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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17226–17231
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Thickness determination of graphene on metal substrate by reflection spectroscopy

Tommi Kaplas, Aleksey Zolotukhin, and Yuri Svirko  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17226-17231 (2011)
http://dx.doi.org/10.1364/OE.19.017226


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Abstract

We show that reflectivity measurements enable the determination of the thickness of multilayered graphene on a metal substrate. The developed technique is based on comparison of the substrate reflectance with and without graphene and relies on the strong absorbance of graphene and high refractive index contrast. We demonstrate the technique by measuring the thickness of the CVD graphene film grown on a copper substrate.

© 2011 OSA

1. Introduction

In this paper we demonstrate a simple approach that can be employed for estimation of the thickness of CVD grown multilayered graphene structures on a copper substrate and can be employed to control and characterize the growth process in situ. The proposed method is based on the measurement of the reflectance change of copper substrate due to graphene deposition and can be implemented using standard equipment available in most laboratories.

2. Experimental methods

Reflectivity of a metal substrate with coated with a homogeneous graphite film of the thickness h can be presented in the following form [13

13. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

]:
R=|r12+r23exp(2iβ)1+r12r23exp(2iβ)|2
(1)
where at normal incidence, r12 = (1-ng)/(1 + ng) and r23 = (ng - n)/(ng + n) are amplitude reflection coefficients of the air-graphite and graphite-metal interfaces, n and ng are refractive indices of the substrate and CVD graphene [14

14. F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010). [CrossRef]

], respectively, β = 2πngh/λ and λ is the light wavelength. When β << 1, the difference between R and reflectance of the bare substrate R0 = |(1-n)/(1 + n)|2 is a linear function of β. Therefore the thickness of the graphite film can be revealed from the measured differential reflectance ΔR/R0 = (R – R0)/R0.

In practice, however, the reflectivity of a bare copper substrate can differ from R0 due to the surface roughness and also the presence of the native oxide layer. In order to examine the relative contribution of both factors we measured of the reflectance of bare copper foil in the visual spectral range. Figure 1
Fig. 1 Measured (dotted line) and calculated using data from [15] (solid line) reflectance spectrum of the copper foil.
shows that in both blue and red parts of the visual spectrum, the measured reflectivity corresponds well to that calculated using the standard copper refractive index data [15

15. E. D. Palik, Handbook of Optical Constants of Solids I (Academic press, 1998).

]. This indicates that in our experimental conditions, the effect of the copper foil roughness is negligible. In the spectral range of 550-600 nm, we observed about ten percent discrepancy between the measured and calculated reflectivity. This discrepancy is probably associated with the interband transition at 571 nm from the filled d band to the unoccupied states in the p conduction band [16

16. H. Ehrenreich and H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128(4), 1622–1629 (1962). [CrossRef]

]. However we will demonstrate below that even in 550-600 nm spectral range, the differential reflectance measurement can be used for the characterization of graphene thickness.

It is worth noting that the oxidation processes, which result in the growth of a few nanometers thick layer of native cupric oxide (CuO), cuprous oxide (Cu2O) and cupric hydroxide (Cu(OH)2) on the air-copper interface [17

17. E. D. Palik, Handbook of Optical Constants of Solids II (Academic press, 1998).

,18

18. J. J. Kim and S.-K. Kim, “Optimized surface pretreatments for copper electroplating,” Appl. Surf. Sci. 183(3-4), 311–318 (2001). [CrossRef]

], can also make a considerable contribution to the substrate reflectivity in the above spectral range. Moreover, since the refractive indices of CuO and Cu2O are comparable with that of graphite [14

14. F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010). [CrossRef]

,17

17. E. D. Palik, Handbook of Optical Constants of Solids II (Academic press, 1998).

,18

18. J. J. Kim and S.-K. Kim, “Optimized surface pretreatments for copper electroplating,” Appl. Surf. Sci. 183(3-4), 311–318 (2001). [CrossRef]

] one may expect that few nanometers thick oxide and graphene films deposited onto copper substrate can give rise to a comparable reflectivity change.

3. Results and discussion

3.1 Effect of copper native oxide layer

In order to visualize the oxidation effect on the copper substrate reflectivity we removed the native oxide layer by etching the copper foil in acetic acid [19

19. K. L. Chavez and D. W. Hess, “A novel method of etching copper oxide using acetic acid,” J. Electrochem. Soc. 148(11), G640–G643 (2001). [CrossRef]

] and studied how reflectivity changes in time. One can observe from Fig. 2
Fig. 2 Temporal evolution of the reflectance of the copper foil etched in acetic acid. One can observe that the reflectivity decreases by 3% at 400 nm and less than 1% at 600 nm during 10 min after oxide removal.
that the oxidation of the etched Cu foil starts instantaneously and results in more than 5% reduction of reflectivity at 400 nm after one hour contact with air due to the strong absorption of Cu oxide in the blue spectral range. In contrast, at 600 nm, the reduction of the reflectance is as low as 1% after one hour, i.e. the effect of the oxide layer on copper reflectance is rather weak. Thus the thickness of the graphene layer can be estimated by comparing reflectivity of the copper substrate with and without graphene at the wavelengths longer than 500 nm. Figure 2 shows that the experimental error due to the presence of the native oxide layer can be suppressed if the reflectivity of the bare copper substrate is performed within five minutes after the oxide removal.

3.2 Reflectivity of the graphene coated copper substrate

The obtained reflectivity R0 of a bare copper substrate with no oxide layer makes it possible to establish a rather straightforward procedure for the graphene film thickness measurement. Specifically, one needs to measure the reflectivity R of the substrate coated with graphene film and to obtain the differential reflectivity ΔR/R0. Since the film is just few nanometers thick, no interference effects occur and the differential reflectivity is proportional to the number of graphene layers. It can be shown that the ΔR/R0 varied from 0.38% at λ = 800 nm to 1.15% at λ = 580 nm per graphene layer, i.e. it is large enough to be detected by the standard techniques. Thus the proposed method can be used for the graphene thickness measurement similarly to the conventional one based on the measurement of the transmittance of the graphene film transferred to a dielectric substrate [8

8. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]

]. The important difference, however, is that the proposed method does not require transferring the graphene film obtained on the copper foil to a transparent substrate and can be employed for the in situ control of the deposition process.

In order to demonstrate the proposed method we used it to measure the thickness of graphene films grown on 25 μm thick copper foil. The foil was annealed for 30 min at the temperature of 950 °C in 10 mBar hydrogen atmosphere. After that the CVD chamber was pumped down and filled by 1:1 H2:CH4 gas mixture. During 30 min of graphitization process the chamber was cooled down to 800 °C in H2:CH4 atmosphere at pressure of 10 mBar. After the process the chamber was pumped down again and cooled down in H2 atmosphere to room temperature. Thus in contrast to the continuous flow system [4

4. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]

], the developed CVD technique allows us to reduce gas consumption. The bare copper substrate, which was used as a reference in differential reflectivity measurements, underwent the same process but in pure hydrogen (i. e. methane free) atmosphere. This allows us to obtain the bare and graphene coated substrates of the same optical quality and to suppress the effect of surface roughness on the differential reflectivity.

To obtain reflectivity of the bare substrate, the reference sample was immersed in acetic acid for 10 minutes in order to remove native oxide layer [18

18. J. J. Kim and S.-K. Kim, “Optimized surface pretreatments for copper electroplating,” Appl. Surf. Sci. 183(3-4), 311–318 (2001). [CrossRef]

,19

19. K. L. Chavez and D. W. Hess, “A novel method of etching copper oxide using acetic acid,” J. Electrochem. Soc. 148(11), G640–G643 (2001). [CrossRef]

]. Reflectance measurement started as soon as 30 seconds after the acid wash and lasted for three minutes. This allowed us to partially suppress the effect of the of newly grown oxide layer on the reflectivity of the bare substrate. We did not observe the oxidation of the graphene-coated copper substrate.

The refelectance measurements were performed for two 2.5 × 2.5 cm2 graphene coated copper substrates. The spectrum of the reflectance R was measured from ten spots for each substrate by Perkin Elmer Lambda-18 spectrophotometer with an integrating sphere. Figure 3
Fig. 3 The measured (dots) and the calculated (solid lines) differential reflectance spectra of the films comprising of 1, 2, 3 and 4 graphene layers. The experimental data at each wavelength are averaged over ten points on the substrate surface. One can observe that variation in the film thickness over substrate surface is less than one graphene layer.
shows the differential reflectivity in the spectral range of 500-800 nm. Solid lines represent differential reflectivity calculated for substrates coated with 1, 2, 3 and 4 graphene layers. By comparing the measured and the calculated spectra in Fig. 3 one can conclude that the film consists of two graphene layers.

In order to verify the obtained results we etched the copper foil in ferric chloride solution, transferred the graphene film to quartz substrate and examined it using conventional Raman and transmission techniques [5

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

,9

9. 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]

,11

11. 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]

]. The Raman spectrum obtained using Renishaw inVia Raman Microscope at excitation wavelength of 514 nm is shown in Fig. 4(a)
Fig. 4 (a) Raman spectrum of multilayer graphene film transferred to a SiO2 substrate. Narrow G peak and a large ratio of 2D and D peaks indicate a high crystallinity of fabricated graphene. The shape and position of the 2D peak indicates that the film consists of 2-4 graphene layers [9,11]. (b) Transmittance of the graphene film transferred onto a SiO2 substrate measured relatively to the transmittance of the bare substrate. Results of the transmittance measurements for different points of the sample are shown. Solid horizontal lines represent calculated transmittance of the graphene coated quartz substrate relatively to the transmittance of the bare substrate [20]. By comparing calculated data with than measured at 800 nm one can conclude that the film is comprised of about 2.6 layers.
. Large 2D/G Raman peaks ratio indicates a high crystalline quality of graphene, while the shape and shift of the 2D peak suggest that the film thickness is between 2 to 4 layers [9

9. 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]

,11

11. 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]

].

Transmittance spectrum is presented in Fig. 4(b). One can observe [20

20. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]

] that the average film thickness is about 2.6 layers, i.e. the difference between the results of the thickness measurements using reflectivity and transmittance techniques is about a half of a graphene layer. The origin of such a discrepancy may be two-fold. First, the discrepancy can be caused by the native oxide layer, which starts growing on etched copper foil surface of the reference sample instantaneously and can effect the obtained differential reflectivity. Second, the counting the number of layers by subtracting 1.87% of the transmittance per layer [20

20. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]

] may be not entirely accurate. This is because in such a case we assume that total optical losses of the fabricated CVD graphene film is N*2.3% where N is the number of layers, while the film is infinitesimally thin. In other words, we assume that the refractive index of the fabricated film along the substrate normal is equal to 1. Such an assumption is probably correct for graphene fabricated by exfoliation of HOPG, however it may be not entirely correct for CVD graphene. It has been shown [20

20. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]

] that the transmission change per layer depends on the finite optical thickness of the multilayer graphene. Nevertheless it is worth noting that both the reflectance (see Fig. 3) and the conventional (Fig. 4) measurement techniques produce almost the same result. This allows us to conclude that the measurement of the differential reflectance is a powerful yet simple tool to control the number of graphene layers grown on metal substrate. The uncertainty caused by the possible oxidation of the substrate can be suppressed by measuring performing reflectivity of the reference sample immediately after oxide removal or in an inert atmosphere. Alternatively this uncertainty can be avoided by quantitative measurement of the growth rate of the oxide layer and adjusting the reflectance of the reference sample accordingly.

4. Conclusion

In conclusion, we have demonstrated a technique that enables the revealing of the thickness of CVD nanographite film deposited on copper substrate by differential reflectivity measurements. We believe that our results offer a reliable yet simple thickness evaluation technique capable of characterising both mono- and multilayered graphene on metal surfaces and of controlling the growth process in situ.

Acknowledgment

We are grateful to Dr. Pertti Silfsten for the helpful discussions. This work was supported by Academy of Finland (Grants No 131165, 124133, and 123252) and EU (project "CACOMEL").

References and links

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(5696), 666–669 (2004). [CrossRef] [PubMed]

2.

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

3.

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,” Nature 457(7230), 706–710 (2009). [CrossRef] [PubMed]

4.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef] [PubMed]

5.

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

6.

W. Cai, Y. Zhu, X. Li, R. D. Piner, and R. S. Ruoff, “Large area few-layer graphene/graphite films as transparent thin conducting electrodes,” Appl. Phys. Lett. 95(12), 123115 (2009). [CrossRef]

7.

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

8.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]

9.

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]

10.

A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, and P. C. Eklund, “Raman scattering from high-frequency phonons in supported n-graphene layer films,” Nano Lett. 6(12), 2667–2673 (2006). [CrossRef] [PubMed]

11.

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]

12.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008). [CrossRef] [PubMed]

13.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

14.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010). [CrossRef]

15.

E. D. Palik, Handbook of Optical Constants of Solids I (Academic press, 1998).

16.

H. Ehrenreich and H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128(4), 1622–1629 (1962). [CrossRef]

17.

E. D. Palik, Handbook of Optical Constants of Solids II (Academic press, 1998).

18.

J. J. Kim and S.-K. Kim, “Optimized surface pretreatments for copper electroplating,” Appl. Surf. Sci. 183(3-4), 311–318 (2001). [CrossRef]

19.

K. L. Chavez and D. W. Hess, “A novel method of etching copper oxide using acetic acid,” J. Electrochem. Soc. 148(11), G640–G643 (2001). [CrossRef]

20.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]

OCIS Codes
(310.3840) Thin films : Materials and process characterization
(160.4236) Materials : Nanomaterials

ToC Category:
Thin Films

History
Original Manuscript: April 18, 2011
Revised Manuscript: July 12, 2011
Manuscript Accepted: July 15, 2011
Published: August 18, 2011

Citation
Tommi Kaplas, Aleksey Zolotukhin, and Yuri Svirko, "Thickness determination of graphene on metal substrate by reflection spectroscopy," Opt. Express 19, 17226-17231 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17226


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References

  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,” Science306(5696), 666–669 (2004). [CrossRef] [PubMed]
  2. A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett.9(1), 30–35 (2009). [CrossRef] [PubMed]
  3. 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]
  4. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science324(5932), 1312–1314 (2009). [CrossRef] [PubMed]
  5. S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. Ri Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol.5(8), 574–578 (2010). [CrossRef] [PubMed]
  6. W. Cai, Y. Zhu, X. Li, R. D. Piner, and R. S. Ruoff, “Large area few-layer graphene/graphite films as transparent thin conducting electrodes,” Appl. Phys. Lett.95(12), 123115 (2009). [CrossRef]
  7. C. Mattevi, H. Kim, and M. Chhowalla, “A review of chemical vapour deposition of graphene on copper,” J. Mater. Chem.21(10), 3324–3334 (2011). [CrossRef]
  8. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010). [CrossRef]
  9. 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]
  10. A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, and P. C. Eklund, “Raman scattering from high-frequency phonons in supported n-graphene layer films,” Nano Lett.6(12), 2667–2673 (2006). [CrossRef] [PubMed]
  11. 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]
  12. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008). [CrossRef] [PubMed]
  13. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).
  14. F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett.97(25), 253110 (2010). [CrossRef]
  15. E. D. Palik, Handbook of Optical Constants of Solids I (Academic press, 1998).
  16. H. Ehrenreich and H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev.128(4), 1622–1629 (1962). [CrossRef]
  17. E. D. Palik, Handbook of Optical Constants of Solids II (Academic press, 1998).
  18. J. J. Kim and S.-K. Kim, “Optimized surface pretreatments for copper electroplating,” Appl. Surf. Sci.183(3-4), 311–318 (2001). [CrossRef]
  19. K. L. Chavez and D. W. Hess, “A novel method of etching copper oxide using acetic acid,” J. Electrochem. Soc.148(11), G640–G643 (2001). [CrossRef]
  20. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser.129, 012004 (2008). [CrossRef]

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