Multiple determination of the optical constants of thin-film coating materials: a Rh sequel

Abstract

We extend the previous investigation by Arndt et al. of the optical properties of a common production run of thin and thick Rh films. Using a first-order expansion of the relevant Fresnel equations, we show that the surprisingly large scatter in the derived values of the optical functions n and k reported in this reference is due to a corresponding scatter in the thicknesses used to calculate them. Specifically, the nominal 0.1% measurement capabilities of photometry and ellipsometry are meaningless here unless the film thicknesses can be determined to ∼1 Å. By eliminating these underlying thickness correlations with the first-order expansion, we find that the photometric results are in good mutual agreement. Similar agreement is found between our new spectroellipsometric data for these films and those previously reported by Arndt et al. By combining these two different sets of data, we take advantage of their significantly different dependences and obtain an accurate purely optical assessment of the film thicknesses and optical functions. The thicknesses are found to agree within 2 Å of the metric values, and the optical functions of the thin and thick films are found to be different. The results clearly demonstrate that combined photometric and ellipsometric measurements are far better able to deal with this class of sample than either technique alone. Finally, we show that the spectroellipsometric data are accurately described over the full 1.5–6.0-eV spectral range by a two-parameter effective medium model originally developed by Sen, Scala, and Cohen to interpret the low-frequency conductance properties of sedimentary rocks. Thus the formerly puzzling optical functions of these films are due to microstructure. The results show that these films are microscopic mixtures of Rh and a dielectric phase, presumably Rh oxides or voids, located primarily at the boundary regions between the metal grains and providing optical isolation between them (metal-rich cermet microstructure). When used with standard spectroellipsometric data reduction methods developed for materials analysis applications in semiconductor technology, this model yields values consistent with those obtained above. Our conclusions are consistent with the results of a deterministic analysis of the film microstructures by transmission electron microscopy.