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基于微波透射法的金属薄膜方块电阻测量理论及其应用

王露 叶鸣 赵小龙 贺永宁

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基于微波透射法的金属薄膜方块电阻测量理论及其应用

王露, 叶鸣, 赵小龙, 贺永宁

Theory and verification of a microwave transmission method of measuring sheet resistance of metallic thin film

Wang Lu, Ye Ming, Zhao Xiao-Long, He Yong-Ning
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  • 贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.
    Metallic thin films deposited on non-conductive substrates are widely used in areas like microwave absorbers, photovoltaic, packaging, electromagnetic shielding, and integrated circuits. From scientific and engineering point of view, measuring sheet resistance of metallic thin films is important. In this study, we develop a theory of evaluating sheet resistance by using transmission coefficient of a rectangular waveguide (RG) and verify it with sputtered silver films of various thickness values. According to the field distribution of RG working under the fundamental mode and corresponding electromagnetic boundary conditions, we first analytically derive the transmission coefficient of an RG with the metallic thin film exactly occupying its cross section. Comparing existing theory, we take the effect of the non-conductive substrate supporting the metallic thin film into consideration. According to this derivation, we establish a method to calculate the sheet resistance of metallic thin films from the amplitude of RG transmission coefficient. To verify our derivation, we also conduct full-wave simulations of a standard WR-75 RG used for characterizing the metallic thin film at 13.65 GHz. Both the analytical derivations and full-wave simulations show that the amplitude of the transmission coefficient depends on the logarithm of the sheet resistance in a linear manner. It is also demonstrated that the substrate effect may not be ignored. To facilitate measurement, we propose a sandwiched structure by placing the metallic thin film between two waveguide flanges. This modification removes the stringent requirements for sample preparation. Simulations of this sandwiched structure indicate that it is possible to realize non-contact measurement if the air gap between metallic thin film and waveguide flange is below 0.1 mm. Through full-wave simulations, we also show the feasibility of metallic thin film evaluation by using such transmission lines as dielectric filled RG, circular waveguide, and coaxial line. Finally, we prepare various silver films with sheet resistances ranging from 20 m/square to 1 /square (measured by the four-point probe technique) on the top of high resistance silicon and glass substrates, respectively. We measure the amplitudes of transmission coefficient of these metal films in RG by using vector network analyzer. The obtained experimental results are well consistent with the derivation and simulation results, thereby verifying the proposed method. It is recommended that the proposed method is suitable for conductive films with sheet resistances ranging from 0.05 /square to 0.5 /square. The results of this study are of potential value for characterizing the conductive thin films in micro/nano fabrication and relevant areas.
      通信作者: 叶鸣, yeming057@mail.xjtu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:61501364)资助的课题.
      Corresponding author: Ye Ming, yeming057@mail.xjtu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61501364).
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    Das R, Goswami S, Borgohain R, Baruah S 2015 International Conference on Energy, Power and Environment:Towards Sustainable Growth Meghalaya, Indian, June 12-15, 2015 p1

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    Enderling S, Brown C L, Smith S, Dicks M H 2006 IEEE. Trans. Semiconduct. M 19 2

    [10]

    Reznik A N, Demidov E V 2013 J. Appl. Phys. 113 2026

    [11]

    Fan M B, Cao B H, Yang X F 2010 Acta Phys. Sin. 59 7570 (in Chinese)[范孟豹, 曹丙花, 杨雪锋2010物理学报59 7570]

    [12]

    Lee M H J, Collier R J 2005 IEEE. Trans. Instrum. Meas. 54 2412

    [13]

    Jan K 2011 Meas. Sci. Technol. 22 085703

    [14]

    Galin M A, Demidov E V, Reznik A N 2014 J. Surf. Investig. 8 477

    [15]

    Li W, Wang H, Feng Z 2016 Rev. Sci. Instrum. 87 045005

    [16]

    Shaforost O, Wang K, Goniszewski S, Adabi M, Guo Z 2015 J. App. Phys. 117 024501

    [17]

    Wang Z, Kelly M A, Shen Z X, Shao L, Chu W K 2005 Appl. Phys. Lett. 86 153118

    [18]

    Krupka J, Mazierska J E, Jacob M V, Hartnett J G, Tobar M E 2003 Microw. Opt. Technol. Lett. 2004 311

    [19]

    Ramey R L, Lewis T S 1968 J. App. Phys. 39 1747

    [20]

    Ramey R L, Kitchen Jr. W J, Lloyd J M, Landes H S 1968 J. App. Phys. 39 3883

    [21]

    Pozar D M (Zhang Z Y, Zhou L Z, Wu D M, Transl) 2006 Microwave Engineering (3rd Ed.) (Beijing:Publishing House of Electronics Industry) pp92-96(in Chinese)[波扎(张肇仪, 周乐柱, 吴德明译) 2006微波工程(三版) (北京:电子工业出版社)第9296页]

  • [1]

    Qu Z, Meng Y, Zhao Q 2015 Front. Mech. Eng. 10 1

    [2]

    Hudaya C, Park J H, Lee J K 2012 Nanoscale. Res. Lett. 7 17

    [3]

    Liu Y, Tan J 2013 Prog. Eletromagn. Res. 140 353

    [4]

    Wang S, Divan R, Rosenmann D, Ocola L E, Sun J, Wang P 2013 IEEE. Microw. Wirel. Co. 23 84

    [5]

    Pan Y L, Tai C C 2012 IEEE. Trans. Magn 48 347

    [6]

    Evseev S B, Nanver L K, Milosaviljevic S 2012 IEEE. Trans. Microw. Theory 60 3542

    [7]

    Krupka J, Usydus L, Koltuniak H 2012 19th International Conference on Microwave Radar and Wireless Communications Warsaw, Poland, May 21-23, 2012 p149

    [8]

    Das R, Goswami S, Borgohain R, Baruah S 2015 International Conference on Energy, Power and Environment:Towards Sustainable Growth Meghalaya, Indian, June 12-15, 2015 p1

    [9]

    Enderling S, Brown C L, Smith S, Dicks M H 2006 IEEE. Trans. Semiconduct. M 19 2

    [10]

    Reznik A N, Demidov E V 2013 J. Appl. Phys. 113 2026

    [11]

    Fan M B, Cao B H, Yang X F 2010 Acta Phys. Sin. 59 7570 (in Chinese)[范孟豹, 曹丙花, 杨雪锋2010物理学报59 7570]

    [12]

    Lee M H J, Collier R J 2005 IEEE. Trans. Instrum. Meas. 54 2412

    [13]

    Jan K 2011 Meas. Sci. Technol. 22 085703

    [14]

    Galin M A, Demidov E V, Reznik A N 2014 J. Surf. Investig. 8 477

    [15]

    Li W, Wang H, Feng Z 2016 Rev. Sci. Instrum. 87 045005

    [16]

    Shaforost O, Wang K, Goniszewski S, Adabi M, Guo Z 2015 J. App. Phys. 117 024501

    [17]

    Wang Z, Kelly M A, Shen Z X, Shao L, Chu W K 2005 Appl. Phys. Lett. 86 153118

    [18]

    Krupka J, Mazierska J E, Jacob M V, Hartnett J G, Tobar M E 2003 Microw. Opt. Technol. Lett. 2004 311

    [19]

    Ramey R L, Lewis T S 1968 J. App. Phys. 39 1747

    [20]

    Ramey R L, Kitchen Jr. W J, Lloyd J M, Landes H S 1968 J. App. Phys. 39 3883

    [21]

    Pozar D M (Zhang Z Y, Zhou L Z, Wu D M, Transl) 2006 Microwave Engineering (3rd Ed.) (Beijing:Publishing House of Electronics Industry) pp92-96(in Chinese)[波扎(张肇仪, 周乐柱, 吴德明译) 2006微波工程(三版) (北京:电子工业出版社)第9296页]

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出版历程
  • 收稿日期:  2017-04-19
  • 修回日期:  2017-06-19
  • 刊出日期:  2017-10-05

基于微波透射法的金属薄膜方块电阻测量理论及其应用

    基金项目: 国家自然科学基金(批准号:61501364)资助的课题.

摘要: 贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.

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