Softened Mechanical Properties of Graphene Induced by Electric Field

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Softened mechanical properties of graphene induced by electric field Peng Huang, Dan Guo, Guoxin Xie, and Jian Li Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02965 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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Softened mechanical properties of graphene induced by electric field Peng Huang1,2, Dan Guo1*, Guoxin Xie1*, Jian Li3 1

State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China

2

Sicence and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621908, Sichuan,

China 3

Wuhan Research Institute of Materials Protection, Wuhan 430030, Hubei, China

Abstract: The understanding on the mechanical properties of graphene under the applications of physical fields is highly relevant to the reliability and lifetime of graphene-based nanodevices. In this work, we demonstrate that the application of electric field could soften the mechanical properties of graphene dramatically on the basis of the conductive AFM nanoindentation method. It has been found that the Young’s modulus and fracture strength of graphene nanosheets suspended on the holes almost stay the same initially, and then exhibit a sharp drop when the normalized electric field strength increases to be 0.18 ± 0.03 V/nm. The threshold voltage of graphene nanosheets before the onset of fracture under the fixed applied load increases with the thickness. Supported graphene nanosheets can sustain larger electric field under the same applied load than the suspended ones. The excessively regional Joule heating caused by the high electric current under the applied load is responsible for the electromechanical failure of graphene. These findings can provide a beneficial guideline for the electromechanical applications of graphene-based nanodevices. Keywords: Graphene, conductive AFM, electric field, Young’s modulus, adhesion force, fracture strength Graphene, the most famous 2D nanomaterial, has been attracting tremendous interests for its prominent physical properties and shows promising applications in electronics, sensors, catalysts, energy conversions, etc1. Graphene exhibits a high in-plane Young’s modulus (~1 TPa)2-6, in-plane tensile elastic strain (up to 25%)3,7 and electron mobility (~2 × 105 cm2V-1s-1)8,9, making it an ideal candidate for the application of nano-electromechanical system (NEMS)10-12. Thus, the electromechanical coupling properties of graphene, mainly the Young’s modulus, fracture strength and adhesion properties of graphene under the electric field, are crucial in the actual applications which determine the system performance. Graphene behaves an excellent piezoresistive property that direct electrical readout of pressure can be observed when exposed to strain transduction10. It also can be electrically resonated to be a mechanical resonator for ultrasensitive force detection and ultralow mass detection11. Previous research has proved that the winkles resulting from the mechanical exfoliation method for the graphene nanosheets will in turn affect the conducting behaviours13. Strain is also an effective way to tune the conductance of graphene nanoribbon14,15. Besides, electric field under the conductive AFM can induce the reduction of graphene oxide16-19 or local anodic oxidation of graphene20. Therefore, the effect of electric field on the mechanical properties of

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graphene need to be systematically investigated since it has been widely used in electronic nanodevices. Electric field might lead to a rippling of graphene by the tip bias of the scanning tunneling microscope (STM)21. Molecular dynamics simulations showed that the Young’s modulus and the critical fracture stress of graphene under the vertical electric field decreases with the increasing electric potential and net charges22. The morphology of a suspended graphene nanoribbon was proved to be affected by the applied gate voltage with a parabolic dependent function23. In situ nanoindentation and electronic transport measurements of graphene proved that moderate uniform strain would not bring band gap opening24. Conductive AFM has been widely used to conduct mechanical and electrical measurements of graphene nanosheets supported on metal substrates and found that the conduction properties were strongly dependent on the thickness25. STM investigation proved that the wrinkles of graphene behaved a lower conductance than the flat areas26. However, the electromechanical researches of graphene are still far from enough. The electromechanical failure is a quite important issue for the design of graphene-based nanodevices. A better understanding on the effects of electric field on the mechanical properties of graphene is necessary for the guidance of graphene-based nanoelectromechanical systems. In this letter, we report a comprehensive investigation of the effect of electric field on the mechanical properties of graphene with the conductive AFM nanoindentation method. The thicknesses of the mechanically fabricated graphene nanosheets were from several to tens of nanometers. The applied load was kept the same and the value was 3 μN for all the nanoindentation process. We found that the adhesion force increased with the bias voltage because of the electrostatic force effect. The Young’s modulus and fracture strength of graphene stayed almost the same initially when the bias was relatively small, and then exhibited a sharp drop with the further increasing bias voltage. The suspended graphene nanosheets behaved a sudden electromechanical fracture with the further increase of electric field under the applied load. It proved that the electric field could soften the mechanical properties of graphene dramatically. Supported graphene nanosheets can sustain larger electric field under the same applied load than the suspended ones. Graphene nanosheets were obtained by mechanical exfoliation onto the pre-prepared SiO2/Si substrate with holes and Cr/Au electrodes (See Supporting Information Figure S1). This kind of design can better fit the actual applications of graphene-based nanodevices. Appropriate graphene nanosheets were chosen by the optical microscope before the AFM experiments, mainly the ones suspended on the holes and connected by the Cr/Au electrodes. Tapping mode was adopted to obtain the morphological parameters of graphene nanosheets, mainly the height and sinking depth of the graphene nanosheets. The thickness of graphene nanosheets ranges from ~20 to ~50 nm and this relatively large range is attributed to the influence of the step height of the Cr/Au electrode (~100 nm). Optical and AFM images of a representative graphene nanosheet are shown in Figure 1 (Other graphene nanosheets see Supporting Information Figure S2). Conductive AFM nanoindentation method was utilized to measure the mechanical properties of graphene nanosheets suspended on the holes under the electric field, as shown in Figure 2(a). Current-voltage (I-V) responses were


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tested before the nanoindentation measurements to check the feasibility of the experimental design and the results are shown in Figure 2(c). Two different areas were chosen to compare the conductivity, one dot is on the graphene nanosheet supported by the SiO2/Si substrate and the other dot is on the Cr/Au electrode. It turns out that the corresponding I-V curves behave an apparent difference. For the location on the Cr/Au electrode, the current can be measured directly when the bias voltage is applied. However, for the graphene supported by the SiO2/Si substrate, there is no apparent current when the bias voltage is less than ~3 V and this is ascribed to the interface effect of graphene/Au contact27,28. This conducting difference of the two locations can be attributed to the zero band gap semimetal property of graphene and excellent metal conductance of Au. An obvious asymmetry of current-voltage response curve can be observed in Figure 2(c) and this is caused by the asymmetric scattering of charged impurities in graphene nanosheets29. The maximum current is limited by the measurement range of the AFM system that a stable value is obtained. The TUNA current-Z sensor displacement curves under the increasing step bias voltages are shown in Supporting Information Figure S3. The distance of piezo movement before the onset of electrical conductance decreases with the bias voltage because of the increasing electrostatic force effect. Furthermore, the conductive-AFM mapping of graphene nanosheet was also obtained, as shown in Figure 3(b). Obvious conducting and insulation states can be observed in the scanning areas. The electrical contact between the AFM tip and the sample is stable and no abrupt changes are observed at the edges between the graphene nanosheet and Cr/Au electrode. The thickness of graphene nanosheet also plays a crucial role in the conducting behavior16. The conductive-AFM mappings of graphene nanosheet under different bias voltages are shown in Supporting Information Figure S4. It turns out that smaller bias voltage may lead to unstable conducting state on the graphene nanosheets and this is in accordance with the results of I-V responses in Figure 2.

Figure 1. (a) Optical image of a desired graphene nanosheet suspended on the holes and connected by the Cr/Au electrodes. (b) AFM image of the graphene nanosheet in the yellow rectangular box of (a). The insets show the height profiles of graphene. The height of the graphene nanosheet is ~33 nm. The sinking depth of the graphene nanosheet suspended on the hole caused by the pretension is ~52 nm.


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Figure 2. (a) Schematic of the conductive AFM nanoindentation. (b) AFM image of a graphene nanosheet supported by the SiO2/Si substrate and connected by the Cr/Au electrode. Two different locations are chosen to test the conducting behaviors. One is on the Cr/Au electrode and the other is on the graphene nanosheet supported by the SiO2/Si substrate. (c) and (d) correspond to the current-voltage responses of the green and light blue dots in the insets of (b). Different conducting behaviors can be observed.

Figure 3. Conductive-AFM mapping of the graphene nanosheet. The bias voltage is set as +5 V. (a) AFM image of a graphene nanosheet connected by the Cr/Au electrode. (b) Conductive current image of the corresponding graphene nanosheet. Obvious conducting state can be observed on the graphene nanosheet and Cr/Au electrodes, as shown by the yellow area. Obvious insulation state with zero current can also be observed on the SiO2/Si substrate, as shown by the blue areas. No obvious fractures are observed on the graphene nanosheet after the conductive AFM mapping. (c) and (d) correspond to the current section lines of the insets of (b).

The adhesion force and Young’s modulus can be obtained from the force-displacement response curves in the conductive AFM nanoindentation process. The adhesion forces between the tip and the graphene under the electric field were investigated. Similarly, two dots on the graphene nanosheet were chosen, one was on the suspended graphene and the other was on the supported graphene, as shown in Figure 4(a). The variations of adhesion force are shown in Figure 4(b). For the supported graphene, the adhesion force increases with the bias voltage at an increasing rate and this is attributed to the increasing electrostatic force effect. This also can be explained by the I-V response curves that the current increases to a threshold value. For the suspended graphene, the adhesion force also increases with the bias voltage initially, then a sharp decrease is observed when the bias voltage comes to +5 V, as shown in the inset of Figure 4(b), and this phenomenon is caused by the fracture of graphene nanosheet. This is also verified by the height images of graphene nanosheets before and after the conductive AFM nanoindentations (see Supporting Information Figure S5 and S6). Figure 5 shows the deflection error maps


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of graphene nanosheet before and after the conductive AFM nanoindentation process with increasing bias voltages. The deflection error maps were obtained after each nanoindentation process with increasing step bias voltage. No obvious variations are observed when the bias voltage is less than +4 V, as shown in (b), (c) and (d). They are in good conformity with the original graphene nanosheet in (a). An apparent fracture hole is observed when the bias voltage increases to +5 V, as shown by the yellow rectangular box in the inset of (e). Small cracks are also observed on the supported graphene, as shown by the light blue circular box in the inset of (e). Severer fractures appear on the suspended graphene with further increase of bias voltage, as shown in (f). Compared with the suspended graphene, the supported graphene can sustain larger electric field under the same applied load because of the smaller deformation and better thermal conduction. Deflection error maps of other graphene samples are shown in Supporting Information Figure S7. The graphene nanosheet can be approximated as a clamped circular membrane for the isotropic elastic property3,30. This model has been proved appropriately for the inhomogeneous polycrystalline CVD-graphene nanosheets which contain irregular grain boundries31. In our research, the graphene nanosheets are fabricated by the mechanical exfoliation from the natural graphite flakes. This sample with bare of defects can also minimize the adverse influence of electric current on the structures of graphene. The tip radius is far smaller than the diameter of the hole and the effect of nonuniform electric field during the nanoindentation process on the force-deformation behavior is negligible. Thus, the force-deformation behavior of graphene under the electric field can be expressed as

= ( ) ∙ ! + (#$)! + (

%

)!

(1)

where F is applied load, E is the Young’s modulus, t is the thickness of the graphene nanosheet, T is the pretension, ! is the deformation at the center point of graphene nanosheet, R is the radius of the hole, & =0.165 is the Poisson’s ratio of graphene, and q=1/(1.05 − 0.15ν − 0.16& + )=0.98 is a dimensionless constant3. The applied load keeps the same for all the nanoindentation measurements to reduce the load effect on the mechanical properties of graphene. The fitting of the force-indentation depth curve can provide the Young’s modulus of the graphene nanosheet (see Supporting Information Figure S8). The damage of graphene nanosheet doesn’t happen at the beginning of the nanoindentation process under the large electric field until the applied load increases to a critical value (See Supporting Information Figure S9). So the early part of the force-deformation curve is utilized to obtain the softened Young’s modulus and fracture strength of graphene. The intrinsic strength empirically equals to ~1/9 of the Young’s modulus of the graphene nanosheets without fractures3. For the broken graphene nanosheet under the applied load, the maximum stress is derived as3 .

/ ,- = ( 0 )/+

(2)

where ,- is the maximum stress at the central location of the circular nanosheet, 1 is the breaking force under the electric field and r is the tip radius. Figure 6(a) shows the variation of Young’s modulus of a representative graphene nanosheet with the


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increasing step bias. The applied load was 3 μN for all the nanoindentation measurements. As we can see, the Young’s modulus almost keeps the same when the bias voltage is less than +4 V. It behaves a sharp drop when the bias voltage reaches +5 V, verifying the failure of suspended graphene nanosheet. This also can be verified by the topographical images of suspended graphene nanosheet. The Young’s moduli obtained in the experiments are a little smaller than the value of pristine monolayer graphene (~1 TPa) and they are in the reasonable range. In order to investigate the influence of fatigue behaviors, AFM nanoindentation processes were repeated ten times on single graphene nanosheet without applying electric field. It turns out that all the force-indentation depth curves overlap very well, as shown in Supporting Information Figure S10. This can exclude the effect of fatigue fracture and verify the softening effect of electric field on the mechanical properties of graphene. The variations of fracture strengths of graphene nanosheets are shown in Figure 6(b). The values of different graphene nanosheets behave a small difference and this is caused by the diverse thicknesses and wrinkles of suspended graphene nanosheets. The fracture strength behaves a similar trend with the Young’s modulus and shows a sudden drop when the bias voltage increases to a threshold value. This softening effect of electric field on the mechanical properties accords with previous MD simulations22. The electric field increases the C-C bond length and makes the graphene break more easily under the same applied load. Raman spectra of graphene under the gate voltage behave an apparent red shift with increasing voltage32,33. Besides, the binding energy of graphene also decreases with the voltage32. These can certify the softening effect of electric field on the mechanical properties of graphene. The excessively regional Joule heating caused by the high electric current in the graphene is responsible for the electromechanical failure of graphene nanosheet34.

Figure 4. Adhesion force variation with the bias voltage. (a) AFM image of the graphene nanosheet. Two different locations are chosen to investigate the interface effect on the graphene nanosheet. One spot is on the suspended graphene, and the other spot is on the supported graphene. (b) Adhesion force variation with the increasing bias voltage. For the supported graphene, the adhesion force slightly increases between 0 to +4 V, then it behaves a sharp increase when the bias voltage is larger than +4 V. This is attributed to the increasing electrostatic force. The stabilization of adhesion force is caused by the maximum current. The adhesion force on the suspended graphene shows a similar variation trend. As shown by the green circle in the inset of (b), an


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apparent drop of adhesion force is observed when the bias voltage comes to +5 V. This is attributed to the fracture of suspended graphene.

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Figure 5. Deflection error maps of graphene nanosheet before and after the conductive AFM nanoindentation process with increasing bias voltages. No obvious variations are observed when the bias voltage is less than +4V. (b), (c) and (d) show the graphene nanosheet without fractures and they are in good conformity with the original graphene in (a). An apparent fracture hole is observed when the bias voltage increases to +5 V, as shown by the yellow rectangular box in the inset of (e). Small cracks are also observed on the supported graphene, as shown by the light blue circular box in the inset of (e). Severer fractures are observed on the suspended graphene with further increase of bias voltage, as shown in (f). The applied load keeps the same for all the nanoindentation measurements. Young's modulus (GPa)

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Figure 6. (a) Variation of Young’s modulus with increasing bias voltages of a representative graphene. The modulus values keep almost the same when the bias voltage is less than +4 V. Then it behaves a sharp decrease when the bias voltage is larger than +5 V. This trend accords with the adhesion force variation of suspended graphene. (b) Variation of fracture strength with increasing bias voltages. They show a similar trend with the Young’s modulus and suffer a sudden failure when the bias increases to a threshold value. The thicker graphene nanosheet can sustain a higher threshold bias under the same applied load. (c) (Left Y axis) The safety threshold bias increases with the thickness of graphene nanosheet under the same applied load (3 μN). The thicker graphene nanosheet can sustain a higher electric field under the same applied load than the thinner ones. (Right Y axis) The electric field strength before the fracture of graphene nanosheet. It nearly shows a decreasing trend with the thickness of graphene nanosheet.


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We also investigated the safety threshold voltages of graphene nanosheets with different thicknesses under the same applied load. It turns out that the safety threshold voltage of graphene nanosheets increases with the thickness, as shown in Figure 6(c). The nearly proportional threshold failure bias voltage to the thickness of graphene nanosheet verifies the Joule heating related electromechanical failure mechanism of graphene nanosheets under the electric field34. The normalized electric field strength before the onset of fracture almost decreases with the thickness of graphene nanosheet. The reasons are as follows. Firstly, the defects in the graphene nanosheet may increase with the thickness and lower the performance of graphene. Besides, The different contact areas of graphene nanosheets are also responsible for this phenomenon because of the interface barrier of graphene/Au contact27,28. The step bias is 1 V and this can lead to the small deviation. Further experiments indicated that the graphene nanosheet suspended on the holes almost suffers no fracture behaviors under the +10 V bias when the thickness increases to ~80 nm. Graphene nanosheets may suffer defects after the electron beam irradiation that affect the elastic modulus of graphene24,35. Thus, SEM experiments are conducted after the AFM measurements to reduce the adverse effects. The SEM images of suspended graphene nanosheet after the conductive AFM nanoindentation measurements are shown in Supporting Information Figure S11. Obvious fractures can be observed when the bias voltage comes to be +5 V. In order to investigate the failure property of graphene nanosheet under the electric field, we increased the bias voltage to a higher value in the conductive AFM nanoindentation measurements. Figure 7 shows the SEM images of a supported graphene nanosheet (~30 nm) after the nanoindentation process. It shows that the graphene nanosheet is totally destroyed when the bias voltage reaches +10 V. Some remnant graphene layers still stick to the SiO2/Si substrate, as shown by the light blue dash dot line in Figure 7(a). It shows that the graphene nanosheet exhibits an interlayer exfoliation curling failure resulting from the electromechanical coupling effect under the large electric field and external applied load. Previous research has proved that the resistance of graphene nanosheets decreased with the applied load25. Thus, the excessively regional Joule heating caused by the high electric current density under the applied load may lead to the fractures or damages. This can account for the failure mechanism of graphene nanosheets under the electric field with external applied load.


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Figure 7. SEM images of the destructive graphene nanosheet after the AFM measurements. (b) is the magnified yellow rectangular area of (a). The graphene nanosheet (~30 nm) suffers a total failure when the bias voltage is +10V. Compared with the original graphene nanosheet, part of the graphene still sticks to the SiO2/Si substrate and exhibits an interlayer exfoliation curling failure.

In summary, the mechanical properties of graphene nanosheets under the electric field are systematically investigated with the conductive AFM nanoindentation method. The adhesion force increases with the bias voltage because of the electrostatic force effect. The Young’s modulus and fracture strength remain stable initially, and then they show a sharp drop when the electric field increases to a threshold value. The safety threshold voltage of graphene nanosheets under the fixed applied load increases with the thickness. A total electromechanical failure of a thin graphene nanosheet can be observed during the nanoindentation process when the bias voltage increases to +10 V. The excessively regional Joule heating caused by the high electric current density under the applied load is responsible for the electromechanical failures of graphene. The electric field has a significant softening influence on the mechanical properties of graphene and the influence increases with the decreasing thickness. These findings can provide beneficial guidances for the electromechanical applications of graphene based nanodevices. Experimental Methods. SiO2/Si substrate with arrays of holes and Cr/Au electrodes were designed and patterned through the photo etching and electronic beam evaporation. The diameters of the holes were ~3 and ~5 μm, respectively. The depth of the holes was ~500 nm. Another experimental design was introduced to repeat the electromechanical investigation of graphene nanosheets in Supporting Information Figure S12-S14. Natural graphite flakes were purchased from Nanjing MKNANO Tech. Co., Ltd (www.mukenano.com). Graphene nanosheets were obtained by mechanical exfoliation onto the SiO2/Si substrate. Appropriate graphene nanosheets were chosen with the optical microscope BX51 (OLYMPUS) before the conductive AFM experiments to increase the experimental efficiency. 20×, 50×, 100× objectives and 10× eyepiece were utilized to obtain the optical images. Dimension Icon (Bruker) was adopted in the AFM experiments. The temperature and relative humidity in the experiment room were 25 ℃ and 10%, respectively. Tapping mode was utilized to obtain the height image and phase image of graphene nanosheets and the pre-prepared substrate. Conductive AFM nanoindentation method was utilized to obtain the force-displacement curves for the calculation of Young’s modulus, adhesion force and fracture strength. PtSi-NCH AFM probe was used to conduct the nanindentation experiments. The resonant frequency is ~330 kHz and the spring constant is ~42 N/m.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the website. In includes the experimental methods, substrate preparation and characterization, optical, AFM and SEM images of graphene nanosheets, calculation of Young’s modulus.


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AUTHOR INFORMATION Corresponding Author. *E-mail: [email protected] E-mail: [email protected] ORCID. Peng Huang: 0000-0003-0530-7338 Dan Guo: 0000-0002-7681-2377 Notes. The authors declare no competing financial interest. ACKNOWLEDGEMENTS The authors thank Mrs. Weiqi Wang, Wenyan Yang and Rong Wang for the useful guidance in the AFM and SEM experiments. This work was financially supported by National Natural Science Foundation of China (Grant Nos. 51375255, 51527901).

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Electrical Characteristics of Graphene Wrinkles Extracted By Conductive Atomic Force Microscopy and Electrical Measurements on Kelvin Structures. 8th International Conference on IEEE, 2013, 182-183. (14) Fu, X.; Liao, Z.; Zhou, J.; Zhou, Y.; Wu, H.; Zhang, R.; Jing, G.; Xu, J.; Wu, X.; Guo, W.; Yu, D., Strain Dependent Resistance in Chemical Vapor Deposition Grown Graphene. Appl. Phys. Lett. 2011, 99, 21310721. (15) Benameur, M. M.; Gargiulo, F.; Manzeli, S.; Autes, G.; Tosun, M.; Yazyev, O. V.; Kis, A., Electromechanical Oscillations in Bilayer Graphene. Nat. Commun. 2015, 6, 8582. (16) Mativetsky, J. M.; Treossi, E.; Orgiu, E.; Melucci, M.; Veronese, G. P.; Samori, P.; Palermo, V., Local Current Mapping and Patterning of Reduced Graphene Oxide. J. Am. Chem. Soc. 2010, 132 (40), 14130-14136. (17) Mativetsky, J. M.; Liscio, A.; Treossi, E.; Orgiu, E.; Zanelli, A.; Samori, P.; Palermo, V., Graphene Transistors via in Situ Voltage-Induced Reduction of Graphene-Oxide under Ambient Conditions. J. Am. Chem. Soc. 2011, 133 (36), 14320-14326. (18) Ekiz, O. O.; Urel, M.; Guner, H.; Mizrak, A. K.; Dana, A., Reversible Electrical Reduction and Oxidation of Graphene Oxide. ACS Nano 2011, 5 (4), 2475-2482. (19) Faucett, A. C.; Mativetsky, J. M., Nanoscale Reduction of Graphene Oxide under Ambient Conditions. Carbon 2015, 95, 1069-1075. (20) Masubuchi, S.; Arai, M.; Machida, T., Atomic Force Microscopy Based Tunable Local Anodic Oxidation of Graphene. Nano Lett. 2011, 11 (11), 4542-4546. (21) Osvath, Z.; Lefloch, F.; Bouchiat, V.; Chapelier, C., Electric Field-controlled Rippling of Graphene. Nanoscale 2013, 5 (22), 10996-11002. (22) Hao, P.; Gao, Y.; Zhou, Y., The Effect of Electric Charge on the Mechanical Properties of Graphene. Sci. China Phys. Mech. Astron. 2013, 56 (6), 1148-1156. (23) Bao, W.; Myhro, K.; Zhao, Z.; Chen, Z.; Jang, W.; Jing, L.; Miao, F.; Zhang, H.; Dames, C.; Lau, C. N., In Situ Observation of Electrostatic and Thermal Manipulation of Suspended Graphene Membranes. Nano Lett. 2012, 12 (11), 5470-5474. (24) Huang, M.; Pascal, T. A.; Kim, H.; Goddard, W. A. I.; Greer, J. R., Electronic-Mechanical Coupling in Graphene from in situ Nanoindentation Experiments and Multiscale Atomistic Simulations. Nano Lett. 2011, 11 (3), 1241-1246. (25) Hauquier, F.; Alamarguy, D.; Viel, P.; Noel, S.; Filoramo, A.; Huc, V.; Houze, F.; Palacin, S., Conductive-probe AFM Characterization of Graphene Sheets Bonded to Gold Surfaces. Appl. Surf. Sci. 2012, 258 (7), 2920-2926 (26) Xu, K.; Cao, P.; Heath, J. R., Scanning Tunneling Microscopy Characterization of the Electrical Properties of Wrinkles in Exfoliated Graphene Monolayers. Nano Lett. 2009, 9 (12), 4446-4451. (27) Maassen, J.; Ji, W.; Guo, H., First Principles Study of Electronic Transport Through a Cu(111)/ Graphene Junction. Appl. Phys. Lett. 2010, 97, 14210514. (28) Gong, C.; Lee, G.; Shan, B.; Vogel, E. M.; Wallace, R. M.; Cho, K., First-principles Study of Metal-Graphene Interfaces. J. Appl. Phys. 2010, 108, 12371112. (29) Kaiser, A. B.; Gomez-Navarro, C.; Sundaram, R. S.; Burghard, M.; Kern, K., Electrical Conduction Mechanism in Chemically Derived Graphene Monolayers. Nano Lett. 2009, 9 (5), 1787-1792. (30) Castellanos-Gomez, A.; Poot, M.; Steele, G. A.; van der Zant, H. S. J.; Agrait, N.; Rubio-Bollinger, G., Elastic Properties of Freely Suspended MoS2 Nanosheets. Adv. Mater. 2012, 24


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(6), 772-775. (31) Lee, G.; Cooper, R. C.; An, S. J.; Lee, S.; van der Zande, A.; Petrone, N.; Hammerherg, A. G.; Lee, C.; Crawford, B.; Oliver, W.; Kysar, J. W.; Hone, J., High-Strength Chemical-Vapor Deposited Graphene and Grain Boundaries. Science 2013, 340 (6136), 1073-1076. (32) Copuroglu, M.; Aydogan, P.; Polat, E. O.; Kocabas, C.; Suzer, S., Gate-Tunable Photoemission from Graphene Transistors. Nano Lett. 2014, 14 (5), 2837-2842. (33) Mao, L.; Wang, J.; Li, L.; Ning, H.; Hu, C., Modeling of Spectral Shift in Raman Spectroscopy, Photo- and Electro-Luminescence Induced by Electric Field Tuning of Graphene Related Electronic Devices. Carbon 2017, 119, 446-452. (34) Yu, T.; Lee, E.; Briggs, B.; Nagabhirava, B.; Yu, B., Bilayer Graphene System: Current-Induced Reliability Limit. IEEE Elec. Dev. Lett. 2010, 31 (10), 1155-1157. (35) Lopez-Polin, G.; Gomez-Navarro, C.; Parente, V.; Guinea, F.; Katsnelson, M. I.; Perez-Murano, F.; Gomez-Herrero, J., Increasing the Elastic Modulus of Graphene by Controlled Defect Creation. Nat. Phys. 2015, 11 (1), 26-31.


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Softened Mechanical Properties of Graphene Induced by Electric Field

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