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].

Structural investigation of superionic AgI-containing orthoborate glasses

“…To analyze the transmittance spectrum, T(m), of a finite flake with complex refractive indexñ ¼ n À ik and thickness d we considered the exact formula for the system vacuum-flake-vacuum taking into account multiple internal reflections of the incident light, as it was employed recently in studies of glassy and crystalline materials [15,16] T ðm; n; k; dÞ…”

Influence of deposition angle on the structural, morphological and optical properties of sputtered AlN thin films

“…Kramers-Kronig (KK) analysis of the first type is related to the normal-incidence reflectivity spectra [8]. Although this approach breaks down for instance for off-normal reflectivity, or for a thin film on a substrate and in many other cases, but a number of analytical and numerical algorithms are suggested to extend the KK method to off-normal reflection [9][10][11][12][13][14][15], transmission [16][17][18][19], attenuated total reflection spectra [20][21][22] as well as to optical data on layered samples [23][24][25][26][27] and low-symmetry crystals [28,29] and non-standard situations. Hence, KK method is explained in many publications and here we briefly describe the method we have used in this work which can be applied to thin films.…”

Preparation and characterization of poly(l-histidine)/poly(l-glutamic acid) multilayer on silicon with nanometer-sized surface structures

“…Reflectance Fourier-transform infrared spectroscopy (FTIR) [46][47][48][49][50][51][52][53][54] was performed on dried (PLH/PGA) 8 films, deposited on bare silicon wafers, and gold-coated silicon wafers. Reflectance FTIR spectra recorded from films on substrates depend on the nature and kind of material of film and substrate, the film thickness as well as the incident angle and polarization of the IR radiation.…”

“…The detection of the individual functional groups was carried out using IR-spectroscopy in reflectance geometry [46][47][48][49][50][51][52][53][54] with silicon and gold-coated silicon wafer substrates. Reflectance FTIR spectroscopy has recently been applied to organic materials [46,52], soils [48], fuels [52], and inorganic materials [53,54].…”

“…Hence, any finite tangential absorption of the coating leads to inverted, ''negative'' signals [46,47,51,52]. The obtained reflectivity is a function of the optical constants, in this case resulting in a maximum where an absorption band was expected [49][50][51]53]. This has been observed for silicon wafers several times [46,[49][50][51]54].…”