IMPOSING BIAXIAL STRAIN ON 2D LAYERED MATERIALS BY LIQUID-INDUCED SWELLING OF SUPPORTING POLYMER

2D layered materials promise to revolutionize the field of electronics, photonics, optoelectronics, energy storage, and sensing, etc. 2D materials have exceptional mechanical properties, with critical elongation >10%. Employing the strain to manipulate the electronic structure of these 2D materials could lead to further improvement of their implementation in many aspects. The ease of manipulation of their electronic structure can be one of the critical factors for their utilization in photonic devices. Apart from the strain, which decreases (increases) the bandgap energy at the rate of ~100 meV under 1% of biaxial tension (compression), also the layer number causes bandgap energy change of, e.g., 0.5 eV between bulk (1.3 eV) and monolayer MoS 2 (1.8 eV). In our work, we focus on using the swelling behavior of PMMA/SU8 polymer in methanol to impose the strain on 2D layered materials. In the first trials, we have shown that it is possible to reach a strain gradient from 0 to ~0.5% of biaxial strain via simple swelling of polymer substrates, both for graphene [1] and transition metal di-chalcogenides (TMDC) like MoS 2 . Raman spectroscopy was used to probe the lattice strain in the materials through measuring changes of vibrational frequencies, and photoluminescence was used to probe the strain-induced bandgap character and energy in TMDC at room temperature. The surface corrugation of the 2D material after the soaking was recorded with the help of atomic force microscope (AFM).


INTRODUCTION
Most of the material's physical properties can be tuned via strain engineering by mechanically modifying its structure. Two-dimensional nanomaterials' unique mechanical properties are particularly promising candidates for strain engineering and related applications because they can withstand considerable strain before structural failure. The atomically thin monolayer graphene exhibits unique chemical and electronic properties. The strain in graphene can change its electronic structure, chemical potential, or induce pseudo magnetic gauge fields. Other than graphene, strain engineering offers great potential to control and modify the optoelectronic structure of transition metal dichalcogenides [1][2][3].
The fast-growing field of flexible devices requires more fundamental research to keep the material science to help the future application. For example, the recent growth of graphene usage in the near field communication (NFC) tags and antennae is the perfect illustration. However, the 2D materials often exhibit a change in their fundamental electrical, optical, and structural properties, requiring further studies and classifications based on their modulation in a real situation under strain/stress. The in-plane stress imposed on a 2D material can be either purely planar or can be manifested by out-of-plane buckling. The buckling patterns can have periodical tensile and compressive strains across the 2D material. Externally imposed deformation such as pressure-induced, tip-induced, blister formation, or substrate bending are the preferential methods in the case of 2D materials [4,5].
A polymer substrate swelled with diffusing fluids can also impose strain on the material. In the present work, we show polymethylmethacrylate (PMMA) swelled by methanol [6][7][8] inducing large deformation in selected 2D material resting on top of it. The strain-dependent change in electronic band structure were detected through the respective characteristic peak shifts in the Raman and photoluminescence spectra (PL) graphene and TMDC flakes [9,10].

EXPERIMENTAL METHODS
Polymethylmethacrylate (PMMA) slabs were coated with ~500nm thick SU8 2000.5 (MicroChem) negative photoresist. The SU8-covered PMMA substrates were annealed at 60°C for 5 minutes to evaporate the solvent present in the SU8. Graphene and MoS2 flakes were mechanically cleaved using scotch tape and directly exfoliated on the SU8-coated PMMA substrates. The exfoliated samples were prebaked at 65°C for 30 minutes to get a conformal adhesion with the SU8 surface on the PMMA slab. The exfoliated graphene and MoS2 sample thickness were identified using optical contrast measurement in an optical microscope. Raman and PL spectroscopy were used to quantify the evolution of the biaxial strain in graphene and MoS2.

Figure 1. Schematic representation of the experiment
The biaxial strain was imposed on the 2D materials (graphene or MoS2) by soaking in methanol in repeated ten-minute intervals [11][12][13]. After every soaking period (10 minutes), the samples were dried in air at room temperature before doing the Raman or PL spectral mapping. Figure 1 represents the experimental scheme. For the graphene samples, the Raman spectral mapping, and for the MoS2 sample, both Raman and PL spectral mapping were performed with LabRAM HR (Horiba). The Raman spectra were measured using a 633nm laser excitation, and PL was measured using 532nm laser excitation, both with 600 l/mm grating. Both Raman and PL maps were recorded with a 2-micrometer (µm) step size. The atomic force microscopy (AFM) images were obtained with the Dimension Icon microscope (Bruker).

RESULTS AND DISCUSSION
Topographically two different graphene samples, named G1 and G2, were considered for the initial swelling experiment. The swollen SU8 imposed strain on the graphene samples, which can be quantified using the insitu Raman spectroscopy, showing a phonon softening (blue shift) of the characteristic Raman peaks [14] [15]. The Raman 2D band, with frequency ω2D ~2680cm -1 , was used to quantify the strain in the graphene samples instead of the G band ωG ~1580cm -1 , because the 2D band is much more sensitive than the G band to biaxial strain effects [10,16,17]. The AFM topography (Figure 1e) shows a large flake with a high level of structural uniformity. The color-coded ω2D map in Figure 1 a-e shows the evolution of the imposed strain for the soaking intervals of 10 minutes. The localized tensile strain in the graphene flake's center region received the maximum interfacial stress transfer from the polymer swelling (to ~2510 cm -1 , corresponding to 0.5 % of biaxial strain) after 40 minutes of soaking time. After that, the stress transfer between the polymer and graphene G1 failed. show the Raman 2D band shift for different soaking times, in G1, and G2, respectively. (f), (l) the AFM topography images of G1 and G2, respectively, before soaking.
In the same fashion, the topography of sample G2 was recorded before the soaking experiment. Sample G2 has more cracks, which separate the graphene into fragments of lateral dimension between 1-3 µm. Figure 1 g-k shows the color-coded Raman spectral maps of the 2D peak for the time intervals of 10 minutes. The imposed strain is not homogenous across the sample. The interfacial stress is very low in the small graphene domains, which results in the small and random strain in the sample G2. Although SU8 and graphene have an excellent interfacial stress transfer, the graphene grain boundaries restrict reaching such high strain levels as in the sample G1. The ω2D and soaking time correlation plot, Figure 2, statistically compares the results from the two samples. Figure 2 proves that smaller strain was imposed on the sample G2 compared to the sample G1. The median of the ω2D shift reached in sample G1 corresponded to ~0.5%, and the maximum to more than 1% [18,19].
In the sample G2, less than 0.1% strain was achieved by the swelling experiment, evidencing the vital role of the grain boundaries present in an otherwise continuous flake. This because of the interfacial stress transfer failure at the edges of the graphene domains, i.e. boundaries [20]. The high stress-transfer in the sample G1 took place due to the absence of such boundaries. With the increasing soaking time, the extending size of the error bars in Figure 2 for both G1 and G2 samples confirms the evolution of a strain gradient across the flakes. This evolution of the strain with the soaking time is evident as is the continuous strain gradient in the achieved biaxial strain on these atomically thin graphene layers [15,21].
We employ the same swelling technique to impose the biaxial strain on another 2D material, namely monolayer MoS2. Since the MoS2 has a different Raman signature than graphene, we considered the frequencies of the in-plane vibrational peak (E' or E2g) at 386cm -1 and the out-of-plane vibrational peak (A1') at 406 cm -1 to quantify the strain evolution in MoS2. Besides the Raman modes, we employed the PL signal of the A exciton at ~1.88eV. The PL redshift as well as the Raman peaks' blue shift correspond to the tensile strain in the MoS2 sample [22,23].
The color-coded maps in Figure 3 a-c show the PL map of the MoS2 flake as a response to the soaking times.
To simplify the analysis, we treated both the A neutral exciton and trion as a single PL peak. Figure 3 d-f and g-i show the E' and A1' peak shifts, respectively, as a result of the different soaking times [9]. As expected, the shift of the E' peak is larger than the shift of the A1' peak for the given soaking time, due to the in-plane character of the E' mode and thus an increased sensitivity to an in-plane deformation. The stress transfer from the polymer to the MoS2 flake failed after 20 minutes of soaking due to small size of the MoS2 flake. Due to a relatively smaller strain-sensitivity of either of the Raman modes to small strains, PL A exciton peak was considered to quantify the imposed strain on the MoS2 flake. Approximately maximum of 0.6% of biaxial strain was imposed on the center of the MoS2 flake after 20 minutes of soaking time [23]. According to the Raman shifts, a potential change in charge-transfer doping during the experiment was negligible, as the ratio of the E' and A1' shifts corresponds to a pure effect of strain [24,25]. The profile across the color-coded PL spectral map in Figure 4 shows the redshift in PL at different soaking times localized at the centre of the continuous MoS2 flake where the highest strain was achieved. The profile extracted from Figure 4 c (i.e. Figure 4 f) shows the PL energy gradient forming a potential energy funnel imposed by the biaxial strain. Such an energy funneling, if even higher strain could be achieved as maxima, could be used in applications to power future devices [26][27][28][29].

CONCLUSION
We evidence that biaxial strain can be imposed on atomically thin monolayers of graphene and MoS2 using the swelling of their polymer substrates by methanol. The Raman spectral shift of the 2D band was used to quantify the strain evolution in graphene, while in the case of MoS2 also photoluminescence was employed.
The stress transfer failed after 40 minutes of soaking time for graphene and after 20 minutes of soaking time for MoS2. The different soaking time is due to the different sizes of the flakes or domains within. The large flake size can bear the more considerable biaxial deformation in the swelling experiment. The smaller flake size or more abundant sample boundaries fail to transfer the strain at an earlier soaking time. In both graphene and MoS2, the biaxial strain is tensile corresponding to the volume swelling of the substrate. Hence, the MoS2 band gap energy was decreased as the effect of the imposed biaxial strain, and the median strain level achieved was 0.5% in both graphene and MoS2.