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

Values of the transmittance T-s and the phase retardation Delta were recorded in situ at two angles during the growth of thin films of tantalum oxide, titanium oxide, and zirconium oxide for deposition angles theta(nu), in the range 40 degrees-70 degrees. 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 psi = tan(-1)(0.5 tan theta(nu)) and that the experimental values fit a modified form of the equation psi = tan(-1) (E-1 tan theta(nu)) 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)(theta(nu)) = A(0) + A(2) theta(nu)(2). (C) 1998 Optical Society of America.