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A new definition of the kilogram is being sought. One approach is to relate the kilogram to an atomic mass through the accurate measurement of the Avogadro constant, and it requires the fabrication of near-perfect spheres from Si single-crystal material by a mechanical polishing process. Knowledge of the composition and structure of a sphere's surface is required when determining its density. In the relevant literature, the silicon surface has been described as a layer of amorphous silicon dioxide. Measurement of the oxide layer thickness is often made with spectroscopic ellipsometry (SE) whose spectra are interpreted by the assumption of an optical model consisting of an abrupt Si-SiO2 interface and optical constants derived from studies of bulk amorphous SiO2. In this present thesis, the application of Rutherford Backscattering Spectroscopy (RBS), X-ray Photoelectron Spectroscopy (XPS) and gravimetric weighing has demonstrated this model is overly simplistic. The main contribution of this thesis is to develop a physical model that accurately describes the surface of highly polished spheres. Si single-crystals of five different orientations - (100), (110), (111), (211), (311) - were mechanically polished with a similar method to that used when fabricating spheres. The surface oxide thickness is determined by RBS with channelling. Sub-surface damage resulting from the polishing process is seen at the Si-SiO2 interface and showed a dependence on crystal orientation. An organic surface overlayer is identified and quantified by XPS, and gravimetric weighing is used to determine the adsorption isotherm of water on polished Si. The values of these parameters are used to build a consistent optical model to fit SE data; the damaged layer and the adsorbed organic and water contaminants are all significant components of the surface "oxide" layer. The new model has been applied for the first time to data obtained on a silicon sphere. A procedure was developed that will enable the oxide thickness to be determined on Avogadro silicon spheres with sufficient accuracy for the determination of the Avogadro constant and the potential re-definition of the kilogram.

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