Measurement System For Determining The Thickness Of The Oxide Layer On The Silicon Sphere By Spectroscopic Ellipsometry

Avogadro constant (NA) is a fundamental physical constant which links the macroscopic and microscopic matter. The accurate determination of NA can be applied to redefine the base units such as"kilogram"and"mole". The X-ray crystal density method is a primary approach to measure NA currently. In order to measuring NA with an uncertainty of 2×10-8 by this method, the thickness of an oxide layer on the surface of the single crystal silicon sphere should be determinated with an uncertainty of about 0.1nm. Based on the analysis of the growth mechanism of this layer, a method for determining the thickness of this layer by means of mapping the surface of the silicon sphere by the spectroscopic ellipsometer (SE) is presented in this dissertation, and a measurement system for mapping the oxide layer on the surface of the silicon sphere is also developed.To improve the surface roughness of a domestic silicon sphere treated with the traditional polishing process, a modified polishing technique is proposed. The roughness (Ra) of the sphere S303 has been reduced to 1.33 nm from initial 15.30 nm, which indicates that the silicon sphere is appropriate for NA measurement.The validity of applying SE to measuring the thickness of the oxide layer on the spherical surface as well as the method of improving the accuracy of SE are discussed at first. The theoretical research indicates that the spherical surface will lead to a mixed polarization of the reflected light of SE, which will result in inaccuracy of the layer's thickness. A solution named as aperture filter is provided to minimize the effect of the mixed polarization, and the uncertainty caused by the spherical surface can be reduced to less than 0.05 nm. In addition, as an indirected measurement method, the thickness of a film obtained by SE is dependent on its optical model, which means the results of SE can not be traced to the base units. A novel method of calibrating SE by the X-ray reflectivity method is thus presented. The calibration results show that the measuremental accuracy of SE can be improved to subnanometrer, and the results of SE can be traced to the wavelength of the X-ray.Since the distribution of the thicknesses of the oxide layer is not uniform on the surface of the silicon sphere, it is essential to scan the surface of the silicon sphere for the purpose of determining the mean thickness of this layer. Considering the features of the silicon sphere (e.g., enveloped overall by optical surface, large size and mass, cannot be damaged), a sphere-rotating mechanism of an elevator type is invented, which can locate and rotate the silicon sphere with high precision. Moreover, a sampling strategy named as"weighted mean based on equal-spherical angle mapping"is proposed to evaluate the mean thickness of the sampled points. Two steps are necessary according to this strategy, i.e., mapping the surface of the silicon sphere by equal-spherical angle at first, and then calculating the weighte mean of the sampled points according to the theory of equal-area projection. This strategy can be realized and extended easily in the experiment as it is insensitive to the angle resolution of the spherical-rotating mechanism.An automatic system for determining the thickness of the oxide layer on the silicon sphere with high precision is designed based on the previous works. The surface of the silicon sphere S303 is mapped with several groups of experiments by this system, and the mean thickness of the oxide layer is determined to be 4.27(10) nm, which means the relative uncertainty of NA can be reduced to 1×10-8 after the error caused by this layer is corrected. The work presented in this dissertation can promote the determination of NA with high accuracy.