Determination of average refractive index of thin CeO₂films with large inhomogeneities

Abstract

Thin films of cerium dioxide were deposited on heated (HS-films) and unheated (US-films) substrates by electron-beam evaporation. An attempt was made to determine their refractive indices from the measurement of their transmittance at normal incidence. All films were found to be optically inhomogeneous (i.e. variation of the refractive index along the depth of the film). The degree of inhomogeneity in the HS-films was far greater than that in the US-films. It is known that films of cerium oxide (HS-films) are far more inhomogeneous than the films of some other metal oxides. Satisfactory dispersion curves could be obtained for the US-films on the basis of a commonly used linear-index-variation-profile. However, in the case of HS-films satisfactory curves could not be obtained when such an index-variation-profile was used. On the other hand for the HS-films, satisfactory curves were obtained by the use of a quadratic-index-variation-profile. A simple model of a growth of film with columnar structure is proposed, for the first time, such as to justify the use of the quadratic-index-variation-profile in the case of a film with large inhomogeneity. The growth model needs to be verified physically by some other means.

Hydrothermal Synthesis of CeO2and Ce0.9Fe0.1O2Nanocrystals

“…The refractive index (n) and extinction coefficient (k) of pure and doped samples were obtained by direct inversion of measured spectroscopic angles Ψ and ∆ using very simple two-phase model (nanocrystalline CeO 2 /air) [15]. Difference in spectral dependence of n and k indicates that optical parameters of CeO 2 nanoparticles are strongly correlated to the synthesis parameters [16,17] (which in our case are type of basic solution and calcination temperature).…”

Structural and optical study of samarium doped cerium oxide thin films prepared by electron beam evaporation

“…The CeO 2 based films have high refractive index (between 1.6 and 2.4), dc permittivity and transparency in the visible and, near-and mid-IR [21][22][23][24][25]. The direct band gap of CeO 2 films varies between 3.2 and 3.6 eV.…”

A method for the determination of the optical constants (nandk) of thin films with large optical inhomogeneities

“…The determination of the optical constants (n and k) of thin films is very important in the development of demanding multilayer optics. Optical inhomogeneity refers to the variation of the index of refraction along the depth of the film [1][2][3][4][5][6]. This inhomogeneity, often due to variations in packing density, is at the root of many anomalies in the optical properties.…”

“…For various practical and economic reasons, however, sometimes processes must be used in which it is impossible to avoid a film microstructure that results in small variations in the profile of the index of refraction along the depth of the film. The existing methods [1][2][3][4][5][6] for determining the optical constants of inhomogeneous thin films deal with non-absorbing films (k ¼ 0). Various models for refractive index variation were investigated including linear, exponential and step variations.…”

“…Various models for refractive index variation were investigated including linear, exponential and step variations. It was found that for films with a large optical inhomogeneity, the refractive index can be adequately described by a quadratic model [5]. Recently, we have developed a method for determining the optical constants of inhomogeneous and absorbing (k 6 ¼ 0) thin films with a small degree of inhomogeneity [8], for which the refractive index variation was described by a linear model.…”