Determination of properties of wedged, nonuniformly thick, and absorbing thin films by using a new numerical method (original) (raw)

Determination of the thickness and optical constants of thin films from transmission spectra

Thin Solid Films, 1996

A method has been developed to determine the thickness and the wavelength-dependent refractive indices and absorption coefficients of thin optical films by fitting a five parameter function to measured transmission spectra. Initial values for the fitting parameters are obtained from the transmission values at the spectral maxima and minima of the interference patterns created by the films. This is followed by a systematic variation of those parameters which can cause a failure of the calculation by reaching local minima of the residual sum of squares. The final fitting is performed with a Mauluardt algorithm. A Monte Carlo simulation has indicated that the accuracy of this method is at least one order of magnitude better than that of the methods utilising only the interference extrema. Eeywovdf: Amorphous reatedals; Optical properties; Optical spectroscopy; Silicon 004040901961515,00 © 1996 Elsevier Science S.A. All dllhts reserved Pii$0040.6090(96)08737.8

Determination of optical parameters and thickness of weakly absorbing thin films from reflectance and transmittance spectra

Applied Optics, 2006

A method for determining the optical constants and the thickness of weakly absorbing thin films on substrates is proposed. In this method only the reflectance and transmittance spectra obtained at a single arbitrary angle of incidence are used, provided that the former reveals several interference extrema. The calculation procedure is based on relatively simple relations suitable for the programmed realization and does not call for the prescription of the initial values of the parameters to be determined. The method proposed is fairly accurate and allows one to uniquely solve the inverse problem of spectrophotometry. The optical constants and the thickness of an As x Se y film formed on a glass substrate have been determined by the proposed method in the visible region of the spectrum.

Cumhuriyet Üniversitesi Fen Fakültesi The optical constants determination of thin-films

A method for calculating the optical constants of weakly absorbing homogeneous thin films of refractive index, n lower than substrate index, s (s < n) and extinction coefficient, k from the spectral Transmission information alone with no prior knowledge of their characteristics was studied. Initially the procedure uses transmission turning point data to estimate the refractive index, n and extinction coefficient, k by an analytical approach. The calculations are done from the knowledge of transmission turning point data, which was obtained from Shimadzu UV3100 spectrophotometer. The data are then fitted to a high order polynomial function that undergoes an iterative refinement routine by means of a goal seek routine to determine with good accuracy the film parameters as a function of wavelength.

Optical Characterization of Nonabsorbing and Weakly Absorbing Thin Films with the Wavelengths Related to Extrema in Spectral Reflectances

Applied Optics, 2001

In this contribution a new efficient modification of a method that enables us to perform the optical characterization of nonabsorbing and weakly absorbing thin films without using the absolute values of the reflectances measured is presented. Namely, this modification is based on determining the values of the wavelengths corresponding to touching the spectral dependences of the reflectances of the studied films measured for several angles of incidence with the envelopes of maxima and minima of these spectral dependences. By means of combining the explicit formulas containing the wavelengths mentioned and the suitable iteration procedure one can evaluate the values of the thicknesses and spectral dependences of the refractive indices of the films analyzed in reliable and precise ways.

Estimation of the Optical Constants and the Thickness of Thin Films Using Unconstrained Optimization

Journal of Computational Physics, 1999

Titanium Dioxide films are one of the most widely used thin films catering to the needs of various sensing and optical filter applications owing to their excellent environmental durability, best reproducibility, lower thermal stress as well as widely tuneable refractive index properties. In this study, TiO2 films were grown on glass substrates by using electron-beam deposition technique under reactive oxygenated environment and the thickness of the film was monitored using quartz crystal in-situ thickness monitoring. This study focuses on estimation of film thicknesses and optical constants by envelope method to verify and validate the data received through in-situ thickness monitoring. This technique was applied to the transmission spectra of three samples which were deposited under identical conditions but in different batches and having different thicknesses. The calculated thicknesses of these samples were found to be almost in accordance with the in-situ thickness monitoring data and can be extended to other films for estimation of optical constants. The thickness computed through this method was used further for estimating other important optical constants like absorption coefficient and extinction coefficient for the samples under study.

Determination of Thickness, Refractive Index, and Thickness Irregularity for Semiconductor Thin Films from Transmission Spectra

Applied Optics, 2002

A simplified theoretical model has been proposed to predict optical parameters such as thickness, thickness irregularity, refractive index, and extinction coefficient from transmission spectra. The proposed formula has been solved for thickness and thickness irregularity in the transparent region, and then the refractive index is calculated for the entire spectral region by use of the interference fringes order. The extinction coefficient is then calculated with the exact formula in the transparent region, and an appropriate model for the refractive index is used to solve for the extinction coefficient in the absorption region ͑where the interference fringes disappear͒. The proposed model is tested with the theoretical predicted data as well as experimental data. The calculation shows that the approximations used for solving a multiparameter nonlinear equation result in no significant errors.

DETERMINATION OF THE OPTICAL CONSTANTS OF THIN FILMS FROM OPTICAL TRANSMISSION DATA

Optical constants and thickness of thin films of ZnO, SnO and A_2 O_3 are obtained by fitting of transmittance data to model equations. The Swanepoel transmission equation was used as the custom equation in the MATLAB Software. Six constants are determined using the curve fitting toolbox in MATLAB application. The Cauchy dispersion equation was used to determine the refractive index, the refractive index of ZnO, SnO and A_2 O_3 are 2.096, 2.000 and 2.046 at 600nm and the extinction coefficients of 0.1056, 0.066256 and 0.143478 respectively. The accuracy of the optical constants and thickness was very accurate compared with those obtained from other methods. Optical constants and thickness can be obtained with high accuracy by fitting transmittance data.

Determination of Optical Constants of Thin Films and Multilayer Stacks by Use of Concurrent Reflectance, Transmittance, and Ellipsometric Measurements

Applied Optics, 2001

Using measurements of reflectance, transmittance, and the ellipsometric parameter ⌬, we have determined the thickness, refractive index, and the absorption coefficient of various thin films and thin-film stacks. ͑⌬, the relative phase between the p-and s-polarized components, is measured for both reflected and transmitted light.͒ These optical measurements are performed with a specially designed system at the fixed wavelength of ϭ 633 nm over the 10°-75°range of angles of incidence. The examined samples, prepared by means of sputtering on fused-silica substrates, consist of monolayers and trilayers of various materials of differing thickness and optical constants. These samples, which are representative of the media of rewritable phase-change optical disks, include a dielectric mixture of ZnS and SiO 2 , an amorphous film of the Ge 2 Sb 2.3 Te 5 alloy, and an aluminum chromium alloy film. To avoid complications arising from reflection and transmission losses at the air-substrate interface, the samples are immersed in an index-matching fluid that eliminates the contributions of the substrate to reflected and transmitted light. A computer program estimates the unknown parameters of the film͑s͒ by matching the experimental data to theoretically calculated values. Although our system can be used for measurements over a broad range of wavelengths, we describe only the results obtained at ϭ 633 nm.

Method for determination of the parameters of transparent ultrathin films deposited on transparent substrates under conditions of low optical contrast

Applied Optics, 2015

In the present work we suggest an original ellipsometric technique for independently determining strongly correlated refractive index and thickness of transparent ultrathin films. We demonstrate significant accuracy improvement for the single-wavelength null-ellipsometry measurements when using multiple incidence angles for the system "transparent film on a transparent substrate" studied in the thickness range of 1.0-20.0 nm and the low-contrast region for the film-substrate surface. A straightforward relationship is obtained between the refractive index n 1 of the transparent film and the incidence angle φ. It follows from invariability ensured for the amplitude ellipsometric parameter Ψ with respect to the film thickness changes.

Optical peculiarities of thin absorbing films

OPTIKA '98: 5th Congress on Modern Optics, 1998

Optical parameters of thin semiconductor films in visible region are investigated with two different methods: use the new analogues of Fresnel's formulas for absorbing media for calculation of reflection and transmission [1] and, use the calculation of an index of refraction on a base of a phase change on reflection. Results of these methods agree well. Thickness dependencies of n(d) and k(d) of Ge,Si,Se, Te were obtained for the experimental data [2]. Curves n(d) have resonance maxima at thicknesses, which are less than light wavelength in a medium in it times. Curves