ARTICLE pubs.acs.org/JPCC
Rapid Determination of the Thickness of Graphene Using the Ratio of Color Difference Yuan-Fu Chen,* Dong Liu, Ze-Gao Wang, Ping-Jian Li,* Xin Hao, Kai Cheng, Yao Fu, Le-Xu Huang, Xing-Zhao Liu, Wan-Li Zhang, and Yan-Rong Li State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China
bS Supporting Information ABSTRACT: An optical method was proposed, based on the ratio of color difference, to identify the thickness of graphene on dielectric/Si substrates. The effect of light source on the color difference of graphene sheets has been investigated. The result shows that for the number of graphene layers N e 10, the ratio between the color differences of N- and single-layer graphene remains almost unchanged under different light sources. It suggests that one can accurately identify the number of graphene layers by comparing the experimental and theoretical ratio of color difference of graphene without knowing the illuminant’s parameters. The method is rapid, nondestructive, and illuminant independent and needs only an optical image to determine the thickness of graphene sheets.
1. INTRODUCTION Graphene is a recently discovered two-dimensional material with unique electronic and physical properties and exhibits exceptionally high crystal and electronic qualities.1,2 Because of its extraordinary properties, graphene is a promising material in both fundamental physics and potential applications. Graphene sheets prepared by micromechanical cleavage or other methods1,3 may not only be single-layer graphene (SLG) but also may contain few-layer graphene (FLG). With the variation of layers, the FLG’s band structure and electronic properties differ from those of SLG.4 On the other hand, for the graphene electronic devices, the graphene is usually located on the top of a Si substrate with a dielectric film (SiO2, Al2 O3). So it is critical to rapidly identify the thickness of graphene sheet on a dielectric/Si substrate for fundamental research and engineering applications. Although atomic force microscopy (AFM) is the most common tool to measure the thickness of graphene, the method is time-consuming and may damage the samples. Raman spectroscopy is a quick way to confirm the SLG for its very sharp and symmetric 2D band,5,6 but the differences between two layers and a few layers of graphene are not obvious and unambiguous in Raman spectra. Recently, as a cheap, quick, and accurate method, the optical method was proposed to identify the number of graphene layers. However, the applications of optical methods have been limited due to instrument requirements. For example, the contrast spectra can be used to determine the number of graphene layers,7,8but r 2011 American Chemical Society
the reflection spectra need to be collected and detected to generate the contrast spectra in this method. A total color difference method, which combines reflection spectra with International Commission on Illumination (CIE) color space, can use optical images of graphene for layer identification,9 but this method needs to know the exact spectral power distribution (SPD) of the light source. So it is significant to simplify optical methods, especially to lower the instrument requirements. In this paper, we proposed an optical method, based on the ratio of color difference (RCD), to identify the thickness of graphene on dielectric/Si substrates. The effect of light source on color difference was discussed. We find that the ratio between the color difference of N-layer graphene and SLG remains almost unchanged with the variation of SPD when the number of graphene layers (N) is less than 10. It means that the RCD method does not need to detect reflection spectra or know the SPD of the light source, and needs only an optical image of graphene on a dielectric/Si substrate. The method has been demonstrated by identifying the graphene samples on the Si substrate with three different dielectric films: 300 nm SiO 2 , 285 nm SiO2 , and 72 nm Al 2 O3 . Received: December 22, 2010 Revised: January 27, 2011 Published: March 16, 2011 6690
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Figure 1. Color difference as a function of the number of graphene layers for different SPDs on 300 nm thick SiO2. S1 = 1; S2 = 1, {λ ∈ (480, 580 nm)}; S3 = |sin(2 107 λ)|.
2. COLOR DIFFERENCE OF GRAPHENE ON A DIELECTRIC/SI SUBSTRATE The theoretical color difference between N-layer graphene and dielectric/Si substrate can be calculated using the equation10,11 DN ¼ jkj 2R 31=2 R ð λ SðλÞðRN ðλÞ - R0 ðλÞÞxðλÞ dλÞ2 þ ð λ SðλÞðRN ðλÞ - R0 ðλÞÞyðλÞ dλÞ2 4 5 3 þðR SðλÞðR ðλÞ - R ðλÞÞzðλÞ dλÞ2 N 0 λ
ð1Þ where κ is a constant; S(λ) is the relative SPD of the light source; RN(λ) and R0(λ) are the reflection spectra of the N-layer graphene and dielectric/Si substrate, respectively; and hx(λ),hy(λ), and z(λ) are the color-matching functions (CMFs). The detailed inference process is shown in the Supporting Information. The experimental color difference can be calculated using the equation D0 N ¼ ½ðXN - X0 Þ2 þ ðYN - Y0 Þ2 þ ðZN - Z0 Þ2 1=2
ð2Þ
where X0, Y0, and Z0 are the tristimulus components of the substrate and XN, YN, and ZN are corresponding components of the N-layer graphene. The XYZ parameters can be obtained from the red-green-blue (RGB) parameters of the optical image using the equation ½X, Y , ZT ¼ M 3 ½r, g, bT
ð3Þ
where M is a transformation matrix and reversible which relies on the reference white light source and other instrumental factors.12,13
3. RESULTS AND DISCUSSION 3.1. Independence of Light Source on the Ratio of Color Difference. To investigate the effect of light source on RCD, we
calculated the color difference of graphene on SiO2/Si substrate for different simulated SPDs of light source (Figure 1). From Figure 1, we observe that although the value of color difference changes with the variation of SPD, the RCD nearly remains constant. For example, the ratios between the color difference of 3-layer graphene and SLG on 300 nm thick SiO2 layer are D3/ D1|S1 = 2.797, D3/D1|S2 = 2.745, and D3/D1|S3 = 2.778. In order to further confirm that the RCD remains constant for any SPD of light source, we fitted (RN(λ) - R0(λ)) by the following equation: RN ðλÞ - R0 ðλÞ ¼ lN ðR1 ðλÞ - R0 ðλÞÞ
ð4Þ
Figure 2. Comparison between RN(λ) - R0(λ) and lN(R1(λ) - R0(λ)) for graphene with 2-10 layers.
As shown in Figure 2, the solid lines represent (RN(λ) - R0(λ)), and the dash dot lines represent lN(R1(λ) - R0(λ)). One can find that when N e 5, the curves are in quite good agreement, and when 5 < N e 10, the deviation can be tolerable. It suggests that (RN(λ) - R0(λ)) and (R1(λ) - R0(λ)) are nearly linearly correlated when N e 10. Combining eqs 1 and 4, the theoretical RCD (DN /D1) for Nlayer graphene and SLG can be simplified as FðlN 3 ðR1 ðλÞ - R0 ðλÞÞÞ DN FðRN ðλÞ - R0 ðλÞÞ ¼ ¼ FðR1 ðλÞ - R0 ðλÞÞ FðR1 ðλÞ - R0 ðλÞÞ D1 ¼
jlN jFðR1 ðλÞ - R0 ðλÞÞ ¼ lN FðR1 ðλÞ - R0 ðλÞÞ
ð5Þ
where F is a functional defined by eq 1. One can find that DN/D1 is equal to lN, which is an intrinsic value of the film system and independent of SPD. We also find that the experimental RCD (D0N/D01) is independent of transformation matrix M (see the Supporting Information). It opens up the possibility for accurate identification of graphene layers without knowing the SPD of the light source by using the RCD. 3.2. Ratio of Color Difference Method. For accurate identification of graphene on a dielectric/Si substrate, we propose a simple, illuminant independent optical method. The detailed procedure is as follows. (1) For a certain dielectric/Si substrate, calculate the theoretical RCD of graphene (DN/D1). Because the RCD is independent of SPD, we take S(λ) =1 for simplifying calculation. Table 1 lists the theoretical value of the RCD of graphene on a Si substrate with three different dielectric films: 300 nm SiO2, 285 nm SiO2, and 72 nm Al2O3, which were usually used in previous reports. (2) Prepare a standard sample: The SLG is prepared by micromechanical cleavage and transferred on the dielectric/Si substrate. The thickness of graphene is identified by using AFM or Raman spectra, and then the experimental color difference of standard SLG (D01) from the optical image was obtained. (3) Transfer the graphene to be identified on the same substrate and obtain the experimental color difference from the optical image (D0N). The experimental RCD can be calculated as D0N/D01. (4) Identify the number of graphene layers by comparing the experimental and theoretical values of RCD. In order to verify our optical method, we selected the optical image of graphene on the Si substrate with a 300 nm SiO2 film 6691
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Table 1. Theoretical RCD of 2-10 Layer Graphenes for S(λ) =1 2 layers
3 layers
4 layers
5 layers
6 layers
7 layers
8 layers
9 layers
10 layers
RCD (300 nm SiO2/Si)
1.9311
2.7967
3.6000
4.3441
5.0319
5.6661
6.2494
6.7843
7.2731
RCD (285 nm SiO2/Si)
1.9379
2.8166
3.6389
4.4075
5.1249
5.7936
6.4159
6.9940
7.5300
RCD (72 nm Al2O3/Si)
1.8925
2.6841
3.3809
3.9888
4.5134
4.9597
5.3330
5.6378
5.8789
Figure 3. (a) Optical image of graphene on the Si substrate with a 300 nm SiO2 film (from ref 14), (b) converted color difference contour plot, (c) corresponding color difference for line regions marked in (a), and (d) comparison of experimental and theoretical RCD values.
from ref 14 (Figure 3a). A 100 objective lens with a numerical aperture of 0.95 was used in their experiment. The SPD of the light source is unknown for us. From Figure 3a, we can observe that the graphene sheet has four different contrast regions marked by 1, 2, 3, and 4, which are correspond to 1, 2, 3, and 4 layers confirmed by Raman spectra. The optical image (Figure 3a) was converted to obtain the experimental color difference by eqs 2 and 3, and the corresponding contour plot is shown in Figure 3b. The red solid curve and blue dash dot curve in Figure 3c are the color differences for line regions marked in Figure 3a. The red solid line passes through region 1 and region 3, and the blue dash dot line passes through region 4 and region 2. The experimental color difference of each region can be obtained from Figure 3c. It is noted that we use region 1 instead of the standard SLG sample (step 2) in this case. Figure 3d shows the experimental and theoretical RCDs with different graphene layers. The good agreement suggests that region 2, 3, 4 is 2, 3, 4 layers, respectively, which is consistent with Raman spectroscopy results from ref 14. We have also demonstrated the RCD method by identifying the two other graphene samples on different substrates. Figure 4a illustrates the optical image of graphene on a Si substrate with a 285 nm SiO2 film from ref 10, and Figure 4b shows the experimental and theoretical RCDs. Figure 4c and d illustrates
Figure 4. (a) Optical image of graphene on the Si substrate with a 285 nm SiO2 film (from ref 10), (b) comparison of experimental and theoretical values, (c) optical image of graphene on the Si substrate with a 72 nm Al2O3 film (from ref 9), and (d) comparison of experimental and theoretical values.
the result of graphene on the Si substrate with a 72 nm Al2O3 film (the optical image of Figure 4c was taken from ref 9). The good agreement suggests that the RCD method can be applied for different substrates. So we conclude that our RCD method can accurately identify the number of graphene layers (N e 10) without knowing the actual value of SPD.
4. CONCLUSIONS We propose a RCD method to rapidly determine the number of graphene layers. The effect of the light source on the color difference of graphene was discussed. The result shows that the RCD of graphene sheets is independent of the SPD of the light source when the number of graphene layers is less than 10. The method has been demonstrated by identifying the graphene samples on the Si substrate with three different dielectric films: 300 nm SiO2, 285 nm SiO2, and 72 nm Al2O3. The RCD method is rapid, nondestructive, and illuminant independent and needs only an optical image. It will be very helpful for the future research and application of graphene-based devices. ’ ASSOCIATED CONTENT
bS
Supporting Information. The detailed inference process for reflection spectroscopy, theoretical color difference, and
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experimental color difference. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Fax þ86 28 8320 2710; e-mail
[email protected] (Y.F.C.),
[email protected] (P.J.L.).
’ ACKNOWLEDGMENT The authors acknowledge the support by the Special Fund for Basic Scientific Research of Central Colleges, University of Electronic Science and Technology of China (UESTC), and the youth foundation and startup research project of UESTC. ’ REFERENCES (1) Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6 (3), 183–91. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; et al. Electric field effect in atomically thin carbon films. Science 2004, 306 (5696), 666–9. (3) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, K. M.; Kim, K. S.; et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009, 457 (5), 706–10. (4) Bostwick, A.; Ohta, T.; McChesney, J. L.; Emtsev, K. V.; Seyller, T.; Horn, K.; et al. Symmetry breaking in few layer graphene films. New J. Phys. 2007, 9 (10), 385. (5) Calizo, I.; Balandin, A. A.; Bao, W.; Miao, F.; Lau, C. N. Temperature dependence of the Raman spectra of graphene and graphene multilayers. Nano Lett 2007, 7 (9), 2645–9. (6) Graf, D.; Molitor, F.; Ensslin, K.; Stampfer, C.; Jungen, A.; Hierold, C.; et al. Spatially resolved Raman spectroscopy of single- and few-layer graphene. Nano Lett. 2007, 7 (2), 238–2. (7) Jung, I. H.; Pelton, M.; Piner, R.; Dikin, D. A.; Stankovich, S.; Watcharotone, S.; et al. Simple approach for high-contrast optical imaging and characterization of graphene-based sheets. Nano Lett. 2007, 7 (12), 3569–75. (8) Casiraghi, C.; Hartschuh, A.; Lidorikis, E.; Qian, H.; Harutyunyan, H.; Gokus, T.; et al. Rayleigh imaging of graphene and graphene layers. Nano Lett. 2007, 7 (9), 2711–7. (9) Gao, L. B.; Ren, W. C.; Li, F.; Cheng, H. M. Total color difference for rapid and accurate identification of graphene. ACS Nano 2008, 2 (8), 1625–33. (10) Ni, Z. H.; Wang, H. M.; Kasim, J.; Fan, H. M.; Yu, T.; Wu, Y. H.; et al. Graphene thickness determination using reflection and contrast spectroscopy. Nano Lett. 2007, 7 (9), 2758–63. (11) Bunting, F. The colorshop color primer; Light Source Computer Images: Larkspur, CA, 1998, p 74. (12) Schanda, J. Colorimetry: Understanding the CIE system; John Wiley & Sons: Hoboken, NJ, 2007, p 30. (13) Henrie, J.; Kellis, S.; Schultz, S. M.; Hawkins, A. Electronic color charts for dielectric films on silicon. Opt. Express. 2004, 12 (7), 1464–9. (14) Ni, Z. H.; Wang, H. M.; Ma, Y.; Kasim, J.; Wu, Y. H.; Shen, Z. X. Tunable stress and controlled thickness modification in graphene by annealing. ACS Nano 2008, 2 (5), 1033–9.
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