INTERFEROMETRIC MEASUREMENTS OF THE DIAMETERS OF A SINGLE-CRYSTAL SILICON SPHERE

A new interferometer has been developed for the accurate determination of the density of a silicon crystal, in which a single-crystal silicon sphere of nearly perfect geometry is placed in a Fabry-Perot etalon of accurately known plate distance, and the diameters are obtained measuring the two gaps between the etalon and the adjacent surface of the sphere. A new method is used to measure the sum of the length of the two gaps by scanning the etalon against the sphere. Two wavelengths, 633 nm from a frequency-stabilized He-Ne laser and 441 nm from a free-running He-Cd laser, are used to determine the order of interference by applying the method of exact fractions. The diameter of about 94 mm has been measured with a resolution of 0.5 nm. Diameter measurements from uniformly distributed directions have shown that the mean diameter has been determined with a standard deviation of 8.6 nm, corresponding to 0.28 ppm in the volume determination. The total uncertainty of the volume is estimated to be 0.34 ppm. Effects of a thin oxide layer and impurities on the bulk density are discussed.