Giant elasto-optic response of gallium selenide on flexible mica

Introduction

Since the discovery of graphene, there has been a surge of research into two-dimensional (2D) van der Waals (vdW) crystals due to their fascinating properties and emerging phenomena. These include a strain-engineered electronic band structure of relevance for the manipulation of electronic and optical properties at the nanoscale^1,2,3. Strain engineering in traditional covalent semiconductors is generally limited by a poor macroscopic elasticity⁴. In contrast, the mechanical flexibility of 2D crystals offer unprecedented opportunities for strain engineering beyond traditional systems^5,6. In fact, a single vdW layer, or even several layers, can sustain a much larger mechanical strain than their bulk counterparts or covalent semiconductors.

Amongst 2D systems, group III-V monochalcogenides, such as GaSe, have emerged as promising semiconductors for strain engineering. GaSe has a relatively small Young’s modulus (E ≈ 82 GPa at T = 300 K)⁷, several orders of magnitude smaller than for graphene (≈1.05 TPa at T = 300 K)⁸ and many 2D vdW crystals⁹. Thus, less stress is needed in GaSe to create the same amount of strain than in many other materials. Also, as for many other 2D materials, such as graphene, 2D GaSe can sustain very large elastic strains. The breaking stress of 2D GaSe corresponds to a strain (compressive or tensile) larger than that for bulk GaSe^7,10: GaSe layers can withstand stresses of up to several GPa and a maximal strain of 5% before breaking, as probed by atomic force microscopy⁷. Furthermore, mechanical properties can be tuned by microstructuring, as required for applications in flexible devices¹¹.

The large mechanical flexibility of GaSe is paralleled by electronic properties that are well suited for modern electronics, such as high intrinsic carrier mobilities, non-linear optical response, efficient optical frequency conversion from the visible to the terahertz range, and absorption resonances in the UV for a broad range of applications spanning from integrated optics to imaging^{12,13,14,15,16,17}. Thus, the prospect of tuning the electronic properties of GaSe via mechanical deformation is of great interest to unveil the versatile functionalities of GaSe in flexible electronics^18,19. The strain-induced change in the band gap energy of GaSe has been predicted in the literature^20,21,22,23 and a red-shift of the photoluminescence (PL) emission of GaSe was measured under bending of bulk crystals²⁴. Also, research on strain engineered 2D GaSe has focussed on experimental studies of irreversible changes of electronic properties. For example, flakes of GaSe on polymer substrates, such as polyvinyl chloride (PVC), polyethylene terephthalate (PET) and poly-dimethylsiloxane (PDMS) can easily be bent, but the bending results in irreversible wrinkles and a non-uniform strain distribution^19,20,25. Thus, GaSe on these substrates would not be suitable for applications that require repeated, reversible changes of electronic properties.

In this work, we report on the reversible bending-dependent optical and vibrational properties of GaSe layers mechanically exfoliated onto a Muscovite mica [KAl₂(Si₃Al)O₁₀(OH)₂] substrate. An increasing value of the tensile uniaxial strain ϵ induces an energy red shift ΔE of the room temperature band edge PL emission, corresponding to a large strain coefficient ΔE/ϵ (~100 eV), larger than that reported for other 2D systems, such as transition metal dichalcogenides, TMDs (~10 eV²⁶. This is paralleled by an increase in the PL intensity. Furthermore, coupled electronic and vibrational states under strain-induced resonant excitation conditions act to enhance forbidden Raman modes.

Results

Gallium selenide bent on flexible mica

The primitive unit cell of ϵ-GaSe contains two layers, each consisting of four closely-packed, covalently bonded, monoatomic sheets in the sequence Se-Ga-Ga-Se along the c-axis, perpendicular to the layer plane. The primitive unit cell has an out-of-plane lattice parameter of c = 15.949 Å. Atoms form hexagons within the basal a–b plane with lattice parameter a = 3.755 Å, as illustrated in Fig. 1a (Methods). The in-plane pseudo-hexagonal crystal structure of Muscovite mica is shown in Fig. 1b. Mica has a monoclinic structure with lattice parameters of a = 5.19 Å, b = 9.00 Å, and c = 20.05 Å²⁷. Flakes of GaSe were mechanically exfoliated using adhesive tape and transferred onto the mica substrate. The mechanical exfoliation of bulk GaSe produces small (micron) area flakes with different layer thicknesses. We carried out the experiments on several flakes of similar thickness (~10’s nm-thick, corresponding to ~10’s vdW layers), all revealing a common large reversible elasto-optic response.

Giant elasto-optic response of gallium selenide on flexible mica — **Fig. 1: Gallium selenide bent on flexible mica.**

Muscovite mica is a highly flexible, transparent, and atomically smooth material that is readily available and widely used in the electronic industry due to its dielectric strength and thermal endurance. In addition, mica has a Young’s modulus of E ≈ 190 GPa at T = 300 K²⁸, which is comparable to that of GaSe. This makes mica a good choice for strain studies of GaSe as the experiments rely on the coupled deformation of the flexible substrate and vdW crystal, as well as the transfer of strain from the substrate onto GaSe. This avoids the formation of permanent wrinkles of the flakes, which can occur when using other substrates, such as PVC or PET¹⁹. Since one surface of the bent mica is in compression and the other in tension, the GaSe layers are subject to a uniform, uniaxial (perpendicular to the axis of bending) strain ϵ = t/2r, where t is the mica layer thickness and r is the radius of curvature of the bent mica (Fig. 1c, d)^25,29. Repeated experiments were conducted to assess the reversibility of the measured effects under the bending of GaSe on mica.

Figure 1c, d shows the set up used for our two-point bending experiments. Once the deformation is applied to the sample, set screws are used to fix the sample holder in place and preserve the deformations in the sample for the Raman and PL measurements using an optical confocal microscope system (see Methods).

Raman spectroscopy of GaSe under bending

Figure 2a shows the Raman spectra of a GaSe/mica sample for different bending radii, from r = ∞ to r = 4 cm, corresponding to a maximum strain of up to ϵ = t/2r = 0.04% (t = 0.03 mm and r = 4 cm). Here, the smallest radius of curvature is restricted by the breaking point of mica. The spectra are normalised to the main vibrational mode of mica, which is centred at 256 cm⁻¹. The Raman experiment was conducted using a He-Ne laser with wavelength λ = 633 nm, corresponding to a stronger Raman scattering efficiency as the laser energy (hv = 1.96 eV) is close to the exciton PL energy. Each Raman spectrum shows three main peaks at A’₁(1) = 133 cm⁻¹, E” = 212 cm⁻¹, and A’₁(2) = 307 cm⁻¹, which we assign to the Raman active (in-plane and out-of-plane) modes of GaSe³⁰. The position of each mode is not affected over the entire range of applied strain (ϵ < 0.1%). However, the Raman spectra also indicate a significant and consistent increase in the intensity of a Raman mode centred at about 245 cm⁻¹, which we assign to the forbidden A”₂ mode³¹. Figure 2b shows the dependence of the intensity of this mode, ({I}_{{A}^{{primeprime} }}), normalised to that of the mica mode, I_mica, versus the applied strain ϵ, as estimated from ϵ = t/2r. This dependence is well described by ({I}_{{A}^{{primeprime} }}/{I}_{mica}=sepsilon) with a constant s ≈ 2 × 10³. We note that the intensity of this mode is returned to the original value when the sample is returned to the initial unbent state.

**Fig. 2: Raman spectroscopy of GaSe bent on mica.**

Different phenomena can account for the enhancement of a Raman mode: (i) an increased Raman scattering under resonant laser excitation conditions^30,31; (ii) the change in the orientation of the laser beam relative to the bent crystal³²; and (iii) defect-related effects³². We exclude that the orientation of the crystal relative to the laser beam has any significant effect on the measured spectra. Under excitation with light polarized along the c-axis of the crystal, a Raman mode can become more or less visible under bending since the electric field of the incident light is no longer perpendicular to the c-axis. However, except for the A”₂ mode, none of the Raman-active modes are influenced by the bending of the layers. Also, we exclude defect-related effects, as those reported in previous studies of GaSe showing that specific vibrational modes can be enhanced in defected GaSe³². Defects in GaSe can arise from stacking faults and areas of high topological variations, causing an enhancement of forbidden Raman modes due to the breaking of Raman selection rules. To avoid these effects, in our experiments we focused on uniform areas and avoided regions with visible wrinkles as a result of exfoliation. Also, we carefully checked the reproducibility and reversibility of the strain-induced effect. In contrast, we note that for unbent GaSe, the intensity of a Raman mode can be enhanced as the photon energy of the laser source approaches the band gap energy of GaSe³⁰. Of particular interest is the resonant behavior of the Raman mode A”₂, which is normally Raman inactive, but can be seen under resonant excitation³¹. In our experiment on bent GaSe, the bending induces a systematic red-shift of the PL emission (Fig. 3), bringing the band edge exciton energy closer to the laser excitation energy (hv= 1.96 eV). Thus, a resonance Raman scattering effect can be achieved by strain in bent GaSe.

**Fig. 3: Photoluminescence spectroscopy of GaSe bent on mica.**

Photoluminescence spectroscopy of GaSe under bending

Figure 3 illustrates the PL spectra of a representative GaSe/mica sample under tensile strain. Under the applied tensile strain, the PL emission red-shifts and its energy peak position shifts by up to ΔE = 34 ± 1 meV for an applied nominal strain of ϵ = 0.029 ± 0.005%. Figure 4 shows the value of ΔE as a function of strain for several GaSe flakes. There is a consistent decrease in the PL peak energy under increasing strain across all GaSe/mica samples. Although the GaSe samples are of different thicknesses, they are all bulky (~10’s vdW layers) flakes for which quantum confinement effects can be neglected. From the data of ΔE at different ϵ in Fig. 4, we derive the strain coefficient ΔE/ϵ (e.g., slope of the PL shift versus strain). This varies across different flakes in the range 46–137 eV and is larger than the typical values reported in previous experimental studies of GaSe (e.g., ΔE/ϵ ≈ 6–10 eV)^19,24. The variability in ΔE/ϵ across different experiments in the literature can arise partly from differences in the effective strain-transfer between the flakes and the supporting substrate. For example, previous experiments used relatively thick GaSe flakes (thickness t = 30 μm) and an intermediate adhesive layer between the flakes and the mica²⁴. A greater GaSe layer thickness has the effect of decreasing the induced strain transferred through the flake, reducing the energy shift³³. The similarity in Young’s moduli of mica and GaSe implies a more efficient strain-transfer in GaSe compared to that achieved using a PET substrate or an intermediate adhesive^24,34. This is further supported experimentally by the absence of any wrinkling of our GaSe layers after the removal of strain. We note that although the thickness of our flakes is smaller than that considered in the literature²⁴, thickness-induced effects on the energy shift are expected to be generally small²⁰. Furthermore, the PL intensity of GaSe has previously been reported to increase²⁴ or decrease under strain¹⁹. In this study, the PL intensity tends to increase with increasing strain (Fig. 3). However, we also note that the change in intensity can be partially affected by the focusing conditions of the laser beam onto the bent flakes.

Discussion

To account for our observations, we note that an applied strain tends to break the hexagonal crystal symmetry of GaSe, hardening/softening, shifting and broadening the vibrational modes¹⁰. The effect on the vibrational modes is dependent on the direction and type of strain induced. The method of using a bending rig to induce an in-plane uniaxial tensile strain is expected to have the effect of broadening all the in-plane vibrational modes and softening parallel vibrations¹⁰. However, for the strain values produced with our bending rig of up to ϵ ≈ 0.04%, the strain induced changes of the vibrational modes of GaSe calculated theoretically should not be measurable¹⁰. In line with our Raman studies, no splitting or shifting of the vibrational modes could be observed (Fig. 2). In our studies, the maximum induced strain on our samples is significantly smaller than the minimum value of strain at which a shift of the Raman modes was previously observed¹⁹ or predicted¹⁰. On the other hand, our measured energy shift of the PL emission, ΔE, is larger than that predicted by theoretical models in the literature (Fig. 4). The values of the calculated strain coefficient ΔE/ϵ from the literature are generally within the range ΔE/ϵ ≈ 9–20 eV^19,20,21,23. This accounts for changes in the hybridization of the Ga and Se orbitals under strain, which modify the band structure and band gap energy. In these models, the strain coefficient is weakly dependent on the layer thickness. Thus, the larger energy shifts measured in the PL experiment and their variation across different flakes suggest that additional effects should be considered.

We note that the broadening and energy peak position of the PL emission vary amongst flakes. This may be caused by slightly different layer thicknesses and non-uniform strain transfer across different flakes. Also, the PL emission is red-shifted relative to the free exciton absorption energy (E_ex > 2 eV at T = 300 K)³⁵. For excitons that are in thermal quasi-equilibrium, the Stokes shift between absorption and emission is related to the degree of carrier thermalization, which depends on the carrier temperature, indirect and direct exciton absorption, and inhomogeneous broadening³⁶. The high-energy side of the exciton distribution function tends to be depressed in the PL spectrum, resulting in a Stokes shift. The strain coefficient measured in the PL experiment is larger than that calculated for the direct band gap energy of GaSe (Fig. 4), suggesting a strain-induced enhancement of the exciton thermalization. The applied strain, in similar fashion as the temperature, can modify the occupation of the exciton states and their contribution to the PL emission. For example, excitons can be localized due to local deformations of the GaSe crystal³⁷. As reported in transition metal dichalcogenides (TMDs), strain can bring defect-related exciton states into resonance with extended states, thus changing their relative contribution to the optical emission³⁸. In particular, in TMDs a tensile strain reduces the PL intensity due to a direct-to-indirect transition of the character of the optical band gap²⁶. In contrast, in GaSe, the tensile strain increases the PL intensity, suggesting an enhancement of the direct exciton recombination whose energy is within a few tens meV from that of the indirect exciton³⁹. The investigation of the effects of strain on the carrier relaxation requires complementary spectroscopy techniques, such as time-resolved PL to study dynamic processes under strain. Also, PL spectroscopy for a range of wavelengths of the laser excitation (PL-excitation, PLE) can help to identify the presence, nature and energy of different excitonic states. Finally, a strain-induced gauge field may also lead to an indirect-to-direct bandgap transition in the vicinity of the minimum energy gap (center of the Brillouin zone for unstrained GaSe). The significance of strain-induced pseudo-gauge fields have been previously discussed in TMDs and graphene, but their effects in GaSe remain unexplored⁴⁰. Thus, we conclude that both intrinsic and extrinsic effects contribute to the strong sensitivity of the PL emission of GaSe to bending, leading to a PL enhancement and a large strain coefficient.

In conclusion, we have investigated the optical, electronic and vibrational properties of GaSe under tensile strain. The flexible mica substrate provides a suitable platform for repeatable bending-induced tensile strain in GaSe. The strain causes an increase of the A”₂ mode, as measured by Raman spectroscopy. This arises from coupling between electronic and vibrational states under strain-induced resonant excitation conditions, as confirmed by the strain-induced shift of the band edge photoluminescence emission. Small applied strains of 0.03% can increase the PL intensity and cause a red-shift of the PL emission by up to 34 meV, corresponding to the largest measured strain coefficient seen in the literature to date. This is partially assigned to the high transfer strain efficiency between mica and GaSe and a strain-induced enhancement of the exciton thermalization. The large modulation and reversibility in the electronic and optical properties of GaSe under strain, via bending, demonstrates that GaSe is a suitable material for strain-dependent optoelectronic devices. Mechanical exfoliation can cause large-scale inhomogeneity in the optical properties of the vdW crystal⁴¹ and produces only small GaSe flakes impractical for future applications. To overcome the limitation of mechanical exfoliation, advanced manufacturing technologies are needed, such as epitaxy of GaSe on mica, which would be possible in light of the compatibility of mica with growth at high temperatures and ultra high vacuum. Epitaxial growth of GaSe directly onto mica would facilitate the development of high-purity, homogeneous crystals⁴² and higher strain-transfer efficiencies between the substrate and thin layers^24,43.

Methods

Materials

Flakes of GaSe were prepared from bulk Bridgman-grown hexagonal ϵ-GaSe crystals⁴⁴. The mica samples were purchased from different suppliers (e.g., Agar scientific, LabTech, and NanoandMore) and compared to identify high-quality mica substrates for the experiment, i.e., mica with surfaces without cracks, as probed by optical microscopy. LabTech provided the highest-quality samples. The mica substrate was cleaved to remove the outermost layers and reduce its thickness to approximately tens of micrometers for improved bending.

Techniques

The set-up in Fig. 1c, d was used for our two-point bending experiments. In this bespoke set-up, an Arduino and an a4988 stepper motor driver drive two carriages. These are used to support a moveable sample holder and to apply controlled deformations to the GaSe-mica samples. The sample holder consists of two brass pieces mounted on stainless steel guide rails, which allows free movement of the sample holder. The samples are mounted to the brass pieces using screw clamps. The brass pieces can be pushed together using the stepper motor, which causes the sample to bend. Once the deformation is applied, set screws are used to fix the sample holder in place and preserve the deformations in the sample. The sample holder can then be removed from the carriages so that the Raman and PL measurements can be performed.

The optical studies were carried out using a Horiba Jobin Yvon LABRAM optical confocal microscope system. The experimental setup comprises of a He-Ne (λ = 633 nm) laser and a frequency-doubled Nd:YVO₄ (λ = 532 nm) laser, an x-y-z motorized stage and an optical confocal microscope system equipped with a 0.5 m-long monochromator and two gratings (1200 grooves/mm and 150 grooves/mm). The signal is detected by a Si-charge-coupled device camera. The laser beam is focused onto the sample down to a spot diameter of ~1 μm using a 100 × objective. Since laser irradiation can induce heating and degradation of surfaces due to thermal oxidation, we have conducted preliminary studies to identify levels of laser powers that are safe to use (P up to 5 Wm⁻²), i.e., they do not cause a temporal change in the PL and/or Raman signal due to heating and/or degradation.