**2. Raman scattering monitoring of mechanical strain on graphene**

To date, several approaches to creating strain in graphene have been proposed [23, 24, 26, 28]. Although the graphene deformation methods are different, the Raman spectroscopy is always accepted as the most powerful and efficient tool to reveal the strain condition on graphene. In this section, we employ Raman scattering technology to observe biaxial strain on monolayer graphene. The strain was induced by deformation from a substrate with an array of SiO2 nanopillars. The nanopillars (1 cm2 in area, 80 nm in height, and 40 nm in pitch) were fabricated by employing a self‐assembled block copolymer through simple dry etching and deposition processes. The graphene sheet was subsequently transferred to the array of SiO2 nanopillars. The creation of biaxial tensile strain in graphene was validated based on high‐resolution micro‐ Raman spectroscopy, and the strain values were quantitatively calculated through the Grüneisen parameter. Atomic force microscopy (AFM) and accompanying finite element simulations were employed to confirm the accuracy and reliability of the Raman spectroscopy monitoring results.

**Figure 1** shows the schematic process to fabricate SiO2 nanopillars patterned by self‐assembled block copolymer. The fabrication began with forming periodic nanopatterns on 300 nm, thermally grown SiO2/Si substrate by using a self‐assembled block copolymer as a pattern template [50, 51]. A block copolymer layer, poly(styrene‐*block*‐methyl methacrylate) (PS‐b‐ PMMA), on top of a ~5 nm neutral PS brush layer was used to define periodic nanopatterns (**Figure 1(a)**–**(c)**). The PMMA cylinders were selectively removed by exposure to UV irradia‐ tion and rinsing with acetic acid (CH3COOH) to form the cylinder‐shaped nanopattern template layer. The brush layer in the patterned cylinders was removed by O2 plasma to allow the following evaporated material to deposit directly to the substrate in the next step. **Figure 2(a)** shows the block copolymer nanotemplate with a pitch (center‐to‐center distance between cylinders) size ~40 nm. A layer of 15 nm thick chromium (Cr) was deposited by e‐ beam evaporation and lifted off (**Figure 1(e)**–**(f)**). The array of Cr nanodots was uniformly created over the entire surface of SiO2/Si substrate (**Figure 2(b)**). Then, the underlying SiO2 layer was etched by Cr nanodots as a mask in the inductively coupled plasma (ICP) and the reactive ion etching (RIE) combination system. Finally, an array of SiO2 nanopillars (80 nm in height and 40 nm in pitch) was formed on Si substrate after removing the Cr nanodots, as shown in **Figure 2(c)**.

**Figure 1.** SiO2 nanopillar fabrication process with assistant of self‐assembled block copolymer. (a) original SiO2/Si sub‐ strate, (b) PS coated on substrate, (c) self‐assembled block copolymer coated on PS layer, (d)nanotemplate formed on substrate, (e) Cr evaporated on sample, (f) Cr nanodot on substrate after lift‐off, (g) SiO2 nanopillar formed after etch‐ ing with Cr nanodot mask, and (h) clean SiO2 nanopillar substrate after removing Cr nanodots.

**Figure 2.** (a) Self‐assembled block copolymer nanotemplate on SiO2/Si substrate, (b) Cr nanodots after lift‐off on SiO2/Si substrate, (c) obtained SiO2 nanopillars on SiO2/Si substrate, and (d) CVD grown monolayer graphene on Cu foil sub‐ strate. From Ref. [52].

The monolayer graphene that was transferred onto the array of SiO2 nanopillars was grown on a 25 μm thick 1″ × 1″ copper (Cu) foil by a chemical vapor deposition (CVD) [53, 54]. **Figure 2(d)** shows the SEM image of the grown monolayer graphene on Cu foil. A layer release‐ transfer method was employed to transfer the monolayer graphene film onto the pre‐pre‐ pared SiO2 nanopillar substrate as shown in **Figure 3**.

Firstly, in order to form a 150 nm thick PMMA supporting layer, the graphene layer on the back side of Cu foil was removed by oxygen plasma, followed by spin‐coating PMMA on the top side of the graphene sample and baked at 130°C for 3 min (**Figure 3(a)**–**(c)**). Secondly, the PMMA‐coated sample was dipped into 0.25 mol of Fe3Cl etchant for 4 h to remove the Cu foil completely, and then the left PMMA/graphene membrane was floated on the solution surface (**Figure 3(d)**–**(e)**). After cleaning the sample in DI water, the floating PMMA/graphene membrane was scooped on the SiO2 nanopillar substrate, and the PMMA layer was removed by acetone to only leave the graphene film on a SiO2 nanopillar substrate (**Figure 3(f)**–**(h)**). The graphene/SiO2 nanopillar substrate was dried on a hot plate at 105 °C for 1 min to evaporate solvent and water from the sample. With the help of water capillary action and van der Waals forces, the graphene film can be driven to follow the substrate profile. Namely, when the graphene/PMMA film was transferred to the SiO2 nanopillar substrate, a 150 nm thick PMMA layer made it remain flat on the SiO2 nanopillars. However, the graphene layer started to sag as the PMMA layer was removed and the capillary action of the water and the van der Waals forces between the graphene layer and the nanopillars helped the graphene layer depress and follow the profile of nanopillars. The schematic illumination for this process is shown in **Figure 4(a)**. During the SiO2 nanopillar fabrication process, we intentionally left several unpatterned regions on the substrate to attach the graphene film tightly without strain after the transfer, which also can be used as unstrained reference regions in the following Raman spectroscopy study. **Figure 4(b)** is the 45°‐angled SEM image showing that the deformed graphene film was supported by numerous and periodic SiO2 nanopillars.

**Figure 1.** SiO2 nanopillar fabrication process with assistant of self‐assembled block copolymer. (a) original SiO2/Si sub‐ strate, (b) PS coated on substrate, (c) self‐assembled block copolymer coated on PS layer, (d)nanotemplate formed on substrate, (e) Cr evaporated on sample, (f) Cr nanodot on substrate after lift‐off, (g) SiO2 nanopillar formed after etch‐

**Figure 2.** (a) Self‐assembled block copolymer nanotemplate on SiO2/Si substrate, (b) Cr nanodots after lift‐off on SiO2/Si substrate, (c) obtained SiO2 nanopillars on SiO2/Si substrate, and (d) CVD grown monolayer graphene on Cu foil sub‐

The monolayer graphene that was transferred onto the array of SiO2 nanopillars was grown on a 25 μm thick 1″ × 1″ copper (Cu) foil by a chemical vapor deposition (CVD) [53, 54]. **Figure 2(d)** shows the SEM image of the grown monolayer graphene on Cu foil. A layer release‐ transfer method was employed to transfer the monolayer graphene film onto the pre‐pre‐

strate. From Ref. [52].

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pared SiO2 nanopillar substrate as shown in **Figure 3**.

ing with Cr nanodot mask, and (h) clean SiO2 nanopillar substrate after removing Cr nanodots.

**Figure 3.** Transfer process of CVD graphene to prepared SiO2 nanopillar substrate. (a) Graphene grown on Cu foil, (b) sample with back side graphene removed, (c)PMMA coated on graphen, (d) sample sunk in FeCl3 solution to remove Cu, (e) PMMA/graphene layer in DI water for clean, (f) PMMA/graphene layer picked up by prepared SiO2 nanopiller substrate, (g)Flat PMMA/graphene on top of SiO2 nanopiller substrate, and (h) deformed graphene on SiO2 nanopiller after removing PMMA.

**Figure 4.** (a) Schematic illumination of graphene deformation process and (b) deformed graphene sheet standing on top of SiO2 nanopillars.

A Horiba micro‐Raman spectrometer (resolution of 0.045 cm−1) with a 50× objective lens (a spot size of about 1 μm) and 18.5 mW of He‐Ne (633 nm) was used to investigate the strain on the transferred monolayer graphene. The graphene on both flat regions and the SiO2 nanopillars was examined at several different positions. From the Raman spectra as shown in **Figure 5(a)** and **(b)**, the intensity of the 2D band is about two times of that of the G band, which is corresponding to monolayer graphene Raman spectra [25, 54]. The graphene on the flat regions (no nanopillars) of the substrate without clear deformation was used as reference to study the strain on graphene. It is clear that there are substantial differences in the Raman spectrum G and 2D bands between the graphene on SiO2 nanopillars and on the flat region. In **Figure 5(a)** and **(b)**, compared to the flat graphene, there are downshifts in the G band (average shift, 7.8 cm−1) and 2D band (average shift, 16.3 cm−1) of graphene on nanopillars in the peak positions. The downshift of the G band and the 2D band is attributed to the local strain on graphene induced by SiO2 nanopillars.

**Figure 5.** Raman spectra of the (a) G peak downshift and (b) 2D peak downshift taken on the flat surface (red) and on the nanopillars (blue). From Ref. [52].

In the Raman spectra of graphene, the G band is related to the doubly degenerated E2g at the center of the Brillouin zone, while the 2D band is related to the momentum conservation of the scattering of two phonons with opposite waver vectors [26, 27]. The mechanical strain can influence the phonon variation in the crystal [3, 55]. The center‐zone phonon vibration change due to the strain is shown in the G band shift, and the change in the double‐resonance condition due to the strain, which affects the actual corresponding phonon, can be reflected by the 2D band in the Raman spectrum measurements. The local biaxial tensile strain induced by SiO2 nanopillar can explain the downshift happening to G and 2D bands.

The Raman shifts were qualitatively studied to discover the biaxial strain through the Grü‐ neisen parameter, which describes the vibrational effect on the crystal lattice property, by the following equation [24, 27, 55]:

$$\gamma = -\frac{1}{\alpha\_0} \frac{\delta \alpha}{\delta \varepsilon\_h} \tag{1}$$

where *ω0* is the Raman band frequency without strain, *δω* is the Raman band shift, *γ* is the Grüneisen parameter for the corresponding band, and *εh* is the hydrostatic strain on the graphene film. For biaxial strain, *εh* can be expressed as *εh* = *εt* + *εl* and *εt* = *εl* , in which *εt* and *εl* are the transversal and longitudinal components of the strain. From Eq. (1), based on previously reported Grüneisen parameters and the downshift characteristic bands collected from the test positions, the biaxial tensile strain *εl* = *εt* can be calculated to have an average value of 0.135 % from the G band and 0.117 % from the 2D band.

**Figure 4.** (a) Schematic illumination of graphene deformation process and (b) deformed graphene sheet standing on

A Horiba micro‐Raman spectrometer (resolution of 0.045 cm−1) with a 50× objective lens (a spot size of about 1 μm) and 18.5 mW of He‐Ne (633 nm) was used to investigate the strain on the transferred monolayer graphene. The graphene on both flat regions and the SiO2 nanopillars was examined at several different positions. From the Raman spectra as shown in **Figure 5(a)** and **(b)**, the intensity of the 2D band is about two times of that of the G band, which is corresponding to monolayer graphene Raman spectra [25, 54]. The graphene on the flat regions (no nanopillars) of the substrate without clear deformation was used as reference to study the strain on graphene. It is clear that there are substantial differences in the Raman spectrum G and 2D bands between the graphene on SiO2 nanopillars and on the flat region. In **Figure 5(a)** and **(b)**, compared to the flat graphene, there are downshifts in the G band (average shift, 7.8 cm−1) and 2D band (average shift, 16.3 cm−1) of graphene on nanopillars in the peak positions. The downshift of the G band and the 2D band is attributed to the local strain on

**Figure 5.** Raman spectra of the (a) G peak downshift and (b) 2D peak downshift taken on the flat surface (red) and on

top of SiO2 nanopillars.

128 Raman Spectroscopy and Applications

graphene induced by SiO2 nanopillars.

the nanopillars (blue). From Ref. [52].

**Figure 6.** (a) Morphology of the transferred graphene film on the SiO2 nanopillar substrate measured by AFM and (b) deformed graphene on four adjacent nanopillars (unit area). From Ref. [52].

In order to confirm the Raman spectroscopy defection results, the wavy morphology of the transferred graphene film on the SiO2 nanopillars substrate was carefully measured by the noncontact‐mode atomic force microscopy (AFM) over a 500 nm× 500 nm area as shown in **Figure 6**. It was clearly observed that the surface morphology of the transferred graphene film followed the SiO2 nanopillar profile. The inserted 2D graphene surface profile in **Figure 6(a)** was taken from two adjacent SiO2 nanopillars, which indicates how much the graphene layer was deformed. The peak‐to‐valley distances are found to have a range of about 0.5–5 nm. A subtle difference in the arrangement of the nanopillars and graphene sag condition creates a different degree of deformation on the graphene film. As described in the previous section, just after transfer, the graphene/PMMA film was kept flat, and the length of the graphene between two pillars was L, while once the PMMA was removed, the graphene began to sag to follow the nanopillar profile, and the length of graphene between two pillars was changed to L + ΔL (**Figure 6(b)**). Then, the mechanical strain on graphene can be calculated by the following equation: strain = ΔL/L [24]. Based on the AFM‐measured morphology of the graphene on the nanopillars, the local strain in the graphene can be extracted in the range from about 0.04 to 0.9 % with an average value about 0.17 % measured in a 1 μm2 area.

**Figure 7.** (a) A schematic illustration of strained graphene on top of a nanopillar. Simulated biaxial tensile strain on transferred graphene transferred by COMSOL Multiphysics; (b) with 0.5 nm; and (c) with 5 nm deformation toward. From Ref. [52].

**Figure 8.** Comparison of the strain extracted from AFM and calculated from Raman band shift.

Furthermore, a strain distribution on graphene based on the deformation values we measured from the AFM was simulated by COMSOL Multiphysics. As shown in **Figure 7(a)**, we used the actual dimensions, structure, and material parameters in the simulation model. For graphene, we used Young's modulus of 1 TPa [11] and Poisson's ratio of 0.3 [56]. We took the two extreme cases, the largest and the smallest deformations which were the 0.5 and 5 nm of the peak‐to‐valley distances. For the smallest graphene deformation, the maximum strain in the graphene near the top part of the nanopillar is about 0.3 %, and most of the region shows an average strain of about 0.07 % as shown in **Figure 7(b)**. On the other hand, for the largest graphene deformation, the minimum strain in the graphene near the top part of the nanopillar is as high as 3.5 %, and most of the region shows the average strain about 0.8 % as shown in **Figure 7(c)**. The simulated results confirm the analysis from the AFM measurement.

just after transfer, the graphene/PMMA film was kept flat, and the length of the graphene between two pillars was L, while once the PMMA was removed, the graphene began to sag to follow the nanopillar profile, and the length of graphene between two pillars was changed to L + ΔL (**Figure 6(b)**). Then, the mechanical strain on graphene can be calculated by the following equation: strain = ΔL/L [24]. Based on the AFM‐measured morphology of the graphene on the nanopillars, the local strain in the graphene can be extracted in the range from

**Figure 7.** (a) A schematic illustration of strained graphene on top of a nanopillar. Simulated biaxial tensile strain on transferred graphene transferred by COMSOL Multiphysics; (b) with 0.5 nm; and (c) with 5 nm deformation toward.

area.

about 0.04 to 0.9 % with an average value about 0.17 % measured in a 1 μm2

**Figure 8.** Comparison of the strain extracted from AFM and calculated from Raman band shift.

Furthermore, a strain distribution on graphene based on the deformation values we measured from the AFM was simulated by COMSOL Multiphysics. As shown in **Figure 7(a)**, we used the actual dimensions, structure, and material parameters in the simulation model. For graphene, we used Young's modulus of 1 TPa [11] and Poisson's ratio of 0.3 [56]. We took the two extreme cases, the largest and the smallest deformations which were the 0.5 and 5 nm of the peak‐to‐valley distances. For the smallest graphene deformation, the maximum strain in the graphene near the top part of the nanopillar is about 0.3 %, and most of the region shows an average strain of about 0.07 % as shown in **Figure 7(b)**. On the other hand, for the largest graphene deformation, the minimum strain in the graphene near the top part of the nanopillar

From Ref. [52].

130 Raman Spectroscopy and Applications

The Raman shift and strain conditions collected from Raman and AFM are shown in **Figure 8**. This biaxial strain value obtained from Raman spectroscopy detection matched to that obtained from accurate AFM measurement. This result demonstrates the accuracy and effectiveness for the Raman scattering technology to monitor the strain on graphene, even if the strain is induced by subtle nanostructures.
