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单晶硅球间微量密度差异测量是阿伏伽德罗常数量子基准定义的重要研究内容, 也是半导体产业中高纯度单晶硅制备工艺质量控制的主要方法. 为了改善现有非接触相移干涉法测量装置复杂和静力称重法测量不确定度低的特点, 根据单晶硅密度精密测量需要, 实现了一种基于静力悬浮原理的单晶硅球密度相对参比测量方法. 通过改变静压力和温度进行三溴丙烷和二溴乙烷混合液体密度的微量调节, 分别使两个待测单晶硅球在液体中悬浮, 根据悬浮状态时的液体温度和悬浮高度计算出待测单晶硅球密度差值. 通过双循环水浴和PID温度控制系统实现±100 μK的恒温液体测量环境. 通过图像识别和迭代拟合算法实现单晶硅球悬浮高度的测量. 使用PID静压力控制系统实现单晶硅球的稳定悬浮控制, 同时减少Joule-Thomson效应引起的液体温度改变. 利用静力悬浮模型中的温度变化和静压力变化线性关系准确测量出标准液体的压缩系数. 试验结果表明, 这种测量方法可以避免液体液面张力的影响, 测量相对标准不确定度达到2.1×10-7, 能够实现单晶硅球密度差值的精密测量.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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Keywords:
- silicon single crystal sphere /
- density difference /
- precise measurement /
- hdrostatic suspension
[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 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 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 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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[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 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 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 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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