Self-consistent optical constants of MgF₂,LaF₃ and CeF₃ films

Luis V. Rodríguez-de Marcos, Juan I. Larruquert, José A. Méndez, and José A. Aznárez

Abstract

Various fluorides are materials in nature that extend their transparency range to the shortest wavelengths in the far ultraviolet (FUV, 100nm<λ<200 nm). These are relevant materials to prepare multilayer coatings in the FUV for demanding applications such as space instrumentation for astrophysics, solar physics and atmosphere physics, as well as free electron lasers, plasma diagnostics, synchrotron radiation, lithography, spectroscopy, etc. Multilayer design requires an optical constant of the coating materials. Multilayers optimally alternate two transparent materials with contrasting refractive indices. The optical constants of a low-index material, MgF₂, and of two high-index materials, LaF₃ and CeF₃, have been determined in a wide spectral range and are presented here. Thin films of MgF₂, LaF₃ and CeF₂ were deposited by boat evaporation onto substrates at 523 K. Transmittance, reflectance, and ellipsometry measurements were performed in ranges jointly covering the 30-950-nm spectral range. This range was extended with literature data and extrapolations to obtain self-consistent optical constants using the Kramers-Kronig (KK) analysis. An iterative, double KK analysis procedure (successive reflectance-phase and k-n KK analyses) was carried out to obtain a self-consistent set of optical constants per material. With the final data sets, the experimental measurements were satisfactorily reproduced. Global self-consistency of the data sets was successfully evaluated through sum rules; additionally, local self-consistency at each photon energy range was also evaluated through a novel sum-rule method which involves window functions. The new sets of optical constant extend the data availability mainly to the FUV and beyond, particularly for CeF₃, where few data had been reported.