This study reports on the optical, structural, and dielectric properties of aluminum tantalum oxide (AlxTayOz) thin films deposited at low temperature on silicon and steel substrates by pulsed direct current reactive magnetron sputtering of a target containing 80 at.% aluminum and 20 at.% tantalum in Ar/O2 atmosphere. Oxygen flow rates ranging from 5.0 sccm to 20 sccm corresponded to O content changes from 57.7 at.% to 69.6 at.% and resulted in large differences in dielectric behavior, from films with no measurable dielectric strength to a dielectric strength of 231 V/mu m, respectively. Ab initio calculations were employed to explain the large property changes, and we show that a decrease in the dielectric strength can be linked to the formation of metal-metal bonds in the material, when the O content is less than what would correspond to a stoichiometric Ta2O5 and Al2O3 mixture. The electronic states corresponding to the metal-metal bonds are located in the band gap close to the top of the valence band, leading to an effective band gap reduction, which is directly supported by X-ray photoelectron spectroscopy valence band measurements and by a broad optical absorption in the visible region.

Three samples of non-uniform polymer-like thin films are characterized using imaging spectroscopic reflectometry, which measures maps of spectral dependencies of reflectance of sample surface. It was necessary to consider transition layers between these films and silicon substrates. The goal of the optical characterization was to determine the maps of local thicknesses, optical constants of the non-absorbing films, and the parameters (thickness and the optical constants) of the transition layers. Because the transition layers have complicated spectral dependencies of the optical constants, it was difficult to correctly determine all parameters. Three methods of data processing were introduced to deal with this problem. In the first approach, the data for each sample were processed separately. The second approach considered the data for all three samples together and assumed that the parameters of the transition layers are the same for all samples. The third approach is a slight extension of the second one, which also assumes the same optical constants of the non-uniform films on all three samples. The processing of the data utilizes the least-squares method, with parameters divided into three groups: those sought within each pixel, those that are the same for all pixels of the given sample (multi-pixel method), and those that are the same for all pixels and all samples (multi-sample method). While the first method considering the samples independently, failed to give reasonable results for the parameters of the transition layer, the other two methods utilizing the multi-sample approach, were successful.

The precise values of the refractive index of crystalline silicon are determined in the infrared region based on the measurements of the interference pattern in 0.25 mm thick wafer. The interference pattern observed for one particular incidence angle allows us to determine the optical thickness precisely, however, the wafer thickness and refractive index, whose product gives the optical thickness, can be determined with much worse accuracy. This limitation could be overcome by using several incidence angles because if the dependence of the period of interference pattern on the incidence angle is considered, it is possible to determine both the thickness and refractive index with high accuracy. The FTIR infrared ellipsometer is used for measurements at oblique incidence angles, while the FTIR spectrophotometer is utilized for measurements at near-normal incidence. To correctly interpret the experimental data, it is necessary to consider the influence of the finite spectral resolution and beam divergence of the instruments and the thickness non-uniformity of the sample. These effects significantly alter the observed interference patterns. The formulae needed to accomplish this task are derived in this work. The values of the refractive index determined using the proposed method for the crystalline silicon show differences smaller than 10-3 from the values obtained by the minimum deviation method.

This study presents a comprehensive optical characterization of tantalum pentoxide (Ta2O5) thin films across a wide spectral range, using a combination of ellipsometric and spectrophotometric data. The films prepared using e-beam evaporation, ranging in thickness from 20 to 250 nm, were analyzed using a complex structural model that integrates inhomogeneous layer profiles with three distinct phases, allowing for a more accurate representation of the material's optical properties. A universal dispersion model was employed to describe the optical constants, revealing the refractive index and extinction coefficient with exceptional precision. This work stands out due to the extensive spectral range covered-extending from the far infrared (400 mu m, 25 cm-1) to the vacuum ultraviolet (116 nm, 10.7 eV)-and the diverse array of instruments used, providing a level of detail and insight into Ta2O5's optical behavior that has not been achieved before. This novel approach offers significant advancements in understanding Ta2O5's optical characteristics, demonstrating its potential for advanced optical coatings and optoelectronic applications. (c) 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Apart from coherent reflectance, which corresponds to specular reflection, the values obtained by real spectrophotometers also include contribution from incoherent reflectance, which represents light scattered by the samples and registered by the detector due to its finite acceptance angle. This work aims to investigate the influence of this second part on reflectance spectra measured for samples with randomly rough surfaces. Three silicon samples with roughened surfaces are investigated. The reflectance is measured using a commercial spectrophotometer with acceptance angles restricted by apertures placed in the incident and reflected beam. The proposed method is based on the simultaneous processing of spectral dependencies of reflectance measured with differently-sized apertures. The utilized theoretical approach is based on the scalar diffraction theory. Because the dependencies on both wavelength and acceptance angle are considered, a model providing correct predictions for these dependencies should also correctly describe how is the total reflectance separated into its coherent and incoherent parts. It is shown that the theoretical predictions for incoherent reflectance are consistent with the changes in the diameter of the apertures. It was possible to determine the RMS value of the heights as well as the estimate for the autocorrelation length and additional parameter controlling the course of the autocorrelation function. A short discussion comparing our results with those achieved using methods employed in earlier works is also provided.

In this study, an optical investigation in a wide spectral range of polymer-like (SiOxCyHz) thin films deposited by plasma-enhanced chemical vapor deposition (PECVD) is presented. The primary focus is on assessing the homogeneity of the grown films. Within the PECVD, it is possible to alter the properties of the deposited material by continually adjusting deposition process parameters and hence allow for the growth of inhomogeneous layers. However, as shown in this study, the growth of homogeneous layers could be similarly challenging. This challenge is especially pronounced at the beginning of the deposition process, where it is necessary to consider the influence of the substrate among other factors, as even slight variations in the deposition conditions can lead to the formation of inhomogeneous layers. Several series of polymer-like thin films were deposited onto silicon substrates with the goal of producing homogeneous layers, i.e. all deposition parameters were held constant. These samples were optically characterized with a special interest in homogeneity, especially at the beginning of the growth. It was found that initial inhomogeneous growth is always present. The thickness of the initial inhomogeneous part was found to be surprisingly large.

In this work, the optical properties of niobium pentoxide (Nb2O5) films were extensively studied across a wide spectral range using heterogeneous data-processing methods, combining ellipsometric and spectrophotometric measurements for five samples with thicknesses between 20 and 250 nm. This study primarily determined the optical constants of Nb2O5 from the far infrared to the vacuum ultraviolet, presenting these constants as dispersion parameters using the universal dispersion model to describe valence electron excitations in ultraviolet region as well as phonon vibrations in infrared region. These comprehensive and reliable data across such a broad spectral range are unprecedented. Secondly, presented optical characterization proofs that Nb2O5 films can be grown without defects such as surface roughness, porosity, or inhomogeneity. This fact, together with its high refractive index, makes Nb2O5 a promising material for optical applications.

The optical characterization of non-absorbing, homogeneous, isotropic polymer-like thin films with correlated, differently rough boundaries is essential in optimizing their performance in various applications. A central aim of this study is to derive the general formulae necessary for the characterization of such films. The applicability of this theory is illustrated through the characterization of a polymer-like thin film deposited by plasma-enhanced chemical vapor deposition onto a silicon substrate with a randomly rough surface, focusing on the analysis of its rough boundaries over a wide range of spatial frequencies. The method is based on processing experimental data obtained using variable-angle spectroscopic ellipsometry and spectroscopic reflectometry. The transition layer is considered at the lower boundary of the polymer-like thin film. The spectral dependencies of the optical constants of the polymer-like thin film and the transition layer are determined using the Campi–Coriasso dispersion model. The reflectance data are processed using a combination of Rayleigh–Rice theory and scalar diffraction theory in the near-infrared and visible spectral ranges, while scalar diffraction theory is used for the processing of reflectance data within the ultraviolet range. Rayleigh–Rice theory alone is sufficient for the processing of the ellipsometric data across the entire spectral range. We accurately determine the thicknesses of the polymer-like thin film and the transition layer, as well as the roughness parameters of both boundaries, with the root mean square (rms) values cross-validated using atomic force microscopy. Notably, the rms values derived from optical measurements and atomic force microscopy show excellent agreement. These findings confirm the reliability of the optical method for the detailed characterization of thin films with differently rough boundaries, supporting the applicability of the proposed method in high-precision film analysis.

Two samples of silicon-single crystal substrates with randomly rough surfaces covered by native oxide layers are investigated by means of angle-resolved scattering, spectroscopic reflectometry and variable-angle spectroscopic ellipsometry. For each sample, the experimental optical data are processed simultaneously to determine the power spectral density functions, which are modeled by exponentials of quadratic splines. The thicknesses of native oxide layers are also determined. The influence of roughness on the reflectance and ellipsometry is described by the combination of the scalar diffraction theory, which is used for the part of roughness with low spatial frequencies, and the Rayleigh–Rice theory, which is used for the part of roughness with high and moderate spatial frequencies. The separation of the roughness into the parts with low and high/moderate spatial frequencies is performed using a bound dependent on the wavelength of the incident light. The PSDFs determined by the optical method are compared with the PSDFs determined by processing the AFM scans.

Angle-resolved scattering was measured for four samples of silicon exhibiting different surface roughnesses. The measurements were performed for three wavelengths: 457.9 nm, 514.5 nm, and 647.1 nm. Three approaches were used to evaluate the experimental data. The first approach corresponds to the exact formula derived using the scalar diffraction theory. This formula is quite complicated, and numerical methods must be used for its evaluation. For this reason, another two approaches representing approximations by much simpler formulae were considered. The use of several wavelengths allowed us not only to recover the power spectral density function in a limited interval of spatial frequencies but also to determine the total rms values of the heights, which represent the quantity of roughness for all spatial frequencies. The possibility of recovering the total rms values of the heights using the multi-wavelength approach is the most important result of this work. The results obtained from the scattering experiment and atomic force microscopy are compared.

The optical characterization of gadolinium fluoride (GdF3) films is performed in a wide spectral range using heterogeneous data-processing methods (the ellipsometric and spectrophotometric measurements for five samples with thicknesses ranging from 20 to 600 nm are processed simultaneously). The main result of the characterization is the optical constants of GdF3 in the range from far infrared to vacuum ultraviolet, both in the form of a table and in the form of dispersion parameters of the universal dispersion model (UDM). Such reliable data in such a broad spectral range have not been published so far. The GdF3 films exhibit several defects related to the porous polycrystalline structure, namely, surface roughness and a refractive index profile, which complicate the optical characterization. The main complication arises from the volatile adsorbed components, which can partially fill the pores. The presented optical method is based on the application of the UDM for the description of the optical response of GdF3 films with partially filled pores. Using this dispersion model, it is possible to effectively separate the optical response of the host material from the response of the adsorbed components. Several recently published structural and dispersion models are used for optical characterization for the first time. For example, a model of inhomogeneous rough films based on Rayleigh–Rice theory or asymmetric peak approximation with a Voigt profile for the phonon spectra of polycrystalline materials.

In this study, a novel approach for characterizing the optical properties of inhomogeneous thin films is presented, with a particular focus on samples exhibiting absorption in some part of the measured spectral range. Conventional methods of measuring the samples only from the film side can be limited by incomplete information at the lower boundary of the film, leading to potentially unreliable results. To address this issue, depositing the thin films onto non-absorbing substrates to enable measurements from both sides of the sample is proposed. To demonstrate the efficacy of this approach, a combination of variable-angle spectroscopic ellipsometry and spectrophotometry at near-normal incidence was employed to optically characterize three inhomogeneous polymer-like thin films. The spectral dependencies of the optical constants were modeled using the Kramers–Kronig consistent model. It was found that it is necessary to consider thin, weakly absorbing transition layers between the films and the substrates. The obtained results show excellent agreement between the fits and the measured data, providing validation of the structural and dispersion models, as well as the overall characterization procedure. The proposed approach offers a method for optically characterizing a diverse range of inhomogeneous thin films, providing more reliable results when compared to traditional one-sided measurements.

Results concerning the optical characterization of two inhomogeneous polymer-like thin films deposited by the plasma enhanced chemical vapor deposition onto silicon single crystal substrates are presented. One of these films is deposited onto a smooth silicon surface while the latter film is deposited on a randomly rough silicon surface with a wide interval of spatial frequencies. A combination of variable-angle spectroscopic ellipsometry and spectroscopic reflectometry applied at near-normal incidence are utilized for characterizing both the films. An inhomogeneity of the films is described by the method based on multiple-beam interference of light and method replacing inhomogeneous thin films by multilayer systems. Homogeneous transition layers between the films and substrates are considered. The Campi-Coriasso dispersion model is used to express spectral dependencies of the optical constants of the polymer-like films and transition layers. A combination of the scalar diffraction theory and Rayleigh-Rice theory is used to include boundary roughness into formulae for the optical quantities of the rough polymer-like film. Within the optical characterization, the spectral dependencies of the optical constants at the upper and lower boundaries of both the polymer-like films are determined together with their thickness values and profiles of the optical constants. Roughness parameters are determined for the rough film. The values of the roughness parameters are confirmed by atomic force microscopy. Moreover, the optical constants and thicknesses of both the transition layers are determined. A discussion of the achieved results for both the polymer-like films and transition layers is performed.

An inhomogeneous polymer-like thin film was deposited by the plasma enhanced chemical vapor deposition onto silicon single-crystal substrate whose surface was roughened by anodic oxidation. The inhomogeneous thin film with randomly rough boundaries was created as a result. This sample was studied using the variable-angle spectroscopic ellipsometry and spectroscopic reflectometry. The structural model including the inhomogeneous thin film, transition layer, and identically rough boundaries was used to process the experimental data. The scalar diffraction theory was used to describe the influence of roughness. The influence of the scattered light registered by the spectrophotometer due to its finite acceptance angle was also taken into account. The thicknesses and optical constants of the inhomogeneous thin film and the transition layer were determined in the optical characterization together with the roughness parameters. The determined rms value of the heights of roughness was found to be in good agreement with values obtained using AFM. The results of the optical characterization of the studied inhomogeneous thin film with rough boundaries were also verified by comparing them with the results of the optical characterization of the inhomogeneous thin film prepared using the same deposition conditions but onto the substrate with a smooth surface.

The roughness of four samples of silicon single-crystal surfaces roughened by anodic oxidation is studied using atomic force microscopy (AFM) and angle-resolved scattering of light. The power spectral density functions (PSDFs) are determined on the basis of the measured values of the intensity of the scattered light. This is done on the basis of three models, which establish relation between the intensity of the light scattered in the given direction and the values of the PSDF at a certain spatial frequency. Two of the models are based on the scalar diffraction theory (SDT), while the third is based on the Rayleigh-Rice perturbation theory. The formulae corresponding to the SDT are derived in the theoretical part of the paper. The condition for the Fraunhofer diffraction is not satisfied if the values of the wavelength, distance to the detector and the dimensions of the illuminated spot on the sample used in the experiment are considered. However, it is shown that if the calculation of the intensity of the scattered light is performed in a certain way, then the validity of the expansion only up to the linear terms in the phase terms, i.e. in the same way as in the Fraunhofer diffraction, is not limited by the dimensions of the light spot but by the autocorrelation length of the randomly rough surface. The results obtained by the optical methods are compared with those obtained by AFM. It is shown that there is a good agreement between these results.

This review paper is devoted to optics of inhomogeneous thin films exhibiting defects consisting in transition layers, overlayers, thickness nonuniformity, boundary roughness and uniaxial anisotropy. The theoretical approaches enabling the inclusion of these defects into formulae expressing the optical quantities of these inhomogeneous thin films are summarized. These approaches are based on the recursive and matrix formalisms for the transition layers and overlayers, averaging of the elements of the Mueller matrix using local thickness distribution or polynomial formulation for the thickness nonuniformity, scalar diffraction theory and Rayleigh-Rice theory or their combination for boundary roughness and Yeh matrix formalism for uniaxial anisotropy. The theoretical results are illustrated using selected examples of the optical characterization of the inhomogeneous polymer-like thin films exhibiting the combination of the transition layers and thickness nonuniformity and inhomogeneous thin films of nonstoichiometric silicon nitride with the combination of boundary roughness and uniaxial anisotropy. This characterization is realized by variable angle spectroscopic ellipsometry and spectroscopic reflectometry. It is shown that using these optical techniques, the complete optical characterization of the mentioned thin films can be performed. Thus, it is presented that the values of all the parameters characterizing these films can be determined.

The effects of thickness non-uniformity on measured optical quantities must be often considered in the optical characterization. The effects of thickness non-uniformity can be taken into account by averaging the Mueller matrices over the distribution of local thicknesses within the measured area. The distribution of local thicknesses can be assumed in a certain form (e.g. the uniform distribution), or it can be derived on the basis of a model assuming a certain shape of thickness non-uniformity. The latter approach is especially useful for the variable-angle spectroscopic ellipsometry since it can take into account dependence on the incidence angle due to the changes in the size of the light spot. This paper presents results of the optical characterization of three polymer-like thin films highly non-uniform in thickness using variable-angle spectroscopic ellipsometry. The shapes of the thickness non-uniform films are determined on the basis of a model assuming local thicknesses given by quadratic polynomials in coordinates along the surfaces of the films. The studied areas on the films were also measured by the imaging spectroscopic reflectometry, which provides a more direct method to determine local thicknesses. The results achieved using the imaging spectroscopic reflectometry and variable-angle spectroscopic ellipsometry were then compared.

The method of variable angle spectroscopic ellipsometry usable for the complete optical characterization of inhomogeneous thin films exhibiting complicated thickness non-uniformity together with transition layers at their lower boundaries is presented in this paper. The inhomogeneity of these films is described by means of the multiple-beam interference model. The thickness non-uniformity is taken into account by averaging the elements of the Mueller matrix along the area of the light spot of the ellipsometer on the films. The local thicknesses are expressed using polynomials in the coordinates along the surfaces of the films. The efficiency of the method is illustrated by means of the optical characterization of a selected sample of the polymer-like thin film of SiOxCyHz prepared by plasma enhanced chemical vapor deposition onto the silicon single crystal substrate. The Campi-Coriasso dispersion model is used to determine the spectral dependencies of the optical constants at the upper and lower boundaries of this film. The profiles of these optical constants are determined too. The thickness non-uniformity is described using a model with local thicknesses given by the polynomial with at most quadratic terms. In this way it is possible to determine the geometry of the upper boundary. The thickness and spectral dependencies of the optical constants of the transition layer are determined as well. Imaging spectroscopic reflectometry is utilized for confirming the results concerning the thickness non-uniformity obtained using ellipsometry.

In this paper formulae expressing the coherent reflectance, coherent transmittance and scattering losses of multilayer systems with correlated randomly rough boundaries derived within a certain approximation are presented. The theoretical approach employed for deriving these formulae is based on the scalar theory of diffraction of light. A brief numerical analysis of the formulae mentioned is performed for chosen rough multilayer systems. These formulae are also utilized for interpreting experimental data of samples of two chosen multilayers with rough boundaries. Moreover, in this paper formulae enabling us to estimate the errors in the optical quantities calculated using the approximate formulae are also presented.

A common approach to non-uniformity is to assume that the local thicknesses inside the light spot are distributed according to a certain distribution, such as the uniform distribution or the Wigner semicircle distribution. A model considered in this work uses a different approach in which the local thicknesses are given by a polynomial in the coordinates x and y along the surface of the film. An approach using the Gaussian quadrature is very efficient for including the influence of the non-uniformity on the measured ellipsometric quantities. However, the nodes and weights for the Gaussian quadrature must be calculated numerically if the non-uniformity is parameterized by the second or higher degree polynomial. A method for calculating these nodes and weights which is both efficient and numerically stable is presented. The presented method with a model using a second-degree polynomial is demonstrated on the sample of highly non-uniform polymer-like thin film characterized using variable-angle spectroscopic ellipsometry. The results are compared with those obtained using a model assuming the Wigner semicircle distribution.