Ellipsometry Modeling with Gradient in Refractive Index Resolves Unrealistic Density Increases in Thin Polymer Films and Demonstrates Inhomogeneous Film Structure Decoupled from Dynamics

We show polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(2-vinylpyridine) (P2VP) all exhibit similar large increases in refractive index with decreasing film thickness for ellipsometry data modeled by a homogeneous Cauchy layer. Such increases in refractive index have been interpreted by others recently as large increases in density (~25%) via the Lorentz-Lorenz relation, despite being physically unrealistic. We demonstrate that an ellipsometric layer model with a gradient in refractive index provides more physically realistic parameters for very thin films, retaining a bulk-like refractive index for much of the film’s interior, while exhibiting a sharp gradient in index near the free surface whose breadth grows from 4 to 9 nm with decreasing film thickness from 50 to 30 nm. Such an inhomogeneous film structure would invalidate the use of homogeneous Cauchy layers and the Lorentz-Lorenz relation whose derivation is based on assuming an isotropic distribution of dipoles. Surprisingly the refractive index gradient has an opposite trend to that based on a simple density correlation to dynamics. A higher refractive index near the free surface could reflect more optimized molecular packing from surface mobility, similar to vapor deposited stable molecular glasses.