The structure and mass of heterogeneous thin films measured with dual polarization interferometry and ellipsometry

Optical techniques for the characterisation of thin films, such as Dual Polarisation Interferometry (DPI), Ellipsometry or Optical Waveguide Lightmode Spectroscopy (OWLS), usually apply a uniform single layer model to the analysis of thin films. Whilst this is the simplest approach, fitting a more realistic density profile would be preferable for heterogeneous films. The influence of a film's density distribution on the optically determined values, assuming a homogeneous isotropic model is thus investigated. New analytic formulae are proposed that give a good approximation to the measured averages for the thickness, refractive index and extinction coefficient of inhomogeneous light absorbing films. It is demonstrated that these equations are valid for optical waveguide techniques, such as DPI and agree closely with ellipsometry. The equations enable non-uniform density distributions of heterogeneous films to be studied and related to the experimentally measured values created using a slab model, without the need for instrument dependent modelling using the often more complicated Drude, Fresnel or Maxwell equations. A non-uniform density distribution model is applied, as an example, to the analysis of data obtained during the deposition of the cationic polyelectrolyte Polyethylenimine (PEI) on silica, measured by DPI and correlated with data obtained using a Quartz Crystal Microbalance with Dissipation (QCM-D). The equations presented are then extended to enable the calculation of the mass of different molecular species in composite films that absorb varying amounts of light. The ability to measure the mass of light absorbing molecules provides more information concerning surface morphology and removes an ambiguity concerning a film's composition, especially when different molecular species compete for sites on a surface.