Tunable biaxial strain device for low-dimensional materials

Strain engineering is one of the key strategies to boost the performance of the latest generation transistors.¹ Beyond performance, tunable properties are paramount to functional electronic devices. In this context, strain is becoming increasingly fashionable to tune the optical and electronic properties of contemporary materials and devices. Strain is of particular interest in low-dimensional materials, starting with graphene² and transition metal dichalcogenides (TMDs).^3,4 The ability to exfoliate these materials into single unit-cell thin crystals and their controlled stacking promote an entirely new approach to material synthesis and functional device assembly.^5,6 Their stretchability makes them particularly susceptible to tune their optical and electromagnetic properties by means of controlled strain.

Strain can be directly embedded into the material or device during its synthesis through an appropriate choice of growth conditions or by combining lattice mismatched materials.^7,8 However, this approach only offers a limited number of possibilities and does not enable any post-fabrication adjustments of the strain. To this end, a number of mechanical devices have been developed to apply tunable strain. They include mounting the sample between movable anvils^9–11 and mounting it on a bending^12–14 or stretching¹⁵ beam or directly onto a piezoelectric crystal.⁷ 

We present a device to apply tunable biaxial strain in a confined space by the controlled bending of a thin substrate. The bending force is applied by means of a pusher actuated by a screw. Our device features two innovations: we introduce a four-points pusher (Fig. 2) that yields a larger region of uniform biaxial strain at the center of the substrate than the single point pushers commonly found in the literature. However, the strain induced at the center of a simple cruciform substrate is smaller with the four-points pusher than with a single point one for the same displacement. To compensate for this reduction, we designed a more elaborate substrate shape where, instead of a simple cruciform shape consisting of two orthogonally intersecting rectangular beams, the inner corners of a standard cross are reinforced with four large radius profiles.

We use a nitinol substrate, a superelastic alloy made of 50% nickel and 50% titanium. Other elastic substrates can be used, although with a reduced range of elastic deformations, hence less applied strain. In order to achieve a 1 nm peak-to-peak roughness compatible with the exfoliation of 2D crystals, we spin-coat a lift-off resist (LOR-10A from micro-resist technology GmbH) onto the nitinol substrate. The material to be strained is either transferred^16,17 or directly exfoliated onto the LOR (Fig. 1). For scanning tunneling microscopy applications, a 2 nm titanium buffer layer and a 5 nm thin gold film are evaporated onto the LOR prior to transferring the exfoliated van der Waals crystals for the purpose of electrically connecting them.

When straining van der Waals materials, we noted that the interlayer forces were often too weak to transfer the strain from the bent substrate to the top layer of thick crystals, resulting in a constant Raman signal despite increasing the applied stress. In order to avoid layer slippage and subsequent strain relaxation, the crystals must be firmly clamped down. For the Raman spectroscopy measurements discussed below, the 2H–MoS₂ crystals were encapsulated in a thin polymer (PMMA) layer, safely preventing any layer slippage.^18,19 For scanning probe applications, the polymer layer is replaced by two thin Au/Ti strips (≈30 nm thick)²⁰ evaporated in situ at a base pressure of 10⁻⁸ mbar over two opposite edges of the crystal through a shadow mask.

The strain in our device is generated by the controlled bending of a 300 μm thick nitinol substrate (Fig. 2). The bending force is applied by means of a pusher actuated by a screw. The substrate is held in place by pressing it against the four arms with the pusher. All the parts of the device are made of steel, including the 2 mm diameter balls from ball-bearings at the top of the pusher. The response of the strain device is checked using commercial metal strip gauges,^21,22 which measure the strain applied along a specific direction from a change in the strip resistance. However, the size of such gauges is too large to capture the small isotropic strain region at the center of our device. The local strain response is obtained by measuring the actual strain applied to the van der Waals material, which we infer from changes in characteristic Raman modes of 2H–MoS₂.^20,23

We start by studying the Raman response of 2H–MoS₂ to uniaxial tensile strain [Fig. 3(a)] applied using a standard device based on the bending of a simple rectangular beam.^20,24 With the increasing tensile strain, the out-of-plane A_1g mode remains unchanged at 407 cm⁻¹ and the in-plane E_2g mode splits into $E2g−$ and $E2g+$ modes. While the split $E2g+$ mode stays at around 382.3 cm⁻¹, there is a clear red shift of the $E2g−$ mode at a rate of about 3.5 cm⁻¹/%, in range with previous findings.^20,24,25 Upon fully relaxing the strain, the initial unstrained Raman spectrum is recovered, demonstrating the reversibility of the applied strain, at least up to 1.6%. Fitting the Raman modes to Lorentzians, we can follow the positions of the modes as a function of strain, as shown in Fig. 3(b).

Next, we measure the Raman response of 2H–MoS₂ under uniform biaxial tensile strain applied with the new device depicted in Fig. 2(a). The corresponding Raman spectra presented in Fig. 3(c) are distinctively different from the Raman response to uniaxial strain discussed above. Both the A_1g and E_2g Raman modes are red shifted with increasing tensile strain, without any splitting of the E_2g mode. Contrary to the uniaxial configuration, uniform biaxial tensile strain preserves the in-plane symmetry of the crystal and therefore the degeneracy of the E_2g mode. The in-plane mode is more sensitive to strain than the out-of-plane mode. Indeed, from 0% to 1.1% strain, the E_2g peak shifts by 4.7 cm⁻¹ from 381.8 to 377.1 cm⁻¹, while the A_1g mode shifts by 1.4 cm⁻¹ from 406.9 to 405.5 cm⁻¹ [Fig. 3(d)]. This 70% difference is a direct consequence of a more important in-plane than out-of-plane deformation under in-plane tensile stress. Upon relaxing the strain, the Raman modes recover their unstrained positions. The close overlap of the peak positions measured as a function of increasing and decreasing strain in Fig. 3(d) illustrates the absence of any significant hysteresis and good reversibility of the applied strain below 1.1%. Additional strain cycles give the same results within 0.5% accuracy.

Numerous devices enabling the application of reproducible uniaxial strain have been described in the literature.^20,24,25 The observed splitting of the in-plane Raman mode in Figs. 3(a) and 3(b) reflects the anisotropic lattice distortion due to the stress applied along one direction only, which lifts their degeneracy.

Applying controlled and uniform biaxial strain is significantly more challenging than applying uniaxial strain. We found both the shape of the bending plate and the shape of the pusher to be critical in achieving the sizable and uniform biaxial in-plane strain demonstrated in Figs. 3(c) and 3(d). Using a simple cruciform nitinol substrate allows us to induce only limited strain at the center of the cross. This is because the central square where the sample is mounted is too rigid to be significantly strained by the four rectangular arms of such a cross. The more elaborate shape shown in Fig. 2(d), where the sharp inner corners of the simple cross are reinforced with quarter circle profiles, overcomes this limitation and allows for the sizable uniform deformation of the central region (up to 2.4% demonstrated so far).

The other key feature of our device is the pusher used to deform the substrate. We designed the four-points pusher because a simpler design using a single point pusher [Fig. 2(c)] did not allow us to obtain uniform biaxial strain in a systematic manner. Typical Raman spectra obtained in this configuration are shown in Figs. 3(e) and 3(f). Both the A_1g and E_2g Raman modes shift to higher frequencies as expected for biaxial strain. However, the in-plane E_2g mode splits into $E2g−$ and $E2g+$ modes with the increasing strain, indicating non-uniform in-plane stresses. The magnitude of this non-uniform applied strain can be quantified based on the shift and splitting of the Raman peaks, which depend approximately linearly on the applied strain.^13,27 At the maximum applied deformation of 3.5 turns, A_1g and the average of the split E_2g peaks in Fig. 3(e) shift by about 2.2 times the shifts observed with an applied isotropic strain of 1.1% in Fig. 3(c). Thus, we estimate that 3.5 turns in Fig. 3(f) correspond to an applied strain of 2.2 × 1.1% = 2.4%. The anisotropy of the applied strain can be estimated by comparing the E_2g peak splitting in Fig. 3(e) with the splitting measured under uniaxial strain. The splitting is about the same at 1.6% strain in Fig. 3(a) and at 3.5 turns in Fig. 3(e), which corresponds to a spurious uniaxial component of about 2/3 of the biaxial component in the single point device that is not observed in the four-points device.

The better performance of the four-points pusher, which allows us to obtain more systematically homogeneous biaxial strain than the single point pusher, can be understood and quantified using finite element analysis. The general setup configurations for the two different pushers are shown in Figs. 4(a) and 4(b). Zooming into the 1.4 × 1.4 mm² central region of the nitinol substrate shows a much wider region with uniform in-plane strain with the four-points pusher [Fig. 4(c)] than with the single point pusher [Fig. 4(d)]. The color scale in these two panels represents the relative strain difference between the orthogonal directions (ϵ_xx − ϵ_yy)/ϵ_xx(0), where ϵ_xx(0) = ϵ_yy(0) is the strain at the center of the substrate. A direct consequence is that the precise positioning of the crystal to apply uniform biaxial strain is much less critical with the four-points pusher.

We have demonstrated a unique device capable of applying a uniform in-plane biaxial strain in excess of 1.1% to low-dimensional single crystals and small devices. Key design features to achieve such uniform strain in a small device are the shapes of the bending substrate and pusher. The device is also capable of generating non-uniform biaxial strain, although the calibration of the strain along the two orthogonal directions remains an open issue. The device is magnetic field, low temperature and ultra-high vacuum compatible. It can be scaled to fit onto standard sample holders, making it compatible with existing experimental setups, including local probes and angular resolved photoemission. The nitinol plates are capable of sustaining even larger strain than 2.4% applied here before plastic deformations start to set in. The limiting factors are the onset of a hysteretic response and the finite range of the in situ actuated pusher in our setup.

This work was supported by the Swiss National Science Foundation (Division II Grant No. 182652).

The authors have no conflicts to disclose.

Vincent Pasquier: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Alessandro Scarfato: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Jose Martinez-Castro: Investigation (equal); Methodology (equal); Validation (equal). Antoine Guipet: Resources (equal). Christoph Renner: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this are openly available in Yareta repository at https://doi.org/10.26037/yareta:l7rgbesfffacfdyeamggm6snva.²⁸