Optical characterization of inhomogeneity of polymer-like thin films arising in the initial phase of plasma-enhanced chemical vapor deposition.

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.

Optical characterization of inhomogeneous thin films with randomly rough boundaries exhibiting wide intervals of spatial frequencies.

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.

Optical characterization of inhomogeneous thin films with randomly rough boundaries.

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.

Ellipsometric characterization of inhomogeneous thin films with complicated thickness non-uniformity: application to inhomogeneous polymer-like thin films.

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.

Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials.

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.

Spectroscopic ellipsometry of inhomogeneous thin films exhibiting thickness non-uniformity and transition layers.

In this paper the complete optical characterization of an inhomogeneous polymer-like thin film of SiOxCyHz exhibiting a thickness non-uniformity and transition layer at the boundary between the silicon substrate and this film is performed using variable angle spectroscopic ellipsometry. The Campi-Coriasso dispersion model was utilized for describing the spectral dependencies of the optical constants of the SiOxCyHz thin film and transition layer. The multiple-beam interference model was used for expressing inhomogeneity of the SiOxCyHz thin film. The thickness non-uniformity of this film was taken into account by means of the averaging of the elements of the Mueller matrix performed using the thickness distribution for the wedge-shaped non-uniformity. The spectral dependencies of the optical constants of the SiOxCyHz thin film at the upper and lower boundaries together with the spectral dependencies of the optical constants of the transition layer were determined. Furthermore, the thickness values of the SiOxCyHz film and transition layer, profiles of the optical constants of the SiOxCyHz thin film and the rms value of local thicknesses corresponding to its thickness non-uniformity were determined. Thus, all the parameters characterizing this complicated film were determined without any auxiliary methods.

Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia.

A dispersion model capable of expressing the dielectric response of a broad class of optical materials in a wide spectral range from far IR to vacuum UV is described in detail. The application of this universal dispersion model to a specific material is demonstrated using the ellipsometric and spectrophotometric characterization of a hafnia film prepared by vacuum evaporation on silicon substrate. The characterization utilizes simultaneous processing of data from multiple techniques and instruments covering the wide spectral range and includes the characterization of roughness, nonuniformity, transition layer, and native oxide layer on the back of the substrate. It is shown how the combination of measurements in light reflected from both sides of the sample and transmitted light allows the separation of weak absorption in films and substrates. This approach is particularly useful in the IR region where the absorption structures in films and substrates often overlap and a prior measurement of the bare substrate may be otherwise necessary for precise separation. Individual phenomena that contribute to the dielectric response, i.e., interband electronic transitions, electronic excitations involving the localized states, and phonon absorption, are discussed in detail. A quantitative analysis of absorption on localized states, permitting the separation of transitions between localized states from transitions between localized and extended states, is utilized to obtain estimates of the density of localized states and film stoichiometry.

Measurement of thickness distribution, optical constants, and roughness parameters of rough nonuniform ZnSe thin films.

Epitaxial ZnSe thin films exhibiting two important defects, i.e., boundary roughness and thickness nonuniformity, prepared on GaAs substrates, are optically characterized using a combination of variable-angle spectroscopic ellipsometry, spectroscopic near-normal reflectometry, and imaging spectroscopic reflectometry (ISR). The influence of boundary roughness is incorporated into optical quantity formulas by the Rayleigh-Rice theory. Thickness nonuniformity is included using averaging of the unnormalized Mueller matrices. The dispersion model of the optical constants of the ZnSe films is based on parametrization of the joint density of electronic states. Very thin overlayers represented by thin films with identically rough boundaries are taken into account on the upper boundaries of the ZnSe films. Standard optical techniques are used to determine the spectral dependencies of the optical constants of the ZnSe films, together with the parameters of roughness and thickness nonuniformity. ISR is then used to find the maps of the local thickness and local rms value of height irregularities. The values of roughness parameters, determined using the standard techniques and ISR, are verified by a comparison with results obtained by atomic force microscopy.

Consolidated series for efficient calculation of the reflection and transmission in rough multilayers.

Fresnel reflectance and transmittance coefficients of a thin film system consisting of an arbitrary number of layers are expressed explicitly in the form of a power series of Fresnel coefficients for individual boundaries and phase terms for the individual films. The series is based on the evaluation of all possible paths light can pass through the system. However, the series is written as consolidated, i. e. all paths corresponding to the same powers are represented using a single term in the series, with multiplicity which is a simple product of binomial coefficients. This result is used to express the normal reflectance of a thin film system with arbitrarily correlated randomly rough boundaries and it is shown that such approach can be computationally efficient in practice.

Influence of cross-correlation effects on the optical quantities of rough films.

Within the Rayleigh-Rice theory the influence of layer boundary roughness on coherently reflected light is expressed using very complex formulae. Therefore we deal with the simplification of these formulae by employing an approximation based on neglecting cross-correlation effects between both the rough boundaries. It is shown that if the mean distance of the boundaries (mean thickness) is sufficiently large in comparison with the lateral dimensions of the roughness it is possible to describe the individual boundaries of the layers by matrices corresponding to isolated rough surfaces. This fact enables us to simplify the formulae for the optical quantities in a substantial way, which also simplifies the numerical calculation needed for the inverse problem. This statement is illustrated by means of a numerical analysis simulating ellipsometric and reflectometric data of rough silicon dioxide layers placed onto silicon single crystal substrates.

Influence of the atomic force microscope tip on the multifractal analysis of rough surfaces.

In this paper, the influence of atomic force microscope tip on the multifractal analysis of rough surfaces is discussed. This analysis is based on two methods, i.e. on the correlation function method and the wavelet transform modulus maxima method. The principles of both methods are briefly described. Both methods are applied to simulated rough surfaces (simulation is performed by the spectral synthesis method). It is shown that the finite dimensions of the microscope tip misrepresent the values of the quantities expressing the multifractal analysis of rough surfaces within both the methods. Thus, it was concretely shown that the influence of the finite dimensions of the microscope tip changed mono-fractal properties of simulated rough surface to multifractal ones. Further, it is shown that a surface reconstruction method developed for removing the negative influence of the microscope tip does not improve the results obtained in a substantial way. The theoretical procedures concerning both the methods, i.e. the correlation function method and the wavelet transform modulus maxima method, are illustrated for the multifractal analysis of randomly rough gallium arsenide surfaces prepared by means of the thermal oxidation of smooth gallium arsenide surfaces and subsequent dissolution of the oxide films.

Theoretical analysis of the atomic force microscopy characterization of columnar thin films.

In this paper, the theoretical analysis of the influence of finite linear dimensions of an atomic force microscope tip on profiles of the upper boundaries of columnar thin films and their statistical quantities is performed. This analysis is based on a numerical evaluation of the main statistical quantities, i.e. the standard deviations of the heights and slopes, one-dimensional distributions of the probability density of heights and slopes and power spectral density function, corresponding to a simulated columnar structure of the thin films. It is shown that the strongest misrepresentation of the measured profiles of the upper boundaries of the columnar films originates in the cases when the linear dimensions of the columns are smaller or comparable with the linear dimensions of the tip. Further, it is shown that using a surface reconstruction procedure one can correct (improve) the boundary profiles and their statistical quantities partially. The results of this analysis enable us to perform rough estimation of the errors achieved within atomic force microscopy studies of the real columnar thin films. Moreover, these results allow to estimate the corrections of the statistical quantities mentioned above to be obtained using the surface reconstruction.