Abstract

In predicting the reflectance, transmittance, and other optical properties of film-covered substrates, the films are usually modeled as uniform, plane parallel layers having constant (complex) refractive indices. However, it is well known that film structure is strongly influenced by the condition of the substrate onto which it is deposited. Optical scattering theories modify the above zero order assumptions by introducing microroughness on the substrate and film surfaces. In first order scattering theories the heights of surface microirregularities are assumed to be much less than the wavelength of light. In order to calculate the angular dependence of the scattered light,¹ it is necessary to know the statistical properties of the microroughness, specifically the autocovariance function or its Fourier transform, the spectral density function. Recent experiments^2,3 have shown that in some cases this information is not enough to correctly predict the complete angular scattering distribution; more detailed modeling of the film structure is needed. In order to better relate optical scattering of thin films to their structural and topographic features, we have made electron micrographs of replicas of film surfaces and their cross sections, and microtopographic measurements on films and bare substrates using a stylus-type profiling instrument having a lateral resolution ~ 0.1 to 0.2 μm. We have also obtained surface profiles from an analysis of microdensitometer traces of electron micrographs of surface replicas.⁴ Films studied include silver and multilayer dielectric stacks deposited onto microscope slides, fused quartz, and Zerodur substrates. When silver films are baked in vacuum, appreciable differences are observed in film structure, and large differences are also observed in the total scattering and its angular dependence. Measured scattering from various film-substrate combinations whose microstructural features have also been measured will be compared with theoretically predicted values. Further modifications to the theory have been proposed⁵ in order to better incorporate observed film microstructure into vector scattering theory.

© 1984 Optical Society of America