Abstract

This work presents an investigation and optimization of the identification of graphene mono- and bilayers on various multilayer substrates. Instead of the mere contrast between substrate and substrate/mono/bilayer systems, weighted color differences are used to obtain optimum visibility. Our approach employs a genetic algorithm that allows finding the most appropriate composition of multilayer systems in terms of materials in use and their respective thicknesses. A major benefit of our approach is the possibility to qualify appropriate layer systems with respect to their manufacturability.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
    [CrossRef]
  2. B. Partoens and F. M. Peeters, “From graphene to graphite: electronic structure around the K-point,” Phys. Rev. B 74, 075404 (2006).
    [CrossRef]
  3. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [CrossRef]
  4. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [CrossRef]
  5. P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
    [CrossRef]
  6. Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
    [CrossRef]
  7. A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
    [CrossRef]
  8. A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
    [CrossRef]
  9. 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, 063124 (2007).
    [CrossRef]
  10. L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
    [CrossRef]
  11. I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
    [CrossRef]
  12. M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
    [CrossRef]
  13. D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
    [CrossRef]
  14. M. Bruna and S. Borini, “Assessment of graphene quality by quantitative optical contrast analysis,” J. Phys. D 42, 175307 (2009).
    [CrossRef]
  15. G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).
  16. Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
    [CrossRef]
  17. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1981).
  18. J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
    [CrossRef]
  19. M. V. Klein and T. E. Furtak, Optics (Springer, 1998).
  20. S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
    [CrossRef]
  21. M. Richter, Einführung in die Farbmetrik, 2nd ed. (Gruyter, 1981).
  22. ISO/CIE 10527: CIE standard colorimetric observers, http://www.cie.co.at/ (2007).
  23. P. J. Bouma, Physical Apsects of Colour, 2nd ed. (Macmillan, 1971).

2010 (2)

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[CrossRef]

2009 (3)

M. Bruna and S. Borini, “Assessment of graphene quality by quantitative optical contrast analysis,” J. Phys. D 42, 175307 (2009).
[CrossRef]

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

2008 (4)

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
[CrossRef]

2007 (5)

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
[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, 063124 (2007).
[CrossRef]

2006 (1)

B. Partoens and F. M. Peeters, “From graphene to graphite: electronic structure around the K-point,” Phys. Rev. B 74, 075404 (2006).
[CrossRef]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

2002 (1)

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Abergel, D. S. L.

D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
[CrossRef]

Ahlers, F. J.

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

Argunova, T.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Avouris, Ph.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Beltram, F.

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[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, 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, 063124 (2007).
[CrossRef]

Borini, S.

M. Bruna and S. Borini, “Assessment of graphene quality by quantitative optical contrast analysis,” J. Phys. D 42, 175307 (2009).
[CrossRef]

Bouma, P. J.

P. J. Bouma, Physical Apsects of Colour, 2nd ed. (Macmillan, 1971).

Bruna, M.

M. Bruna and S. Borini, “Assessment of graphene quality by quantitative optical contrast analysis,” J. Phys. D 42, 175307 (2009).
[CrossRef]

Calado, V. E.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[CrossRef]

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, 063124 (2007).
[CrossRef]

Charrier, A.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Cheng, H.

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

Chiu, H.-Y.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Coati, A.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Debever, J.-M.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Dikin, D. A.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Dimitrakopoulos, C.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Dresselhaus, M. S.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Fal’ko, V. I.

D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
[CrossRef]

Fan, B.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Fan, H. M.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Farmer, D. B.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Feng, Y. P.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Flege, J.-I.

P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
[CrossRef]

Forbeaux, I.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Friedemann, M.

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

Furtak, T. E.

M. V. Klein and T. E. Furtak, Optics (Springer, 1998).

Gao, L.

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

Garreau, Y.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Geim, A. K.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[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, 063124 (2007).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1981).

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Grill, A.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Guinea, F.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Guo, Z.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Hausner, M.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Hill, E. W.

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, 063124 (2007).
[CrossRef]

Jenkins, K. A.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

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, 063124 (2007).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Jiao, K.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Jung, I.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Kasmin, J.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

Klein, M. V.

M. V. Klein and T. E. Furtak, Optics (Springer, 1998).

Kong, J.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Li, F.

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

Lin, Y.-M.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Liu, Z.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Neto, A. H. C.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Ni, Z.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Ni, Z. H.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Novoselov, K. S.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[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, 063124 (2007).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Partoens, B.

B. Partoens and F. M. Peeters, “From graphene to graphite: electronic structure around the K-point,” Phys. Rev. B 74, 075404 (2006).
[CrossRef]

Peeters, F. M.

B. Partoens and F. M. Peeters, “From graphene to graphite: electronic structure around the K-point,” Phys. Rev. B 74, 075404 (2006).
[CrossRef]

Pellegrini, V.

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

Pelton, M.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Peres, N. M. R.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Piazza, V.

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

Pierz, K.

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

Pinchaux, R.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Piner, R.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Pingue, P.

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

Reina, A.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Ren, W.

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

Richter, M.

M. Richter, Einführung in die Farbmetrik, 2nd ed. (Gruyter, 1981).

Roddaro, S.

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

Ruoff, R. S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Russell, A.

D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
[CrossRef]

Sauvage-Simkin, M.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Shen, Z.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Shen, Z. X.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Son, H.

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

Stankovich, S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Stosch, R.

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

Sutter, E. A.

P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
[CrossRef]

Sutter, P. W.

P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
[CrossRef]

Teo, G.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Themlin, J.-M.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

Thibaudau, F.

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

van de Sanden, M. C. M.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[CrossRef]

Wang, H.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Wang, H. M.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Watcharotone, S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Weber, J. W.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[CrossRef]

Wu, Y.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Wu, Y. H.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

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, 063124 (2007).
[CrossRef]

Yu, T.

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

Zhang, J.

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

ACS Nano (1)

L. Gao, W. Ren, F. Li, and H. Cheng, “Total color difference for rapid and accurate identification of graphene,” ACS Nano 2, 1625–1633 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

M. Friedemann, K. Pierz, R. Stosch, and F. J. Ahlers, “Graphene on gallium arsenide: engineering the visibility,” Appl. Phys. Lett. 95, 102103 (2009).
[CrossRef]

D. S. L. Abergel, A. Russell, and V. I. Fal’ko, “Visibility of graphene flakes on a dielectric substrate,” Appl. Phys. Lett. 91, 063125 (2007).
[CrossRef]

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[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, 063124 (2007).
[CrossRef]

J. Appl. Phys. (2)

G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” J. Appl. Phys. 12, 124302 (2008).

A. Charrier, A. Coati, T. Argunova, F. Thibaudau, Y. Garreau, R. Pinchaux, I. Forbeaux, J.-M. Debever, M. Sauvage-Simkin, and J.-M. Themlin, “Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films,” J. Appl. Phys. 92, 2479 (2002).
[CrossRef]

J. Phys. Chem. Lett. (1)

A. Reina, H. Son, K. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and identification of single- and few-layer graphene on arbitrary substrates,” J. Phys. Chem. Lett. 112, 17741–17744 (2008).
[CrossRef]

J. Phys. D (1)

M. Bruna and S. Borini, “Assessment of graphene quality by quantitative optical contrast analysis,” J. Phys. D 42, 175307 (2009).
[CrossRef]

Nano Lett. (3)

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, “Simple approach for high-contrast optical imaging and characterization of graphene-based sheets,” Nano Lett. 7, 3569–3575 (2007).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasmin, 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, 2758–2763 (2007).
[CrossRef]

S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, and F. Beltram, “The optical visibility of graphene: interference colors of ultrathin graphite on SiO2,” Nano Lett. 7, 2707–2710(2007).
[CrossRef]

Nature (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

Nature Materials (1)

P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nature Materials 7, 406–411 (2008).
[CrossRef]

Phys. Rev. B (1)

B. Partoens and F. M. Peeters, “From graphene to graphite: electronic structure around the K-point,” Phys. Rev. B 74, 075404 (2006).
[CrossRef]

Rev. Mod. Phys. (1)

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100 GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662(2010).
[CrossRef]

Other (5)

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1981).

M. V. Klein and T. E. Furtak, Optics (Springer, 1998).

M. Richter, Einführung in die Farbmetrik, 2nd ed. (Gruyter, 1981).

ISO/CIE 10527: CIE standard colorimetric observers, http://www.cie.co.at/ (2007).

P. J. Bouma, Physical Apsects of Colour, 2nd ed. (Macmillan, 1971).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Comparison of simulated (left) and measured (right) colors and (b) RGB values for the following multilayer systems on Si: (1) 117nm WTO SiO2, (2) 324nm PECVD Si3N4, (3) 234nm PECVD SiO2 on 67nm PECVD Si3N4, (4) 301nm WTO SiO2, (5) 519nm WTO SiO2, (6) 62nm WTO SiO2 on 324nm PECVD Si3N4 (1048-8), (7) 317nm Si on 400nm SiO2 (SOI), (8) 81nm Si on 400nm SiO2 (SOI).

Fig. 2.
Fig. 2.

Comparison of simulated (left) and measured (right) colors of graphene on 301nm SiO2.

Fig. 3.
Fig. 3.

Visibility of graphene on different dielectric layers depending on their thicknesses in comparison to SiO2.

Fig. 4.
Fig. 4.

Visibility of graphene (a) on a SiO2-BaTiO3-Si system depending on SiO2 and BaTiO3 thicknesses and (b) on a SiO2-HfO2-Si system depending on SiO2 and HfO2 thicknesses. The right panels show the colors of the optimized multilayer systems with (a) 67nmSiO2/36nmBaTiO3 on Si and (b) 44nmSiO2/45nmHfO2 on Si.

Fig. 5.
Fig. 5.

Graphene on (a) 101nm SiO2 - 34nm BaTiO3 - 125nm HfO2 - Si (wcd: 140), (b) 29nm SiO2 - 47nm Al2O3 - 12nm BaTiO3 - Si (wcd: 127), (c) 52nm Al2O3 - 10nm Si3N4 - 16nm SrTiO3 (wcd: 117), (d) 45nm Al2O3 - 80nm HfO2 - 361nm SiO2 - Si (wcd: 80) in comparison to (e) 300nm SiO2 - Si (wcd: 54). The color of a mono- and a bilayer are surrounded by the color of the surface of the corresponding multilayer system.

Equations (14)

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

S=H1,2·L2··Ln1·Hn1,n=(S11S12S21S22),
Hij=(1ϱijϱij1)·1τij,Lj=(eiβj00e+iβj),
ϱij=ϱ+ϱ2andτij=τ+τ2
ϱ=n˜icosΦin˜jcosΦjn˜icosΦi+n˜jcosΦj,ϱ=n˜jcosΦin˜icosΦjn˜icosΦj+n˜jcosΦi,
τ=2n˜jcosΦin˜icosΦi+n˜jcosΦj,τ=2n˜jcosΦjn˜icosΦi+n˜jcosΦi,
Rk(λ)=|ϱ(λ)|2=|S12S22|2,
Rk(λ)=2π0ΦmaxRk(λ,Φ)W(Φ)sinΦdΦ,
X=380780Rk(λ)S(λ)x¯(λ)dλ
Y=380780Rk(λ)S(λ)y¯(λ)dλ
Z=380780Rk(λ)S(λ)z¯(λ)dλ,
(RGB)=(+3.2401.5370.4990.969+1.876+0.042+0.0560.204+1.057)·(XYZ).
r=380780r¯(λ)dλ,g=380780g¯(λ)dλ,b=380780b¯(λ)dλ,
wcdj=r·(ΔR)2+g·(ΔG)2+b·(ΔB)2,
wcd=jwcdj.

Metrics