Determining mean thickness of the oxide layer by mapping the surface of a silicon sphere

To determine Avogadro constant with a relative uncertainty of better than 2 x 10(-8), the mean thickness of the oxide layer grown non-uniformly on the silicon sphere should be determined with about 0.1 nm uncertainty. An effective and flexible mapping strategy is proposed, which is insensitive to the angle resolution of the sphere-rotating mechanism. In this method, a sphere-rotating mechanism is associated with spectroscopic ellipsometer to determine the distribution of the layer, and a weighted mean method based on equal-area projection theory is applied to estimate the mean thickness. The spectroscopic ellipsometer is calibrated by X-ray reflectivity method. Within 12 hours, eight hundred positions on the silicon sphere are measured twice. The mean thickness is determined to be 4.23 nm with an uncertainty of 0.13 nm, which is in the acceptable level for the Avogadro project.