Mastering the Wrinkling of Self-supported Graphene

We present an approach that allows for the preparation of well-defined large arrays of graphene wrinkles with predictable geometry. Chemical vapor deposition grown graphene transferred onto hexagonal pillar arrays of SiO2 with sufficiently small interpillar distance forms a complex network of two main types of wrinkle arrangements. The first type is composed of arrays of aligned equidistantly separated parallel wrinkles propagating over large distances, and originates from line interfaces in the graphene, such as thin, long wrinkles and graphene grain boundaries. The second type of wrinkle arrangement is composed of non-aligned short wrinkles, formed in areas without line interfaces. Besides the presented hybrid graphene topography with distinct wrinkle geometries induced by the pre-patterned substrate, the graphene layers are suspended and self-supporting, exhibiting large surface area and negligible doping effects from the substrate. All these properties make this wrinkled graphene a promising candidate for a material with enhanced chemical reactivity useful in nanoelectronic applications.

. Demonstration of wrinkled edges of the graphene sheet for the GN@pillar_B sample, with almost smooth graphene in the central parts of graphene layers. Completely smooth graphene parts in the AFM topography (left) and phase (right) images are highlighted by black dashed lines. Table S1. Parameters of wrinkled graphene sheet in the GN@pillars_B sample. Percentage of surface area of the sample covered with graphene, A GN , number of different types of the graphene areas within individual samples with the list of individual area types, surface area attributed to the different area types, A/A GN , surface area of graphene, S GN , calculated contact area of graphene and nanopillar, S cont , typical wrinkle length, l wr and median peak to valley distance for different area types, R tm , corresponding to the slack of graphene between individual wrinkles. *wrinkles formed in the direction perpendicular to the graphene hole edge Raman spectroscopy of the GN@nanopillars_B sample Figure S3. (a) Typical Raman spectra of the GN@pillars_B sample for region of freestanding graphene (red data points) and graphene supported by the Si/SiO 2 nanopillars (grey data points). (b) Intensity map of the transverse optical (TO) phonon mode of Si together with the typical size of the laser spot (green dot). It has to be noted that depending on the position of the laser spot, one Raman spectrum contains information both about the suspended and supported graphene due to the finite laser spot size. The Raman shift of the G 1 (c), 2D 1 (d) and 2D' (e) modes of graphene. Scale bar in all maps represents 1 µm. Figure S4 proves that large optically visible wrinkles (folds) are not the source of the aligned wrinkle formation, as they do not form continuous constraint boundary. Figure S4. Visualisation of the optically visible wrinkle (left image) on AFM topography image (right). Left image shows typical optical pattern of graphene transferred on the nanopillar array, with thin wrinkles (visible by AFM only, marked with red arrows) serving as the source of the parallel wrinkle formation.

Major and minor wrinkles (2D FFT filtration) and wrinkle propagation geometry (2D FFT)
The long-range (major) and short-range (minor) wrinkles can be separated well using 2D FFT filtration. An example of this procedure is shown in Fig. S5, where the topography image of the GN@pillars_A (Fig. 3a) is split into long-range ( Fig. 3b) and short-range ( Fig. 3c) wrinkles. Figure S5. Left column: the AFM topography image (a) of the GN@pillars_A sample with the long-range (b) and short-range (c) frequency components separated using the 2D-FFT filtration. Right column: Example of the 2D FFT images for typical wrinkle areas, demonstrating symmetry of wrinkle propagation and visualising the angles between main propagation directions. Yellow star marks directions with highest intensity, hence the most preferred direction of wrinkle propagation for individual wrinkle area type. Figure S6. Visualisation of the wrinkle location with respect the nanopillar positions for image containing all three specific wrinkle areas. Image was created as a subtraction of the AFM topography and phase images -AFM topography image shows the complete wrinkle network, whereas the phase image visualises both the topography corrugations (wrinkle peaks, graphene line boundaries) as well as the objects hidden beneath the graphene layer which are in direct mechanical contact with the graphene (pillar tops). Combination of both images via image arithmetic allows visualisation of topography together with mechanical perturbations of scanned surface.

Line boundaries -evidence for graphene on flat substrate
The area of the graphene transferred on the substrate is approximately 1cm 2 , whereas the central part of the sample where the nanopillar array is located is only 1mm 2 large. Graphene transferred on the bare Si/SiO 2 substrate is used as an area to explore origin of the thin lines on the phase images.

Mechanical properties mapping
We mapped samples using the PF-QNM method, where simultaneously the AFM topography, adhesion and deformation can be measured. Deformation was correlated with the topography; it can be seen in Figures S10 -S13 that deformation of the regions with free standing (suspended) graphene is much lower than the deformation of supported graphene on nanopillars. Moreover, deformation reached for graphene in the GN@pillars_A sample is much larger than deformation reached in the GN@pillars_B sample, pointing to higher strain of the graphene layer and better adhesion of graphene to larger pillars. Larger strain of the layer should lead to smoothening of wrinkles and more flat-like profile of graphene layer, which was observed for the GN@pillars_B sample. Better attachment of the graphene to pillars for the GN@pillars_B sample was indirectly confirmed with adhesion, which is higher than for the GN@pillars_A sample ( Figures S12 and S13).   Figure S12 and S13 show that phase contrast for the wrinkles located in between pillars is dominated by adhesion, whereas pillar regions are dominated by deformation. Figure S12. a) Topography, b) adhesion and c) deformation for the GN@nanopilars_A sample. Figure S13. a) Topography, b) adhesion and c) deformation for the GN@nanopilars_A sample.

Calculation of the peak-to-peak amplitude of the layer (R tm )
To calculate the median peak-to-peak amplitude of the graphene layer R tm (median distance between wrinkle height and inter-wrinkle valley depth) for individual area types, we built procedure for the MATLAB network.
Calculation of the R tm parameter (Eq. 1 in the manuscript file) works as follows. The individual area types (random, aligned and mixed wrinkle areas) were cut out from the large topography AFM images, producing images with m x n pixels. Then all the peak maxima (p i ) and minima (v i ) were found for each individual line m in the image. Finally, the median R tm was calculated from median peak height (p m ) and valley depths (v m ) of whole area using Eq. 1. Example of the one image line of the 'mixed area' with highlighted p i and v i is depicted in Figure S14. Additional comments on the Raman spectroscopy data and analysis Figure S16: Close up of the G mode (top panel) and 2D mode (lower panel) regions, magnified from Fig. 2 in the main text, of typical Raman spectra of the GN@pillars_A sample for regions with randomly wrinkled graphene (grey data points) and aligned wrinkles (red data points). It is clearly visible that the G mode of the random area (grey data points) is rather symmetric, whereas the aligned area (red data points) clearly exhibits an asymmetric G mode. This asymmetry is fitted using a larger G 2 component and one, although small, extra peak function (G 3 ) that accounts for the long wrinkles. Figure 16 shows the close-ups of the G and 2D regions (from Fig. 2 in the main text) of the GN@pillars_A sample. As indicated in the main text, the strain differences were estimated through the analysis of the 2D' mode. However, several interesting observations can be made regarding the shape of the G mode, especially concerning its asymmetry in the spectra from the aligned wrinkle areas. The larger asymmetry usually indicates the presence of regions with more defined state (doping/strain) of the graphene within the laser spot [S1]. If the regions are not so well defined, in other words there are many areas with only slightly differing strain/doping within the spot, then the G peak becomes simply broader and shifted towards the average values. We can see this is indeed the case of the difference between the aligned and random areas in our GN@pillars_A sample. The doping and strain (level and direction) are much more random in the area where the wrinkles are oriented randomly, while there is a limited number of strain/doping configurations with specific Raman shifts in the aligned area. On the other hand it is difficult to draw any further conclusions, for example from the widths of the particular components, since apart from homogeneity of the sample, both the doping and strain influence the width of the G mode.