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Method of accurately measuring silicon sphere density difference based on hydrostatic suspension principls

Wang Jin-Tao Liu Zi-Yong

Method of accurately measuring silicon sphere density difference based on hydrostatic suspension principls

Wang Jin-Tao, Liu Zi-Yong
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  • The micro density difference between silicon single crystal spheres is not only important for the research on the redefinition of Avogadro constant based on quantum standard, but also a key solution for quality control for the production of silicon single crystal with ultra-high purity in semi-conductor industry. To overcome the complexity of non-contact laser interferometer method and improve the accuracy of hydro-weight method, a method based on the hydrostatic suspension principle is realized. The silicon single spheres to be measured are immersed into mixture liquid including 1,2,3-tribromopropane and 1,2-dibromoethane, and floated freely by adjusting the temperature and pressure of the liquid. The micro density difference between two silicon single crystal spheres is calculated based on a mathematical model by using liquid temperature, pressure, and central floatation height difference in the floatation condition. The stable constant temperature liquid with maximal error ± 100 μ K is realized by two-cycle water bath and PID control system. The floatation height of silicon single crystal sphere is determined by binary image and iterative algorithm. The stable suspension is achieved by the PID pressure control system, and the temperature fluctuation due to Joule-Thomson effect is reduced. By means of linearity between changes of temperature and pressure in hydrostatic suspension model, the compressibility of mixture liquid is measured. The experimental results show that the influence from liquid surface tension is avoided by using the hydrostatic suspension method, and accurate measurement of density difference between silicon single crystal spheres can be achieved with an uncertainty of 2.1× 10-7 (expand factor k=1).
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51105347), the Special Fund for Quality and Inspection Research in the Public Interest, China (Grant No. AHY0711) and National Science Supported Planning Projects, China (Grant No. 2011BAI02B03).
    [1]

    Fujii K, Waseda A, Kuramoto, N, Mizushima S, Becker P, Bellin H, Nicolaus A, Kuetgens U, Valkiers S, Tayler P, de Biever P, Mare G, Massa E, Matyi R, Kessler J, Emerst G B, Hamke M 2005 IEEE Trans. Instrum. Meas. 54 854

    [2]

    Yun J F, Zhu H N 2007 Physics. 36 543 (in Chinese) [岳峻峰, 朱鹤年 2007 物理 36 543]

    [3]

    Luo Z Y, Yang L F, Gu Y Z, Guo L G, Ding J A, Chen Z H 2008 Acta Meirolocica Sinica 29 211 (in Chinese) [罗志勇, 杨丽峰, 顾英姿, 郭立功, 丁京安, 陈朝晖 2008 计量学报 29 211]

    [4]

    Fujii K, Tanaka M, Nezu Y, 1999 Metrologia 36 455

    [5]

    Becker Peter 2001 Report On Progress In Physics. 64 1945

    [6]

    Wu C Y, Gu J H, Feng Y Y, Xue Y, Lu J X 2012 Acta Phys. Sin. 61 157803 (in Chinese) [吴晨阳, 谷锦华, 冯亚阳, 薛源, 卢景霄 2012 物理学报 61 157803]

    [7]

    Elwenspoek M, Jansen M H 2006 Silicon Micromachining (Beijing: Chemical Industry Press) p10 (in Chinese) [M.埃尔温斯波克, H.扬森 2006 硅微机械加工技术 (北京: 化学工业出版社) 第10页]

    [8]

    Xu J, Li F L, Yang D R 2007 Acta Phys. Sin. 56 4113 (in Chinese) [徐进, 李福龙, 杨德仁 2007 物理学报 56 4113]

    [9]

    Martin J, Bettin H, Kuetgens U, Schiel D, Becker P 1999 IEEE Trans. Instrum. Meas. 48 216

    [10]

    Bettin H, Toth H 2006 Measurement Science and Technology 17 2567

    [11]

    Luo Z Y 2004 Acta Me'irolocica Sinica 25 138 (in Chinese) [罗志勇 2004 计量学报 25 138]

    [12]

    Kuramoto N, Fujii K 2005 IEEE Trans. Instrum. Meas. 54 868

    [13]

    Kozdon A F, Spieweck F 1992 IEEE Trans. Instrum. Meas. 41 420

    [14]

    Nicolaus R A, Fujii K 2006 Meas. Sci. Technol. 17 2527

    [15]

    Luo Z Y, Yang L F, Gu Y Z, 2007 Chinese Science Bulletin. 52 2881

    [16]

    Kang Y H, Zhu J G, Luo Z Y, Ye S H 2008 Acta Optica Sinica 11 2148 (in Chinese) [康岩辉, 邾继贵, 罗志勇, 叶声华 2008 光学学报 11 2148]

    [17]

    Borsch G, Bohme H 1989 Optik 82 161

    [18]

    Nicolaus R A, Bonsch G 2005 Metrologia 42 24

    [19]

    Luo Z Y, Yang L F, Chen Y C 2005 Acta Phys. Sin. 54 3051 (in Chinese) [罗志勇, 杨丽峰, 陈允昌 2005 物理学报 54 3051]

    [20]

    Luo Z Y, Gu Y Z, Zhang J T, Yang L F, Guo L G 2010 IEEE Trans. Instrum. Meas. 59 2991

    [21]

    Kuramoto N, Fujii K 2003 IEEE Trans. Instrum. Meas. 52 631

    [22]

    Nicolaus R A, Geckeler R D 2007 IEEE Trans. Instrum. Meas. 56 517

    [23]

    Waseda A, Fujii K 2001 Meas. Sci. Technol. 12 2039

    [24]

    Bettin, H, Glaser M, Spieweck F, Toth H, Saceoni A, Peut A, Fajii K, Tanake M, Nezu Y 1997 IEEE Trans. Instrum. Meas. 46 556

    [25]

    Fujii K, Waseda A, Tanaka M 2001 IEEE Trans. Instrum. Meas. 50 616

    [26]

    Fujii K, Tanaka M 2006 14th International Conference on the Properties of Water and Steam Kyoto, Japan, August 29-September 3, 2006 p132

    [27]

    Fujii K, Waseda A, Kuramoto N, Mizushima S, Valkiers S, Taylor P, Bievre D 2003 IEEE Trans. Instrum. Meas. 52 646

    [28]

    Mykolajewycz R, Kalnajs J, Smakula A 1964 J. Appl. Phys. 35 1773

    [29]

    Seyfried P, Balhorn R, Kochsiek M, Kozdon A F, Rademacher H J, Wagenbreth H, Peuto A M, Sacconi A 1987 IEEE Trans. Instrum. Meas. 36 161

  • [1]

    Fujii K, Waseda A, Kuramoto, N, Mizushima S, Becker P, Bellin H, Nicolaus A, Kuetgens U, Valkiers S, Tayler P, de Biever P, Mare G, Massa E, Matyi R, Kessler J, Emerst G B, Hamke M 2005 IEEE Trans. Instrum. Meas. 54 854

    [2]

    Yun J F, Zhu H N 2007 Physics. 36 543 (in Chinese) [岳峻峰, 朱鹤年 2007 物理 36 543]

    [3]

    Luo Z Y, Yang L F, Gu Y Z, Guo L G, Ding J A, Chen Z H 2008 Acta Meirolocica Sinica 29 211 (in Chinese) [罗志勇, 杨丽峰, 顾英姿, 郭立功, 丁京安, 陈朝晖 2008 计量学报 29 211]

    [4]

    Fujii K, Tanaka M, Nezu Y, 1999 Metrologia 36 455

    [5]

    Becker Peter 2001 Report On Progress In Physics. 64 1945

    [6]

    Wu C Y, Gu J H, Feng Y Y, Xue Y, Lu J X 2012 Acta Phys. Sin. 61 157803 (in Chinese) [吴晨阳, 谷锦华, 冯亚阳, 薛源, 卢景霄 2012 物理学报 61 157803]

    [7]

    Elwenspoek M, Jansen M H 2006 Silicon Micromachining (Beijing: Chemical Industry Press) p10 (in Chinese) [M.埃尔温斯波克, H.扬森 2006 硅微机械加工技术 (北京: 化学工业出版社) 第10页]

    [8]

    Xu J, Li F L, Yang D R 2007 Acta Phys. Sin. 56 4113 (in Chinese) [徐进, 李福龙, 杨德仁 2007 物理学报 56 4113]

    [9]

    Martin J, Bettin H, Kuetgens U, Schiel D, Becker P 1999 IEEE Trans. Instrum. Meas. 48 216

    [10]

    Bettin H, Toth H 2006 Measurement Science and Technology 17 2567

    [11]

    Luo Z Y 2004 Acta Me'irolocica Sinica 25 138 (in Chinese) [罗志勇 2004 计量学报 25 138]

    [12]

    Kuramoto N, Fujii K 2005 IEEE Trans. Instrum. Meas. 54 868

    [13]

    Kozdon A F, Spieweck F 1992 IEEE Trans. Instrum. Meas. 41 420

    [14]

    Nicolaus R A, Fujii K 2006 Meas. Sci. Technol. 17 2527

    [15]

    Luo Z Y, Yang L F, Gu Y Z, 2007 Chinese Science Bulletin. 52 2881

    [16]

    Kang Y H, Zhu J G, Luo Z Y, Ye S H 2008 Acta Optica Sinica 11 2148 (in Chinese) [康岩辉, 邾继贵, 罗志勇, 叶声华 2008 光学学报 11 2148]

    [17]

    Borsch G, Bohme H 1989 Optik 82 161

    [18]

    Nicolaus R A, Bonsch G 2005 Metrologia 42 24

    [19]

    Luo Z Y, Yang L F, Chen Y C 2005 Acta Phys. Sin. 54 3051 (in Chinese) [罗志勇, 杨丽峰, 陈允昌 2005 物理学报 54 3051]

    [20]

    Luo Z Y, Gu Y Z, Zhang J T, Yang L F, Guo L G 2010 IEEE Trans. Instrum. Meas. 59 2991

    [21]

    Kuramoto N, Fujii K 2003 IEEE Trans. Instrum. Meas. 52 631

    [22]

    Nicolaus R A, Geckeler R D 2007 IEEE Trans. Instrum. Meas. 56 517

    [23]

    Waseda A, Fujii K 2001 Meas. Sci. Technol. 12 2039

    [24]

    Bettin, H, Glaser M, Spieweck F, Toth H, Saceoni A, Peut A, Fajii K, Tanake M, Nezu Y 1997 IEEE Trans. Instrum. Meas. 46 556

    [25]

    Fujii K, Waseda A, Tanaka M 2001 IEEE Trans. Instrum. Meas. 50 616

    [26]

    Fujii K, Tanaka M 2006 14th International Conference on the Properties of Water and Steam Kyoto, Japan, August 29-September 3, 2006 p132

    [27]

    Fujii K, Waseda A, Kuramoto N, Mizushima S, Valkiers S, Taylor P, Bievre D 2003 IEEE Trans. Instrum. Meas. 52 646

    [28]

    Mykolajewycz R, Kalnajs J, Smakula A 1964 J. Appl. Phys. 35 1773

    [29]

    Seyfried P, Balhorn R, Kochsiek M, Kozdon A F, Rademacher H J, Wagenbreth H, Peuto A M, Sacconi A 1987 IEEE Trans. Instrum. Meas. 36 161

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  • Received Date:  15 August 2012
  • Accepted Date:  05 September 2012
  • Published Online:  05 February 2013

Method of accurately measuring silicon sphere density difference based on hydrostatic suspension principls

  • 1. Division of Mechanics and Acoustic, National Institute of Metrology, Beijing 100013, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 51105347), the Special Fund for Quality and Inspection Research in the Public Interest, China (Grant No. AHY0711) and National Science Supported Planning Projects, China (Grant No. 2011BAI02B03).

Abstract: The micro density difference between silicon single crystal spheres is not only important for the research on the redefinition of Avogadro constant based on quantum standard, but also a key solution for quality control for the production of silicon single crystal with ultra-high purity in semi-conductor industry. To overcome the complexity of non-contact laser interferometer method and improve the accuracy of hydro-weight method, a method based on the hydrostatic suspension principle is realized. The silicon single spheres to be measured are immersed into mixture liquid including 1,2,3-tribromopropane and 1,2-dibromoethane, and floated freely by adjusting the temperature and pressure of the liquid. The micro density difference between two silicon single crystal spheres is calculated based on a mathematical model by using liquid temperature, pressure, and central floatation height difference in the floatation condition. The stable constant temperature liquid with maximal error ± 100 μ K is realized by two-cycle water bath and PID control system. The floatation height of silicon single crystal sphere is determined by binary image and iterative algorithm. The stable suspension is achieved by the PID pressure control system, and the temperature fluctuation due to Joule-Thomson effect is reduced. By means of linearity between changes of temperature and pressure in hydrostatic suspension model, the compressibility of mixture liquid is measured. The experimental results show that the influence from liquid surface tension is avoided by using the hydrostatic suspension method, and accurate measurement of density difference between silicon single crystal spheres can be achieved with an uncertainty of 2.1× 10-7 (expand factor k=1).

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