Oxide Layer Mass Determination at the Silicon Sphere of the Avogadro Project

Within the International Avogadro Project, two spheres of highly enriched <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">28</sup> Si crystals have been produced to perform new determination of Avogadro constant N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> . The mass of the oxide layer of the spheres has to be measured as one of the critical tasks. For this purpose, a method consisting of precise thickness measurements and density determinations is proposed and tested. Part of this procedure is the thermal oxidation of the Si spheres to produce a SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer with a well-defined structure and stoichiometry. Consecutively, its thickness is determined by a combination of X-ray reflectometry (XRR) for absolute thickness determination and spectral ellipsometry for mapping. Starting with the analysis of the assumed uncertainty budget, the allowed uncertainties of each part of the procedure were estimated to realize the required uncertainty in an oxide layer mass of 10 mug. The measurements at the test spheres have been carried out to show that an uncertainty of u(d) = 0.1 nm for the thickness measurements directly at the silicon spheres can be achieved, e.g., the thickness of the SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer at the PTB-01 sphere at a (100) lattice plane has been determined to be d = 6.2(1) nm. The second major part of the procedure described in this paper is the determination of the density of the oxide layer of the sphere by pressure of floatation at an additional test sphere. A value of rho = 2228(18) kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> has been determined and confirmed in a remeasurement, with the resulting value of rho = 2223(15) kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> .