Interpolating the optical properties of varied composition silicon nitride

Abstract

We develop a method for interpolating the optical properties of silicon nitride formed with different deposition parameters. Published refractive index measurements for eight silicon nitride films formed by in-line microwave plasma-enhanced chemical-vapour deposition with a range of ammonia to silane gas-flow ratios are modelled and interpolated. The measurements are fitted by a physical model for the optical properties of silicon nitride. The model considers 16 different silicon-centred, silicon, nitrogen, hydrogen tetrahedron bond configurations in an effective medium with vacuum. An average root mean squared error (RMSE) of 0.36, was calculated when using the physical model, which is high when compared to a simple semi-physical model which achieves an average RMSE of 0.06. The semi-physical model is similar to the tetrahedron model. However, the scale and shifts variables are used as fit parameters compared to being calculated for a physical tetrahedron configuration. The poor fitting of the tetrahedron model empirically suggests that additional bond arrangements need be considered, in particular tetrahedra with vacant bonds. Our global interpolation over the optical properties measured for multiple films mitigates measurement and modelling error. It leads to a smooth optical function with changing gas ratio which aides in optimisation of multi-layer and graded anti-reflection coatings.