As one of the reference measurement methods for future realization of the unit of mass (kilogram) and Avogadro constant NA, the silicon (Si) sphere method employs the ellipsometry for the measurement of the thickness of the ultrathin (< 10 nm) silicon oxide layer (OL) with high accuracy. Depending on the reference standard used, the application of ellipsometer is generally divided into the internal and external calibrations, respectively. For the former, the Si sphere itself is used as the reference standard to directly compare the ellipsometric and another independent high-accuracy thickness measurement method, thus achieving an uncertainty of u(d(OL)) approximate to 0.1 nm. For the latter, the uncertainty is enlarged because the transfer standards of wafer samples are essentially not the same as the Si sphere. In spite of the different level of uncertainty, the external calibration method provides more practical approach for dissemination and maintenance of the new mass unit. Both methods are studied in detail for practical guidance. (C) 2017 Elsevier B.V. All rights reserved.