2
J. Pu, 1 Y. Zhang, 2 Y. Wada, 1 J. T.-W. Wang, 3 L.-J. Li, 3,a) Y. Iwasa, 2,4,5 and T. Takenobu 1,a)
1 Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan
2 Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
3 Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
4 Correlated Electron Research Group, RIKEN, Wako 351-0198, Japan
5 Quantum-Phase Electronics Center, The University of Tokyo, Tokyo 113-8656, Japan
* E-mail: takenobu@waseda.jp
*E-mail address: takenobu@waseda.jp 1

Figure S1 (a) shows the schematic configuration of the stretch test of the Au electrode. These electrodes were thermally deposited onto the PDMS substrates. DC measurements were performed to investigate the variation in the Au electrode conductance under different applied tensile tensions.
Figure S1 (b) presents the strain dependence of the Au conductivity (red). The variation in the Au conductivity is negligible within a strain of 20% because the Au conductivity is four magnitudes larger than that of the MoS
2
TFTs on the PDMS substrate (blue line shown in Fig. S1 (b)). The inset shows the optical image of the relaxation between the two Au electrodes. The applied strains were determined by directly observing the expansion of the distance between the two electrodes, which corresponded to the channel region in the transistors. These results allow for the stretchability of the electrical performance in semiconductors to be tested using an Au electrode.
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Figure S2 (a) presents the geometry of the ion-gel/Au interface capacitor on the PDMS substrate.
Impedance measurements were performed across the top and bottom electrodes with an applied tensile tension. Figure S2 (b) shows the frequency profile of the specific capacitance under the following three strain conditions: 0% (red), 11% (orange), and 22% (blue). The capacitance at 100
Hz is 9.05 (μF/cm 2 ). The inset presents the phase angle as a function of the applied frequency, and these results strongly suggest that the capacitance obtained at 100 Hz is reasonable because a phase angle of -90º corresponds to a purely capacitive response. Figure S2 (c) demonstrates the strain dependence of the ion-gel capacitance. This result demonstrates the stretchability of the ion-gel capacitor under high strains because the capacitance was nearly constant during stretching at up to
20% strain.
3

Evidence of deformation in 2-D nanosheet materials is provided by the strain-induced peak splitting in the Raman spectrum, which has already been observed for graphene.
1-3 Figure S3(a) presents the Raman spectra of the MoS
2
films transferred onto the PDMS substrates under different strains. The two characteristic Raman peaks correspond to the E 1
2g
mode at ~ 377 cm -1 and the A
1g mode at ~ 400 cm -1 . The peak energy difference measured between the E 1
2g
and A
1g
modes (~ 23 cm -1 ) agrees reasonably well with the results for tri-layer MoS
2
films produced by the mechanical exfoliation method.
4,5 Because the stretching of the MoS
2
crystal structure should change the
S-Mo-S hexagonal geometry, changes in the Raman E 1
2g
and A
1g
peak energies are expected.
6
However, we did not observe any clear change in the Raman spectra of the MoS
2
films up to a strain of 7%, suggesting negligible deformation of these films. These results are completely inconsistent with the degradation of the transport properties under strain that is shown in Fig. 2.
Another possible experimental signature of uniaxial deformation in MoS
2
is the closure of the band gap. Very recently, several groups reported the effect of tensile strain on mono- and bi-layer
MoS
2
films using first-principle calculations.
6-9 These studies predicted that the band gap of MoS
2 decreases as the strain increases and that a semiconductor-metal transition can be induced at a strain of 10%.
7-9 Following this theoretical prediction, to confirm the deformation of the MoS
2
films, we measured the absorption spectra under uniaxial strain. As shown in Fig. S3(b), we observed minor variations below a strain of 15%, indicating negligible deformation of these films. Moreover, a similar robustness up to a 7% strain was revealed in the photoluminescence spectra (Fig. S3(c)).
These optical and spectroscopic characterizations obviously indicate that the MoS
2
lattice structure was not strongly deformed by uniaxial strain, and they conflict with the results of the transistor measurements.
References
(1) M. Huang, H. Yan, C. Chen, D. Song, T. F. Heinz, and J. Hone, Proc. Natl. Acad. Sci. U.S.A. 106 ,
7304 (2009).
(2) T. M. G. Mohiuddin, A. Lombardo, R. R. Nair, A. Bonetti, G. Savini, R. Jalil, N. Bonini, D. M.
Basko, C. Galiotis, N. Marzari, K. S. Novoselov, A. K. Geim, and A. C. Ferrari, Phys. Rev. B. 79 ,
205433 (2009).
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Funct. Mater. 22 , 1385 (2012).
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(7) E. Scalise, M. Houssa, G. Pourtois, V. Afanas’ev, and A. Stesmans, Nano Res. 5 , 43 (2012).
(8) Q. Yue, J. Kang, Z. Shao, X. Zhang, S. Chang, G. Wang, S. Qin, and J. Li, Phys. Lett. A. 376 ,
1166 (2012).
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FIG. S3. Optical and spectroscopic characterizations of the MoS
2
thin films on PDMS substrates. (a)
Raman spectra of the MoS
2
thin films under two strain conditions. The two characteristic Raman peaks correspond to the E 1
2g
mode and the A
1g
mode. The energy difference between the two peaks was ~ 23 cm -1 . (b) The absorption and (c) Photoluminescence (PL) spectra are shown as a function of energy. The Raman and PL spectra were measured with an excitation laser wavelength of 532 nm.
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Below 5% of strain, the applied deformation is relaxed by the ripples structure and transistors are stable, as shown in Fig. S4. On the other hand, when the strain is larger than 5%, we observed the degradation in transistor performance (Figs. 3). During the transistor experiments, we observed a clear expansion of the channel length, which was measured directly as the distance between the source and drain electrodes (Fig. 2). However, as shown in Figs. S3, optical and spectroscopic characterizations deny the deformation of MoS
2
films. These contradictory results lead to the conclusion that the origin of the degradation of transport properties in CVD-grown MoS
2
films is the strain relaxation in the domain boundaries (Fig. S4). Although the harder single-crystalline part of the CVD-grown MoS
2
films is not seriously deformed by the stretching, the softer domain boundaries change their bonding angles and distances, resulting in strain release. Because most of the CVD-grown MoS
2
films are single crystalline, the effective area of the domain boundaries is very small. Therefore, optical and spectroscopic characterizations are not able to detect the deformation of the boundaries. In contrast, because the undeformable single-crystalline part of the films is inevitably surrounded by the deformable boundaries, the carriers must cross them, and the transport properties are affected by strong stretching. This mechanism explains the strain dependence of polycrystalline, CVD-grown nanosheet materials, such as graphene and MoS
2
films.
FIG. S4. Schematic views of the stretching of a polycrystalline MoS
2
thin film. Polycrystalline MoS
2 thin films consist of single-crystalline MoS
2
domains. In relatively weak strain (< 5%), the applied strain is relaxed by the ripple structures. The domain boundaries play an important role in farther stretching. Because the stiff MoS
2
single crystals are undeformable, the domain boundaries deform and relax the applied strain. This mechanism may explain the origin of the stretchability and degradation of polycrystalline, CVD-grown, 2-D nanosheet materials.
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