A general and simple method for evaluating the electrical transport performance of graphene by the van der Pauw–Hall measurement

Accepted Manuscript Article A general and simple method for evaluating the electrical transport performance of graphene by the van der Pauw-Hall measurement Fangzhu Qing, Yang Shu, Linsen Qing, Yuting Niu, He Guo, Shuyi Zhang, Chunlin Liu, Changqing Shen, Wanli Zhang, Samuel S. Mao, Wenjuan Zhu, Xuesong Li PII: DOI: Reference:

S2095-9273(18)30504-8 https://doi.org/10.1016/j.scib.2018.10.007 SCIB 519

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Science Bulletin

Received Date: Revised Date: Accepted Date:

17 July 2018 17 September 2018 30 September 2018

Please cite this article as: F. Qing, Y. Shu, L. Qing, Y. Niu, H. Guo, S. Zhang, C. Liu, C. Shen, W. Zhang, S.S. Mao, W. Zhu, X. Li, A general and simple method for evaluating the electrical transport performance of graphene by the van der Pauw-Hall measurement, Science Bulletin (2018), doi: https://doi.org/10.1016/j.scib.2018.10.007

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Article Received 17 July 2018 Received in revised form 17 September 2018 Accepted 30 September 2018

A general and simple method for evaluating the electrical transport performance of graphene by the van der Pauw-Hall measurement Fangzhu Qinga, c, Yang Shua, Linsen Qingb, Yuting Niua, He Guoa, Shuyi Zhanga, Chunlin Liua, Changqing Shena, Wanli Zhanga, Samuel S. Maod, e, Wenjuan Zhuf, Xuesong Lia, * a

State Key Laboratory of Electronic Thin Films and Integrated Devices & School of Electronic

Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China b

Chengdu Institute of Biology, Chinese Academy of Sciences, Chengdu 610041, China

c

National Engineering Research Center of Electromagnetic Radiation Control Materials, University of

Electronic Science and Technology of China, Chengdu 610054, China d

Institute of New Energy, Shenzhen 518031, China

e

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720,

USA f

Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign,

Urbana, IL 61801, USA *Corresponding author. E-mail address: [email protected] (X. Li) ABSTRACT: Expected for many promising applications in the field of electronics and optoelectronics, a reliable method for the characterization of graphene electrical transport properties is desired to predict its device performance or provide feedback for its synthesis. However, the commonly used methods of extracting carrier mobility from graphene field effect transistor or Hall-bar is time consuming, expensive, and significantly affected by the device fabrication process other than graphene itself. Here we reported a general and simple method to evaluate the electrical transport performance of graphene by the van der Pauw-Hall measurement. By annealing graphene in vacuum to remove the adsorbed dopants and then exposing it in ambient surroundings, carrier mobility as a function of density can be measured with the increase of carrier density due to the dopant re-adsorption from the surroundings. Further, the relationship between the carrier mobility and density can be simply fitted with a power equation to the first level approximation, with which any pair of measured carrier mobility and density can be normalized to an arbitrary carrier density for 1

comparison. We experimentally demonstrated the reliability of the method, which is much simpler than making devices and may promote the standard making for graphene characterization. Keywords: graphene, van der Pauw, Hall, chemical vapor deposition (CVD)

1.

Introduction Graphene has been attracting great interests because of its unique properties and many

promising applications since its re-discovery in 2004[1]. One of the characteristics of graphene is its electronic properties. Graphene has remarkable high carrier mobility at room temperature up to 200,000 cm2 V-1 s-1 at a carrier density of 1012 cm-2 for the suspended monolayer graphene[2]. Although graphene is not directly suitable for digital electronics because it has no band gap, it is very promising for analog, high frequency applications [3-5] and interconnects[6,

7]

. Correspondingly, the sheet

resistance of graphene can be as low as 30 Ω/□, together with its high optical transmittance of ~97.7%, it can also be used as a transparent conductive electrode[8]. In addition, graphene also has very good mechanical robustness. Even with extreme deformation, excellent conductivity can still be preserved, showing great potential for the applications in flexible electronics[9-11]. Most of graphene’s applications in the electronic and optoelectronic fields require the film have a wafer scale or even larger size in area. Nowadays, such kind of large-area graphene films are mainly synthesized by chemical vapor deposition (CVD) method, typically using Cu as the catalytic substrate[12-14]. Before its application, the electronic properties of graphene need to be evaluated as the synthetic graphene normally has various defects. As the electronic properties of graphene are tightly correlated to its crystal structure, they are also usually used to evaluate the quality (crystallinity) of graphene. The most common method for graphene electronic property characterization is to extract its carrier mobility from graphene field effect transistor (FET) with the Drude model as follows, µ = (enρ)-1, and the carrier density, n = Cg(Vg-Vdirac)/e, where Cg is the gate capacitance[15]. Although making graphene FET is compatible with the modern microelectronic technology, which is already quite mature, the device fabrication process actually has significant effect on the final results rather than the quality of graphene itself. In addition, the device fabrication is time consuming and expensive. Furthermore, the most important issue is that the carrier mobility is highly related to the substrate and carrier density[16]. Much higher carrier mobility of graphene on h-BN substrates can be achieved than that on SiO2/Si substrates as there is less substrate surface polar phonon scattering on h-BN[17, 18]. For graphene on SiO2/Si substrates, the mobility decreases with increasing carrier density, due to short range scattering and optical phonon scattering from SiO2[19]. It is known that the water and oxygen in air can introduce doping in graphene and increase the carrier density at zero gate voltage[20]. Thus, the mobilities measured in vacuum condition may have higher values than that in ambient environment. It is not reliable to compare the mobility of graphene on different substrates or with different initial 2

carrier densities directly, which has been overlooked in many previous literatures [21-24]. Graphene mobility can also be extracted by making graphene Hall bars, which however suffers from similar issues as graphene FETs. Another method is to measure the sheet resistance of graphene, for example, by the linear 4-probe measurement or the van der Pauw (VDP) method, which can characterize the graphene film on the insulated substrate in the macroscale without further device fabrication process. Sheet resistance is directly related to applications such as transparent conductive electrode, but it is not accurate to evaluate graphene crystallinity as it is also a function of carrier density, which varies with surrounding conditions. By applying the gate voltage on the VDP geometry can also extract the carrier mobility, similar to the FET case but with the conductivity measured by the 4-probe VDP method without any photolithographic process[25]. However, it usually requires the sample little doped, e.g., measured in a vacuum chamber. Otherwise, it is not easy to locate the Dirac point at low voltage. Raman spectroscopy is another strong tool for graphene characterization and has been correlated to the carrier mobility as well, but the errors are too large to make it not actually useful in practice [26-28]. Therefore, a general method to evaluate the electrical transport performance of graphene with comparable data is still desired and the standard needs to be set up. VDP-Hall (VDP-H) measurement is a common technique for the characterization of thin film. Similar to the measurement of the sheet resistance, large-area graphene on the insulated substrate can be characterized directly. Other than the sheet resistance, with the application of the magnetic field, both carrier density and mobility can be extracted as well[28-30]. However, when being conducted in ambient conditions, as different samples may have different carrier density due to unintentional doping, the measured mobility cannot be compared directly. In this work, we experimentally measured the changes of carrier mobility as a function of carrier density that was tuned by the unintentional doping from the ambient surroundings. We found that the decrease of the carrier mobility with the increase of carrier density could be well fitted with a power equation, with which the carrier mobility can be normalized to any carrier density (in a practical range) for comparison. Our work provides a simple and reliable method which can be generally used for evaluating the electrical transport performance of graphene in the macroscale and may promote the standardization of graphene characterization. 2.

Materials and methods Graphene was synthesized on Cu substrates by the CVD method and then transferred to 285-nm

SiO2/Si wafer substrates with the wet transfer technique with poly(methyl methacrylate) (PMMA) as carrier film and FeCl3 aqueous solution to etch Cu[12]. According to the parameters we used, the synthetic graphene films were polycrystalline with domain size in a range of several to tens of micrometers. Typically, the graphene samples were cut into ~(1 × 1) cm2 square pieces and the substrates were a little bit larger. Silver paint was used as the electrodes at the four corners of the graphene films, as shown in Fig. 1a. 3

Fig. 1. (Color online) Typical graphene sample for the VDP-H measurement. (a) Picture of a transferred graphene sample with silver paint at the four corners for the VDP-H measurement. (b) Optical microscopy image of the transferred graphene with typical monolayer and continuous features. The scale bar is 10 µm. Inset is the AFM image with a scanning area of (5×5) µm2. (c) Typical Raman spectrum of the sample.

Optical microscopy, atomic force microscopy (AFM, Bruker Dimension Icon), and Raman spectroscopy (Renishaw Invia, laser wave length of 532 nm) were used for materials characterization. The VDP-H measurement was performed with an ECOPIA HMS-5000 Hall measurement system. The measurements were conducted in ambient surroundings with temperature of ~297 K and relative humidity of 47%-55%. A constant current and magnetic field of 20 mA and 0.55 T were used, respectively. To achieve carrier mobility at various carrier densities, the transferred graphene film was firstly annealed in a vacuum chamber (background pressure less than 0.1 Pa) at 200 oC for 30 min to remove the adsorbates. After cooling down to room temperature, the sample was taken out of the vacuum chamber and then loaded onto the VDP-H measurement stage as quickly as possible (within several minutes). Then the VDP-H measurements were conducted at a frequency of one time per ~23 s (1/23 s-1) until the carrier density was almost stable (adsorption of the dopants from surroundings was almost saturated). 3.

Results and discussion

3.1 Reliability of the VDP-H measurement To confirm the reliability of the VDP-H measurement, a graphene sample was cycled between ambient surroundings and the vacuum annealing while the VDP-H measurements were conducted. That is, the sample was annealed and then performed the VDP-H measurement (G1-1). Then the sample was annealed again and performed the VDP-H measurement for the second time (G1-2),

subsequently for G1-3 and G1-4. Fig. 1b is the optical microscopy image of the transferred graphene used here showing its typical monolayer and continuous features, which is also confirmed with the inset AFM image. The lines in the AFM image correspond to the copied morphology of the Cu steps. Fig. 1c is the typical Raman spectrum of the sample, which has no detectable D band, indicating a very low defect density. Fig. 2a shows the plots of carrier mobility vs. density (the µ-n plots). It can be seen that except the 1st one, the last three are almost overlapped, indicating the very good repeatability of the measurements. The difference between the 1st one and the others may be attributed to the fact that annealing may help to enhance graphene performance by removing transfer residues and relaxing strains. Fig. 2b shows the carrier density as a function of time. The different 4

increase rates of n may be attributed to the fluctuating adsorption rate of the dopants due to the non-constant humidity of the surroundings.

Fig. 2. (Color online) Cycled VDP-H measurements on a transferred graphene sample. The last number of the labels in the legend, G1-i, means the VDP-H measurements were conducted after the ith annealing. (a) Plots of µ vs. n. (b) Plots of n vs. t. 3.2 Carrier density dependence of the mobility and sheet resistance At room temperature, the dominant scattering mechanism is Coulomb scattering by impurities (µC), the short-range scattering by defects (µsr), the graphene acoustic phonon (µ gr), and substrate surface polar phonon scattering (µox) [16]. The overall mobility for monolayer graphene is given using the Matthiessen’s rule µ–1≈µC–1 + µsr–1 + µgr–1 + µox–1≈SC–1 + n/Ssr + nT/Sgr + nβf(T)/Sox

,

(1)

where SC, Ssr, Sgr, Sox, and β are corresponding fitting parameters and f(T) is a function of temperature [16]

. For specific temperature (for this case, at 297 K), Eq. (1) can be simplified as µ–1≈ A + Bn+Cnβ

,

(2)

or µ≈ 1/(A + Bn + Cnβ) ,

(3)

where A = SC–1, B = 1/Ssr + 297/Sgr, C = f(297)/Sox. To the first level approximation of Eq. (3) we can get µ≈µi(n/ni) –α

,

(4)

where ni is an arbitrary value and µi is the carrier mobility at the density ni. For simplicity, here subscript i of ni corresponds to the carrier density ni = i × 1012 (cm-2). α is between 0 and 1. The fitting parameters for the four plots in Fig. 2a are listed in Table 1 (for clarification, only the fitting curve for G1-1 is shown in Fig. 2a). The close-to-1 determination coefficients (R2) indicate the fittings are good. Table 1. Fitting parameters for the data in Figs. 2a and 3a at n1= 1012 cm-2, respectively. Sample No.

µ1 (cm2 V-1 s-1)

α

R2

G1-1

3,984.4

0.525

0.9989

G1-2

4,223.8

0.538

0.9985

G1-3

4,245.8

0.531

0.9989

G1-4

4,339.1

0.541

0.9997

5

S1

4,243.3

0.53

0.9991

S2

3,073.4

0.437

0.9989

S3

2,002.2

0.567

0.9988

As the sheet resistance Rs = 1/(neµ), from Eq. (4) we can get Rs = Rsi(n/ni)α–1

,

(5)

where Rsi is the sheet resistance at the carrier density ni. 3.3 Evaluation of the electrical transport performance of graphene Now we can consider how to evaluate the electrical transport performance of graphene by the VDP-H measurement. Although n is affected by the surroundings, the fluctuation is negligible in the time scale of the measurement. Thus normally the VDP-H measurement can only get one pair of (µ, n) and usually n varies from samples. For instance, Fig. 3 shows the measured results from three samples. The square markers correspond to the single pair for each sample and the cycle markers after annealing. From the single pairs in Fig. 3a we can see µ(S2-P) >µ(S1-P) >µ(S3-P), which may be thought an indication that the electrical performance or sample quality of S2 is the best and then S1 and then S3. On the other hand, sheet resistance is also used as the judgement of graphene quality and in Fig. 3b Rs(S1-P) µ(S2) >µ(S3) and from Fig. 3b Rs(S1) S2 > S3.

Fig. 3. (Color online) Plots of µ (a) and Rs (b) v.s. n for three different samples. The square markers correspond to individual measurements and the cycle markers after annealing. The dash lines are using the fitting parameters from the annealed samples. The solid lines are determined with the individual measured (µ, n) pairs by taking α = 0.5. Normalization of the carrier mobility.

Sometimes the µ vs. n plots may not have overlapped carrier density region or the samples are not allowed to be annealed or for any case that only individual (µ, n) pairs can be measured. For this case, we can normalize the measured carrier mobility to one at a certain carrier density. From Eq. (4), we have 6

µi≈µ(n/ni)α

.

(6)

If we had a universal value of α, then with any measured pair of (µ, n), we could simply normalize the mobility to an arbitrary carrier density ni with Eq. (6). However, α depends on the number of charged impurities vs. neutral physical defects. It should be also affected by the substrates. Thus, the issue becomes to find an approximate value with error as small as possible. By testing a variety of graphene samples with various defect densities as characterized by Raman spectroscopy and different preparation methods, including ID/IG = 0.02-0.16, wafer substrates from different venders and with different surface pretreatments, graphene grown with different CVD systems and parameters, different annealing conditions, different sample sizes and VDP-H measurement equipment, we found that all the data we had got showed similar fitting rules with α = 0.4-0.6 (Tables S1, S2 and Figs. S1, S2 online).We did also found that when using other substrate such as polyethylene terephthalate or if the graphene film is too defective (e.g., ID/IG> 0.2), although the µ-n plot could still be fitted with a power equation, the value of the power might change a lot (results are not shown here and will be further discussed in our future work). Thus, we conclude that for graphene transferred on the 285-nm SiO2/Si wafer substrate and with ID/IG< 0.2, we can take α = 0.5 as a universal value to normalize any pair of (µ, n) for comparison. The relative error of the normalized µi, Δµi/µi is Δ

,

(7)

where Δα = 0.5 – α and |Δα| < 0.1. Although here the graphene samples are limited to a range of ID/IG< 0.2, our method is still practically efficient. This is because according to present CVD technique, it is easy to produce graphene with such quality. Thus, α = 0.5 is in fact suitable for most of the cases. Even though for the case that the graphene sample is too defective, it can be pre-characterized with Raman spectroscopy. Compared with the complete measurement of the carrier mobility over a range of density as in the previous section, although with some more errors, this simplification here provides the easiness for graphene characterization with just one measurement without annealing treatment of the sample and long-time multiple measurements. From Eq. (7), we can also see that the closer the normalized carrier density ni to the measured n, the smaller the relative error. Now we take the individual pairs (µ, n) in Fig. 3a as an example. To compare a group of samples and minimize the errors in general, we should choose nmin
Δ

.

7

(8)

Keeping in mind that Δα = ± |Δα|, we can approximately get .

(9)

Then from Eq. (9) we have ni = (2.9 × 22.5)0.5 = 8.08×1012 cm-2. The normalized mobility and relative errors are shown in Table 2. It can be seen µ8.08(S1) >µ8.08(S2) >µ8.08(S3), in consistence with what we have got by comparing the plots in Fig. 3a.

Table 2. Normalization of the measured individual pairs (µ, n) in Fig. 3a to n8.08 = 8.08×1012 cm-2 by taking α = 0.5. Sample

Measured n

Measured µ

No.

(1012 cm-2)

(cm2 V-1 s-1)

S1-P

7.7

S2-P S3-P

µ8.08

Fitted α

Δα

1,430

0.53

–0.030

1,396

0.14

2.9

1,910

0.437

0.063

1,144

–6.17

22.5

320

0.567

–0.067

534

–6.64

(cm2 V-1 s-1)

Δµi/µi (%)

In fact, according to Eq. (4) we can draw a µ-n chart as shown in Fig.4. In this chart we use logarithmic scale for both the two axes and draw lines of µ∝n–0.5. Then we can simply compare any two pairs of (µ, n) in the chart that the one close to the bottom-left corner is worse than that up-right, for instance, samples S1-P, S2-P, and S3-P. The Rs-n chart can be made in the same way.

Fig. 4. (Color online) The µ-n chart for the comparison of measure (µ, n) pairs. The dashed slant lines are drawn as µ∝n–0.5. The individual (µ, n) pairs for S1-P, S2-P, and S3-P are shown here as an example.

Furthermore, we can take ni = n1 = 1012 cm-2 since most of the measurements of FETs are performed in vacuum condition in which the carrier density is close to 10 12 cm-2. With this we can approximately compare the normalized mobility µ1, with those reported in the literatures. We can also take ni = n10 = 1013 cm-2 because the carrier density of graphene film in the ambient environment is normally stabilized in the range of (5-15) ×1013 cm-2. Thus we can compare the samples in general. 4.

Conclusions We reported how to evaluate the electrical transport performance of graphene by the VDP-H

measurement, demonstrated its reliability, and analyzed its accuracy. Characterization of graphene with the VDP-H measurement can be conducted with a full process or a simplified process. With the 8

full process, the graphene sample is firstly annealed to remove the adsorbed dopants and then the changes of carrier mobility as a function of density can be measured with the increase of carrier density due to the dopant re-adsorption from the surroundings, which can be simply fitted with a power equation. With the simplified process, by using a universal value of the power to the first level approximation, a measured pair of carrier mobility and density can be normalized to an arbitrary density and thus to compare with other data. Compared with Raman spectroscopy and FET or Hall-bar, the VDP-H measurement shows advantages of simplicity, low cost, few damages induced by extra steps and macroscale characterization and may be made as a standard for graphene characterization. Conflict of interest The authors declare that they have no conflict of interest. Acknowledgments This work was supported by the National Natural Science Foundation of China (51772043 and 51802036), the Open Foundation of National Engineering Research Center of Electromagnetic Radiation Control Materials (ZYGX2017K003-3) and Sichuan Science and Technology Program (2018GZ0434). Samuel S. Mao acknowledges the support from the Shenzhen Peacock Plan (1208040050847074). Wenjuan Zhu would like to acknowledge the ONR support Grant (NAVY N00014-17-1-2973). References [1] Novoselov KS, Fal'Ko VI, Colombo L, et al. A roadmap for graphene. Nature 2012; 490: 192-200 [2] Chen JH, Jang C, Xiao S, et al. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nat Nanotechnol 2008; 3: 206-9 [3] Lin YM, Jenkins KA, Valdes-Garcia A, et al. Operation of graphene transistors at gigahertz frequencies. Nano Lett 2009; 9: 422-6 [4] Lin YM, Dimitrakopoulos C, Jenkins KA, et al. 100-GHz transistors from wafer-scale epitaxial graphene. Science 2010; 327: 662 [5] Wu Y, Lin YM, Bol AA, et al. High-frequency, scaled graphene transistors on diamond-like carbon. Nature 2011; 472: 74-8 [6] Geim AK, Novoselov KS. The rise of graphene. Nat Mater 2007; 6: 183-91 [7] Shao Q, Liu G, Teweldebrhan D, et al. High-temperature quenching of electrical resistance in graphene interconnects. Appl Phys Lett 2008; 92: 202108 [8] Nair RR, Blake P, Grigorenko AN, et al. Fine structure constant defines visual transparency of graphene. Science 2008; 320: 1308 [9] Kim KS, Zhao Y, Jang H, et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009; 457: 706-10 [10] Li X, Zhu Y, Cai W, et al. Transfer of large-area graphene films for high-performance transparent conductive electrodes. Nano Lett 2009; 9: 4359-63 [11] Bae S, Kim H, Lee Y, et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat Nanotechnol 2010; 5: 574-8

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Fangzhu Qing is now an Assistant Professor of University of Electronic Science and Technology of China. She received her Ph.D. in Materials Science from Sichuan University. Dr. Qing’s

research interests are synthesis and functionalization of graphene films and their applications in biotechnology.

Xuesong Li is currently a Professor of University of Electronic Science and Technology of China . He received his B.S. and M.S. from Tsinghua University and Ph.D. from Rensselaer Polytechnic Institute, USA. His research interests are synthesis and applications of graphene films and other two-dimensional materials.

16

Van der Pauw – Hall measurement

Carrier density increases due to the unintentional doping from the ambient surroundings