Mechanically-induced reverse phase transformation of MoS₂ from stable 2H to metastable 1T and its memristive behavior

Abstract

The 1T phase of MoS₂ is attracting much attention due to its metallic property and potential applications for supercapacitors, photothermal agents, and memristors. However, because the 1T phase is metastable, it can easily be transferred to the stable 2H phase by heating. In this work, it is the first time we observe the mechanically-induced reverse phase transformation (from stable 2H to metastable 1T) for MoS₂ by HAADF-STEM images. Furthermore, XPS revealed that the content of the 1T phase increased with increasing mechanical ball-milling time. Furthermore, the mechanically generated 1T MoS₂ exhibited memristive behavior.

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1 Introduction

Since the discovery of graphene, great efforts haves been devoted to exploring two-dimensional (2D) layer materials.^1–9 Furthermore, transition metal dichalcogenides (TMDs), which present a MX₂ stoichiometry and are composed of atomically thin 2D layers, are currently a primary focus in 2D materials.¹⁰ Each MX₂ layer is three-atoms-thick and consists of transition metal atom (M) sheets sandwiched between two sheets of chalcogen atoms (X).² The intralayer metal–chalcogen bond is predominantly covalent, but the adjacent layers stack together by weak van der Waals interlayer forces.^4,11 Such a weak interlayer interaction allows TMDs to be exfoliated into a single layer or few layers.¹²

As a representative MX₂, molybdenum disulfide (MoS₂) possesses unique properties, such as tuneable band gap, high mobility, and quantum confinement,^4,13–16 which make it an attractive material for electronic and optoelectronic devices,^{13,14,17–22} sensing platforms,^23–25 and energy storage.^26,27 MoS₂ has two main types of phases (2H and 3R). 2H phase is dominant in nature and more stable than 3R phase. Different from 3R phase, in which three layers per unit cell stack in the rhombohedral symmetry with trigonal prismatic coordination, 2H phase possesses two layers per unit cell stacked in the hexagonal symmetry with trigonal prismatic coordination.²⁸ A metastable 1T metallic phase, which has one-layer unit cell in the tetragonal symmetry with octahedral coordination, was obtained in MoS₂ nanosheets prepared by intercalation-assisted-exfoliation.^15,29,30

1T metallic phase MoS₂ is a very promising material for electrical devices and energy conversion processes. Chhowalla et al. revealed that 1T phase MoS₂ is an excellent electrode material.^31,32 Chou et al. demonstrated its effectiveness of 1T phase MoS₂ as a near-infrared (NIR) photothermal agent.³³ 1T phase MoS₂ nanosheets were explored as effective catalysts for hydrogen evolution reaction (HER).^34–36 Recently, we demonstrated that 1T phase MoS₂ nanosheets can be used to fabricate an odd-symmetric memristor.³⁷

Metastable 1T phase can easily transform into stable 2H phase by heating treatment.^6,30 Furthermore, the reverse transformation from stable 2H to metastable 1T phase could be obtained by ion intercalation exfoliation (including lithium ion, sodium ion, potassium ion, ammonium ion, and alkali metal alloy),^38–41 chemical exfoliation,⁴² electron beam irradiation treatment,⁴³ and plasmonic hot electron injection.⁴⁴ So far, to our best knowledge, although mechanical ball-milling method was used to change particle sizes and shapes,^45,46 no mechanical process has be explored for the phase transformation of MoS₂ from 2H to 1T.

In this work, we demonstrated the mechanically-induced phase transformation of MoS₂ from 2H into 1T at room temperature. Furthermore, the mechanically-treated MoS₂ nanoparticles with phase transformation exhibited memristive behaviors.

2 Experimental section

2.1 Materials and characterization

Bulk MoS₂ (2H phase, purchased from Sigma-Aldrich), which was placed inside a stainless steel container alongside three stainless steel milling balls at room temperature, was subjected to the ball milling using SPEX 8000 Mixer/Mill for 2, 5, or 10 hours. The obtained samples, which were denoted as MoS₂-bm-2 h, MoS₂-bm-5 h, and MoS₂-bm-10 h, respectively, were characterized as follows. X-ray diffraction (XRD) measurements were carried out using a Scintag XDS-2000 powder diffractometer with Cu Kα (λ = 1.54062 Å) radiation at a scan speed of 1° min⁻¹ and a step size of 0.03° in 2θ. A field emission scanning electron microscope (FE-SEM, Hitachi S-4700) was exploited to evaluate morphologies. The height profile of MoS₂ samples was depicted by an atomic force microscopy (AFM, Veeco Dimension 3000) at room temperature. Raman spectra were obtained using a Jobin-Yvon LabRAM HR800 Raman Spectrometer with a helium–neon laser operating at 632.8 nm in air ambient environment. The high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of MoS₂ samples were obtained by a JEOL JEM3100R05 double Cs-corrected analytical electron microscope. X-ray photoelectron spectra (XPS) of MoS₂ samples were collected using a Kratos Ultra AXIS DLD XPS instrument with a monochromated Al source for composition analysis.

2.2 Fabrication and tests of MoS₂-based memristive devices

The MoS₂ sample was dispersed in 2-propanol solution (purchased from Sigma-Aldrich) with the concentration of 0.1 mg mL⁻¹ at room temperature. The obtained suspension was uniformly spin-coated onto the top of a cleaned silver foil (0.1 mm thick and the area of 0.1 mm²), followed by heating at 90 °C for 12 h. The thickness of the coated MoS₂ film was about 550 nm. After that, a thin layer of silver was uniformly coated on the surface of the MoS₂ film by conductive paste (purchased from Sigma-Aldrich) and cured at 90 °C for 1 h, forming the Ag/MoS₂/Ag memristive device.

Hysteresis I–V curves were collected by an electrochemical workstation (Princeton Potentiostat/Galvanostat Model 273A) which allowed the measurement of currents from 100 nA to 1 A.

3 Results and discussion

To evaluate the mechanically-induced phase transformation of MoS₂, bulk MoS₂ with 2H phase was ball-milled. The obtained samples were subjected to XRD characterization. Fig. 1 showed all diffraction peaks became smaller and broader with increasing ball-milling time. The crystal size, which was estimated from XRD peaks, decreased from 54 nm to 23, 16, and 15 nm (corresponding to 35, 25, and 23 layers) for ball-millings of 2, 5, and 10 h, respectively. Furthermore, the structures of MoS₂ nanoparticles were depicted by Raman spectra. As shown in Fig. 2a, the in-plane E¹_2g peak (due to opposite vibration of two S atoms with respect to the Mo atom)⁴⁵ and out-of-plane A_1g peak (resulting from the vibration of only S atoms in opposite directions)⁴⁵ were exhibited for both bulk and mechanically-induced MoS₂. It was clear that the frequency of A_1g peak decreased from 402.8 to 402.5 cm⁻¹ (red-shift) after bulk MoS₂ was mechanically ball-milled. This is reasonable because interlayer van der Waals force decreases with decreasing the number of layers, atomic vibration becomes more strenuous in MoS₂, thus both E¹_2g peak and A_1g peak are expected to soften (red-shift). However, on the contrary, the frequency of E¹_2g peak increased from 375.9 to 376.7 cm⁻¹ (blue-shift), reflecting the dominant influence of stacking induced structure changes or long-range coulombic interlayer interactions.^47–49 In addition, the thickness-dependent shift of E¹_2g and A_1g peaks supports that the MoS₂ layer number was decreased gradually with increasing ball-milling time. More importantly, the additional J₁, J₂ and J₃ peaks at 145.2, 234.1 and 336.1 cm⁻¹ (Fig. 2b), which are absent in the spectrum of bulk MoS₂, indicating the presence of 1T phase MoS₂.^6,50,51 The presence of these three peaks are attributed to a zone-folding mechanism resulting from the formation of a superlattice in the basal planes.⁵¹

Fig. 1 XRD patterns of bulk MoS₂ (black), MoS₂-bm-2 h (red), MoS₂-bm-5 h (green), and MoS₂-bm-10 h (blue).

Fig. 2 Raman spectra of bulk MoS₂ (black), MoS₂-bm-2 h (red), MoS₂-bm-5 h (green), and MoS₂-bm-10 h (blue) using 632.8 nm laser line.

Because 1T and 2H has the same XRD diffraction pattern, we are unable to distinguish the two phases with XRD. To further identify the existence of 1T phase in mechanically-ball-milled MoS₂, a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), which is an extremely powerful tool in revealing the atomic structure of materials,³¹ was used to evaluate MoS₂ with and without ball-milling. As shown in Fig. 3, the HAADF-STEM image of bulk MoS₂ exhibited a honeycomb lattice structure in which blue and yellow dots represent Mo and S atoms respectively, confirming that bulk MoS₂ possesses the 2H phase with an ABA stacking sequence.⁵² The signal of S atoms is comparable to that of Mo atoms due to the overlap of two sulphur atoms along the electron beam direction.⁵³ However, the image of MoS₂ treated with ball-milling for 5 hours contains a hexagonal lattice structure in which blue dots displayed Mo atoms, because S atoms are evenly distributed around Mo atoms, leading to the strong contrast between Mo and S atoms (Fig. 4). This provides the evidence of 1T phase with an ABC stacking sequence,^6,31 which can be attributed to the mechanically-induced S plane glide motion. The coexistence of 1T and 2H phase demonstrates that mechanically-induced MoS₂ possesses a highly heterogeneous structure (Fig. 4). Furthermore, X-ray photoelectron spectroscopy (XPS) was exploited to evaluate the contents of 1T and 2H phase in mechanically-induced MoS₂. The binding energies of Mo 3d_5/2, Mo 3d_3/2, S 2p_3/2, and S 2p_1/2 are 228.25, 231.45, 161.0, and 162.2 eV for 1T-phase and 229.05, 232.25, 161.8, and 163.0 eV for 2H phase, respectively (Fig. 5). Generally, compared with 2H phase MoS₂, 1T-type MoS₂ is down-shifted by 0.8 eV, which is in agreement with previous reports from different groups.^6,31,54 Furthermore, the content of 1T phase, which was calculated from XPS, increased with increasing ball-milling time (0% for bulk MoS₂, 8% for MoS₂-bm-2 h, 16% for MoS₂-bm-5 h, and 20% for MoS₂-bm-10 h). The property of mechanically-induced 1T MoS₂ is different from that of 1T MoS₂ prepared by lithium ion intercalation exfoliation. The exfoliated MoS₂ is usually very thin with few layers, whereas mechanically-induced 1T MoS₂, which consists of 23–35 layers, is thick. As a result, the distance between E¹_2g peak and A_1g peak in the Raman spectrum is 24 cm⁻¹ for the exfoliated MoS₂,³⁷ but it is 25.8 cm⁻¹ for MoS₂-bm-10 h.

Fig. 3 HAADF-STEM image of bulk MoS₂ (blue and yellow dots representing Mo and S atoms show a honeycomb lattice for 2H phase).

Fig. 4 HAADF-STEM image of MoS₂-bm-5 h nanoparticles (blue dots indicating Mo atoms exhibit a hexagonal lattice for 1T phase; blue and yellow dots representing Mo and S atoms show a honeycomb lattice for 2H phase).

Fig. 5 XPS spectra of Mo 3d and S 2p species in bulk MoS₂ (black), MoS₂-bm-2 h (red), MoS₂-bm-5 h (green), and MoS₂-bm-10 h (blue) (orange and cyan curves represent 2H and 1T phase, respectively).

Recently-invented memristors, which were predicted by Chua,⁵⁵ are expected to revolutionize electrical devices, such as fast non-volatile memory for computers. This has stimulated an increasing interest to explore new memristive materials.^37,56,57 Recently, we demonstrated that 2H phase MoS₂ possesses an ohmic feature, whereas 1T phase MoS₂ nanosheets exhibited a unique memristive behavior due to its voltage-dependent resistance change.³⁷ Herein, to verify whether mechanically-generated 1T MoS₂ phase has memristive properties, Ag/MoS₂/Ag device system was fabricated and tested. Fig. 6 shows I–V characteristic for the Ag/MoS₂/Ag switch based on ball-milled MoS₂ (for 2 hours). When sweeping a bias voltage from 0 mV → 200 mV → −200 mV → 0 mV, an obvious pinched hysteresis loop (following the arrows) was recorded (Fig. 6b). Initially, the current was very low, indicating a very high resistance (OFF state). Then sweeping the applied voltage to positive values on the top Ag electrode, the current suddenly rose at 95 mV, corresponding to a switch to a very low resistance state (ON state). Subsequently, increasing the bias voltage to 200 mV and then sweeping back to negative values, the device transformed into OFF state at −26 mV. The switch of OFF/ON state happened because electrical field could cause the displacement of ions in 1T phase MoS₂, which induces a lattice distortion, leading to resistant change.³⁷ Both the alternation between ON and OFF states and the feature of a pinched hysteresis loop made this device an asymmetric switch. The logarithmic scale shown in Fig. 6c indicated an ON/OFF current ratio with five orders of magnitude, which is an impressive value. The negligible change during 1000-cycle sweeping reflected that MoS₂-bm-2 h based device possessed the excellent stability of memristive behavior (Fig. 6d). To further confirm the memristive behavior of mechanically-induced MoS₂, another device was fabricated with MoS₂-bm-10 h. A stable pinched hysteresis loop was also observed, but the switching voltages for ON and OFF states were 77 and −39 mV, the ON/OFF current ratio was ∼10³ (Fig. 7). MoS₂-bm-10 h has more 1T phase than MoS₂-bm-2 h and thus a smaller resistance, because 1T phase MoS₂ is 10⁷-times more conductive than 2H phase.³¹ As a result, a lower bias voltage is required to induce a lattice distortion (transform into ON state), but a higher bias voltage to recover the distortion (transform into OFF state). In contrast, no switching behavior was observed (Fig. S1 in ESI†) for the device with bulk MoS₂ (pure 2H phase) without ball-milling. Therefore, mechanically-generated 1T phase MoS₂ possesses unique memristive behavior.

Fig. 6 I–V characteristic of MoS₂-bm-2 h based switch. (a) Schematic structure of Ag/MoS₂/Ag switch. (b) Typical I–V characteristic of Ag/MoS₂/Ag switch at room temperature. (c) Typical I–V characteristic of Ag/MoS₂/Ag switch in the logarithmic scale at room temperature. (d) Typical I–V characteristic of Ag/MoS₂/Ag switch at the 1st (red), 500th (green), and 1000th (blue) cycle at room temperature.

Fig. 7 I–V characteristic of MoS₂-bm-10 h based switch. (a) Schematic structure of Ag/MoS₂/Ag switch. (b) Typical I–V characteristic of Ag/MoS₂/Ag switch at room temperature. (c) Typical I–V characteristic of Ag/MoS₂/Ag switch in the logarithmic scale at room temperature. (d) Typical I–V characteristic of Ag/MoS₂/Ag switch at the 1st (red), 500th (green), and 1000th (blue) cycle at room temperature.

4 Conclusion

In conclusion, the mechanical ball-milling could induce the reverse phase transformation from stable 2H to metastable 1T, which was confirmed by Raman and XPS spectra as well as HAADF-STEM images. Furthermore, it was found that the content of 1T phase increased with increasing ball-milling time. The mechanically-generated 1T MoS₂ phase exhibited unique memristive behavior, which can be used for memristor devices. This work provides a simple approach to generate 1T metallic phase MoS₂ from its bulk 2H material.

Acknowledgements

This work was supported by the U.S. National Science Foundation (CBET-0931587). Y. H. H. also thanks Charles and Carroll McArthur for their great support. The JEOL JEM 3100R05 double Cs-corrected AEM and the Krato XPS were supported by NSF Grant No. DMR-0723032 and Grant No. DMR-0420785, respectively.

References

1. A. K. Geim, Science, 2009, 324, 1530–1534.
2. J. N. Coleman, M. Lotya, A. O'Neill, S. D. Bergin, P. J. King, U. Khan, K. Young, A. Gaucher, S. De, R. J. Smith, I. V. Shvets, S. K. Arora, G. Stanton, H.-Y. Kim, K. Lee, G. T. Kim, G. S. Duesberg, T. Hallam, J. J. Boland, J. J. Wang, J. F. Donegan, J. C. Grunlan, G. Moriarty, A. Shmeliov, R. J. Nicholls, J. M. Perkins, E. M. Grieveson, K. Theuwissen, D. W. McComb, P. D. Nellist and V. Nicolosi, Science, 2011, 331, 568–571.
3. X. Huang, X. Qi, F. Boey and H. Zhang, Chem. Soc. Rev., 2012, 41, 666–686.
4. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147–150.
5. X. Huang, Z. Zeng and H. Zhang, Chem. Soc. Rev., 2013, 42, 1934–1946.
6. G. Eda, H. Yamaguchi, D. Voiry, T. Fujita, M. Chen and M. Chhowalla, Nano Lett., 2011, 11, 5111–5116.
7. Y. Li, H. Wang, L. Xie, Y. Liang, G. Hong and H. Dai, J. Am. Chem. Soc., 2011, 133, 7296–7299.
8. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli and F. Wang, Nano Lett., 2010, 10, 1271–1275.
9. Y. Zhang, J. Ye, Y. Matsuhashi and Y. Iwasa, Nano Lett., 2012, 12, 1136–1140.
10. G. R. Bhimanapati, Z. Lin, V. Meunier, Y. Jung, J. Cha, S. Das, D. Xiao, Y. Son, M. S. Strano, V. R. Cooper, L. Liang, S. G. Louie, E. Ringe, W. Zhou, S. S. Kim, R. R. Naik, B. G. Sumpter, H. Terrones, F. Xia, Y. Wang, J. Zhu, D. Akinwande, N. Alem, J. A. Schuller, R. E. Schaak, M. Terrones and J. A. Robinson, ACS Nano, 2015, 9, 11509–11539.
11. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov and A. K. Geim, Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 10451–10453.
12. D. Voiry, A. Mohite and M. Chhowalla, Chem. Soc. Rev., 2015, 44, 2702–2712.
13. Y. Yoon, K. Ganapathi and S. Salahuddin, Nano Lett., 2011, 11, 3768–3773.
14. H. S. Lee, S.-W. Min, Y.-G. Chang, M. K. Park, T. Nam, H. Kim, J. H. Kim, S. Ryu and S. Im, Nano Lett., 2012, 12, 3695–3700.
15. K. F. Mak, C. Lee, J. Hone, J. Shan and T. F. Heinz, Phys. Rev. Lett., 2010, 105, 136805.
16. Z. Yin, Z. Zeng, J. Liu, Q. He, P. Chen and H. Zhang, Small, 2013, 9, 727–731.
17. H. Xu, J. Wu, Q. Feng, N. Mao, C. Wang and J. Zhang, Small, 2014, 10, 2300–2306.
18. Z. Yin, H. Li, H. Li, L. Jiang, Y. Shi, Y. Sun, G. Lu, Q. Zhang, X. Chen and H. Zhang, ACS Nano, 2012, 6, 74–80.
19. H. Wang, L. Yu, Y.-H. Lee, Y. Shi, A. Hsu, M. L. Chin, L.-J. Li, M. Dubey, J. Kong and T. Palacios, Nano Lett., 2012, 12, 4674–4680.
20. J. Pu, Y. Yomogida, K.-K. Liu, L.-J. Li, Y. Iwasa and T. Takenobu, Nano Lett., 2012, 12, 4013–4017.
21. S. Kim, A. Konar, W.-S. Hwang, J. H. Lee, J. Lee, J. Yang, C. Jung, H. Kim, J.-B. Yoo, J.-Y. Choi, Y. W. Jin, S. Y. Lee, D. Jena, W. Choi and K. Kim, Nat. Commun., 2012, 3, 1011.
22. B. Radisavljevic, M. B. Whitwick and A. Kis, ACS Nano, 2011, 5, 9934–9938.
23. D. J. Late, Y.-K. Huang, B. Liu, J. Acharya, S. N. Shirodkar, J. Luo, A. Yan, D. Charles, U. V. Waghmare, V. P. Dravid and C. N. R. Rao, ACS Nano, 2013, 7, 4879–4891.
24. H. Li, Z. Yin, Q. He, H. Li, X. Huang, G. Lu, D. W. H. Fam, A. I. Y. Tok, Q. Zhang and H. Zhang, Small, 2012, 8, 63–67.
25. Q. He, Z. Zeng, Z. Yin, H. Li, S. Wu, X. Huang and H. Zhang, Small, 2012, 8, 2994–2999.
26. Y. Chen, B. Song, X. Tang, L. Lu and J. Xue, Small, 2014, 10, 1536–1543.
27. L. Yang, S. Wang, J. Mao, J. Deng, Q. Gao, Y. Tang and O. G. Schmidt, Adv. Mater., 2013, 25, 1180–1184.
28. A. R. Beal, J. C. Knights and W. Y. Liang, J. Phys. C: Solid State Phys., 1972, 5, 3540.
29. L. Wang, Z. Xu, W. Wang and X. Bai, J. Am. Chem. Soc., 2014, 136, 6693–6697.
30. A. N. Enyashin, L. Yadgarov, L. Houben, I. Popov, M. Weidenbach, R. Tenne, M. Bar-Sadan and G. Seifert, J. Phys. Chem. C, 2011, 115, 24586–24591.
31. M. Acerce, D. Voiry and M. Chhowalla, Nat. Nanotechnol., 2015, 10, 313–318.
32. R. Kappera, D. Voiry, S. E. Yalcin, B. Branch, G. Gupta, A. D. Mohite and M. Chhowalla, Nat. Mater., 2014, 13, 1128–1134.
33. S. S. Chou, B. Kaehr, J. Kim, B. M. Foley, M. De, P. E. Hopkins, J. Huang, C. J. Brinker and V. P. Dravid, Angew. Chem., Int. Ed., 2013, 52, 4160–4164.
34. D. Voiry, M. Salehi, R. Silva, T. Fujita, M. Chen, T. Asefa, V. B. Shenoy, G. Eda and M. Chhowalla, Nano Lett., 2013, 13, 6222–6227.
35. U. Maitra, U. Gupta, M. De, R. Datta, A. Govindaraj and C. N. R. Rao, Angew. Chem., Int. Ed., 2013, 52, 13057–13061.
36. M. A. Lukowski, A. S. Daniel, F. Meng, A. Forticaux, L. Li and S. Jin, J. Am. Chem. Soc., 2013, 135, 10274–10277.
37. P. Cheng, K. Sun and Y. H. Hu, Nano Lett., 2016, 16, 572–576.
38. Q. Liu, X. Li, Q. He, A. Khalil, D. Liu, T. Xiang, X. Wu and L. Song, Small, 2015, 11, 5556–5564.
39. J. Zheng, H. Zhang, S. Dong, Y. Liu, C. Tai Nai, H. Suk Shin, H. Young Jeong, B. Liu and K. Ping Loh, Nat. Commun., 2014, 5, 2995.
40. B. K. Miremadi, T. Cowan and S. R. Morrison, J. Appl. Phys., 1991, 69, 6373–6379.
41. H. Feng, Z. Hu and X. Liu, Chem. Commun., 2015, 51, 10961–10964.
42. R. Raja, P. Sudhagar, A. Devadoss, C. Terashima, L. K. Shrestha, K. Nakata, R. Jayavel, K. Ariga and A. Fujishima, Chem. Commun., 2015, 51, 522–525.
43. Y.-C. Lin, D. O. Dumcenco, Y.-S. Huang and K. Suenaga, Nat. Nanotechnol., 2014, 9, 391–396.
44. Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, J. Lou and Z. Fang, Adv. Mater., 2014, 26, 6467–6471.
45. L. Takacs, P. Baláž and A. R. Torosyan, J. Mater. Sci., 2006, 41, 7033–7039.
46. A. Ambrosi, X. Chia, Z. Sofer and M. Pumera, Electrochem. Commun., 2015, 54, 36–40.
47. H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier and D. Baillargeat, Adv. Funct. Mater., 2012, 22, 1385–1390.
48. C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone and S. Ryu, ACS Nano, 2010, 4, 2695–2700.
49. T. J. Wieting and J. L. Verble, Phys. Rev. B: Solid State, 1972, 5, 1473–1479.
50. D. Yang, S. J. Sandoval, W. M. R. Divigalpitiya, J. C. Irwin and R. F. Frindt, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 43, 12053–12056.
51. S. Jiménez Sandoval, D. Yang, R. F. Frindt and J. C. Irwin, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 44, 3955–3962.
52. G. Eda, T. Fujita, H. Yamaguchi, D. Voiry, M. Chen and M. Chhowalla, ACS Nano, 2012, 6, 7311–7317.
53. P. Hartel, H. Rose and C. Dinges, Ultramicroscopy, 1996, 63, 93–114.
54. Z. Tang, Q. Wei and B. Guo, Chem. Commun., 2014, 50, 3934–3937.
55. L. O. Chua, IEEE Trans. Circuit Theory, 1971, 18, 507–519.
56. V. K. Sangwan, D. Jariwala, I. S. Kim, K.-S. Chen, T. J. Marks, L. J. Lauhon and M. C. Hersam, Nat. Nanotechnol., 2015, 10, 403–406.
57. A. M. van der Zande, P. Y. Huang, D. A. Chenet, T. C. Berkelbach, Y. You, G. H. Lee, T. F. Heinz, D. R. Reichman, D. A. Muller and J. C. Hone, Nat. Mater., 2013, 12, 554–561.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra12735e

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