Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

Citation:

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
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • 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.
    • 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).
    [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

  • [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

  • [1] Liao Yong-Quan, Zhang Xiao-Xue, Liu Hui, Zhu Xiang-Yu, Chen Xu-Dong, Lin Zhi-Li. Self-reference interferometric measurement of scattering medium transmission matrix based on digital micromirror device superpixel method. Acta Physica Sinica, 2023, 72(22): 224201. doi: 10.7498/aps.72.20230660
    [2] Dai Mei-Qin, Zhang Qing-Yue, Zhao Qiu-Ling, Wang Mao-Rong, Wang Xia. Controllable characteristics of interface states in one-dimensional inverted symmetric photonic structures. Acta Physica Sinica, 2022, 71(20): 204205. doi: 10.7498/aps.71.20220383
    [3] Li Geng, Guo Hui, Gao Hong-Jun. Novel two-dimensional materials and their heterostructures constructed in ultra-high vacuum. Acta Physica Sinica, 2022, 71(10): 106801. doi: 10.7498/aps.71.20212407
    [4] Wu Min, Fei Hong-Ming, Lin Han, Zhao Xiao-Dan, Yang Yi-Biao, Chen Zhi-Hui. Design of asymmetric transmission of photonic crystal heterostructure based on two-dimensional hexagonal boron nitride material. Acta Physica Sinica, 2021, 70(2): 028501. doi: 10.7498/aps.70.20200741
    [5] Wang Cheng, Fan Zhi-Guo, Jin Hai-Hong, Wang Xian-Qiu, Hua Dou. Design and optimization analysis of imaging system of polarized skylight pattern of full polarization. Acta Physica Sinica, 2021, 70(10): 104201. doi: 10.7498/aps.70.20210104
    [6] Wang Xing-Yue, Zhang Hui, Ruan Zi-Lin, Hao Zhen-Liang, Yang Xiao-Tian, Cai Jin-Ming, Lu Jian-Chen. Research progress of monolayer two-dimensional atomic crystal materials grown by molecular beam epitaxy in ultra-high vacuum conditions. Acta Physica Sinica, 2020, 69(11): 118101. doi: 10.7498/aps.69.20200174
    [7] Huang Li, Li Geng, Zhang Yu-Yang, Bao Li-Hong, Huan Qing, Lin Xiao, Wang Ye-Liang, Guo Hai-Ming, Shen Cheng-Min, Du Shi-Xuan, Gao Hong-Jun. Construction, physical properties and applications of low-dimensional atomic/molecular crystals. Acta Physica Sinica, 2018, 67(12): 126801. doi: 10.7498/aps.67.20180846
    [8] Zhang Xi-Cheng, Fang Long-Jie, Pang Lin. Transmission matrix optimization based on singular value decomposition in strong scattering process. Acta Physica Sinica, 2018, 67(10): 104202. doi: 10.7498/aps.67.20172688
    [9] Li Qian-Li, Wen Ting-Dun, Xu Li-Ping, Wang Zhi-Bin. Effect of uniaxial stress on photon localization of one-dimensional photonic crystal with a mirror symmetry. Acta Physica Sinica, 2013, 62(18): 184212. doi: 10.7498/aps.62.184212
    [10] Wu Feng-Tie, Ma Liang, Zhang Qian-An, Zheng Wei-Tao, Pu Ji-Xiong. Experimental and theoretical study on the reconstruction of focused high order Bessel-Gauss beam. Acta Physica Sinica, 2012, 61(1): 014202. doi: 10.7498/aps.61.014202
    [11] Wang Guang-Huai, Wang Qing-Cai, Wu Xiang-Yao, Zhang Si-Qi, Wang Jing, Liu Xiao-Jing, Ba Nuo, Gao Hai-Xin, Guo Yi-Qing. Research on one-dimensional function photonic crystals. Acta Physica Sinica, 2012, 61(13): 134208. doi: 10.7498/aps.61.134208
    [12] Yang Zhi-Chun, Wu Feng, Guo Fang-Zhong, Zhang Chun-Ping. Symplectic symmetry feature of thermoacoustic network. Acta Physica Sinica, 2011, 60(8): 084303. doi: 10.7498/aps.60.084303
    [13] Huang Jian-Liang, Wei Yang, Ma Wen-Quan, Yang Tao, Chen Liang-Hui. On detection wavelength and electron-hole wave function overlap of type Ⅱ InAs/InxGa1-xSb superlattice infrared photodetector. Acta Physica Sinica, 2010, 59(5): 3099-3106. doi: 10.7498/aps.59.3099
    [14] Xu Hui, Cui Mai-Ling, Ma Song-Shan. Heat conduction in one-dimensional Fibonacci chain with on-site potential. Acta Physica Sinica, 2010, 59(10): 7266-7270. doi: 10.7498/aps.59.7266
    [15] Frequency response of photonic heterostructures consisting of single-negative materials. Acta Physica Sinica, 2007, 56(12): 7280-7285. doi: 10.7498/aps.56.7280
    [16] Tong Yuan-Wei, Zhang Ye-Wen, He Li, Li Hong-Qiang, Chen Hong. The band structure in microwave frequency for quasi-1-D coaxial photonic crystals. Acta Physica Sinica, 2006, 55(2): 935-940. doi: 10.7498/aps.55.935
    [17] Wang Xiao-Ping, Liu Lei, Hu Hai-Long, Zhang Kun. Study of tip-sample contact process and phase contrast in tapping mode atomic force microscopy. Acta Physica Sinica, 2004, 53(4): 1008-1014. doi: 10.7498/aps.53.1008
    [18] Yuan Xian-Zhang, Lu Wei, Li Ning, Chen Xiao-Shuang, Shen Xue-Chu, Zi Jian. Photocurrent spectra of very long wavelength GaAs/AlGaAs quantum well infrared photodetector. Acta Physica Sinica, 2003, 52(2): 503-507. doi: 10.7498/aps.52.503
    [19] Zhou Peng, You Hai-Yang, Wang Song-You, Li He-Yin, Yang Yue-Mei, Chen Liang-Rao. . Acta Physica Sinica, 2002, 51(10): 2276-2280. doi: 10.7498/aps.51.2276
    [20] ZHOU YUN-SONG, JIE DONG, CHEN JIN-CHANG, LIN DUO-LIANG. . Acta Physica Sinica, 2001, 50(1): 153-158. doi: 10.7498/aps.50.153
Metrics
  • Abstract views:  6245
  • PDF Downloads:  1444
  • Cited By: 0
Publishing process
  • Received Date:  14 December 2012
  • Accepted Date:  08 January 2013
  • Published Online:  05 June 2013

/

返回文章
返回