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Graphene films grown on metallic substrates by chemical vapor deposition have wide potential applications, such as serving as transparent electrodes, transistors, sensors, etc. The coverage of graphene on metal surface can influence many performance parameters, such as square resistance and transparence, after it has been transferred to other substrates. As most of the performance parameters cannot be measured while graphene is still on the metal, it is very useful to evaluate the coverage of graphene before further actions. In this paper, we present a method to measure the coverage of graphene on metal by using scanning electron microscopy and image processing software. We also calculate and measure the uncertainty of the measured coverage. There are two main factors, namely the determination of the boundary between the covered areas and the uncovered areas, and the number of the graphene islands or vacancy islands in view, which can bring uncertainty to the coverage. The former factor raises the uncertainty of the coverage while the number of graphene (vacancy) islands in view is higher, because the more the islands in view, the smaller the islands are, therefore the total boundaries become more. The latter factor reduces uncertainty with the number of islands increasing, because of the quantum fluctuation. The uncertainty of the latter factor is proportional to 1/√N, where N is the number of islands in view. As we can see, the number of islands in view is the key parameter to balance the two factors. We measure the graphene coverage with different graphene islands in view, and also measure the uncertainty by using the statistics knowledge. Meanwhile, we also build a model to calculate the uncertainty under different numbers of islands in view. The experiments and the calculations accord with each other reasonably well. By these carefully modeling and experimentations, we optimize and balance the two faces and suggest the number of islands in view to reduce the uncertainty of the measured coverage to a lowest value. The use of these measured data can ensure the accuracy of the graphene coverage measurement with minimal time cost.
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Keywords:
- graphene /
- coverage rate /
- uniformity /
- scanning electron microscopy
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[1] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
[2] Geim A K 2009 Science 324 1530
[3] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[4] Hernandez Y, Nicolosi V, Lotya M, Blighe F M, Sun Z Y, De S, McGovern I T, Holland B, Byrne M, Gun’ko Y K, Boland J J, Niraj P, Duesberg G, Krishnamurthy S, Goodhue R, Hutchison J, Scardaci V, Ferrari A C, Coleman J N 2008 Nat. Nanotechnol. 3 563
[5] Park S, Ruoff R S 2009 Nat. Nanotechnol. 4 217
[6] Berger C, Song Z M, Li X B, Wu X S, Brown N, Naud C, Mayou D, Li T B, Hass J, Marchenkov A N, Conrad E H, First P N, de Heer W A 2006 Science 312 1191
[7] Emtsev K V, Bostwick A, Horn K, Jobst J, Kellogg G L, Ley L, McChesney J L, Ohta T, Reshanov S A, Rohrl J, Rotenberg E, Schmid A K, Waldmann D, Weber H B, Seyller T 2009 Nat. Mater. 8 203
[8] Yu Q, Lian J, Siriponglert S, Li H, Chen Y P, Pei S S 2008 Appl. Phys. Lett. 93 113103
[9] Reina A, Jia X T, Ho J, Nezich D, Son H, Bulovic V, Dresselhaus M S, Kong J 2009 Nano Lett. 9 3087
[10] Sutter P W, Flege J I, Sutter E A 2008 Nat. Mater. 7 406
[11] Kim K S, Zhao Y, Jang H, Lee S Y, Kim J M, Kim K S, Ahn J H, Kim P, Choi J Y, Hong B H 2009 Nature 457 706
[12] Li X S, Cai W W, An J, Kim S, Nah J, Yang D X, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee S K, Colombo L, Ruoff R S 2009 Science 324 1312
[13] Levendorf M P, Ruiz-Vargas C S, Garg S, Park J 2009 Nano Lett. 9 4479
[14] Lee Y, Bae S, Jang H, Jang S, Zhu S E, Sim S H, Song Y I, Hong B H, Ahn J H 2010 Nano Lett. 10 490
[15] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
[16] Wang X, Zhi L, Mllen K 2008 Nano Lett. 8 323
[17] Blake P, Brimicombe P D, Nair R R, Booth T J, Jiang D, Schedin F, Ponomarenko L A, Morozov S V, Gleeson H F, Hill E W, Geim A K, Novoselov K S 2008 Nano Lett. 8 1704
[18] Li X, Zhang G, Bai X, Sun X, Wang X, Wang E, Dai H 2008 Nature Nanotechnol. 3 538
[19] Becerril H A, Mao J, Liu Z, Stoltenberg R M, Bao Z, Chen Y 2008 ACS Nano 2 463
[20] Huang P Y, Ruiz-Vargas C S, Zande A M, Whitney W S, Levendorf M P, Kevek J W, Garg S, Alden J S, Hustedt C J, Zhu Y, Park J, McEuen P L, Muller D A 2011 Nature 469 389
[21] 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 2012 Science 336 1143
[22] Li X S, Zhu Y W, Cai W W, Borysiak M, Han B, Chen D, Piner R D, Colombo L, Ruoff R S 2009 Nano Lett. 9 4359
[23] Zhao Z J, Shan Z F, Zhang C K, Li Q Y, Tian B, Huang Z Y, Lin W Y, Chen X P, Ji H X, Zhang W F, Cai W W 2015 Small 11 1418
[24] Hao Y F, Bharathi M S, Wang L, Liu Y Y, Chen H, Nie S, Wang X H, Chou H, Tan C, Fallahazad B, Ramanarayan H, Magnuson C W, Tutuc E, Yakobson B I, McCarty K F, Zhang Y W, Kim P, Hone J, Colombo L, Ruoff R S 2013 Science 342 720
[25] Wang H, Wang G Z, Bao P F, Yang S L, Zhu W, Xie X, Zhang W J 2012 J. Am. Chem. Soc. 134 3627
[26] Dong G C, Frenken J W M 2013 ACS Nano 7 7028
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