Procedure for determining the optical constants of metals from the results of measurements of the self-radiation of a sample

A procedure is described for determining the optical constants of metals in the infrared region of the spectrum.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 6, pp. 1066–1069, June, 1979.     

Far-ultraviolet reflectance measurements and optical constants of unoxidized aluminum films

The far-UV reflectance of thin unoxidized aluminum films prepared and maintained in ultra-highvacuum conditions was measured versus the angle of incidence, and the complex refractive index was obtained from those measurements on several wavelengths from 82.6 to 113.5 nm. Measurements were made on two perpendicular planes of incidence to deal with the unknown of the polarization state of the radiation beam. The surface roughness was characterized by atomic force microscopy. The refractive index is obtained for the first time, to our knowledge, from direct optical measurements in this spectral range. Current results match well the former values in the literature that were calculated through the Kramers-Kronig analysis by using in the above interval reflectances estimated from electron-energy-loss spectra and from optical measurements on surfaces of unstated roughness.     

Unified measurements in determining traces of dissolved metals by optical spectroscopy

Basic methods are given for determining traces of dissolved heavy metals at concentrations in the range 10⁻⁹–10⁻⁴%. Spectroscopic methods can be combined: atomic absorption, atomic emission, and atomic fluorescence. Unified measurements in this area are considered together with apparatus for the purpose. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 60–63, March, 2000.     

Inversion of light-scattering measurements for particle size and optical constants: theoretical study

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt-Hilbert eigenfunctions and a set of supplemental basis functions, which have been orthogonalized with respect to the Schmidt-Hilbert eigenfunctions by using the Gram-Schmidt orthogonalization procedure. We use the orthogonality properties of the basis functions and of the eigenvectors of the kernel covariance matrix to obtain the solution that minimizes the residual errors subject to a trial function constraint. The inversion process is described, and results from the inversion of several simulated data sets are presented.     

Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet-soft-x-ray region

The refractive index n = 1 - delta + ibeta of Si in the energy range 50-180 eV is investigated with angle-dependent reflectance measurements. The optical constants delta and beta are both determined by fitting to the Fresnel equations. The results of this method are compared with the values in the atomic tables derived from experimental data for beta and implementation of the Kramers-Kronig relations for delta. The samples were prepared by UV irradiation and HF:ethanol dipping to H passivate the surface. It is found that the values of delta in the atomic tables are 8-15% too high in the region 50-90 eV. This is attributed to missing oscillator strength in the tabulated absorption coefficient for Si. The measured values of beta for crystalline Si exhibit structure below the L (2,3) edge (99.8 eV), as was previously observed in transmission measurements of Si(111). It is also found that the method of least-squares fitting reflectance data to obtain optical constants is most effective for energies well below the edge, where delta > beta, while for a range of energies around and above the edge, where delta < beta, the optical constants are determined with large uncertainties. This behavior is not unique to the Si L(2,3) edge.     

Ellipsometric measurements on tantalum and tantalum oxide films and variation of the optical constants with structure

The optical constants n and k for films of tantalum and naturally grown tantalum oxide were determined at wavelengths of 4960 Å, 5487 Å and 6049 Å using an ellipsometer at two angles of incidence. The tantalum films were prepared at a pressure equal to or less than 2 × 10^-8 Torr during evaporation. Values are compared with those of other workers. Optical observations on films with mixed b.c.c. and f.c.c. structures (as determined from X-ray measurements) indicate the presence of a b.c.c. and f.c.c. mixture throughout; this is contrary to previous suggestions by other workers that the f.c.c. phase was present in very thin films only and was converted to b.c.c. in thick films.     

Simultaneous determination of the optical constants and thickness of very thin films by using soft-x-ray reflectance measurements

A nonlinear, least-squares curve-fitting method is described that simultaneously determines the optical constants and the thickness of a very thin (? 100-?) film from reflectance versus angle of incidence (R - θ) data measured in the soft-x-ray region. The method is applied to R - θ data obtained for very thin, sputtered films of carbon (65 ? thick) and gold (94 ? thick) at photon energies of 60-900 eV. The results show that the present method is capable of accurately determining the thickness of very thin films even for transparent materials, and that the obtained optical constants are in good agreement with values reported for films with a thickness of 1000 ?.     

Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements

We propose a new and simple procedure to overcome the ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements. The basis for the proposed method is an error analysis with the help of an error simulation technique and an error variation technique. We show that in practice (owing to experimental errors) it is not possible to overcome the problem of ambiguity by normal-incidence spectroscopic measurements alone. At least one oblique-incidence measurement is necessary for unambiguously determining the optical constants of the film. We discuss the consequences of experimental errors of the measured transmittance and reflectance values for the determination of the optical constants.     

Temperature-dependent optical constants of water ice in the near infrared: new results and critical review of the available measurements

The optical constants of water ice have been determined in the near infrared from 4000 to 7000 cm(-1). Polycrystalline ice films with thickness as great as ~1164 mum were formed by condensation of water vapor on a cold silicon substrate at temperatures of 166, 176, 186, and 196 K. The transmission of light through the ice films was measured during their growth from 0 to 1164 mum over the frequency range of approximately 500-7000 cm(-1). The optical constants were extracted by means of simultaneously fitting the calculated transmission spectra of films of varying thickness to their respective measured transmission spectra with an iterative Kramers-Kronig technique. Equations are presented to account for reflection losses at the interfaces when the sample is held in a cell. These equations are used to reanalyze the transmission spectrum of water ice (358-mum sample at 247 K) recorded by Ockman in 1957 [Philos. Mag. Suppl. 7, 199 (1958)]. Our imaginary indices for water ice are compared with those of Gosse et al. [Appl. Opt. 34, 6582 (1995)], Kou et al. [Appl. Opt. 32, 3531 (1993)], Grundy and Schmitt [J. Geophys. Res. 103, 25809 (1998)], and Warren [Appl. Opt. 23, 1206 (1984)], and with the new indices from Ockman's spectrum. The temperature dependence in the imaginary index of refraction observed by us between 166 and 196 K and that between our data at 196 K and the data of Gosse et al. at 250 K are compared with that predicted by the model of Grundy and Schmitt. On the basis of this comparison a linear interpolation of the imaginary indices of refraction between 196 and 250 K is proposed. We believe that the accuracy of this interpolation is better than 20%.     

Improved method for determination of optical constants of organic thin films from reflection and transmission measurements

A new technique for determining the optical properties of organic thin films is presented. A detailed evaluation of the accuracy of the determined optical constants has been performed, and the best combination of measured values yielding the smallest errors in the index of refraction for realistic experimental uncertainties has been found. The proposed method utilizes the fact that optical constants are smooth continuous functions, which reduces the possibility of encountering multiple solutions. The method consists of two steps. In the first step the optical constants at all wavelengths and the film thickness are determined. In the second step the thickness and the imaginary part of the index of refraction are kept fixed while we reevaluate the real part of the index of refraction by using a different objective function with improved sensitivity to the refractive index. After verifying that the proposed method is capable of an accurate estimation of optical constants, we determine the index of refraction data of vanadyl-phthalocyanine in the visible spectral range.