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石墨烯等二维原子晶体薄片样品的光学衬度计算及其层数表征

韩文鹏 史衍猛 李晓莉 罗师强 鲁妍 谭平恒

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石墨烯等二维原子晶体薄片样品的光学衬度计算及其层数表征

韩文鹏, 史衍猛, 李晓莉, 罗师强, 鲁妍, 谭平恒

The numerical-aperture-dependent optical contrast and thickness determination of ultrathin flakes of two-dimensional atomic crystals: A case of graphene multilayers

Han Wen-Peng, Shi Yan-Meng, Li Xiao-Li, Luo Shi-Qiang, Lu Yan, Tan Ping-Heng
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  • 本文以鉴别机械剥离法制备的高质量石墨烯样品的层数为例, 阐明了如何利用传输矩阵来计算二维原子晶体薄片样品的光学衬度, 并进一步精确地鉴别其层数. 计算结果表明测试时所选用的显微物镜数值孔径对精确确定薄片样品的层数非常重要, 并为实验所证实. 同时提出了使用两个激光波长可以快速地表征样品尺寸接近物镜衍射极限的薄片样品层数的方法. 本文所采用的传输矩阵形式非常适合于计算二维原子晶体薄片样品的光学衬度, 并可以方便地推广到更复杂的多层衬底结构, 以便快速和准确地鉴别各种衬底上二维原子晶体薄片样品的厚度.
    The optical and electronic properties of two-dimensional atomic crystals including graphene are closely dependent on their layer numbers (or thickness). It is a fundamental issue to fast and accurately identify the layer number of multilayer flakes of two-dimensional atomic crystals before further research and application in optoelectronics. In this paper, we discuss in detail the application of transfer matrix method to simulate the optical contrast of ultrathin flakes of two-dimensional atomic crystals and further to identify their thickness, where numerical aperture of microscope objective is considered. The importance of numerical aperture in the thickness determination is confirmed by the experiments on the graphene flakes. Furthermore, two lasers with different wavelengths can be serviced as light sources for the thickness identification of flakes of two-dimensional atomic crystals with a size close to the diffraction limit of the microscope objective. The transfer matrix method is found to be very useful for the optical-contrast calculation and thickness determination of flakes of two-dimensional atomic crystals on multilayer dielectric substrate.
    • 基金项目: 国家重点基础研究发展计划(批准号: 2009CB929301) 和国家自然科学基金(批准号: 11225421, 10934007)资助的课题.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. G2009CB929301), and the National Natural Science Foundation of China (Grant Nos. 11225421, 10934007).
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    Zhao W J, Tan P H, Zhang J, Liu J 2010 Phys. Rev. B 82 245423

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    Zhao W J, Tan P H, Liu J, Ferrari A C 2011 J. Am. Chem. Soc. 113 5941

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    Kang C Y, Tang J, Li L M, Yan W S, Xu P S, Wei S Q 2012 Acta Phys. Sin. 61 037302 (in Chinese) [康朝阳, 唐军, 李利民, 闫文盛, 徐彭寿, 韦世强 2012 物理学报 61 037302]

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    Blake P, Hill E W, Castro Neto A H, Novoselov K S, Jiang D, Yang R, Booth T J, Geim A K 2007 Appl. Phys. Lett. 91 063124

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    Ni Z H, Wang H M, Kasim J, Fan H M Yu T Wu Y H, Feng Y P, Shen Z X 2007 Nano Lett. 7 2758

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    Wang Y Y, Ni Z H, Shen Z X, Wang H M, Wu Y H 2008 Appl. Phys. Lett. 92 043121

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    Yoon D, Moon H, Son Y W, Choi J S, Park B H, Cha Y H, Kim Y D, Cheong H 2009 Phys. Rev. B 80 125422

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    Born M, Wolf E 1999 Principles of Optics (7th Edn) (London: Cambridge University Press) p58

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    Liu X J, Zhang B J, Wang J, Zhang S Q, Ba N, Li H, Wu X Y, Guo Y Q 2012 Acta Phys. Sin. 61 237801 (in Chinese) [刘晓静, 张伯军, 王婧, 张斯淇, 巴诺, 李宏, 吴向尧, 郭义庆 2012 物理学报 61 237801]

    [17]

    Tan P H, Deng Y M, Zhao Q, Cheng W C 1999 Appl. Phys. Lett. 74 1818

    [18]

    Tan P H, An L, Liu L Q, Guo Z X, Czerw R, Carroll D L, Ajayan P M, Zhang N, Guo H L 2002 Phys. Rev. B 66 245410

    [19]

    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

    [20]

    Kravets V G, Grigorenko A N, Nair R R, Blake P, Anissimova S, Novoselov K S Geim A K 2010 Phys. Rev. B 81 155413

    [21]

    Palik E D Ed. 1985 Handbook of Optical Constants of Solids (New York: Academic Press)

    [22]

    Zhang X, Han W P, Wu J B, Milana S, Lu Y, Li Q Q, Ferrari A C, Tan P H arXiv 1212 6796

    [23]

    Zhao W, Ghorannevis Z, Chu L, Toh M, Kloc C, Tan PH, Eda G 2012 ACS Nano, DOI: 10.1021/nn305275h, accepted for publication.

    [24]

    Hu P A, Wen Z Z, Wang L F, Tan P H, Xiao K 2012 ACS Nano 6 5988

  • [1]

    Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451

    [2]

    Mak K F Lee C, Hone J Shan J, Heinz T F 2010 Phys. Rev. Lett. 105 136805

    [3]

    Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C Y, Galli G, Wang F 2010 Nano Lett. 10 1271

    [4]

    Cao T, Wang G, Han W P, Ye H Q, Zhu C R, Shi J R, Niu Q, Tan P H, Wang E G, Liu B L, Feng J 2012 Nature Communications 3 887

    [5]

    Zhang Y, He K, Chang C Z, Song C L, Wang L L, Chen X, Jia J F, Fang Z, Dai X, Shan W Y, Shen S Q, Niu Q, Qi X L, Zhang S C, Ma X C, Xue Q K 2010 Nat. Phys. 6 584

    [6]

    Tan P H, Han W P, Zhao W J, Wu Z H, Chang K, Wang H, Wang Y F, Bonini N, Marzari N, Savini G, Lombardo A, Ferrari A C 2012 Nature Materials 11 294

    [7]

    Ferrari A C, Meyer J C, Scardaci V, Casiraghi C Lazzeri M, Mauri F, Piscanec S, Jiang D, Novoselov K S, Roth S, Geim A K 2006 Phys. Rev. Lett. 97 187401

    [8]

    Zhao W J, Tan P H, Zhang J, Liu J 2010 Phys. Rev. B 82 245423

    [9]

    Zhao W J, Tan P H, Liu J, Ferrari A C 2011 J. Am. Chem. Soc. 113 5941

    [10]

    Kang C Y, Tang J, Li L M, Yan W S, Xu P S, Wei S Q 2012 Acta Phys. Sin. 61 037302 (in Chinese) [康朝阳, 唐军, 李利民, 闫文盛, 徐彭寿, 韦世强 2012 物理学报 61 037302]

    [11]

    Blake P, Hill E W, Castro Neto A H, Novoselov K S, Jiang D, Yang R, Booth T J, Geim A K 2007 Appl. Phys. Lett. 91 063124

    [12]

    Ni Z H, Wang H M, Kasim J, Fan H M Yu T Wu Y H, Feng Y P, Shen Z X 2007 Nano Lett. 7 2758

    [13]

    Wang Y Y, Ni Z H, Shen Z X, Wang H M, Wu Y H 2008 Appl. Phys. Lett. 92 043121

    [14]

    Yoon D, Moon H, Son Y W, Choi J S, Park B H, Cha Y H, Kim Y D, Cheong H 2009 Phys. Rev. B 80 125422

    [15]

    Born M, Wolf E 1999 Principles of Optics (7th Edn) (London: Cambridge University Press) p58

    [16]

    Liu X J, Zhang B J, Wang J, Zhang S Q, Ba N, Li H, Wu X Y, Guo Y Q 2012 Acta Phys. Sin. 61 237801 (in Chinese) [刘晓静, 张伯军, 王婧, 张斯淇, 巴诺, 李宏, 吴向尧, 郭义庆 2012 物理学报 61 237801]

    [17]

    Tan P H, Deng Y M, Zhao Q, Cheng W C 1999 Appl. Phys. Lett. 74 1818

    [18]

    Tan P H, An L, Liu L Q, Guo Z X, Czerw R, Carroll D L, Ajayan P M, Zhang N, Guo H L 2002 Phys. Rev. B 66 245410

    [19]

    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

    [20]

    Kravets V G, Grigorenko A N, Nair R R, Blake P, Anissimova S, Novoselov K S Geim A K 2010 Phys. Rev. B 81 155413

    [21]

    Palik E D Ed. 1985 Handbook of Optical Constants of Solids (New York: Academic Press)

    [22]

    Zhang X, Han W P, Wu J B, Milana S, Lu Y, Li Q Q, Ferrari A C, Tan P H arXiv 1212 6796

    [23]

    Zhao W, Ghorannevis Z, Chu L, Toh M, Kloc C, Tan PH, Eda G 2012 ACS Nano, DOI: 10.1021/nn305275h, accepted for publication.

    [24]

    Hu P A, Wen Z Z, Wang L F, Tan P H, Xiao K 2012 ACS Nano 6 5988

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出版历程
  • 收稿日期:  2012-12-14
  • 修回日期:  2013-01-08
  • 刊出日期:  2013-06-05

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