NANO LETTERS
Spontaneous Formation of Nanostructures in Graphene
2009 Vol. 9, No. 10 3599-3602
Zhongjun Li, Zengguang Cheng, Rui Wang, Qiang Li, and Ying Fang* National Center for Nanoscience and Nanotechnology of China, Zhongguancun, Beijing 100190, People’s Republic of China Received June 8, 2009
ABSTRACT We report in-depth studies of nanostructures formed in graphene on soft substrates. Periodic buckles with amplitude of nanometer scale spontaneously appear at edges of single-layer membranes after cooling of samples from above the substrate’s glass-transition temperature. Stress modulation at step-edges between single- and few-layer further induces penetrating nanobuckles into the few-layer. The evolvement of single-layer folding into double and triple-layer stacks at elevated temperature was also probed in detail, and we show that the developed interfaces are clear of polymer contamination. Our results underscore the possibility to construct diverse nanostructures and to design novel devices based on graphene.
Graphene is attracting tremendous interests because of high crystal quality and unique properties,1-4 and efforts are being devoted to develop applications with it.5-8 In particular, introducing nanostructures in graphene may find applications in, for example, tailoring of its physical properties and consequently its functionalities as building blocks.8-11 Central to explore structure engineering based on graphene is to understand its transition and its interactions with the medium,12 although these points have been poorly addressed by experiments so far. Conventional mechanical exfoliation transfers graphene to silicon oxide (SiO2) substrate, but the strong van der Waals interaction between graphene and its substrate suggests that the morphology of graphene will be largely set by that of SiO213,14 whose covalent network structure renders an extremely thermal-stable surface. On the other hand, most polymers exhibit glass transitions at moderately elevated temperatures to facilitate movements of polymer chains,15 which can therefore assist dynamical behaviors near the polymer surface. Further, the difference in the thermal expansion coefficient of graphene and polymer may be adopted to generate stress-related changes in graphene’s elastic membrane.10,16 We have undertaken and report herein investigations of graphene on top of polymer substrates and its thermally induced structure changes. Atomic force microscopy (AFM) measurements were carried out to deliver nanometer-scale information that represents the most interesting scenario in structure engineering based on the ultimate two-dimensional membranes. * To whom correspondence should be addressed. E-mail: fangy@ nanoctr.cn. 10.1021/nl901815u CCC: $40.75 Published on Web 08/05/2009
2009 American Chemical Society
A 300 nm thick polymethylmethacrylate (PMMA 950K) layer with glass transition temperature of ∼105 °C was spin coated on the silicon substrate then baked at 180 °C for 30 min to completely remove the solvent chlorobenzene.16 Graphene flakes were then deposited on top of the polymer by mechanical exfoliation of natural graphite. The thickness of the PMMA was chosen as such to give the optimized contrast of graphene as shown in Figure 1a.17,18 The sample was then annealed at 170 °C for 30 seconds then quickly cooled to room temperature, and its optical image (Figure 1b) revealed no detectable changes in the single-layer region when compared with that taken before annealing (Figure 1a). Raman characterization has been demonstrated to be a powerful tool to envisage properties of graphene,19,20 so we compared the Raman spectra at the center of the single-layer before and after annealing (Figure 1c). The absence of D band in the spectra shows that annealing does not result in any damage to the integrity of the nanomembrane, which is further confirmed when the integrated intensity ratio of 2D to G band (I2D/IG) stays unchanged after annealing.21 Surprisingly, both G and 2D bands of the single-layer shifted to higher frequency after annealing with ∆G ) 6 cm-1 and ∆2D ) 10 cm-1 compared with those before annealing. The blue-shifted Raman bands cannot be accounted by the optical images. AFM (Dimension 3100 Veeco) measurements were therefore carried out on the same sample to gain more insight of its structure. The AFM was under ambient conditions and scanned in tapping mode, and valuable information was immediately revealed in Figure 2a. Nanometer-high buckles were formed along the two edges of the single-layer after short thermal cycling, and we note similar
Figure 1. (a) Optical image of graphene transferred on a 300 nm PMMA layer. Single-layer and few-layer regions of the sample are indicated by SL and FL. (b) Optical image after cooling down to room temperature from 170 °C. Scale bars are both 5 µm. (c) Raman spectra recorded at the center of the single-layer, marked with black and red dots in (a) and (b), before and after annealing. The spectra are offset for clarity, and the I2D/IG values are indicated for each curve.
structures have been reproduced frequently in single-layer samples on PMMA substrates. Figure 2b is the AFM height profile illustrating periodic buckles of ∼4 nm high and ∼200 nm long along the edge of the single-layer. Former finite element simulations on graphene have predicted the existence of intrinsic buckles at edges of the suspended single-layer, although their calculation gave much smaller buckles than our results.22 The observed nanobuckles in our system are likely due to the generated stress from the difference of thermal expansion between the single-layer and the polymer. PMMA has a thermal expansion coefficient of ∼5 × 10-5/ °C. Although the thermal expansion coefficient of graphene has not been measured experimentally, bulk graphite has a thermal expansion coefficient of ∼10-6/°C and provides an approximation for graphene. Therefore, the large shrinkage of polymer during cooling places the single-layer under compressive stress, and the edges of the single-layer spontaneously buckle to relieve this stress. The blue shift of the single layer’s Raman bands in Figure 1c is also consistent with the existence of compressive stress in it.20,23 Periodic buckles also appeared in the few-layer along its step edge connecting the single-layer (Figure 2a and Figure 3a). The AFM height profiles of these buckles are summarized in Figure 3b,c, and we found that the propagating of the buckles along the step edge follows a sinusoid waveform with a period of λ ) 0.55 µm. Further, the penetration of the buckles into the few-layer is best fitted 3600
Figure 2. (a) AFM topographic image of the graphene after annealing. The height of the single-layer is 1 nm. The height of the connecting few-layer is about 2.5 nm. Scale bar is 5 µm. (b) AFM height profile along the dashed line marked in (a). The profile shows periodic buckles at the edge of the single-layer.
by a linear decay of (1 - x2/d), where d is the total penetration depth of ∼2.5 µm (Figure 3c). So the structure of the buckles in the few-layer can be presented as y ) A(1 - x2 /d)sin(2πx1 /λ)
(1)
where y is the height of the buckles, x1 is along the step edge, x2 is perpendicular to the step edge, and A ) 4.9 nm is half of the averaged buckle amplitude at the step edge. The origin of the buckles in the few-layer is discussed next. The propagation of the buckles along the step edge stops at the end of the single-layer (Figure 2a), and combined with the fact that the amplitude of the buckles decays when penetrating in the few-layer, we reach the conclusion that the buckles in the few-layer were produced by the relative configuration changes between the single-layer and the fewlayer. We define the relative compression of the single-layer to the few-layer after thermal cycling as
R)
∫
(( ) ) ∫ (( ) ) ∂y ∂x1
2
+ 1 dx1 -
∂y ∂x1
2
∫ dx
1
(2)
+ 1 dx1 Nano Lett., Vol. 9, No. 10, 2009
Figure 4. (a-c) Optical images of graphene on PMMA substrate before annealing, initially folded when annealed for 1 min, and extensively folded when annealed for another minute, respectively. The areas within the dashed boxes in (b) and (c) were studied by high resolution AFM in detail. Scale bars are 5 µm. (d,f) AFM image and constructed cartoon of the initially folded graphene, the AFM measurements were performed after the sample was cooled down to room temperature. (e,g) AFM image and constructed cartoon of the extensively folded graphene. Dashed boxes in (e) mark the areas used to calculate surface roughness of PMMA substrate (1), single-layer (2), and folded-layer (3), respectively. Each box consists 1764 data points which are 6 nm apart from each other in the lateral directions. Scale bars in (d,e) are both 1 µm. Figure 3. (a) Tapping mode AFM images showing details of the buckles in the few-layer. Scale bar is 5 µm. (b) AFM height profiles along the solid lines marked in (a), showing the propagation of buckles in the few-layer at different distances from the step edge. The green dashed line is a sinusoid fit of y ) 4.9 sin(2πx1/0.55) at the step edge. (c) Height profiles along the dashed lines marked in (a), showing the penetration of a buckle into the few-layer. The red curve is along the peak of the buckle and the blue curve is along the valley of the buckle. The black curve was constructed by subtracting the blue from the red curve to show the decaying of the buckle’s amplitude.
and the AFM result in Figure 3a gives R ) 0.1% along the whole step edge. On the basis of continuum model,24 the strain energy stored in the few-layer can be estimated with U ) ≈
(
∫ 21 ∫ MF 1 + ( ∂x∂y ) dx 2
1
∫ ( 21 ∫ F (1EI- ν ) dx )dx 2
2
Nano Lett., Vol. 9, No. 10, 2009
1
2
)
1
)
dx2
Et3 24(1 - ν2)
A
( )
∂2y 2 dx1 dx2 ∂x12 (3)
where M is the bending moment, F is the local bending radius, I is the area moment of inertia, E ) 1.0 TPa is the Young modulus of graphite, ν ) 0.16 is the Poisson’s ratio,25,26 and t ) 2.5 nm is the thickness of the few-layer. Equation 3 is calculated under the condition of the sinusoidlike waveform in eq 1, which yields the strain energy in the few-layer of ∼380 eV per period (0.55 µm × 2.5 µm). The rich nature of graphene’s transition is further supported when a single-layer folds into double- or triple-layer (Figure 4a-c) above the substrate’s glass transition temperature. Corresponding AFM studies were also carried out at different stages (Figure 4d,e). Figure 4 panels d and f are the AFM and simulated cartoon images at the initial stage of folding. Two of 0.2 µm wide folding structures were formed in the single-layer, but we will focus our discussion on the triple-layer in the middle since only it underwent migration in the next step. The folded structure in the middle is measured to be 1.3 nm higher than the single-layer (Figure 4d), and this number is larger than 0.7 nm height of a natural Bernal double-layer. The observed difference is due to the misaligned stacking between layers,27 although the interlayer 3601
coupling between the misaligned layers is still strong enough to drive the folded area to enlarge to 1.2 µm wide as show in Figure 4e. Next, we compared the AFM surface roughness of the PMMA substrate and the graphene in Figure 4e. Each measurement was done within a 0.25 µm × 0.25 µm square window, and the root-mean-square (rms) roughness (Rq) were calculated as
∑ n
Rq )
|yi - jy | 2
i)1
n
(4)
where jy is the mean height of the data in the square window. The results for the PMMA substrate, the single-layer, and the developed triple-layer graphene were measured to be 0.27, 0.17, and 0.21 nm, respectively. The difference between the triple-layer and the single-layer is within the vertical resolution of our instrument. The comparable surface roughness in the folded region to the single-layer indicates that the contacts between layers are smooth and clean of PMMA residues.28,29 This observation substantiates the potential of our method to engineer graphene into homogeneous threedimensional structures. In conclusion, we have utilized AFM to study nanoscale structures formed during thermally induced configuration changes of graphene on top of PMMA substrates. Nanometer-high buckles were found at both the single-layer’s edges and the connecting few-layer. Detailed analysis suggests that penetrating buckles in the few-layer were induced by relative configuration changes between the single-layer and the fewlayer. We also demonstrated that a single-layer can stack into few-layers with clean interfaces, and the coupling between layers drives the folded area to expand to micrometer size. Our method represents a novel approach to fabricate diverse nanostructures based on graphene and to further explore their fundamental physical properties, for example, combined with the merit that graphene on PMMA can be readily transferred to SiO2 substrate,30 it will be interesting to investigate effects of nanobuckles on electronic properties of graphene. Acknowledgment. The authors thank Yan Fang for helpful discussion on continuum mechanics. Y.F. acknowledges support of this work by Special Presidential Foundation of the Chinese Academy of Sciences, China (08172911ZX) and “973” Fund (2009CB930200). Supporting Information Available: Methods, AFM image showing PMMA residues on graphene surface after lithography-like process, optical and AFM studies of configuration changes in graphene on PMMA-MMA Copolymer. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U.S.A. 2005, 102 (30), 10451–10453.
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NL901815U
Nano Lett., Vol. 9, No. 10, 2009
