Direct four-probe measurement of grain-boundary resistivity and mobility in millimeter-sized graphene

Transcription

1 Supporting Information Direct four-probe measurement of grain-boundary resistivity and mobility in millimeter-sized graphene Ruisong Ma 1,2, Qing Huan 1, Liangmei Wu 1,2, Jia-Hao Yan 1,2, Wei Guo 3, Yu-Yang Zhang 1, Shuai Wang 3, Lihong Bao 1,2,*, Yunqi Liu 4, Shixuan Du 1,2, Sokrates T Pantelides 5,1, 1, 2,* Hong-Jun Gao 1 Institute of Physics &University of Chinese Academy of Sciences, Chinese Academy of Sciences, P.O. Box 603, Beijing , People s Republic of China 2 Beijing Key Laboratory for Nanomaterials and Nanodevices, Beijing, , People s Republic of China 3 School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan , People s Republic of China 4 Beijing National Laboratory for Molecular Sciences, Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing , People s Republic of China 5 Department of Physics and Astronomy and Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37235, United States * Corresponding author. lhbao@iphy.ac.cn, hjgao@iphy.ac.cn 1

2 Methods CVD growth of graphene on Cu foil and transfer technique. Before growth, the Cu foil (Alfa Aesar, 99.8%) was ultrasonically cleaned by solvents (solution mixed by deionized H 2 O, ethanol, and acetic acid with equal volume ratio), followed by rinsing with copious amounts of deionized H 2 O and blowing dry with N 2. After that, the foil was put into the middle of a 1 in. quartz tube and heated to 1040 C in 10 sccm H 2 (99.99%) and 320 sccm Ar (99.99%) mixed atmosphere within 30 min. Next, graphene growth was initiated by introducing sccm CH 4 (0.9% diluted in Ar), sccm O 2 (0.9% diluted in Ar), and 3-25 sccm H 2 mixed in 320 sccm Ar into the CVD system. Following the growth process, the O 2 flow was shut off. Finally, the CVD system was quickly cooled down to 700 C and slowly cooled down to ambient temperature. The as-grown graphene flakes on the Cu foil were transferred onto a Si/SiO 2 substrate by the poly (methyl, methacrylate)-assisted method. 1 Characterization. Raman spectra were measured using a Horiba Jobin Yvon LabRAM HR-800 Raman microscope (laser wavelength = 532 nm, power = 1 mw, beam spot = 1 µm) at ambient temperature and pressure. Electrical transport measurements were carried out by a home-designed UHV four-probe STM system at room temperature and a base pressure of Torr with an additional Keithley 4200-SCS instrument. Before loaded into the STM chamber, the graphene@si/sio 2 sample was glued onto the sample holder by silver paste and was then degassed in the STM chamber at 500 K and pressure of 2

3 Torr for at least 24 hours. Electrochemically etched Au probes are used in the electrical transport measurement. When the probes approach the sample, the capacitance between the probes and the gate electrode is monitored as a real-time feedback signal for the approaching process. 2 The original capacitance value indicates the distributed capacitance of wires both in and out the UHV chamber. Additional value coming from the parallel capacitor formed by the gate electrode and the graphene flake on the SiO 2 /Si wafer is detected once the probe contacts the graphene flake. The approaching process is stopped as long as the reading capacitance becomes stable. The STM and AFM images are obtained in air at ambient temperature by the Nanoscope IIIa SPM (Digital Instruments). STM probes are mechanically cut from platinum/iridium (80% Pt/20% Ir) wires with diameter of 0.25 mm. The STM images are obtained in constant current mode while the AFM image is acquired in the tapping mode. Extraction of intra-grain and inter-grain sheet resistance The measured resistance R I1V23 by I 1 V 23 setup can be expressed as V 23 /I 1 (in unit Ω). Considering the geometry factors in these configurations, 3, 4 the sheet resistance R (in unit Ω/ ) of grain-1 (R 1 ), grain-2 (R 2 ) and inter-grain measurement (R inter-gain ) at a certain carrier density can be obtained from R I1V23 by 3, 4 2 R R IV ln( ) s s 1 23, (S1) s13s where s ij (=s ji ) is defined as the distance between point i and j in Figures 3a-c. For example, s 12 in Eq (S1) refers to the distance from probe 1 to probe 2. If the four probes 3

4 exactly form a standard square, i.e., s 12 =s 23 =s 34 =s 41 =s, the sheet resistance R can be simplified as 3, 4 R 2 ln 2 R. (S2) IV 1 23 Extending the 1D GB defect into a 2D domain According to the Poisson s equation, the current density and the electric field distributions caused by probes 1 and 4 can be derived separately in the four-probe measurement. For a homogenous 2D material, the current injected by a single STM probe (e.g. probe 1) spreads radially to all directions in plane as presented in Figure S4a. If another probe (e.g. probe 4) contacts the sample and is grounded (see Figure S4b), the total current density distribution can be obtained by summing the current density vectors that result from the two current probes separately, as is shown in Figure S4c. The summed current density distributions are shown in Figure S4d, wherein I indicates current injection while G means the ground. Red arrows demonstrate the current directions in plane and the color bar on the right reveals the current density values in logarithmic form (a.u.). As can be seen from Figure S4d, the current passes perpendicularly through the symmetry axis of the two current probes. If the GB exactly coincides with this symmetry axis, the current also passes approximately through the GB without a parallel component, like the case in the device measurement. 5-7 In the four-probe case, if a GB coincides with the symmetry axis, the effect of the GB on electrons, especially for those moving along the normal to the GB, can also be considered 4

5 as an extension of the conductance channel. 7 This extension can be characterized by an effective parameter λ: R GB, (S3) where ρ GB is defined as the GB resistivity (in unit kω μm) and R (in unit Ω/ ) is the intra-grain sheet resistance. 7 In this way, the sheet resistance in the extended area (dark green area with an effective extent λ), indicated by dark green arrow in Figure S3, shares the same sheet resistance with the pristine graphene grain (R ). Consequently, the 1D defect has been transformed into an extended 2D area, referred to the pristine graphene grain, as if electrons move a longer way through the GB. 7, 8 Derivation of the expression of the sheet resistance crossing the grain boundary R inter-grain If R 1 R 2 =R, the model illustrated in Figure S3 can be simplified into the case shown in Figure S5a. In this case, according to Eq (S2), the measured resistance R I1V23 crossing the GB and the intra-grain sheet resistance R satisfies: 2 R R IV ln( ) rr 1 23, (S4) rr where r ij (=r ji ) is defined as the distance between point i and j in Figures S3 and S5, and shows the spacing between different points after extended in our model. According to Eq (S1), the sheet resistance crossing the grain boundary R inter-grain can be calculated from 5

6 intra-grain sheet resistance R by rr ln( ) 2 rr Rinter-grain RIV 1 23 R s13s42 s13s42. (S5) ln( ) ln( ) s s s s where s ij (=s ji ) is defined as the distance between point i and j in Figures 3a-c. As for the case wherein the four probes form a standard square and the GB line lies in the symmetry axis of the square, the Eq (S5) can be simplified to 2 2 R s ( s ) Rinter-grain f ( R, s, ) ln( ) 2, (S6) ln 2 s in which s is the side length of the square (s=s 12 =s 23 =s 34 =s 41 ) and λ represents the extent. In this sense, the inter-grain sheet resistance only changes as a function of R, s and the effective parameter λ. Estimation of GB resistivity for the case with R 1 R 2 In a more complicated case when the GB stitches two pristine graphene domains with obviously different sheet resistance (R 1 R 2 ) shown in Figure S5b, the GB resistivity can also be estimated. However, the expression for the inter-grain sheet resistance (R inter-grain ) is more complicated than Eq (S6). The 2D resistivity of grain-1 and grain-2 is denoted as R 1 and R 2, respectively. In this case, the effective parameter λ can be defined by λ=ρ GB /R 2 (R 1 can also be used in obtaining the parameter λ). Therefore, the original GB line splits into two boundary lines, GB-L and GB-R. Since grain-2 and the extended area share the same resistivity, GB-L can be ignored as depicted in Figure S5c. 6

7 The connecting line of probes 1 and 3 intersects with GB-R at point M while the analogous node for probes 2 and 4 is labeled as N. Since only GB-R remains, in order to estimate the GB resistivity, the current ejected by the current probe is supposed to preserve the radial diffusing scheme even encountering the GB-R as shown in Figure S5d. However, the current experiences different resistivity after crossing GB-R, i.e., R 1 and R 2 as presented in Figure S5d. On condition that the current entering via probe 1 is I 1, the current density J 1 is given by () I J1 r 2 rt 7 1, (S7) where r is the distance away from probe 1 in Figure S5d and t is the graphene membrane thickness. The electric field yielded by J 1 at grain-1 is expressed by E( r) ( ) I R I d Vr ( ), (S8) 2 rt 2 r dr J1 r where ρ 1 is the bulk resistivity of grain-1 and V(r) is the potential at position r away from probe 1. Accordingly, potential at probe 2 can be written as d Vr ( ) R1 I1 R1 I1 V2 0 dr dr ln( r12 ) r12 dr. (S9) r12 2 r 2 In the case of the potential at probe 3, the current passes through two grains with different resistivity. At point M, the potential is given by R I R I d ln( ). (S10) 2 r VM r r r 1M 1Μ The potential difference between point M and point 3 caused by the diffusing current at grain-2 can be described by R2 I 1 R2 I1 VM V3 ln( r1m ) ln( r13 ). (S11) 2 t 2 t Therefore, according to Eq (S10) and (S11), V 3 is deduced to be

8 R I R I R I R I R I V r r r r ln( 1M ) ln( 1M) ln( 13) ln( 1M) ln( ) r1m r. (S12) Then the expression for the measured voltage difference of probes 2 and 3 can be derived from Eq (S9) and (S12): R I r R I V23 V2 V3 2 r 2 r r 1 1 1M ln( ) ln( ) 12 1M, (S13) Taking only probe 4 into consideration which is grounded (without influence from other probes), the voltage drop between probes 3 and 2 is V 32 R2 I4 r4n R1 I4 r42 ln( ) ln( ), (S14) 2 r 2 r 43 4N where I 4 represents the electrical current leaving the sample. Since I 1 =-I 4 =I, the final expression of the measured resistance R I1V23 in view of all probes should be R IV 1 23 V23 R1 r1m r42 R2 r13 r4n ln( ) ln( ). (S15) I 2 r r 2 r r 12 4N 1M 43 Accordingly, the expression of the inter-grain sheet resistance is illustrated below: R inter-grain 2 R r r R s s s s s s ln( ) ln( ) ln( ) s s s s s s 1 1M N RIV 1 23 ln( ) ln( ) r12 r4n r1m r r r. (S16) When the four probes form a standard square with a GB lying in the symmetry axis of the square, Eq (S16) can be simplified to R s ( s ) ( 2 ) ( ) 1 R s s s 2 Rinter-grain f ( R1, R2, s, ) ln( ) ln( ), (S17) 2 ln 2 s 2 ln 2 s in which s and s+λ are the side length of the rectangular in Figure S5b. As for GB-S1 and GB-S2, the intra-grain sheet resistances on either side are obviously different, thus the 8

9 GB resistivity can be extracted based on Eq (S17). By supposing that R =R 1 =R 2 (the case in the previous section), the equation above can be simplified as inter-grain R s ( s ) ln 2 s 2 2 (,, ) ln( ) 2, R f R s which is exactly the same as Eq (S6). Converting the gate voltage to sheet carrier densities of graphene In our experiment, a series of gate voltage is applied to the gate electrode in order to tune the charge carrier densities of the graphene on SiO 2 /Si substrate. The sheet charge carrier densities n s can be calculated using n s CoxV e G0, (S18) where C ox =ε ox /t ox is the capacitance per unit area for the dielectric layer, ε ox is the permittivity of SiO 2, t ox is the thickness of the oxide layer, e is the elementary charge, and V G0 =V G V Dirac is the gate voltage referenced to Dirac voltage (charge neutrality point). 9 With regard to the 300 nm SiO 2 layer, C ox = F cm Extraction of hole and electron mobility for a 2D sample According to the Drude model for the conductivity, ne s, (S19) where μ is the electrical mobility and σ is the conductivity for a 2D domain. As a 9

10 consequence, the electrical mobility μ can be obtained from the derivative of the Drude formula in the linear region near the charge neutrality point (positive carrier densities for electrons and negative values for holes): 1 d. (S20) e dn s Ratio of mobility at GB electronic transition region with intra-grain mobility Based on Eq (1) and (3) in the main text, the relation of sheet resistance at GB transition region R GB with the intra-grain sheet resistance R is described by: R GB R. (S21) W In combination with Eq (S19), the relationship of the mobility in the GB electronic transition region with that in the pristine graphene grain (intra-grain mobility) satisfies: GB pristine W. (S22) Similarly, the same method can be applied to the case regarding graphene wrinkle. Width of the graphene wrinkle As is already mentioned, a graphene wrinkle (labeled as wrinkle-1) on grain-2 is indicated by a light blue arrow in Figure 2a in the main text. An optical micrograph of this graphene wrinkle-1 is presented in Figure S14a, where the width ranges from 2.3 to 4.3 μm (3.3 μm on average) measured at twenty positions. The AFM image in Figure S14b reveals the details of the wrinkle area indicated by a red square in Figure S14a. 10

11 According to the AFM line profile in Figure S14c, which is along the red dash line in Figure S14b, the large graphene wrinkle consists of about ten small wrinkles and the height of the small wrinkles is in the range of 10 nm. Since the effective extent is 14.3 μm, 3~5 times the structural width (2.3 to 4.3 μm), these small wrinkles behave like folded graphene membranes with 3~5 layers stacking if the simple diffusive model holds

12 References: (1) Guo, W.; Jing, F.; Xiao, J.; Zhou, C.; Lin, Y.; Wang, S. Adv. Mater. 2016, 28 (16), (2) Ma, R.; Huan, Q.; Wu, L.; Yan, J.; Zou, Q.; Wang, A.; Bobisch, C. A.; Bao, L.; Gao, H.-J. Rev. Sci. Instrum. 2017, 88 (6), (3) Li, A.-P.; Clark, K. W.; Zhang, X.-G.; Baddorf, A. P. Adv. Funct. Mater. 2013, 23 (20), (4) Miccoli, I.; Edler, F.; Pfnur, H.; Tegenkamp, C. J. Phys.: Condens. Matter 2015, 27 (22), (5) Jauregui, L. A.; Cao, H. L.; Wu, W.; Yu, Q. K.; Chen, Y. P. Solid State Commun. 2011, 151 (16), (6) Yu, Q.; Jauregui, L. A.; Wu, W.; Colby, R.; Tian, J.; Su, Z.; Cao, H.; Liu, Z.; Pandey, D.; Wei, D.; Chung, T. F.; Peng, P.; Guisinger, N. P.; Stach, E. A.; Bao, J.; Pei, S.-S.; Chen, Y. P. Nat. Mater. 2011, 10 (6), (7) Tsen, A. W.; Brown, L.; Levendorf, M. P.; Ghahari, F.; Huang, P. Y.; Havener, R. W.; Ruiz-Vargas, C. S.; Muller, D. A.; Kim, P.; Park, J. Science 2012, 336 (6085), (8) Ji, S.-H.; Hannon, J. B.; Tromp, R. M.; Perebeinos, V.; Tersoff, J.; Ross, F. M. Nat. Mater. 2012, 11 (2), (9) Dorgan, V. E.; Bae, M.-H.; Pop, E. Appl. Phys. Lett. 2010, 97 (8), (10) Choi, M. S.; Lee, S. H.; Yoo, W. J. J. Appl. Phys. 2011, 110 (7), (11) Zhu, W. J.; Low, T.; Perebeinos, V.; Bol, A. A.; Zhu, Y.; Yan, H. G.; Tersoff, J.; Avouris, P. Nano lett. 2012, 12 (7),

13 (a) (b) 100 nm 100 nm (c) (d) 100 nm 70 nm Figure S1. Large-area STM images of graphene-covered Cu foil substrates. These STM images show quite different morphologies of the Cu substrate underneath the graphene at varied substrate locations. Imaging parameters: (a) I t =300 pa and V sample =67.92 mv; (b) I t =358.6 pa and V sample =87.16 mv; (c) I t =240.3 pa and V sample =82.02 mv; (d) I t =200 pa and V sample =97.17 mv. 13

14 (a) (b) (c) 3 nm 2 nm 1 nm (d) (e) (f) 3 nm 2 nm 1 nm Figure S2. Atomically resolved STM images of graphene on Cu foil. (a), (b) and (c) are STM morphology images with atomic resolution in constant current mode. (d), (e) and (f) are the corresponding current images for (a), (b) and (c), respectively. As can be seen from these images, the defect-free graphene is continuously grown across different surface topographies on the Cu substrate. Imaging parameters: (a) and (d) I t =800 pa and V sample =89.12 mv; (b) and (e) I t =367.3 pa and V sample =82.02 mv; (c) and (f) I t =367.3 pa and V sample =82.02 mv. 14

15 Probe 3 Extended GB area Probe 2 Probe 4 V V Probe 1 Grain-2 SiO 2 P ++ Si (gate) G λ I Grain-1 λ=ρ GB /R I 1 V 23 Figure S3. Extent of the GB. In our model, the presence of a GB can be considered as simply an extent of the conductance channel with an effective parameter λ where λ=ρ GB /R. In this expression, ρ GB is the GB resistivity and R is defined as the sheet resistance of the extended GB domain. The size in these drawings is not to scale. 15

16 4 Current density (a.u.) 4 4 (a) Current in (b) Current out 3 3 R 2 R 2 I 4 I 1 1 I 4 =-I 1 1 J1 distributions J 4 distributions (c) Superposition (d) 3 G (probe 4) I (probe 1) -2-3 R I 4 =-I 1 J J 1 J total 1 4 Symmetry axis Logarithmic form -6-7 Figure S4. Current density distributions of a single probe and two probes on a homogenous graphene (sheet resistance R ) during I 1 V 23 measurement. (a) Current density distributions (J 1 ) if only I 1 (current which goes into the flake at probe 1) is considered. I 1 will diffuse radially out of the contact point in the plane as indicated by the red arrow. (b) Current density distributions (J 4 ) caused by probe 4 alone. Since I 1 goes out of the graphene at probe 4, I 4 can be treated as reverse of I 1, i.e. I 4 =-I 1. The blue arrow demonstrates that the current I 4 leaves the sample at probe 4. (c) Simple superposition of 16

17 the current density distributions in (a)-(b). The black arrow shows the main direction of the overall current density J total, which is compounded by vectors from J 1 and J 4. (d) The overall J distributions in logarithmic form. The red arrows indicate the current directions in the plane of graphene membrane. The color bar reveals the current density in logarithmic form (a.u.). As can be seen from this image, the current passes perpendicularly through the symmetry axis of the two current probes in this geometry. 17

18 (a) V 3 3 λ=ρ GB /R V 2 2 (b) V 3 3 GB-L GB-R V 2 2 R R R s R 2 R 2 R 1 s G 4 s+ G 4 λ=ρ GB /R 2 s+ 1 I 1 (c) 3 GB-R (d) 3 GB-R V 3 R 2 N V 2 2 R 2 2 M R 1 M R 1 G 4 I 1 I I 1 Figure S5. The model to extract the GB resistivity. (a) The schematic showing model wherein the intra-grain sheet resistances of grains on both sides are the same. (b) The schematic of four-probe measurement with different intra-grain sheet resistances on either side. The GB is extended into a 2D GB area (green area) referred with sheet resistance R 2. The extent of GB is represented with an effective parameter λ where λ=ρ GB / R 2. Hence, the original GB line is split into two boundary lines in which GB-L connects the extended area with grain-1 and GB-R connects with grain-2. (c) Equivalent model as (b). Since the resistivity of the extended area is set to be the same as grain-2, the extended 18

19 area and grain-2 can be merged together and only line GB-R is left. The connecting line for probes 1 and 3 intersects with GB-R at point M. As for probes 2 and 4, the crossing point is labeled as N. (d) Assumption proposed in our model for GB stitching grains with different resistivity. Current injected by probe 1 diffuses radially to all directions within the plane and preserves its propagation direction even encountering the GB-R separating the areas with different resistivity. 19

20 Figure S6. Effective parameter λ as function of carrier densities n s for GB-S1. The line defect GB-S1 shown in Figure S7a stiches two grains with nearly zero rotation angle. The value λ is calculated according to Eq (1) in the main text. The effective parameter λ shows small variations with different carrier densities tuned by gate voltage, especially near the neutral point. 20

21 (a) GB-S2 Grain-S3 Grain-S2 GB-S1 Grain-S1 200 μm (b) Figure S7. Optical image and Raman spectra of another polycrystalline graphene on SiO 2 /Si substrate. (a) Three merged hexagonal graphene grains stitched by two GBs with nearly zero rotation angle. The expected GB lines are indicated by white dash lines. The edges of each graphene grain are indicated by the colored dash line (blue for grain-s1, red for grain-s2 and black for grain-s3, respectively). (b) Raman spectra for the three grains in (a) with an excitation wavelength of 532 nm of the laser. The spectra are offset vertically for clarity. The fact that the intensity of 2D peak is about two times higher than that of G peak and the 2D peak can merely be fitting by one Lorentz curve 21

22 confirms the monolayer nature of this merged graphene flake. Occurrence of D peak reveals additional non-negligible defects of this graphene flake. 22

23 Figure S8. Experimental data and fitting results for GB-S1 and GB-S2. (a) Sheet resistance of grain-s1 (blue) and grain-s2 (red) shown in Figure S7a. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for GB-S1 is 4.6 μm. (c) Electrical conductivity of GB-S1 as a function of carrier densities. The extracted hole and electron mobility values for GB-S1 are ± and 1.892±0.036 cm 2 V -1 s -1, respectively. (d)-(f) Analogous results of GB-S2 characterized in Figure S7a. The parameter λ for GB-S2 is 1.7 μm. For GB-S2, the extracted hole and electron mobility values are 2.453±0.132 and 6.917±0.280 cm 2 V -1 s -1, respectively. 23

24 Fig. S9. Experiment data and fitting results for GB-S3. (a) Sheet resistance of grain-1 (blue), grain-2 (red) and inter-grain (black) measurement across GB-S3. The inset shows the micrograph of the four-probe measurement across the GB-S3. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for GB-S3 is 28.8 μm. (c) Extracted resistivity of GB-S3 under a series of carrier densities.(d) Electrical conductivity of GB-S3 as a function of carrier densities. The extracted hole and electron mobility values for GB-S3 are ± and ± cm 2 V -1 s -1, respectively. 24

25 Fig. S10. Experiment data and fitting results for GB-S4. (a) Sheet resistance of grain-1 (blue), grain-2 (red) and inter-grain (black) measurement across GB-S4. The inset shows the micrograph of the four-probe measurement across the GB-S4. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for GB-S4 is 14.3 μm. (c) Extracted resistivity of GB-S4 under a series of carrier densities.(d) Electrical conductivity of GB-S4 as a function of carrier densities. The extracted hole and electron mobility values for GB-S4 are ± and ± cm 2 V -1 s -1, respectively. 25

26 Fig. S11. Experiment data and fitting results for GB-S5. (a) Sheet resistance of grain-1 (blue), grain-2 (red) and inter-grain (black) measurement across GB-S5. The inset shows the micrograph of the four-probe measurement across the GB-S5. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for GB-S5 is 19.7 μm. (c) Extracted resistivity of GB-S5 under a series of carrier densities.(d) Electrical conductivity of GB-S5 as a function of carrier densities. The extracted hole and electron mobility values for GB-S5 are ± and ± cm 2 V -1 s -1, respectively. 26

27 Fig. S12. Experiment data and fitting results for GB-S6. (a) Sheet resistance of grain-1 (blue), grain-2 (red) and inter-grain (black) measurement across GB-S6. The inset shows the micrograph of the four-probe measurement across the GB-S6. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for GB-S6 is 10.0 μm. (c) Extracted resistivity of GB-S6 under a series of carrier densities.(d) Electrical conductivity of GB-S6 as a function of carrier densities. The extracted hole and electron mobility values for GB-S6 are 1.091± and 0.947± cm 2 V -1 s -1, respectively. 27

28 Fig. S13. Experiment data and fitting results for wrinkle-s1. (a) Sheet resistance of intra-grain (red) and inter-grain measurements (black) across wrinkle-s1. The left inset shows the micrograph of the four-probe measurement across the wrinkle-s1. The right inset shows a magnified micrograph of wrinkle-s1. The averaged width of this wrinkle is about 3.0 μm. (b) Fitting results of measured resistance (black) under I 1 V 23 setup with the calculated data (orange) based on the model. The parameter λ for wrinkle-s1 is 17.9 μm. (c) Extracted resistivity of wrinkle-s1 under a series of carrier densities.(d) Electrical conductivity of wrinkle-s1 as a function of carrier densities. The extracted hole and electron mobility values for wrinkle-s1 are 150.1±2.9 and 121.9±2.5 cm 2 V -1 s -1, respectively. 28

29 (a) Wrinkle 10 μm (b) 2 μm (c) 29

30 Figure S14. Optical and AFM characterization of graphene wrinkle-1 on Si/SiO 2 substrate. (a) Optical micrograph of graphene wrinkle-1 on SiO 2 /Si substrate. The width of wrinkle area ranges from 2.3 to 4.3 μm measured at twenty positions. The average width of this defect is 3.3 μm. (b) AFM image of graphene wrinkle-1 on Si/SiO 2 substrate which corresponds to the area indicated by red square in (a). The red arrows indicate the preserved graphene wrinkle formed on Cu foil by differential thermal expansion of metal substrate and graphene during post-growth cooling. (c) AFM line profile of the graphene wrinkle along the red dashed line shown in (b). 30

31 (a) 100 nm (b) Figure S15. STM characterization of graphene GB on Cu substrate. (a) STM image of a graphene GB on Cu foil. The underneath Cu substrates share the same features as that shown in Figure S1c. (b) Line profile of the GB along the red dashed line shown in (a). The width of this GB is about 10 nm. 31