave Technol.29(18), 2732–2739 (2011).
[CrossRef]

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

A. K. Mishra and S. Ramaprabhu, “Functionalized graphene-based nanocomposites for supercapacitor application,” J. Phys. Chem. C115(29), 14006–14013 (2011).
[CrossRef]

C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
[CrossRef]

2010 (7)

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

S. K. Saha, M. Baskey, and D. Majumdar, “Graphene quantum sheets: a new material for spintronic applications,” Adv. Mater.22(48), 5531–5536 (2010).
[CrossRef] [PubMed]

H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
[CrossRef] [PubMed]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

2009 (6)

A. K. Geim, “Graphene: status and prospects,” Science324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

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]

P. E. Gaskell, H. S. Skulason, C. Rodenchuk, and T. Szkopek, “Counting graphene layers on glass via optical reflection microscopy,” Appl. Phys. Lett.94(14), 143101 (2009).
[CrossRef]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

V. Yu and M. Hilke, “Large contrast enhancement of graphene monolayers by angle detection,” Appl. Phys. Lett.95(15), 151904 (2009).
[CrossRef]

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

2008 (5)

Y. N. Eroshenko, “Physics news on the Internet (based on electronic preprints),” Physics-Uspekhi51(1), 107–108 (2008).
[CrossRef]

C. Ritter, S. S. Makler, and A. Latge, “Energy-gap modulations of graphene ribbons under external fields: a theoretical study,” Phys. Rev. B77(19), 195443 (2008).
[CrossRef]

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
[CrossRef]

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

2007 (5)

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007).
[CrossRef] [PubMed]

2006 (1)

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]

Ahn, J. H.

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Albrektsen, O.

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Alves, L.

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

Arsat, R.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Avouris, P.

P. Avouris and C. Dimitrakopoulos, “Graphene: synthesis and applications,” Mater. Today15(3), 86–97 (2012).
[CrossRef]

Bae, S.

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

Baskey, M.

S. K. Saha, M. Baskey, and D. Majumdar, “Graphene quantum sheets: a new material for spintronic applications,” Adv. Mater.22(48), 5531–5536 (2010).
[CrossRef] [PubMed]

Belsley, M.

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

Blake, P.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

Booth, T. J.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

Bozhevolnyi, S. I.

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Breedon, M.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Brown, L.

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Cai, Z. P.

Casiraghi, C.

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

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]

Castro Neto, A. H.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

Chan-Park, M. B.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Chekushin, A.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

Chen, L. J.

Chen, P.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Cheon, S.

Choe, M.

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

Choi, J. Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Choi, W.

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

Cote, L. J.

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

Dimitrakopoulos, C.

P. Avouris and C. Dimitrakopoulos, “Graphene: synthesis and applications,” Mater. Today15(3), 86–97 (2012).
[CrossRef]

Dong, J.

Dong, X.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Dorn, M.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

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).
[CrossRef]

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D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
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O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
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Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
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C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
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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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H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
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K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

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T. Premkumar and K. E. Geckeler, “Graphene-DNA hybrid materials: assembly, applications, and prospects,” Prog. Polym. Sci.37(4), 515–529 (2012).
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A. K. Geim, “Graphene: status and prospects,” Science324(5934), 1530–1534 (2009).
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T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
[CrossRef]

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
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A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007).
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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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R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
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C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

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H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

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C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
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K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

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D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

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G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

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K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
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C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

Harutyunyan, H.

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

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R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

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D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

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V. Yu and M. Hilke, “Large contrast enhancement of graphene monolayers by angle detection,” Appl. Phys. Lett.95(15), 151904 (2009).
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P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

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S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
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S. Cheon, K. D. Kihm, J. S. Park, J. S. Lee, B. J. Lee, H. Kim, and B. H. Hong, “How to optically count graphene layers,” Opt. Lett.37(18), 3765–3767 (2012).
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K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Huang, J. X.

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

Huang, W.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Huang, Y.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Jang, H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Jiang, D.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[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).
[CrossRef] [PubMed]

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G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

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R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Jungen, A.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

Kahng, Y. H.

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

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R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Kaner, R. B.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Kang, Y. S.

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

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O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Kasim, J.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Kihm, K. D.

Kim, F.

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

Kim, H.

Kim, J.

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

Kim, J. M.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Kim, K. S.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Kim, P.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Kim, S. J.

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

Lahiri, I.

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

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M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

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C. Ritter, S. S. Makler, and A. Latge, “Energy-gap modulations of graphene ribbons under external fields: a theoretical study,” Phys. Rev. B77(19), 195443 (2008).
[CrossRef]

Lazzeri, M.

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]

Lee, B. J.

Lee, J. S.

Lee, S.

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

Lee, S. Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Lee, T.

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

Lidorikis, E.

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

Long, Q.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Luo, Z. Q.

Majumdar, D.

S. K. Saha, M. Baskey, and D. Majumdar, “Graphene quantum sheets: a new material for spintronic applications,” Adv. Mater.22(48), 5531–5536 (2010).
[CrossRef] [PubMed]

Makler, S. S.

C. Ritter, S. S. Makler, and A. Latge, “Energy-gap modulations of graphene ribbons under external fields: a theoretical study,” Phys. Rev. B77(19), 195443 (2008).
[CrossRef]

Malard, L. M.

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]

Mauri, F.

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]

Meyer, J. 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]

Mishra, A. K.

A. K. Mishra and S. Ramaprabhu, “Functionalized graphene-based nanocomposites for supercapacitor application,” J. Phys. Chem. C115(29), 14006–14013 (2011).
[CrossRef]

Molitor, F.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

Moura, C.

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

Ni, Z. H.

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Novikov, S. M.

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Novoselov, K. S.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007).
[CrossRef] [PubMed]

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]

Park, J.

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Park, J. S.

Park, W.

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

Parkinson, P.

D. K. Venkatachalam, P. Parkinson, S. Ruffell, and R. G. Elliman, “Rapid, substrate-independent thickness determination of large area graphene layers,” Appl. Phys. Lett.99(23), 234106 (2011).
[CrossRef]

Paulava, V.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

Peres, N. M. R.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
[CrossRef]

Peters, K.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

Pimenta, M. A.

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]

Piscanec, S.

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]

Premkumar, T.

T. Premkumar and K. E. Geckeler, “Graphene-DNA hybrid materials: assembly, applications, and prospects,” Prog. Polym. Sci.37(4), 515–529 (2012).
[CrossRef]

Qian, H.

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

Rabe, J. P.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

Ramakrishna Matte, H. S. S.

C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
[CrossRef]

Ramaprabhu, S.

A. K. Mishra and S. Ramaprabhu, “Functionalized graphene-based nanocomposites for supercapacitor application,” J. Phys. Chem. C115(29), 14006–14013 (2011).
[CrossRef]

Rao, C. N. R.

C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
[CrossRef]

Ritter, C.

C. Ritter, S. S. Makler, and A. Latge, “Energy-gap modulations of graphene ribbons under external fields: a theoretical study,” Phys. Rev. B77(19), 195443 (2008).
[CrossRef]

Rodenchuk, C.

P. E. Gaskell, H. S. Skulason, C. Rodenchuk, and T. Szkopek, “Counting graphene layers on glass via optical reflection microscopy,” Appl. Phys. Lett.94(14), 143101 (2009).
[CrossRef]

Roling, C.

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Roth, S.

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]

Ruffell, S.

D. K. Venkatachalam, P. Parkinson, S. Ruffell, and R. G. Elliman, “Rapid, substrate-independent thickness determination of large area graphene layers,” Appl. Phys. Lett.99(23), 234106 (2011).
[CrossRef]

Ruiz-Vargas, C. S.

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Saha, S. K.

S. K. Saha, M. Baskey, and D. Majumdar, “Graphene quantum sheets: a new material for spintronic applications,” Adv. Mater.22(48), 5531–5536 (2010).
[CrossRef] [PubMed]

Scardaci, V.

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]

Schall, D.

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Schellenberg, P.

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

Seelaboyina, R.

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

Severin, N.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

Shafiei, M.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Shen, Z. X.

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Shin, D.

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

Simonsen, A. C.

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

Skulason, H. S.

H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
[CrossRef] [PubMed]

P. E. Gaskell, H. S. Skulason, C. Rodenchuk, and T. Szkopek, “Counting graphene layers on glass via optical reflection microscopy,” Appl. Phys. Lett.94(14), 143101 (2009).
[CrossRef]

Spizziri, P. G.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Stampfer, C.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

Stauber, T.

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
[CrossRef]

Subrahmanyam, K. S.

C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
[CrossRef]

Szkopek, T.

H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
[CrossRef] [PubMed]

P. E. Gaskell, H. S. Skulason, C. Rodenchuk, and T. Szkopek, “Counting graphene layers on glass via optical reflection microscopy,” Appl. Phys. Lett.94(14), 143101 (2009).
[CrossRef]

Teo, G. Q.

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Thiesen, P. H.

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Tittel, A.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

Vaupel, M.

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Venkatachalam, D. K.

D. K. Venkatachalam, P. Parkinson, S. Ruffell, and R. G. Elliman, “Rapid, substrate-independent thickness determination of large area graphene layers,” Appl. Phys. Lett.99(23), 234106 (2011).
[CrossRef]

Wang, H. M.

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Wang, J.

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Wang, Y. Y.

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

Wang, Z. H.

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Wegscheider, W.

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Weiss, D.

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Weng, J.

Wirtz, L.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

Wlodarski, W.

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Wojcik, M.

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Wu, D. D.

Wu, Y. H.

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Wurstbauer, U.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

Xu, H. Y.

Yang, R.

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

Ye, C. C.

Yu, T.

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

Yu, V.

V. Yu and M. Hilke, “Large contrast enhancement of graphene monolayers by angle detection,” Appl. Phys. Lett.95(15), 151904 (2009).
[CrossRef]

Zhang, J.

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

Zhao, Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Zhou, M.

ACS Nano (1)

R. W. Havener, S. Y. Ju, L. Brown, Z. H. Wang, M. Wojcik, C. S. Ruiz-Vargas, and J. Park, “High-throughput graphene imaging on arbitrary substrates with widefield Raman spectroscopy,” ACS Nano6(1), 373–380 (2012).
[CrossRef] [PubMed]

Adv. Mater. (1)

S. K. Saha, M. Baskey, and D. Majumdar, “Graphene quantum sheets: a new material for spintronic applications,” Adv. Mater.22(48), 5531–5536 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (7)

P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett.91(6), 063124 (2007).
[CrossRef]

H. Gonçalves, M. Belsley, C. Moura, T. Stauber, and P. Schellenberg, “Enhancing visibility of graphene on arbitrary substrates by microdroplet condensation,” Appl. Phys. Lett.97(23), 231905 (2010).
[CrossRef]

P. E. Gaskell, H. S. Skulason, C. Rodenchuk, and T. Szkopek, “Counting graphene layers on glass via optical reflection microscopy,” Appl. Phys. Lett.94(14), 143101 (2009).
[CrossRef]

V. Yu and M. Hilke, “Large contrast enhancement of graphene monolayers by angle detection,” Appl. Phys. Lett.95(15), 151904 (2009).
[CrossRef]

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett.99(19), 191912 (2011).
[CrossRef]

U. Wurstbauer, C. Roling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett.97(23), 231901 (2010).
[CrossRef]

D. K. Venkatachalam, P. Parkinson, S. Ruffell, and R. G. Elliman, “Rapid, substrate-independent thickness determination of large area graphene layers,” Appl. Phys. Lett.99(23), 234106 (2011).
[CrossRef]

Chem. Phys. Lett. (1)

R. Arsat, M. Breedon, M. Shafiei, P. G. Spizziri, S. Gilje, R. B. Kaner, K. Kalantar-Zadeh, and W. Wlodarski, “Graphene-like nano-sheets for surface acoustic wave gas sensor applications,” Chem. Phys. Lett.467(4-6), 344–347 (2009).
[CrossRef]

Crit. Rev. Sol. State (1)

W. Choi, I. Lahiri, R. Seelaboyina, and Y. S. Kang, “Synthesis of graphene and its applications: a review,” Crit. Rev. Sol. State35(1), 52–71 (2010).
[CrossRef]

J. Am. Chem. Soc. (1)

J. Kim, L. J. Cote, F. Kim, and J. X. Huang, “Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy,” J. Am. Chem. Soc.132(1), 260–267 (2010).
[CrossRef] [PubMed]

J. Appl. Phys. (3)

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys.108(10), 106101 (2010).
[CrossRef]

O. Albrektsen, R. L. Eriksen, S. M. Novikov, D. Schall, M. Karl, S. I. Bozhevolnyi, and A. C. Simonsen, “High resolution imaging of few-layer graphene,” J. Appl. Phys.111(6), 064305 (2012).
[CrossRef]

G. Q. Teo, H. M. Wang, Y. H. Wu, Z. B. Guo, J. Zhang, Z. H. Ni, and Z. X. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys.103(12), 124302 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Phys. Chem. C (1)

A. K. Mishra and S. Ramaprabhu, “Functionalized graphene-based nanocomposites for supercapacitor application,” J. Phys. Chem. C115(29), 14006–14013 (2011).
[CrossRef]

Mater. Today (1)

P. Avouris and C. Dimitrakopoulos, “Graphene: synthesis and applications,” Mater. Today15(3), 86–97 (2012).
[CrossRef]

Mod. Phys. Lett. B (1)

C. N. R. Rao, K. S. Subrahmanyam, H. S. S. Ramakrishna Matte, and A. Govindaraj, “Graphene: synthesis, functionalization and properties,” Mod. Phys. Lett. B25(07), 427–451 (2011).
[CrossRef]

Nano Lett. (3)

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, “Graphene thickness determination using reflection and contrast spectroscopy,” Nano Lett.7(9), 2758–2763 (2007).
[CrossRef] [PubMed]

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett.7(9), 2711–2717 (2007).
[CrossRef] [PubMed]

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett.7(2), 238–242 (2007).
[CrossRef] [PubMed]

Nano Res. (1)

Z. H. Ni, Y. Y. Wang, T. Yu, and Z. X. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res.1(4), 273–291 (2008).
[CrossRef]

Nanoscale (1)

X. Dong, Q. Long, J. Wang, M. B. Chan-Park, Y. Huang, W. Huang, and P. Chen, “A graphene nanoribbon network and its biosensing application,” Nanoscale3(12), 5156–5160 (2011).
[CrossRef] [PubMed]

Nanotechnology (2)

G. Jo, M. Choe, S. Lee, W. Park, Y. H. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology23(11), 112001 (2012).
[CrossRef] [PubMed]

H. S. Skulason, P. E. Gaskell, and T. Szkopek, “Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers,” Nanotechnology21(29), 295709 (2010).
[CrossRef] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007).
[CrossRef] [PubMed]

Nature (1)

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature457(7230), 706–710 (2009).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rep. (1)

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]

Phys. Rev. B (2)

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008).
[CrossRef]

C. Ritter, S. S. Makler, and A. Latge, “Energy-gap modulations of graphene ribbons under external fields: a theoretical study,” Phys. Rev. B77(19), 195443 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Phys. Scr. T (1)

S. Bae, S. J. Kim, D. Shin, J. H. Ahn, and B. H. Hong, “Towards industrial applications of graphene electrodes,” Phys. Scr. TT146, 014024 (2012).
[CrossRef]

Physics-Uspekhi (1)

Y. N. Eroshenko, “Physics news on the Internet (based on electronic preprints),” Physics-Uspekhi51(1), 107–108 (2008).
[CrossRef]

Proc. SPIE (1)

H. Gonçalves, P. Schellenberg, M. Belsley, L. Alves, C. Moura, and T. Stauber, “New optical techniques to improve the visibility of graphene on multiple substrates,” Proc. SPIE8001(80014G), 80014G-8 (2011).
[CrossRef]

Prog. Polym. Sci. (1)

T. Premkumar and K. E. Geckeler, “Graphene-DNA hybrid materials: assembly, applications, and prospects,” Prog. Polym. Sci.37(4), 515–529 (2012).
[CrossRef]

Science (1)

A. K. Geim, “Graphene: status and prospects,” Science324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) The contrast as a function of the immersion index medium for a monolayer (red), bilayer (blue) and trilayer (black) deposited on a glass substrate. Figure 1(b) The contrast of graphene layers as a function of the substrate index in air.

Fig. 2
Fig. 2

Schematics of the optical reflection microscope set-up with the addition of immersion oil between the glass and the graphene and a prism to prevent reflections from the back of the substrate. For clarity the reflected beam is drawn in a different colour (yellow) compared to the incoming beam (orange).

Fig. 3
Fig. 3

Images of the same graphene flake in air (a), glycerol (b), immersion oil (c), and quinoline (d). The broken blue line shown in image b indicates the positions for the profile taken in each of the images to create Fig. 4. The blue rectangle represents the region used in Fig. 5 for the contour maps.

Fig. 4
Fig. 4

The graphs displays a comparison of the contrast profile in the flake within the squares of the images presented in Fig. 3 for air, microscopy immersion oil, glycerol and quinoline.

Fig. 5
Fig. 5

Contour maps showing averaged contrast as a function of pixel position for the same region using air (a), oil (b) and quinoline (c) as a medium. The sample area depicted in these maps is indicated as squares in the images in Fig. 3. The bluish coloured areas represent the substrate baseline, while the yellow areas shows a monolayer and the red areas show a bilayer. The perspective of (a) and (b) is identical, the one of (c) is slightly altered to give an improved view of the negative contrast valley of the double layer graphene.

Equations (4)

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

C= I(m)I(m=0) I(m=0)
r= n 1 n 2 mπα n 1 + n 2 +mπα
C= 4m n 1 πα( n 1 2 + n 2 ( n 2 +mπα)) ( n 1 n 2 ) 2 ( n 1 + n 2 +mπα) 2
C= 4m n 1 πα( n 1 2 + n 2 ( n 2 +mπα)) ( ( n 1 n 2 ) 2 + ( n 1 + n 2 ) 2 R)( ( n 1 + n 2 +mπα) 2

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