- Email: [email protected]
Sample rotation angle dependence of graphene thickness measured using atomic force microscope
CARBON
8 1 ( 2 0 1 5 ) 2 1 0 –2 1 5
Available at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/carbon
Sample rotation angle dependence of graphene thickness measured using atomic force microscope Duk Hyun Lee a, Mi Jung Lee a, Yeon Soo Kim a, Jin Sik Choi b, Bae Ho Park
a,*
a
Division of Quantum Phases & Devices, Department of Physics, Konkuk University, Seoul 143-701, Republic of Korea Creative Research Center for Graphene Electronics, Electronics and Telecommunications Research Institute (ETRI), Daejeon 305-700, Republic of Korea b
A R T I C L E I N F O
A B S T R A C T
Article history:
A precise measurement of graphene thickness is required for the design and development
Received 30 June 2014
of nano-devices based on the material. Many factors affect this measurement when using
Accepted 16 September 2014
scanning tunneling microscope (STM) and atomic force microscope (AFM), including the
Available online 27 September 2014
interaction between the scanning tip and ripples on graphene; such effects have not previously been explored. To investigate this, we measure the sample rotation angle dependence of graphene thickness as determined by contact mode and tapping mode AFM. The graphene thickness as determined by contact mode AFM follows a cosine modulus function of sample rotation angle, while tapping mode AFM reveals a constant graphene thickness, independent of sample rotation angle. For comparison, the AFM torsion signal is measured and follows a sine function of the sample rotation angle. All the measured sample rotation angle dependences can be explained by the interaction between linearly aligned ripples on graphene and the AFM tip in contact with the graphene. 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
Following the discovery of graphene prepared by the micromechanical cleavage technique [1], much research has been carried out on the material due to its outstanding characteristics, including its electrical [2,3] and mechanical properties [4,5]. However, the experimentally observed physical properties are inferior to those predicted by theory, and possible causes of this relate to intrinsic structural defects such as distortions, disorder, wrinkles or ripples [6–8]. Formation of these defects is inevitable because they provide structural stability of the two-dimensional graphene layer when under external stress [7]. Being able to measure the exact thickness of mono-layer graphene is a very important issue when considering
* Corresponding author. E-mail address: [email protected] (B.H. Park). http://dx.doi.org/10.1016/j.carbon.2014.09.051 0008-6223/ 2014 Elsevier Ltd. All rights reserved.
applications to nano-devices whose performance strongly depends on the dimensions of the constituent nano-materials. The thickness of mono-layer graphene, (i.e. the distance between the surface and the substrate on which it lies), has experimentally been determined to be in a wide range, from 0.3 nm to 1.5 nm, using scanning tunneling microscope (STM) or atomic force microscope (AFM) with atomic-scale resolution; theoretically, the thickness has been predicted to be 0.34 nm [9–12]. Thickness measurements of graphene using STM or AFM may in principle be perturbed by the interaction between the scanning tip and intrinsic structural defects, but such interaction dependence has not previously been explored. Thickness measurement using AFM is performed by monitoring a bending force of AFM cantilever during tip
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scanning. A torsion force of AFM cantilever is also induced during tip scanning and can be measured using friction force microscopy mode of AFM. We already found that the torsion force of AFM cantilever, which was obtained during tip scanning on graphene surface, followed a sine modulus function of sample rotation angle with 180 periodicity [13]. Such sample rotation angle dependence of the torsion force was attributed to linearly aligned ripple structures formed on graphene. If there would be linearly aligned ripple structures on graphene, bending force of AFM cantilever measured on graphene, which is proportional to thickness of graphene, should show sample rotation angle dependence with 180 periodicity. However, sample rotation angle dependence of graphene thickness has not been experimentally demonstrated yet. In this paper, we demonstrate that the graphene thickness determined by contact mode AFM topography follows a cosine modulus function of the sample rotation angle. For comparison, we measure the sample rotation angle dependence of the AFM torsion signal, as well as the graphene thickness as determined by tapping mode AFM. The AFM torsion signal shows a sine function dependence, while the tapping mode AFM measurements reveal a constant thickness of graphene. All the measured sample rotation angle dependences can be explained by the interaction between linearly
211
aligned ripples on graphene and an AFM tip in contact with the graphene.
2.
Experimental
Graphene flakes were prepared using the mechanical cleavage method, and deposited onto a thermally oxidized 300 nm thick SiO2 substrate in an ambient environment. Samples were sorted using an optical microscope, and Raman spectroscopy (with a 532 nm Nd:YAG laser source) was used to discriminate between mono-, bi-, and multi-layer graphene material. AFM topography and torsion images were obtained using a Seiko SPA-300HV system at room temperature, this being equipped with a 15-degree-step rotational sample holder. The scan speed and loading force were fixed at 10 lm/s and 0 nN, respectively, during the entire AFM measurement. We used silicon AFM tips from Nanosensors for all measurements. In contact mode, topographic images were obtained with tips having a typical curvature radius of 4.0 lm (model CDT-CONR), and lateral friction tips were used for torsion imaging (PPP-LFMR with spring constant of 0.2 N/m). Tapping mode topographic images were obtained using NCHR tips.
Fig. 1 – (a) Optical microscope image of a graphene flake mechanically exfoliated onto a SiO2 substrate. The lower inset shows the contact mode AFM topography image of the region depicted by the red square in the main figure. 1L and 2L denote the mono-layer and bi-layer graphene, respectively. (b) Raman spectra obtained at the red and blue spots in the lower inset of (a). (c) Contact mode AFM topography images obtained after rotating the sample by 30: in each case, the scan direction of AFM cantilever was the same as denoted in the upper inset of (a). (d) Sample rotation angle dependences of the distances: (i) between the mono-layer graphene and SiO2 (red dots); (ii) between the bi-layer graphene and SiO2 (blue dots); (iii) between the mono- and bi-layer graphene (black dots). These are averaged values measured on the red, blue, and black dashed rectangles in the inset of Fig. 1a, respectively. The red, blue, and black lines denote the fitting curves for the measured corresponding data. (A colour version of this figure can be viewed online.)
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Results and discussion
The optical microscope image shown in Fig. 1a reveals that graphene samples with different numbers of layers coexist within a single graphene flake that has been mechanically exfoliated onto a SiO2 substrate. Contact mode AFM topography was undertaken within the red square region (5 lm · 5 lm) shown in Fig. 1a, which contained two distinguishable regions of graphene with different thicknesses, as shown in the inset to Fig. 1a. To confirm the local number of graphene layers, Raman spectroscopy measurements were performed on the areas designated by red and blue spots shown in the inset. The Raman spectra in Fig. 1b show two intense bands: G band at 1580 cm 1; 2D band at 2700 cm 1. Raman spectrum obtained at the red spot has sharp 2D band and 2D/G intensity ratio of 2.8, which are typical features of mono-layer graphene [14]. In contrast, Raman spectrum obtained at the blue spot reveals broad 2D band with shoulder and 2D/G intensity ratio 1 implying that the blue spot area is bi-layer graphene [14]. Therefore, the Raman spectra verify that the red and blue spots are located on mono- and bi-layer graphene, respectively.
In order to determine the sample rotation angle dependence of the graphene thickness, we obtained contact mode AFM topography images (Fig. 1c) after rotating the sample sequentially by 30 (but leaving the scan direction of AFM cantilever same). The regions with brighter contrast correspond to thicker layers. Fig. 1c shows that the graphene thickness determined by contact mode AFM topography changes with the sample rotation angle. For more quantitative analysis, we plotted the thicknesses of mono- and bi-layer graphene samples as functions of sample rotation angle (Fig. 1d); these are the average thicknesses (Fig. S1 of Supplementary data) measured on the red and blue dashed rectangles in the inset of Fig. 1a, respectively. The thickness of the mono-layer graphene on SiO2 follows a cosine modulus function of sample rotation angle with 180 periodicity and 0.25 nm amplitude. The thickness of the bi-layer graphene on SiO2 shows a very similar dependence on sample rotation angle. However, measurements of the distance between the surfaces of monoand bi-layer graphene (which is the average thickness measured on the black dashed rectangle in the inset of Fig. 1a) remains constant at 0.4 nm during sample rotation. Given the experimental results, we can argue that a typical
Fig. 2 – (a) Optical microscope image of a graphene flake mechanically exfoliated onto a SiO2 substrate. The lower right inset shows the contact mode AFM topography image of red square region. The lower left inset shows the Raman spectra obtained at the red spot in the lower right inset. (b) Contact mode AFM topography images obtained after rotating the sample by 60 each while scan direction of AFM cantilever was kept fixed as denoted in the upper inset of (a). Gray dashed lines delineate the boundaries between domains with different contrasts. White dashed rectangles indicate the domain-1 regions where average thicknesses are measured. (c) Sample rotation angle dependences of mono-layer graphene thicknesses determined using contact mode AFM topography at domain-1 (black dot), domain-2 (blue square) and domain-3 (red triangle), which are average values measured on the white, blue, and red dashed rectangles in the lower right inset of (a), respectively. Orange inverted triangles show sample rotation angle dependence of mono-layer graphene thicknesses determined using tapping mode AFM topography. (d) AFM torsion images obtained after rotating the sample by 60; in each case, the longitudinal scan direction of AFM cantilever was kept fixed, as denoted in the upper inset of (a). (A colour version of this figure can be viewed online.)
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repulsive van der Waals force is dominant between the SiO2 surface and an AFM tip during scanning for contact mode topography, but a significant force (which follows a cosine modulus function of sample rotation angle) is added to it between the surfaces of mono- or bi-layer graphene and an AFM tip. This additional force is expected to be identical for mono- and bi-layer graphene owing to the similar amplitude (0.25 nm) of the cosine modulus functions that are followed by both (see Fig. 1d). In order to confirm the reproducibility of such intriguing sample rotation angle dependence of graphene thickness, we measured contact mode AFM topography on the red square area (5 lm · 5 lm) of another graphene, as shown in Fig. 2a. The Raman spectra shown in the left inset of Fig. 2a was obtained at the red spot and revealed that it was located on mono-layer graphene. Just like previous experiments, we achieved contact mode AFM topography images after rotating the sample, as shown in Fig. 2b. The images reveal domain structures on graphene, whose boundaries are denoted by the gray dashed lines, as well as anisotropic behavior. It is interesting that there is a thickness difference between
213
domains in the mono-layer graphene (Figs. S2 and S3 of Supplementary data). Specifically, we can argue that the graphene thickness determined using contact mode AFM topography is non-uniform and dependent on sample rotation angle. Fig. 2c shows the sample rotation angle dependences of mono-layer graphene thicknesses determined using contact mode AFM topography at domain-1 (black dot), domain-2 (blue square), and domain-3 (red triangle), which are average values measured on the white, blue, and red dashed rectangles in the lower right inset of Fig. 2a, respectively. In each case, a cosine modulus function is followed with 180 periodicity and 0.25 nm amplitude, similar to Fig. 1d, and is shifted by 60 from that in its adjacent domain. The mean value of the mono-layer graphene thickness in Fig. 2c is different from that in Fig. 1d, because the mean value is affected by the interaction between mono-layer graphene and a substrate; this in turn depends on the physical environment during mechanical exfoliation. For comparison, we obtained tapping mode AFM topography images, but they show a constant thickness of mono-layer graphene on SiO2 (orange inverted
Fig. 3 – (a) Longitudinal (TLON) and (b) lateral (TLAT) scan torsion images obtained on the graphene sample shown in Fig. 2(a). The torsion images are obtained by subtracting torsion values in the positive and negative scan directions. The insets denote a top view of the cantilever body and respective scan direction of an AFM tip. The calculated dependences of (c) TLON and (d) TLAT on the rotation angle of ripple from the forward lateral direction of the cantilever body. The shaded area exhibits the possible ripple directions of a domain denoted by the corresponding colored number in (a) and (b). (e) Resultant ripple directions determined by comparing TLON and TLAT images. (f) Sample rotation angle dependence of TLON in each domain, which are estimated (colored lines) and experimentally obtained (colored dots). (A colour version of this figure can be viewed online.)
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triangle in Fig. 2c). These results imply that the sample rotation angle dependence of graphene thickness is induced by a contact force between graphene and an AFM tip, which probably results from linearly aligned ripples of graphene [13]. In order to identify the interaction between ripples in mono-layer graphene and an AFM tip in contact with it, we obtained the AFM torsion images of the red square area in Fig. 2a, after rotating the graphene sample sequentially by 60. As shown in Fig. 2d, domain structures appear in monoand bi-layer graphene of these images that are dependent on the rotation angle, indicating that linearly aligned ripples are formed in each domain [13]. We can determine the ripple direction by comparing the cantilever torsion values obtained during longitudinal (TLON) and lateral (TLAT) scanning to the cantilever body (insets of Fig. 3a and b) of an AFM tip [4,8], as respectively shown in Fig. 3a and b. The cantilever torsion images reveal that a mono-layer graphene consists of three domains. The three domains show the torsion values of TLON,3 > TLON,1 > TLON,2 and TLAT,1 < TLAT,2 TLAT,3. From these results, the ripple direction of each domain can be estimated as follows. If cantilever torsions are induced by the interaction between an AFM tip and linearly aligned ripples, TLON and TLAT show sin h and |sin h| dependences (Fig. 3c and d), respectively, where h ( 90 < h < 90) is the (counter-clockwise) rotation angle of the ripple away from the forward lateral direction of the cantilever body [13]. Considering that the ripple direction of one domain is rotated by 60 or 60 from that of an adjacent domain, we can estimate the ripple direction of each domain within a range of 60 from an
individual AFM torsion image. The domains with bright (3), medium (1), and dark (2) contrasts in a TLON image (Fig. 3a) have h values in the range of 30 to 90, 30 to 30, and 90 to 30, respectively (Fig. 3c). However, the contrast of TLAT image (Fig. 3b) implies that 30 < h1 < 30 and |sin h2| |sin h3| where |h2 h3| = 60. By comparing h values estimated from the TLON and TLAT images, we can determine the precise ripple direction of each domain: h1 = 0; h2 = 60, which corresponds to 120 because of 180 periodicity of ripple direction; h3 = 60, as denoted by the colored two-way arrows in Fig. 3e. The estimated ripple direction of each domain can provide us with the expected sample rotation angle dependence (colored line) of TLON in each domain, as shown in Fig. 3f. The colored dots denote experimentally obtained TLON data of the same colored domains in the sample rotated by 0, 60, 90, 120, 150, and 180: we note that data expected for the TLON lines of three domains at these angles are in good agreement with corresponding data obtained from experiments. Based on our findings, we can argue that a contact force between linearly aligned ripples and an AFM tip affects both contact mode topography and cantilever torsion images. In general, contact mode AFM topography image is obtained by measuring longitudinal bending of cantilever body when an AFM tip scans on a surface in contact with the tip. The existence of ripple structure in graphene can affect not only torsion [8,13] of cantilever body but also longitudinal cantilever bending during AFM tip scanning on graphene. As illustrated in Fig. 4a, we describe the contact force (normal action force) and its reaction force (normal reaction force) on a ripple when
Fig. 4 – (a) An illustration explaining the forces between linearly aligned ripples and an AFM tip which longitudinally scans in contact mode. (b) Bending and torsion forces on cantilever when h is varied from 60 to 60. (A colour version of this figure can be viewed online.)
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an AFM tip is scanned along the longitudinal direction. The normal reaction force whose amplitude is A can be divided into a bending force (A|cos h|) leading to the topography signal and a torsion force (Asin h) resulting in cantilever torsion signal. The force components successfully elucidate the cosine and sine function dependences of topography (Figs. 1d and 2c) and cantilever torsion (Fig. 3f) signals, respectively. Fig. 4b explicitly shows that a bending force follows a cosine modulus function while a torsion force is fitted well by a sine function when h is varied from 60 to 60. The normal reaction force is negligible during tapping mode measurement, which leads to constant thickness measurements (Fig. 2c) of graphene, independent of ripple direction and sample rotation angle.
4.
Conclusions
We demonstrate experimentally that mono-layer graphene thickness determined by contact mode AFM follows a cosine modulus function of sample rotation angle, while that determined by tapping mode AFM remains constant. The sample rotation angle dependence is well explained by the interaction between an AFM tip and linearly aligned ripples on graphene in contact with the AFM tip. These findings can be extensively applied to determining exact thicknesses of two-dimensional atomic crystals, such as graphene, MoS2, and h-BN.
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIP) (No. 2013R1A3A2042120, 2011-0030229, and 20080061893 (QMMRC)).
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon. 2014.09.051.
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R E F E R E N C E S
[1] Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric field effect in atomically thin carbon films. Science 2004;306:666–9. [2] Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, et al. Two-dimensional atomic crystals. Proc Natl Acad Sci USA 2005;102:10451–3. [3] Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005;438:197–200. [4] Scarpa F, Adhikari S, Srikantha Phani A. Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 2009:065709–11. [5] Lee C, Wei X, Kysar JW, Hone J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008;321:385–8. [6] Morozov SV, Novoselov KS, Katsnelson MI, Schedin F, Ponomarenko LA, Jiang D, et al. Strong suppression of weak localization in graphene. Phys Rev Lett 2006;9:016801–16804. [7] Fasolino A, Los JH, Katsnelson MI. Intrinsic ripples in graphene. Nat Mater 2007;6:858–61. [8] Choi JS, Kim J-S, Byun IS, Lee DH, Lee MJ, Park BH, et al. Friction anisotropy-driven domain imaging on exfoliated monolayer graphene. Science 2011;333:607–10. [9] Lui CH, Liu L, Mak KF, Flynn GW, Heinz TF. Ultraflat graphene. Nature 2009;462:339–41. [10] Lee C, Li Q, Kalb W, Liu XZ, Berger H, Carpick RW, et al. Frictional characteristics of atomically thin sheets. Science 2010;328:76–80. [11] Dean CR, Young AF, Meric I, Lee C, Wang L, Sorgenfrie S, et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 2010;5:722–6. [12] Cheng Z, Zhou Q, Wang C, Li Q, Wang C, Fang Y. Toward intrinsic graphene surfaces: a systematic study on thermal annealing and wet-chemical treatment of SiO2-supported graphene devices. Nano Lett 2011;11:767–71. [13] Choi JS, Kim J-S, Byun IS, Lee DH, Hwang IR, Park BH, et al. Facile characterization of ripple domains on exfoliated graphene. Rev Sci Instrum 2012;83:073905–73907. [14] Ferrari AC, Meyer JC, Scardaci V, Casiraghi C, Lazzeri M, Mauri F, et al. Raman spectrum of graphene and graphene layers. Phys Rev Lett 2006;97:187401–4.
8 1 ( 2 0 1 5 ) 2 1 0 –2 1 5
Available at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/carbon
Sample rotation angle dependence of graphene thickness measured using atomic force microscope Duk Hyun Lee a, Mi Jung Lee a, Yeon Soo Kim a, Jin Sik Choi b, Bae Ho Park
a,*
a
Division of Quantum Phases & Devices, Department of Physics, Konkuk University, Seoul 143-701, Republic of Korea Creative Research Center for Graphene Electronics, Electronics and Telecommunications Research Institute (ETRI), Daejeon 305-700, Republic of Korea b
A R T I C L E I N F O
A B S T R A C T
Article history:
A precise measurement of graphene thickness is required for the design and development
Received 30 June 2014
of nano-devices based on the material. Many factors affect this measurement when using
Accepted 16 September 2014
scanning tunneling microscope (STM) and atomic force microscope (AFM), including the
Available online 27 September 2014
interaction between the scanning tip and ripples on graphene; such effects have not previously been explored. To investigate this, we measure the sample rotation angle dependence of graphene thickness as determined by contact mode and tapping mode AFM. The graphene thickness as determined by contact mode AFM follows a cosine modulus function of sample rotation angle, while tapping mode AFM reveals a constant graphene thickness, independent of sample rotation angle. For comparison, the AFM torsion signal is measured and follows a sine function of the sample rotation angle. All the measured sample rotation angle dependences can be explained by the interaction between linearly aligned ripples on graphene and the AFM tip in contact with the graphene. 2014 Elsevier Ltd. All rights reserved.
1.
Introduction
Following the discovery of graphene prepared by the micromechanical cleavage technique [1], much research has been carried out on the material due to its outstanding characteristics, including its electrical [2,3] and mechanical properties [4,5]. However, the experimentally observed physical properties are inferior to those predicted by theory, and possible causes of this relate to intrinsic structural defects such as distortions, disorder, wrinkles or ripples [6–8]. Formation of these defects is inevitable because they provide structural stability of the two-dimensional graphene layer when under external stress [7]. Being able to measure the exact thickness of mono-layer graphene is a very important issue when considering
* Corresponding author. E-mail address: [email protected] (B.H. Park). http://dx.doi.org/10.1016/j.carbon.2014.09.051 0008-6223/ 2014 Elsevier Ltd. All rights reserved.
applications to nano-devices whose performance strongly depends on the dimensions of the constituent nano-materials. The thickness of mono-layer graphene, (i.e. the distance between the surface and the substrate on which it lies), has experimentally been determined to be in a wide range, from 0.3 nm to 1.5 nm, using scanning tunneling microscope (STM) or atomic force microscope (AFM) with atomic-scale resolution; theoretically, the thickness has been predicted to be 0.34 nm [9–12]. Thickness measurements of graphene using STM or AFM may in principle be perturbed by the interaction between the scanning tip and intrinsic structural defects, but such interaction dependence has not previously been explored. Thickness measurement using AFM is performed by monitoring a bending force of AFM cantilever during tip
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scanning. A torsion force of AFM cantilever is also induced during tip scanning and can be measured using friction force microscopy mode of AFM. We already found that the torsion force of AFM cantilever, which was obtained during tip scanning on graphene surface, followed a sine modulus function of sample rotation angle with 180 periodicity [13]. Such sample rotation angle dependence of the torsion force was attributed to linearly aligned ripple structures formed on graphene. If there would be linearly aligned ripple structures on graphene, bending force of AFM cantilever measured on graphene, which is proportional to thickness of graphene, should show sample rotation angle dependence with 180 periodicity. However, sample rotation angle dependence of graphene thickness has not been experimentally demonstrated yet. In this paper, we demonstrate that the graphene thickness determined by contact mode AFM topography follows a cosine modulus function of the sample rotation angle. For comparison, we measure the sample rotation angle dependence of the AFM torsion signal, as well as the graphene thickness as determined by tapping mode AFM. The AFM torsion signal shows a sine function dependence, while the tapping mode AFM measurements reveal a constant thickness of graphene. All the measured sample rotation angle dependences can be explained by the interaction between linearly
211
aligned ripples on graphene and an AFM tip in contact with the graphene.
2.
Experimental
Graphene flakes were prepared using the mechanical cleavage method, and deposited onto a thermally oxidized 300 nm thick SiO2 substrate in an ambient environment. Samples were sorted using an optical microscope, and Raman spectroscopy (with a 532 nm Nd:YAG laser source) was used to discriminate between mono-, bi-, and multi-layer graphene material. AFM topography and torsion images were obtained using a Seiko SPA-300HV system at room temperature, this being equipped with a 15-degree-step rotational sample holder. The scan speed and loading force were fixed at 10 lm/s and 0 nN, respectively, during the entire AFM measurement. We used silicon AFM tips from Nanosensors for all measurements. In contact mode, topographic images were obtained with tips having a typical curvature radius of 4.0 lm (model CDT-CONR), and lateral friction tips were used for torsion imaging (PPP-LFMR with spring constant of 0.2 N/m). Tapping mode topographic images were obtained using NCHR tips.
Fig. 1 – (a) Optical microscope image of a graphene flake mechanically exfoliated onto a SiO2 substrate. The lower inset shows the contact mode AFM topography image of the region depicted by the red square in the main figure. 1L and 2L denote the mono-layer and bi-layer graphene, respectively. (b) Raman spectra obtained at the red and blue spots in the lower inset of (a). (c) Contact mode AFM topography images obtained after rotating the sample by 30: in each case, the scan direction of AFM cantilever was the same as denoted in the upper inset of (a). (d) Sample rotation angle dependences of the distances: (i) between the mono-layer graphene and SiO2 (red dots); (ii) between the bi-layer graphene and SiO2 (blue dots); (iii) between the mono- and bi-layer graphene (black dots). These are averaged values measured on the red, blue, and black dashed rectangles in the inset of Fig. 1a, respectively. The red, blue, and black lines denote the fitting curves for the measured corresponding data. (A colour version of this figure can be viewed online.)
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Results and discussion
The optical microscope image shown in Fig. 1a reveals that graphene samples with different numbers of layers coexist within a single graphene flake that has been mechanically exfoliated onto a SiO2 substrate. Contact mode AFM topography was undertaken within the red square region (5 lm · 5 lm) shown in Fig. 1a, which contained two distinguishable regions of graphene with different thicknesses, as shown in the inset to Fig. 1a. To confirm the local number of graphene layers, Raman spectroscopy measurements were performed on the areas designated by red and blue spots shown in the inset. The Raman spectra in Fig. 1b show two intense bands: G band at 1580 cm 1; 2D band at 2700 cm 1. Raman spectrum obtained at the red spot has sharp 2D band and 2D/G intensity ratio of 2.8, which are typical features of mono-layer graphene [14]. In contrast, Raman spectrum obtained at the blue spot reveals broad 2D band with shoulder and 2D/G intensity ratio 1 implying that the blue spot area is bi-layer graphene [14]. Therefore, the Raman spectra verify that the red and blue spots are located on mono- and bi-layer graphene, respectively.
In order to determine the sample rotation angle dependence of the graphene thickness, we obtained contact mode AFM topography images (Fig. 1c) after rotating the sample sequentially by 30 (but leaving the scan direction of AFM cantilever same). The regions with brighter contrast correspond to thicker layers. Fig. 1c shows that the graphene thickness determined by contact mode AFM topography changes with the sample rotation angle. For more quantitative analysis, we plotted the thicknesses of mono- and bi-layer graphene samples as functions of sample rotation angle (Fig. 1d); these are the average thicknesses (Fig. S1 of Supplementary data) measured on the red and blue dashed rectangles in the inset of Fig. 1a, respectively. The thickness of the mono-layer graphene on SiO2 follows a cosine modulus function of sample rotation angle with 180 periodicity and 0.25 nm amplitude. The thickness of the bi-layer graphene on SiO2 shows a very similar dependence on sample rotation angle. However, measurements of the distance between the surfaces of monoand bi-layer graphene (which is the average thickness measured on the black dashed rectangle in the inset of Fig. 1a) remains constant at 0.4 nm during sample rotation. Given the experimental results, we can argue that a typical
Fig. 2 – (a) Optical microscope image of a graphene flake mechanically exfoliated onto a SiO2 substrate. The lower right inset shows the contact mode AFM topography image of red square region. The lower left inset shows the Raman spectra obtained at the red spot in the lower right inset. (b) Contact mode AFM topography images obtained after rotating the sample by 60 each while scan direction of AFM cantilever was kept fixed as denoted in the upper inset of (a). Gray dashed lines delineate the boundaries between domains with different contrasts. White dashed rectangles indicate the domain-1 regions where average thicknesses are measured. (c) Sample rotation angle dependences of mono-layer graphene thicknesses determined using contact mode AFM topography at domain-1 (black dot), domain-2 (blue square) and domain-3 (red triangle), which are average values measured on the white, blue, and red dashed rectangles in the lower right inset of (a), respectively. Orange inverted triangles show sample rotation angle dependence of mono-layer graphene thicknesses determined using tapping mode AFM topography. (d) AFM torsion images obtained after rotating the sample by 60; in each case, the longitudinal scan direction of AFM cantilever was kept fixed, as denoted in the upper inset of (a). (A colour version of this figure can be viewed online.)
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repulsive van der Waals force is dominant between the SiO2 surface and an AFM tip during scanning for contact mode topography, but a significant force (which follows a cosine modulus function of sample rotation angle) is added to it between the surfaces of mono- or bi-layer graphene and an AFM tip. This additional force is expected to be identical for mono- and bi-layer graphene owing to the similar amplitude (0.25 nm) of the cosine modulus functions that are followed by both (see Fig. 1d). In order to confirm the reproducibility of such intriguing sample rotation angle dependence of graphene thickness, we measured contact mode AFM topography on the red square area (5 lm · 5 lm) of another graphene, as shown in Fig. 2a. The Raman spectra shown in the left inset of Fig. 2a was obtained at the red spot and revealed that it was located on mono-layer graphene. Just like previous experiments, we achieved contact mode AFM topography images after rotating the sample, as shown in Fig. 2b. The images reveal domain structures on graphene, whose boundaries are denoted by the gray dashed lines, as well as anisotropic behavior. It is interesting that there is a thickness difference between
213
domains in the mono-layer graphene (Figs. S2 and S3 of Supplementary data). Specifically, we can argue that the graphene thickness determined using contact mode AFM topography is non-uniform and dependent on sample rotation angle. Fig. 2c shows the sample rotation angle dependences of mono-layer graphene thicknesses determined using contact mode AFM topography at domain-1 (black dot), domain-2 (blue square), and domain-3 (red triangle), which are average values measured on the white, blue, and red dashed rectangles in the lower right inset of Fig. 2a, respectively. In each case, a cosine modulus function is followed with 180 periodicity and 0.25 nm amplitude, similar to Fig. 1d, and is shifted by 60 from that in its adjacent domain. The mean value of the mono-layer graphene thickness in Fig. 2c is different from that in Fig. 1d, because the mean value is affected by the interaction between mono-layer graphene and a substrate; this in turn depends on the physical environment during mechanical exfoliation. For comparison, we obtained tapping mode AFM topography images, but they show a constant thickness of mono-layer graphene on SiO2 (orange inverted
Fig. 3 – (a) Longitudinal (TLON) and (b) lateral (TLAT) scan torsion images obtained on the graphene sample shown in Fig. 2(a). The torsion images are obtained by subtracting torsion values in the positive and negative scan directions. The insets denote a top view of the cantilever body and respective scan direction of an AFM tip. The calculated dependences of (c) TLON and (d) TLAT on the rotation angle of ripple from the forward lateral direction of the cantilever body. The shaded area exhibits the possible ripple directions of a domain denoted by the corresponding colored number in (a) and (b). (e) Resultant ripple directions determined by comparing TLON and TLAT images. (f) Sample rotation angle dependence of TLON in each domain, which are estimated (colored lines) and experimentally obtained (colored dots). (A colour version of this figure can be viewed online.)
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triangle in Fig. 2c). These results imply that the sample rotation angle dependence of graphene thickness is induced by a contact force between graphene and an AFM tip, which probably results from linearly aligned ripples of graphene [13]. In order to identify the interaction between ripples in mono-layer graphene and an AFM tip in contact with it, we obtained the AFM torsion images of the red square area in Fig. 2a, after rotating the graphene sample sequentially by 60. As shown in Fig. 2d, domain structures appear in monoand bi-layer graphene of these images that are dependent on the rotation angle, indicating that linearly aligned ripples are formed in each domain [13]. We can determine the ripple direction by comparing the cantilever torsion values obtained during longitudinal (TLON) and lateral (TLAT) scanning to the cantilever body (insets of Fig. 3a and b) of an AFM tip [4,8], as respectively shown in Fig. 3a and b. The cantilever torsion images reveal that a mono-layer graphene consists of three domains. The three domains show the torsion values of TLON,3 > TLON,1 > TLON,2 and TLAT,1 < TLAT,2 TLAT,3. From these results, the ripple direction of each domain can be estimated as follows. If cantilever torsions are induced by the interaction between an AFM tip and linearly aligned ripples, TLON and TLAT show sin h and |sin h| dependences (Fig. 3c and d), respectively, where h ( 90 < h < 90) is the (counter-clockwise) rotation angle of the ripple away from the forward lateral direction of the cantilever body [13]. Considering that the ripple direction of one domain is rotated by 60 or 60 from that of an adjacent domain, we can estimate the ripple direction of each domain within a range of 60 from an
individual AFM torsion image. The domains with bright (3), medium (1), and dark (2) contrasts in a TLON image (Fig. 3a) have h values in the range of 30 to 90, 30 to 30, and 90 to 30, respectively (Fig. 3c). However, the contrast of TLAT image (Fig. 3b) implies that 30 < h1 < 30 and |sin h2| |sin h3| where |h2 h3| = 60. By comparing h values estimated from the TLON and TLAT images, we can determine the precise ripple direction of each domain: h1 = 0; h2 = 60, which corresponds to 120 because of 180 periodicity of ripple direction; h3 = 60, as denoted by the colored two-way arrows in Fig. 3e. The estimated ripple direction of each domain can provide us with the expected sample rotation angle dependence (colored line) of TLON in each domain, as shown in Fig. 3f. The colored dots denote experimentally obtained TLON data of the same colored domains in the sample rotated by 0, 60, 90, 120, 150, and 180: we note that data expected for the TLON lines of three domains at these angles are in good agreement with corresponding data obtained from experiments. Based on our findings, we can argue that a contact force between linearly aligned ripples and an AFM tip affects both contact mode topography and cantilever torsion images. In general, contact mode AFM topography image is obtained by measuring longitudinal bending of cantilever body when an AFM tip scans on a surface in contact with the tip. The existence of ripple structure in graphene can affect not only torsion [8,13] of cantilever body but also longitudinal cantilever bending during AFM tip scanning on graphene. As illustrated in Fig. 4a, we describe the contact force (normal action force) and its reaction force (normal reaction force) on a ripple when
Fig. 4 – (a) An illustration explaining the forces between linearly aligned ripples and an AFM tip which longitudinally scans in contact mode. (b) Bending and torsion forces on cantilever when h is varied from 60 to 60. (A colour version of this figure can be viewed online.)
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8 1 (2 0 1 5) 2 1 0–21 5
an AFM tip is scanned along the longitudinal direction. The normal reaction force whose amplitude is A can be divided into a bending force (A|cos h|) leading to the topography signal and a torsion force (Asin h) resulting in cantilever torsion signal. The force components successfully elucidate the cosine and sine function dependences of topography (Figs. 1d and 2c) and cantilever torsion (Fig. 3f) signals, respectively. Fig. 4b explicitly shows that a bending force follows a cosine modulus function while a torsion force is fitted well by a sine function when h is varied from 60 to 60. The normal reaction force is negligible during tapping mode measurement, which leads to constant thickness measurements (Fig. 2c) of graphene, independent of ripple direction and sample rotation angle.
4.
Conclusions
We demonstrate experimentally that mono-layer graphene thickness determined by contact mode AFM follows a cosine modulus function of sample rotation angle, while that determined by tapping mode AFM remains constant. The sample rotation angle dependence is well explained by the interaction between an AFM tip and linearly aligned ripples on graphene in contact with the AFM tip. These findings can be extensively applied to determining exact thicknesses of two-dimensional atomic crystals, such as graphene, MoS2, and h-BN.
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIP) (No. 2013R1A3A2042120, 2011-0030229, and 20080061893 (QMMRC)).
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon. 2014.09.051.
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