Most transition metal disulfides MX₂ (M = Mo, W, Ta, Re; X = S, Se, Te) are semiconductors with outstanding performance and have been widely investigated and applied. Two-dimensional MX₂ has the similar intra-layer honeycomb lattice as graphene and the van der Waals interaction is responsible for the weak interlayer coupling. This allows one to obtain few-layer MX₂ flakes by mechanical exfoliation from bulk crystals just like graphene. Compared to pristine graphene with zero energy gap, MX₂ has a gap of 1–2 eV, which is a large advantage for applications.^[1–3] Furthermore, its higher mobility^[4] is particularly essential to semiconducting devices such as logical devices,^[3,5] sensors,^[6] photo-diodes,^[7] and photo-detectors.^[8] The unique valley polarization revealed in MX₂ provides us with a new degree of freedom for device design.^[3,9–13]

External strain is a conventional and convenient way to tune energy gap and lattice vibrations in low-dimensional semiconductors. The subtle changes induced by strain can be easily probed by the micro-Raman technique. In fact, the strain-modulated effects have been extensively investigated in graphene^[14,15] and MoS₂.^[16–19] First-principles calculations predicted that strain can substantially change the band structure of monolayer MX₂ and drive a transition from direct gap to indirect gap.^[20–24] Interestingly, strain can also modulate magnetic properties of few-layer MX₂^[20,21] and provide possible scenarios for some optical devices or solar cells.^[25] Among few-layer MX₂ compounds, MoSe₂ has attracted special attention since its energy gap under zero strain (∼ 1.55 eV), is exactly close to the optimum value balanced between the optimum utilization of the solar spectrum and the maximum efficiency of conversion into electricity.^[26] This means that two-dimensional MoSe₂ may play an important role in the future opto-electric applications.

In this work, we carried out careful Raman scattering studies of strain-induced effects in mono- and bi-layer MoSe₂. The linear dependence of energy gaps on strain was observed and quantitatively determined. The strain effect can be well understood in term of the change of Se–Mo–Se bond angle. We have comparatively discussed the strain effects, which may help us get insight into exciton physics in MoSe₂ and provide a solid basis for applications.

MoSe₂ bulk crystals were grown through vapor transport equilibration under strict conditions.^[27] Similar to graphene, mono- and bi-layer MoSe₂ flakes used in this work were mechanically exfoliated from bulk crystals but transferred to flexible polyethylene terephthalate (PET) substrate instead of conventional SiO₂/Si substrate, to carry out measurements under strain. As shown in Fig. 1(a), the monolayer piece is a nearly isosceles triangular area with a side length of ∼ 8 microns. The bilayer piece is the neighboring parallelogram. Monolayer MoSe₂ flake was determined by the A_1g phonon frequency (240.5 cm^{− 1}, Fig. 1(b)) and the PL peak position located at 1.55 eV. The extremely strong PL intensity under very low-intensity excitation light further confirmed its thickness since it is a direct-gap semiconductor only in the monolayer case. Then one can further determine the bilayer flake which becomes an indirect-gap semiconductor and its PL intensity is lower than the monolayer case by a factor of ∼ 1/20.

Fig. 1.

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Fig. 1. (a) Optical image of monolayer and bilayer MoSe2. (b) Raman phonon in the monolayer case. (c) Home-made setup for applying strain on films. (d) Schematic of quantitatively estimated strain. The arc length of bended PET substrate is L and its thickness is d. If the straight-line distance between any two points on the PET substrate is taken as x, one can calculate the radius of curvature R. Tuning R by changing x gives variable strains e. For accuracy, the two points should be as close as possible to the arc top.

The home-made setup for applying strain is illustrated in Fig. 1(c). By changing the screw positions, one can adjust the curvature radius of the PET substrate.^[18] External strain can be applied to the flakes through the mediation of van der Waals interaction between flake and substrate. The calculation details can be found in Fig. 1(d). The applied strain e is defined as e = d/2R in units of mm. The maximum applied strain was limited to 0.75%, since the flake may slip off from the substrate under a strain higher than 0.8%.^[18]

PL and Raman scattering measurements were performed with a Jobin–Yvon HR800 system equipped with liquid-nitrogen cooled CCD and a He–Ne excitation laser of 633 nm (MellesGriot). The configuration of backscattering was adopted in our measurements. The laser power was monitored and controlled at a level of 60 μW to protect the flakes and the focus spot is around 2 microns in diameter. All the measurements were carried out at room temperature.

PL spectra of mono- and bi-layer MoSe₂ under various strains are shown in Fig. 2. The evolutions of PL peaks with strain are distinguished in two flakes. PL peak position or energy gap of A-exciton moves down almost linearly with increasing strain in the monolayer sample, and its width remains little changed. In bilayer MoSe₂, PL intensities are significantly weakened because of its indirect gap. Its position has the similar linear strain dependence but its width is obviously reduced by strain. The PL peak positions and widths extracted from Fig. 2 are summarized in Fig. 3. The linear behaviors are clearly seen in both samples in Fig. 3. The fitting in the monolayer case gives a slope of −42 meV/% strain, which is well consistent with first-principles calculations using the GGA method.^[28,29] The calculated rate of strain change is −45 meV/% strain for the direct gap. In the bilayer sample, the fitted slope is −35 meV/% strain, slightly smaller than that in the monolayer case. In comparison, the slope is −45 meV/% strain and −53 meV/% strain in mono- and bilayer MoS₂,^[17] respectively. Considering the different energy gaps (1.55 eV and 1.82 eV for monolayer MoSe₂ and MoS₂, respectively), we obtained the rate of energy-gap change with strain, ∼ 2.7% per 1% strain for MoSe₂ and ∼ 2.4% per 1% strain for MoS₂. This means that the excitonic gap of MoSe₂ is even more sensitive to strain than MoS₂. However, this is reversed in the bilayer case, i.e., 2.3% per 1% strain for MoSe₂ and 2.9% per 1% strain for MoS₂.

Fig. 2.

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	Fig. 2. PL spectra in monolayer (a) and bilayer (b) MoSe2 with applying strain from 0 to 0.75%.

Fig. 3.

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	Fig. 3. (a) Strain dependence of A-exciton PL peak positions in mono- and bi-layer MoSe2. (b) Strain dependence of A-exciton PL peak widths in mono- and bi-layer MoSe2.

The difference can be understood in terms of the different interlayer coupling in both samples. Generally the uniaxial strain stretches the Mo–Se bond and reduces the Se–Mo–Se bond angle. The valence bands of MoSe₂ contain five d orbits of Mo and 4p orbits of Se. In detail, the conduction bands at K points and the valence bands at Γ points are dominated by orbits, while d_{x² − y²} and d_xy orbits contribute to the valence bands at K points. The rest d_xz, d_yz orbits and 4p orbits of Se have a smaller contribution. The application of in-plane uniaxial strain increases the distance between Mo and Se atoms and reduces the Mo–Se–Mo bond angle. Consequently, it brings an effective increase of the vertical distance between Mo and Se atoms, and hence a reduction of the hybridization between p_z orbits of Se and orbits of Mo. This moves down the bottom of the conduction bands at K points and moves down the top of the valence bands at Γ points.

On the other hand, the decrease of the Mo–Se–Mo bond angle under strain reduces the distance between Mo and Se layers. This enhances the coupling between p_x/p_y orbits of Se and d_{x² − y²} and d_xy orbits of Mo. However, the absolute distance between Mo and Se is against the enhancement. The net effect of strain on the valence band top becomes very small. Taking all the factors discussed above, we will see that strain modulates the direct gap at K points by changing the conduction band bottom and keeping the valence band top fixed. Larger strain gives a smaller gap and vice versa. If strain is too large to move up the valence band top at Γ points over that at K points, monolayer MoSe₂ will become an indirect-gap semiconductor.^{[20–24,28–30]}

Figure 3(b) shows the evolution of PL peak width with strain. Under zero strain, the PL peak of the bilayer sample is about two times wider than that in the monolayer one. The width remains unchanged with strain in monolayer MoSe₂, while it clearly becomes sharper with strain in the bilayer sample. This can also be explained by the reduction of Se–Mo–Se bond angle under strain.^[30] The angle reduction effectively decreases the thickness of the MoSe₂ layer or is equivalent to the increase of the interlayer distance, which weakens the interlayer coupling and decreases the A-exciton PL peak width.

We first observed the direct energy-gap evolution with strain in mono- and bilayer MoSe₂. The measured rates of change are consistent with the calculated ones. We further discussed the possible mechanisms in both cases in terms of interlayer coupling. The reduction of the Mo–Se–Mo bond angle under strain modifies the hybridization between the d orbits and p orbits of Se, and further shifts the conduction and valence bands. This effectively reduces the band gap. The studies on excitonic energy gaps under strain are important to the applications and provide fundamental insight to exciton physics in this two-dimensional system.