Determination of the Analytical Relationship between Refractive Index and Density of $SiO_{2}$ Layers

The main goal of the work was the elaboration of the analytical functional relationship between refractive index n and density ρ of $SiO_{2}$ layers on silicon substrates. Such ρ (n) relationship will give possibility to determine elastic and non-elastic strains in $SiO_{2}$ layers on silicon substrates. Ellipsometric measurements by using variable angle spectroscopic ellipsometer of J.A. Woollam Company allowed determination of thicknesses and refractive indexes of silica layers. Measured $SiO_{2}$ masses and calculated volumes of the layers gave possibility to define the degree of densification of silicon dioxide layers on silicon substrates. The Hill approximation function curve turned out to be the best fitting. The obtained Hill curve shows saturation for the density of silicon dioxide equal to ca. 4.53 g/$cm^{3}$. This value corresponds to the value nearby the one of the crystalline polytypic silicon dioxide (stishovite). It seems to be physically established that degree of densification tends to the limiting value.