Efficient strain modulation of 2D materials via polymer encapsulation

Strain engineering is a promising method to manipulate the electronic and optical properties of two-dimensional (2D) materials. However, with weak van der Waals interaction, severe slippage between 2D material and substrate could dominate the bending or stretching processes, leading to inefficiency strain transfer. To overcome this limitation, we report a simple strain engineering method by encapsulating the monolayer 2D material in the flexible PVA substrate through spin-coating approach. The strong interaction force between spin-coated PVA and 2D material ensures the mechanical strain can be effectively transferred with negligible slippage or decoupling. By applying uniaxial strain to monolayer MoS2, we observe a higher bandgap modulation up to ~300 meV and a highest modulation rate of ~136 meV/%, which is approximate two times improvement compared to previous results achieved. Moreover, this simple strategy could be well extended to other 2D materials such as WS2 or WSe2, leading to enhanced bandgap modulation.

, which is consistent with direct exfoliation of 2D materials on various pre-fabricated substrate (e.g., SiO2). We note applying AFM measurement on soft substrate (PVA in our case) tends to show low resolution due to the smaller Young's modulus, which will mask the true height information of the monolayer MoS2 (<1 nm), hence, we use multi-layer MoS2 (5-12 nm) samples for the AFM measurement, which won't impact the demonstration of structure difference between PVA encapsulated device and conventional exfoliated device.

Device failure mode and its mechanism
For our encapsulated devices, the strong interaction force and high modulation rate are achieved through the intimate contact and possible chemical bonds between 2D materials and the spin-coated PVA substrate. With increasing the applying strain value above a threshold value, these chemical bonds may eventually break, leading to the relaxation of strain for the 2D materials (with vdW contact towards the substrate) and the device failure, as schematically illustrated in the Supplementary Figure 5a-c. This process can be further confirmed using PL measurement. As shown in Supplementary   Figure 5d,e, the device shows linearly PL peak shift from 1.88 eV to 1.69 eV with strain from 0% to 1.49%. With further increasing the strain above 1.7%, the PL peak changes back to 1.81 eV, suggesting the strain relax and device failure.

Tape peeling test
Tape peeling test is a simple mechanical test method of the interaction force between a sample and a given substrate, by using typical tape. Here we use two commonly used

Effect of substrate Young's modulus on bandgap modulation.
To investigate the impact of substrate Young's modulus, we have measured the MoS2 devices exfoliated on different substrates using conventional direct-exfoliation method, as shown in Supplementary Figure 11a below. The device exfoliated on PDMS substrate shows much smaller modulation rate (7 meV/%) compared to device exfoliated on prefabricated PVA substrate (46 meV/%), suggesting the high EYoung is important to improve the strain transfer rate, which is consistent with previous report 1 .
Furthermore, we have also investigated the impact of the PVA molecular weight (MW) used for our spin-coating encapsulation method. We have spin-coated the PVA with lower molecular weight (MW) of ~31,000 g/mol (EYoung ~2.3 GPa) onto monolayer MoS2, and measured the strain modulation rate, as shown in Supplementary Figure 11b below. The device exhibits similar strain modulation rate (120 meV/%) compared to our measurement results using high molecular weight of 130,000 g/mol (EYoung ~10 GPa), which is consistent with our FE simulation in Supplementary Figure 10g

Thermal expansion experiment
During the thermal expansion experiment, both the PVA encapsulated samples (using CVD grown WSe2) and the conventional direct exfoliated samples (2D material on prefabricated PVA) are fabricated using previously described methods, as shown in the schematics in Supplementary Figure 12a using conventional exfoliation method (with weak vdW interaction). With increasing temperature to 120 °C , tensional strain ~2.32% is generated inside PVA due to thermal expansion, as calibrated by gold marker (golden solid dots). While the graphene flake expanded from 117.9 μm to 118.2 μm with a strain of 0.25%, suggesting an inefficiency strain transfer efficiency. b,d,f,h, Thermal expansion of 2D material (CVD WSe2) using our spin-coating method. With increasing temperature to 120 °C , the WSe2 flake expanded from 83.5 μm to 85.0 μm with a strain of 1.80%, similar as strain inside the PVA substrate (calibrated by golden cross marker) with a value of 1.82%, suggesting near unity transfer efficiency using our encapsulation approach. Data points and error bars represent the mean and standard deviation respectively for each sample.

Non-repeatable PL spectrums for traditional exfoliation method
In traditional exfoliation method with vdW interaction forces between 2D materials and substrate, the 2D materials would slip during the tensile deformation. Although the vdW force is not strong enough to prevent the slippage during the loading process, it is enough to provide little in-plane compression during releasing or unloading steps 2,3 , as schematically illustrated in Supplementary Figure 13a-c. Therefore, the PL peak position will normally blueshift a bit (due to the compression) compared to its initial state (Supplementary Figure 13a) and yields a non-reproducible strain cycle.