Visibility study of graphene multilayer structures

Transcription

1 Visibility study of graphene ultilayer structures Guoquan Teo and Haoin Wang Departent of Electrical and Coputer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore and Data Storage Institute, 5 Engineering Drive 1, Singapore Yihong Wu * Departent of Electrical and Coputer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore Zaibing Guo and Jun Zhang Data Storage Institute, 5 Engineering Drive 1, Singapore Zhenhua Ni and Zexiang Shen Division of Physics and Applied Physics, School of Physical and Matheatical Sciences, Nanyang Technological University, 1 Nanyang Walk, Block 5, Level 3, Singapore * Author to who correspondence should be addressed; electronic ail: elewuyh@nus.edu.sg

2 ABSTRACT: The visibility of graphene sheets on different types of substrates has been investigated both theoretically and experientally. Although single layer graphene is observable on various types of dielectrics under an optical icroscope, it is invisible when it is placed directly on ost of the seiconductor and etallic substrates. We show that coating of a resist layer with optiu thickness is an effective way to enhance the contrast of graphene on various types of substrates and akes single layer graphene visible on ost seiconductor and etallic substrates. Experients have been perfored to verify the results on quartz and NiFe-coated Si substrates. The results obtained will be useful for fabricating graphene-based devices on various types of substrates for electronics, spintronics and optoelectronics applications.

3 I. INTRODUCTION The recent success in extracting a single layer of carbon fro highly ordered pyrolytic graphite (HOPG) using a technique called icroechanical cleavage has stiulated a large interest in both the fundaental properties and potential applications of graphene. 1,2 Although graphene can also be fored epitaxially on SiC 3 through theral annealing, currently echanical exfoliation of graphite is still the ost efficient way to obtain high-quality graphene saples. As it is reported in literature 4, echanical exfoliation of graphite usually results in single layer graphene (SLG), bilayer graphene (BLG) and few layer graphene (FLG) sheets. Therefore, the first step to fabrication of graphene-based devices is to identify graphene flakes with different nuber of layers and deterine their relative positions on the wafer with respect to the pre-fored alignent arks. In order to ake this first step happen one ust find a way to ake the graphene visible under an optical icroscope. Although graphene sheets can be seen by atoic force, scanning electron and optical icroscopes, the first two techniques cause either daage or containation to the graphene sheets. 1,2 Therefore, currently only optical icroscopy allows a non-destructive recognition of graphene sheets. The advantage of optical icroscopy is that, in addition to optical contrast, Raan spectra are also helpful in deterining the thickness of graphene sheets So far, several papers have been published on visibility of graphene on SiO 2 coated Si substrates with or without a resist Fro application point of view, however, it is also of interest to know if graphene can be seen on other types of substrates or layers, in particular, those that are widely used for existing or will be potentially used for future electronic, optoelectronic and spintronic devices. Based on this background, in this paper we report on the visibility study of SLG, BLG and FLG on a wide range of etal, seiconductor and oxide layers or substrates. We show by siulation that the contrast of graphene can be enhanced substantially with the addition of a resist layer with optiu thickness on alost all types of substrates. This

4 will ake SLG visible on ost seiconductor and etallic substrates which is otherwise unobservable under an optical icroscope. Experients have been perfored to verify the results on quartz and NiFe-coated Si substrates. II. THEORETICAL MODEL The visibility of graphene on different types of substrates with or without under/capping layer originates fro both the relative phase shift and aplitude odification induced by the graphene layer. Although graphene is only one atoic layer thick, its refractive index was found to be very close to that of graphite. Therefore, the reflection spectru of a ultiple layer structure containing graphene can be readily obtained using the 2 2 atrix ethod. 12 Fig. 1 shows a typical ultilayer structure consisting of air, N layers of hoogeneous edia and supporting substrate. The thickness and refractive index of each layer are d, d i (i = 1 to N), d S and n, n i (i = 1 to N), n S, respectively. Here, the reflective indices are in general coplex nubers. We also assue that d and d s approaches infinity. Assuing that electroagnetic wave travels in zx plane and the edia are hoogeneous in z-direction, the electrical field that satisfies the Maxwell i( ωt βz) equation can be written as [ ] E = A( x) + B( x) e, where β is the z coponent of the wave vector, ω is the angular frequency, t is tie, and A(x) and B(x) are aplitude of the righttravelling and left-travelling waves, respectively. The electroagnetic wave can be either a p- wave or an s-wave. The aplitude of the electrical field inside the air and those after passing through the Nth layer and substrate interface are related by the following equation: A = D B 1 N = 1 D P D 1 D S A B S S, where

5 D = n 1 cosφ n 1 cos φ for s wave D cosφ = n cosφ n for p wave P e iω = iω e ω 2πn d = λ Here, n is the refractive index of the th layer, d is the thickness of th layer, λ is wavelength, and φ k is angle of incidence. If we let D 1 N D = 1 P D D T = T T S, 21 T22 then the reflectance is given by T T R =. For unpolarized light, one can take an average of the contributions fro both the s wave and p wave. The contrast C induced by the graphene layer is then given by R(no_graphene) R(with_graphene) C =. R(no_graphene) The siulation has been carried out using Matlab. The incident wave is assued to be perpendicular to the plane of the ultiple layers; hence the angle of incident φ k was set at zero degree. The coplex refractive indices of all aterials used in the paper are adopted fro

6 literature 13 except ZnO. Single layer graphene is assued to have a thickness.34 n, and ultilayer graphene which consists of n onolayers is assued to have a thickness of n.34 n. The refractive index of graphene is assued to be the sae as that of bulk graphite and is independent of λ, i.e., n G (λ) = i. III. RESULTS AND DISCUSSION A. Contrast spectra of graphene sheets on Au, Si and Al 2 O 3 The siplest structure involving graphene is a layer of SLG or FLG on a flat substrate, as shown scheatically in Fig. 2(a). As representative exaples of, oxides, seiconductor and etal, we have calculated the contrast spectra of graphene sheets with different thicknesses on sapphire (Al 2 O 3 ), silicon (Si) and gold (Au). The results are shown in Figs. 2(b), (c) and (d), respectively, for graphene sheets with nuber of layers ranging fro 1 to 1. As can be seen fro the figures, graphene on Al 2 O 3 and Si exhibits a negative contrast while graphene on Au shows a positive one. In other words, graphene on Al 2 O 3 and Si appears brighter than the substrate while graphene on Au is darker than the substrate. Fro Figs. 2(b), (c) and (d), it is observed that the visibility for single layer graphene on gold or silicon (contrast of.27 for gold and -.66 for silicon) is not as good as that for single layer graphene on a sapphire substrate (contrast of -.664) and is practically difficult to be seen under an optical icroscope. On the other hand, single layer graphene sheets on sapphire are not difficult to be seen because the contrast is close to.9, alost the sae as that for SLG on SiO 2 (3 n) / Si structure. 6,9 As both the absorption and phase odification contribute to the contrast foration echanis, the contrast generally increases with the nuber of layers, as shown in Figs. 2(b)-(d). B. Contrast spectra of PMMA / graphene / substrate structures As it has been reported in literature, the contrast for single layer graphene can be increased substantially by adding a layer either underneath or atop the graphene layer. The forer also

7 facilitate the fabrication of field-effect devices if the inserted layer can also function as a gate oxide like SiO 2 and HfO 2. On the other hand, the latter can be a resist layer, such as polyethylethacrylate (PMMA), which is a coonly used resist for e-bea lithography. The scheatic of such a structure is shown in Fig. 3. The advantage of using PMMA over-layer is twofold. One of the advantages is that the thickness of PMMA can be controlled precisely through optiizing the resist solution and its coating process. In addition to adjustable thicknesses, the resist can also be used to pattern the graphene for device fabrication. Figs. 4(a) to 4(f) show the siulated contrast of graphene as a function of wavelength for PMMA thicknesses ranging fro to 4 n on different types of oxide and nitride substrates: (a) SiO 2, (b) Si 3 N 4, (c) HfO 2, (d) Al 2 O 3, (e) MgO and (f) TiO 2. Although the contrast is not high when graphene along is placed on these substrates, the contrast is significantly enhanced with the addition of a PMMA overlayer, especially for SiO 2, Al 2 O 3 and MgO substrates over a wide range of the spectru. In the case of Si 3 N 4, HfO 2 and TiO 2 substrates, viewing of graphene under the icroscope would probably require the use of a narrow band pass filter as contrast of graphene is greatly enhanced only over a narrow band of the spectru. It is also noted that, in ost cases, positive contrasts are obtained, in which graphene is darker than the background and also ore iportantly, the contrasts are coparable, if not better than the current graphene-sio 2 -Si structure for identifying graphene. Figs. 5(a) to 5(f) show the siulated contrast of graphene as a function of wavelength for PMMA thicknesses ranging fro to 4 n on different types of seiconductor substrates: (a) Si, (b) Ge, (c) GaAs, (d) GaN, (e) ZnO and (f) ZnSe substrate. Although iproveents have been obtained in all cases, only the contrast on GaN, ZnO and ZnSe has been increased to a level that is coparable to that of graphene-sio 2 -Si structure. As it is in the cases of Si 3 N 4, HfO 2 and TiO 2 substrates, the contrast enhanceent for GaN and ZnO substrates is obtained only in a narrow

8 band of the spectru; therefore, a narrow band pass filter is probably needed for viewing graphene under the icroscope. Zinc oxide is the only seiconductor aong the six that shows a positive contrast, and the rest has a negative contrast. In the case of Si, Ge and GaAs, it would probably still be possible to see graphene even though the contrast values are at the lower liit of the observable range of naked eyes. Figs. 6(a) to 6(f) show the siulated contrast of graphene as a function of wavelength for PMMA thicknesses ranging fro to 4 n on different types of etallic substrates: (a) Co, (b) Ni, (c) Fe, (d) NiFe, (e) Au and (f) Cu. It is worth noting that the contrasts for the etals have ore or less doubled. Although the enhanceent is significant, the absolute value of contrast is still rather low, which akes the identification of graphene a difficult task on etal substrates. Gold and copper are the two aong the six etals having a higher contrast that could be observed easily under the icroscope with the naked eyes. In Table I, we suarize the axiu contrasts obtained on different types of substrates with or without a resist layer of optiu thickness and the corresponding enhanceent ratio. Based on our experiental experience, the lower contrast liit to see graphene by naked eyes is about.2. Therefore, it is possible to see graphene under an optical icroscope on ost of the substrates after the coating of a PMMA layer with optiu thickness. As shown in Figs. 4-6, the optiu thickness for PMMA ranges fro 5 to 1 n in the visible wavelength range, the approach is technically feasible. Fig. 7(a) to 7(d) shows soe of the siulation results for thicker graphene layers (N = 1 to 4) on different types of substrates, with the thickness of PMMA optiized for axiu contrast: (a) silicon dioxide substrate with 275 n of PMMA, (b) silicon substrate with 13 n of PMMA, (c) galliu arsenide substrate with 38 n of PMMA and (d) cobalt substrate with 31

9 n of PMMA. It can be seen clearly that as the nuber of layers increases, the contrast increases linearly as well. Hence, few layer graphene sheets can be easily identified on various types of substrates and distinguished fro single layer ones. C. Experiental verification Experients were perfored to verify the siulation results on two representative substrates: quartz and NiFe (6 n) coated Si wafer. The graphite flakes obtained by echanical exfoliation were transferred to the substrates which include SLG, BLG and FLG sheets. Subsequently, the contrast and Raan spectra were easured to identify SLG and BLG sheets. After that, a thin layer (~ 38 n for quartz and ~ 325 n for NiFe ) of PMMA was coated on the substrates with graphene sheets, followed by the second round of optical easureents. Fig. 8 (a) copares the easured contrast spectra for a SLG and BLG with the siulation results on quartz substrate. The easured contrast is about half that of the siulated value in the entire visible wavelength range, which ight be caused by the influence of reflection fro the back surface. As shown in Fig. 8(b), the coating of a 38 n PMMA enhances slightly the contrast in the wavelength range of 466 n 616 n, but changes the contrast fro negative to positive in the range of 55 n 75 n. The experiental data are in good agreeent with the siulation results. In the case of NiFe, which is the ost coonly used aterial for spintronics, we could not obtain any contrast when it was not coated with PMMA. However, as shown in Fig. 8(c), a reasonably high contrast is obtained for saples coated with a PMMA layer near the blue wavelength region for both SLG and BLG. Again, a good agreeent is obtained between siulated and easured data. SLG becae visible under optical icroscope, though it is not as clear as when it is on the quartz substrate. Therefore, PMMA coating is a technically feasible way to enhance graphene contrast on different types of substrates. IV. SUMMARY

10 In suary, we have studied theoretically the visibility of graphene on different types of substrates with or without a resist layer. These aterials include oxides, nitride, seiconductors and etals. It was found that SLG can be directly observed on oxide and nitride while it is invisible on ost seiconductors and etals by optical icroscope. The coating of a PMMA layer with optiu thickness is an effective way to enhance the contrast of SLG on all types of substrates investigated and it also akes SLG visible on ost seiconductors and etals. Experients were perfored to verify the results on quartz and NiFe/Si substrates. The results will be useful for fabricating graphene-based electronic, spintronic and optoelectronic devices on various types of substrates. ACKNOWLEDGEMENT The work at the National University of Singapore was supported by A*-STAR under Grant No. R

11 Figure Captions FIG. 1. A ultilayer odel used in the transfer atrix siulation. FIG. 2. (a) Scheatic of light reflection fro a graphene sheet on a substrate; (b)-(d) Optical contrast spectra of graphene sheets with thickness ranging fro 1 to 1 layers on: (b) sapphire substrate, (c) Si substrate and (d) Au substrate. FIG. 3. Scheatic of light reflection fro a graphene sheet on a substrate coated with a PMMA overlayer. FIG. 4. Contrast of graphene as a function of wavelength fro 4 n to 75 n and PMMA thickness fro to 4 n on different types of substrates or layers: (a) SiO 2, (b) Si 3 N 4, (c) HfO 2, (d) sapphire, (e) MgO and (f) TiO 2. FIG. 5. Contrast of graphene as a function of wavelength fro 4 n to 75 n and PMMA thickness fro to 4 n on different types of seiconductor substrates: (a) Si, (b) Ge, (c) GaAs, (d) GaN, (e) ZnO, (f) ZnSe.. FIG. 6. Contrast of graphene as a function of wavelength fro 4 n to 75 n and PMMA thickness fro to 4 n on different types of etallic substrates or thin fils: (a) Co, (b) Ni, (c) Fe, (d) NiFe, (e) Au, (f) Cu. FIG. 7. Contrast of graphene as a function of wavelength on (a) silicon dioxide substrate with 275 n of PMMA, (b) Si substrate with 13 n of PMMA, (c) GaAs substrate with 38 n of

12 PMMA, and (d) Co with 31 n of PMMA (d). The arrows indicate that the nuber of graphene layers increases fro 1 to 4. FIG. 8. Experiental and siulation results of contrast spectra of SLG and BLG for (a) graphene/quartz, (b) PMMA (38 n)/graphene/quartz, and (c) PMMA (325 n)/graphene / NiFe (6 n) /Si.

13 z n n 1 n 2 n i. n N-1 n N n S A A 1 A 2 A i A N-1 A N A S B B 1 B 2 B i B N-1 B N B S x d 1 d 2 d i d N-1 d N FIG. 1 GQ Teo et al. J. Appl. Phys.

14 Contrast graphene n 1 d (a) air: n λ substrate: n n s (c) 1L 1L Contrast Contrast (b) 1L 1L L (d) 1L FIG. 2 GQ Teo et al. J. Appl. Phys.

15 λ air: n =1 PMMA graphene substrate n 1 n 2 n 3 d 1 d 2 FIG. 3 GQ Teo et al. J. Appl. Phys.

16 (a) (b) (c) (e) (d) (f) 7 (f) FIG. 4 GQ Teo et al. J. Appl. Phys.

17 7 (a) (c) 7 (e) (b) (d) (f) FIG. 5 GQ Teo et al. J. Appl. Phys.

18 7 (a) (c) (e) (b) (d) (f) FIG. 6 GQ Teo et al. J. Appl. Phys.

19 Contrast.4 4L (a) 1L L L (b) Contrast Contrast -.4 1L (c).1.6 (d) 4L -.8 4L.2 1L Contrast FIG. 7 GQ Teo et al. J. Appl. Phys.

20 Contrast (a) 1L siulation results 2L siulation results 1L experiental results 2L experiental results Contrast Contrast (b) -.1 1L siulation results 2L siulation results -.2 1L experiental results 2L experiental results (c) 1L siulation result 2L siulation result 1L experiental result 2L experiental result FIG. 8 GQ Teo et al. J. Appl. Phys.

21 Table I. Suary of axiu contrasts obtained on different types of substrates with or without a resist layer of optiu thickness and the corresponding enhanceent ratio. Type Substrate Max Contrast (w/o Max Contrast Thickness of PMMA) (w PMMA) PMMA (n) Iproveent SiO % Si 3 N % Insulator HfO % Al 2 O % MgO % TiO % TCO ITO % Si % Seicondu ctor Metal Ge % GaAs % GaN % ZnO % ZnSe % Co % Ni % Fe % NiFe % Au % Cu %

22 1 K. S. Novoselov, A. K. Gei, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, M. I. Katsenlson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (25). 2 Y. Zhang, Y. W. Tan, H. L. Storer, and P. Ki, Nature 438, 21 (25). 3 C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, Science 312, 1191 (26). 4 A.K. Gei and K. S. Novoselov, Nature Materials 6, 183 (27). 5 D. S. L. Abergel, A. Russell, V. I. Fal'ko, Appl. Phys. Lett. 91, (27). 6 P. Blake, K. S. Novoselov, A. H. Castro Neto, D. Jiang, R. Yang, T. J. Booth, A. K. Gei, E. W. Hill, Appl. Phys. Lett. 91, (27). 7 S. Roddaro, P. Pingue, V. Piazza, V. Pellegrini, F. Beltra, Nano Lett. 7, 277 (27). 8 C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, A. C. Ferrari, Nano Lett. 7, 2711 (27). 9 Z. H. Ni, H. M.Wang, J. Kasin, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, Nano Lett. 7, 2758 (27). 1 I. Jung I., M. Pelton, R. Piner, A. D. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, Nano Lett., ASAP Article 1.121/nl K. Chang, J. T. Liu, J. B. Xia, and N. Dai, Appl. Phys. Lett. 91, (27). 12 P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988). 13 E. D. Palik (ed.), Handbook of Optical Constants of Solids (Acadeic Press, Orlando, 1985).