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

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).