Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide

Abstract

Values of the transmittance T _s and the phase retardation Δ were recorded in situ at two angles during the growth of thin films of tantalum oxide, titanium oxide, and zirconium oxide for deposition angles θ_ν in the range 40°–70°. Column angles for the same films were determined ex situ from scanning electron microscopy photographs of deposition-plane fractures. We show that the experimental column angles are smaller than the corresponding values predicted by the tangent-rule equation ψ = tan^-1(0.5 tan θ_ν) and that the experimental values fit a modified form of the equation ψ = tan^-1 (E ₁ tan θ_ν) where E ₁ is less than 0.5. We also show that the principal refractive indices are represented well by quadratic functions of the deposition angle, for example, n ₁(θ_ν) = A ₀ + A ₂ θ_ν ².

© 1998 Optical Society of America

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