Making graphene visible P. Blake, E. W. Hill Department of Computer Sciences, University of Manchester, Manchester, M13 9PL, UK A. H. Castro Neto Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215,USA K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, A. K. Geim Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK Microfabrication of graphene devices used in many experimental studies currently relies on the fact that graphene crystallites can be visualized using optical microscopy if prepared on top of Si wafers with a certain thickness of SiO2. We study graphene���s visibility and show that it depends strongly on both thickness of SiO2 and light wavelength. We have found that by using monochromatic illumination, graphene can be isolated for any SiO2 thickness, albeit 300 nm (the current standard) and, especially, ���100 nm are most suitable for its visual detection. By using a Fresnel-law-based model, we quantitatively describe the experimental data. Since it was reported in 2004 [1], graphene���a one-atom- thick flat allotrope of carbon���has been attracting increasing interest [1, 2, 3]. This interest is supported by both the realistic promise of applications and the remarkable electronic proper- ties of this material. It exhibits high crystal quality, ballistic transport on a submicron scale (even under ambient condi- tions) and its charge carriers accurately mimic massless Dirac fermions [2, 3, 4]. Graphene samples currently used in exper- iments are usually fabricated by micromechanical cleavage of graphite: a euphemism for slicing this strongly layered ma- terial by gently rubbing it against another surface [5]. The ability to create graphene with such a simple procedure en- sures that graphene was produced an uncountable number of times since graphite was first mined and the pencil invented in 1565 [6]. Although graphene is probably produced every time one uses a pencil, it is extremely difficult to find small graphene crystallites in the ���haystack��� of millions of thicker graphitic flakes which appear during the cleavage. In fact, no mod- ern visualization technique (including atomic-force, scanning- tunneling and electron microscopies) is capable of finding graphene because of their extremely low throughput at the re- quired atomic resolution or the absence of clear signatures dis- tinguishing atomic monolayers from thicker flakes. Even Ra- man microscopy, which recently proved itself as a powerful tool for distinguishing graphene monolayers, [7] has not yet been automated to allow search for graphene crystallites. Un- til now, the only way to isolate graphene is to cleave graphite on top of an oxidized Si wafer and then carefully scan its surface in an optical microscope. Thin flakes are sufficiently transparent to add to an optical path, which changes their in- terference color with respect to an empty wafer [1]. For a certain thickness of SiO2, even a single layer was found to give sufficient, albeit feeble, contrast to allow the huge image- processing power of the human brain to spot a few micron- sized graphene crystallites among copious thicker flakes scat- tered over a mm-sized area. So far, this detection technique has been demonstrated and widely used only for a SiO2 thickness of 300 nm (purple-to- violet in color) but a 5% change in the thickness (to 315nm) can significantly lower the contrast [2]. Moreover, under nom- inally the same observation conditions, graphene���s visibility strongly varies from one laboratory to another (e.g. see im- ages of single-layer graphene in Refs [1, 4]), and anecdo- tal evidence attributes such dramatic differences to different cameras, with the cheapest ones providing better imaging [8]. Understanding the origin of this contrast is essential for op- timizing the detection technique and extending it to different substrates, aiding experimental progress in the research area. FIG. 1: (Color online) Graphene crystallites on 300 nm SiO2 im- aged with white light (a), green light [8] (b) and another graphene sample on 200 nm SiO2 imaged with white light (c). Single-layer graphene is clearly visible on the left image (a), but even 3 layers are indiscernible on the right (c). Image sizes are 25��25��m. Top and bottom panels show the same flakes as in (a) and (c), respec- tively, but illuminated through various narrow bandpass filters with a bandwidth of ���10 nm. The flakes were chosen to contain areas of different thickness so that one can see changes in graphene���s vis- ibility with increasing numbers of layers. The trace in (b) shows step-like changes in the contrast for 1, 2 and 3 layers (trace averaged over 10-pixel lines). This proves that the contrast can also be used as a quantitative tool for defining the number of graphene layers on a given substrate. In this letter, we discuss the origin of this optical contrast arXiv:0705.0259v3 [cond-mat.mes-hall] 22 Sep 2007

2 and show that it appears due not only to an increased optical path but also to the notable opacity of graphene. By using a model based on the Fresnel law, we have investigated the dependence of the contrast on SiO2 thickness and light wave- length, ��, and our experiments show excellent agreement with the theory. This understanding has allowed us to maximize the contrast and, by using narrow-band filters, to find graphene crystallites for practically any thickness of SiO2 and also on other thin films such as Si3N4 and PMMA. Figure 1 illustrates our main findings. It shows graphene viewed in a microscope (Nikon Eclipse LV100D with a 100��, 0.9 numerical aperture, NA, objective) under normal, white- light illumination on top of a Si wafer with the standard 300nm thickness of SiO2 (Fig. 1a). For comparison, Fig. 1c shows a similar sample but on top of 200 nm SiO2, where graphene is completely invisible. In our experience, only flakes thicker than 10 layers could be found in white light on top of 200 nm SiO2. Note that the 10-layer thickness also marks the commonly accepted transition from graphene to bulk graphite [2]. Top and bottom panels in Fig. 1 show the same samples but illuminated through various narrow-band filters. Both flakes are now clearly visible. For 300 nm SiO2, the main contrast appears in green (see Fig. 1b), and the flake is undetectable in blue light. In comparison, the use of a blue filter makes graphene visible even on top of 200 nm SiO2 (see lower panels). FIG. 2: Contrast as a function of wavelength for three different thicknesses of SiO2. Circles are the experimental data curves the calculations. Inset: the geometry used in our analysis. To explain the observed contrast, we consider the case of normal light incidence from air (refractive index, n0 = 1) onto a tri-layer structure consisting of graphene, SiO2 and Si (see inset of Fig. 2). The Si layer is assumed to be semi-infinite and characterized by a complex refractive in- dex n3(��) that, importantly, is dependent on ��, (for exam- ple, n3(�� = 400nm) ��� 5.6 - 0.4i) [9]. The SiO2 layer is described by thickness d2 and another ��-dependent refractive index n2(��) but with a real part only [9] (n2(400nm) ��� 1.47). We note that these n2(��) and n3(��) accurately describe the whole range of interference colors for oxidized Si wafers [10]. Single-layer graphene is assumed to have a thickness d1 equal to the extension of the �� orbitals out of plane [11] (d1 = 0.34 nm) and a complex refractive index n1(��). While n1(��) can be used in our calculations as a fitting parameter, we avoided this uncertainty after we found that our results were well de- scribed by the refractive index of bulk graphite n1(��) ��� 2.6 - 1.3i, which is independent of �� [9, 12]. This can be attributed to the fact that the optical response of graphite with the electric field parallel to graphene planes is dominated by the in-plane electromagnetic response. Using the described geometry, it is straightforward to show that the reflected light intensity can be written as [13]: I(n1) = r1ei(��1+��2) + r2e-i(��1-��2) + r3e-i(��1+��2) + r1r2r3ei(��1-��2) �� ei(��1+��2) + r1r2e-i(��1-��2) + r1r3e-i(��1+��2) + r2r3ei(��1-��2) -1 2 , (1) where r1 = n0 - n1 n0 + n1 , r2 = n1 - n2 n1 + n2 , r3 = n2 - n3 n2 + n3 (2) are the relative indices of refraction. ��1 = 2��n1d1/�� and ��2 = 2��n2d2/�� are the phase shifts due to changes in the optical path. The contrast C is defined as the relative intensity of reflected light in the presence (n1 = 1) and absence (n1 = n0 = 1) of graphene: C = I(n1 = 1) - I(n1) I(n1 = 1) . (3) For quantitative analysis, Fig. 2 compares the contrast observed experimentally with the one calculated by using eq. (3). The experimental data were obtained for single-layer graphene on top of SiO2/Si wafers with 3 different SiO2 thick- nesses by using 12 different narrow-band filters. One can see excellent agreement between the experiment and theory. The contrast reaches up to ��� 12%, and the peaks in graphene���s visibility are accurately reproduced by our model [14]. Note, however, that the theory slightly but systematically overesti- mates the contrast. This can be attributed to deviations from normal light incidence (because of high NA) and an extinction