Determination of the Complex Refractive Index of Materials via Infrared Measurements

Abstract

In this work, methods are presented for obtaining the real, n, and imaginary, k, parts of the complex refractive index of materials considered as semi-infinite and finite from infrared reflectance, R(ν), and/or transmittance, T(ν), spectra. In semi-infinite samples, with negligible T(ν), only R(ν) is measured, and n and k can derive from the Kramers–Kronig (K–K) transformation or the modeling of the dielectric function of the material. In finite samples, the interference fringes due to multiple internal reflections can significantly alter the measured spectra. It was demonstrated that whenever the period of the fringes is on the order of a few cm⁻¹, n and k can be equivalently obtained by the extended K–K analysis for T(ν) spectra, the modeling of the dielectric function, and the inversion of low-resolution R(ν) and T(ν) spectra, as well as the acquisition of a single high-resolution R(ν) or T(ν) spectrum. Otherwise, n and k can be calculated by modeling the dielectric function of the material once the optical effects are carefully removed. These methods were applied in infrared measurements of crystalline Si wafer and of glassy 0.20AgI·0.80[Ag₂O·2B₂O₃].