Vacuum evaporated SiO2 thin films are very important in a design and manufacturing of optical devices produced in optics industry. In this contribution a reliable and precise optical characterization of such SiO2 thin films is performed using the combined method of spectrophotometry at normal incidence and variable-angle spectroscopic ellipsometry applied over spectral range from far IR to extreme UV (0.01-45 eV). This method uses the Universal Dispersion Model based on parametrization of the joint density of states and structural model comprising film defects such as nanometric boundary roughness, inhomogeneity and area non-uniformity. The optical characterization over the wide spectral range provides not only the spectral dependencies of the optical constants of the films within the wide range but, more significantly, it enables their correct and precise determination within the spectral range of interest, i.e. the range of their transparency. Furthermore, measurements in the ranges of film absorption, i. e. phonon excitations in IR and electron excitations in UV, reveal information about the material structure. The results of the optical characterization of the SiO2 thin films prepared on silicon single crystal substrates under various technological conditions are presented in detail for two selected samples. Beside film thicknesses and values of dispersion parameters and spectral dependencies of the optical constants of the SiO2 films, the characterization also enables quantification of film defects and their parameters are presented as well. The results concerning the optical constants of SiO2 films are compared with silica optical constants determined in our earlier studies.
It is possible to encounter thin films exhibiting various defects in practice. One of these defects is area non-uniformity in optical parameters (e.g. in thickness). Therefore it is necessary to have methods for an optical characterization of nonuniform thin films. Imaging spectroscopic reflectometry provides methods enabling us to perform an efficient optical characterization of such films. It gives a possibility to determine spectral dependencies of a local reflectance at normal incidence of light belonging to small areas (37 μm × 37 μm in our case) on these non-uniform films. The local reflectance is measured by individual pixels of a CCD camera serving as a detector of an imaging spectroscopic reflectometer. It is mostly possible to express the local reflectance using formulas corresponding to a uniform thin film. It allows a relatively simple treatment of the experimental data obtained by imaging spectroscopic reflectometry. There are three methods for treating these experimental data in the special case of thickness non-uniformity, i.e. in the case of the same optical constants within a certain area of the film - single pixel imaging spectroscopic reflectometry method, combination of single-pixel imaging spectroscopic reflectometry method and conventional methods (conventional single spot spectroscopic ellipsometry and spectrophotometry), and multi-pixel imaging spectroscopic reflectometry method. These methods are discussed and examples of the optical characterization of thin films non-uniform in thickness corresponding to these methods are presented in this contribution.
Development of antireflective coatings realized by thin film systems requires their characterization and optimization of their properties. Functional properties of such interference devices are determined by optical constants and thicknesses of the individual films and various defects taking place in these systems. In optics industry the characterization of the films is mostly performed in a relatively narrow spectral range using simple dispersion models and, moreover, the defects are not taken into account at all. This manner of characterization fails if applied to real-world non-ideal thin film systems because the measured data do not contain sufficient information about all the parameters describing the system including imperfections. Reliable characterization requires the following changes: extension of spectral range of measurements, combination of spectrophotometry and ellipsometry, utilization of physically correct dispersion models (Kramers-Kronig consistency, sum rules), inclusion of structural defects instrument imperfection into the models and simultaneous processing of all experimental data. This enables us to remove or reduce a correlation among the parameters searched so that correct and sufficiently precise determination of parameter values is achieved. Since the presence and properties of the defects are difficult to control independently by tuning of the deposition conditions, the optimization does not in general involve the elimination of defects. Instead they are taken into account in the design of the film systems. The outlined approach is demonstrated on the characterization and optimization of ultraviolet antireflective coating formed by double layer of Al2O3 and MgF2 deposited on fused silica.
In the optics industry thin film systems are used to construct various interference devices such as antireflective coatings, high-reflectance mirrors, beam splitters and filters. The optical characterization of complex optical systems can not be performed by measurements only in the short spectral range in which the interference devices will be employed because the measured data do not contain sufficient information about all relevant parameters of these systems. The characterization of film materials requires the extension of the spectral range of the measurements to the IR region containing phonon absorption and to the UV region containing the electronic excitations. However, this leads to necessity of a dispersion model suitable for the description of the dielectric response in the wide spectral range. Such model must respect the physical conditions following from theory of dispersion, particularly Kramers-Kronig relations and integrability imposed by sum rules. This work presents the construction of a universal dispersion model composed from individual contributions representing both electronic and phonon excitations. The efficiency of presented model is given by the fact that all the contributions are described by analytical expressions. It is shown that the model is suitable for precise modeling of spectral dependencies of optical constants of a broad class of materials used in the optical industry for thin film systems such as MgF2, SiO2, Al2O3, HfO2, Ta2O5 and TiO2 in the spectral range from far IR to vacuum UV.
A new optical characterization method based on imaging spectroscopic reflectometry (ISR) is presented and illustrated on the characterization of rough non-uniform epitaxial ZnSe films prepared on GaAs substrates. The method allows the determination of all parameters describing the thin films exhibiting boundary roughness and non-uniformity in thickness, i.e. determination of the spectral dependencies of the optical constants, map of local thickness and map of local rms values of heights of the irregularities for the rough boundaries. The local normal reflectance spectra in ISR correspond to small areas (37×37 μm2) on the thin films measured within the spectral range 270{900 nm by pixels of a CCD camera serving as the detector of imaging spectrophotometer constructed in our laboratory. To our experience the small areas corresponding to the pixels are sufficiently small so that the majority of the films can be considered uniform in all parameters within these areas. Boundary roughness is included into the reflectance formulas by means of the scalar diffraction theory (SDT) and the optical constant spectra of the ZnSe films were expressed by the dispersion model based on the parametrization of the joint density of electronic states (PJDOS). In general, there is a correlation between the searched parameters if the individual local reflectance spectra are fitted separately and, therefore, the local reflectance spectra measured for all the pixels are treated simultaneously using so called multi-pixel method in order to remove or reduce this correlation and determine the values of all the parameters with a sufficient accuracy. The results of the optical characterization of the same selected sample of the epitaxial ZnSe thin film obtained using the method presented here and combined method of variable-angle spectroscopic ellipsometry, spectroscopic reflectometry and single-pixel immersion spectroscopic reflectometry are introduced in the contribution as well.
A new approach to surface roughness measurement based on the digital two-wavelength holographic interference
microscopy with the synthetic wavelength is presented. Two holograms of a randomly rough surface are recorded step by
step at two wavelengths by means of a CCD camera. Both holograms are numerically reconstructed. Two reconstructed
waves obtained numerically interfere. The surface roughness parameters may be determined from the interferogram.
Spectroscopic ellipsometry (SE) with microscopic measurement spot is applied to extract geometrical parameters of a bi-periodic array of holes patterned on the top of an Si wafer, namely the holes' diameter and depth, while the period of the patterning is assumed same as the value intended by the manufacturer. The SE response of the structure is simulated by the rigorous coupled-wave analysis implemented as the Airy-like internal reflection series, whose detailed description for the case of 2D gratings is provided with a brief demonstration of its convergence properties. The result of the extraction by SE is compared with results obtained by scanning electron microscopy (SEM) with reasonable agreement. The difference between some of the SE, SEM, and nominal parameters are discussed and the possibility to increase the accuracy of SE-based metrology is suggested.
In this paper the method of imaging spectrophotometry enabling us to characterize non-absorbing thin films non-uniform in the optical parameters is described. This method is based on interpreting the spectral dependences of the local absolute reflectances measured at the normal incidence of light. It is shown how to determine the area distribution of thickness and refractive index of the non-absorbing non-uniform thin films by treating these reflectances. Moreover, the generalization of the method for the optical characterization of slightly absorbing non-uniform thin films is also indicated. Furthermore, the two-channel imaging spectrophotometer enabling us to apply the method of imaging reflectometry is described. The procedure for determining the spectral dependences of the local absolute reflectance in the points aligned in a matrix situated on the illuminated area of the non-uniform thin film by means of the spectrophotometer is also presented. The practical advantages of the method are specified. The method is illustrated by means of the optical characterization of a selected epitaxial ZnSe thin film prepared using molecular beam epitaxy onto gallium arsenide single-crystal substrate.
In this paper the mathematical formalism enabling us to include defects of thin films into the formulae expressing their optical quantities is presented. The attention is devoted to the defects consisting in boundary roughness and inhomogeneity corresponding to the refractive index profile. This mathematical formalism is based on 2x2 matrix algebra. The Rayleigh-Rice theory (RRT) is used for describing boundary roughness. The refractive index profile is included into the matrix formalism by means a special procedure based on combination of the Drude and Wentzel-Kramers-Brillouin-Jeffries (WKBJ) approximations. The mathematical formalism is applied for the optical characterization of thin films of TiO2 and As-S chalcogenides. Using this formalism the experimental data corresponding to the ellipsometric quantities, reflectance measured from the ambient side, reflectance measured from the substrate side and transmittance are treated. The corrections of the systematic errors connected with the reflection accessory of the spectrometer used is carried out using the special procedure.
In this paper the mechanical stresses taking place in diamond like thin films prepared by the plasma enhanced chemical vapor deposition onto silicon single crystal substrates are studied. For determination of the stress values the Stoney's formula is used. The values of the film thicknesses are determined using the combined
method of variable angle spectroscopic ellipsometry and near-normal spectroscopic reflectometry. The values of the curvature radii of the deformed silicon substrates in consequence of the film stresses are evaluated using interferometric method based on two-beam interferometry and chromatic aberration method. The dependence of
the mechanical stress inside these films on their thickness values is determined. It is found that this dependence can be approximate by the straight-line. The results achieved for the mechanical stresses obtained by both the optical methods, i.e. by the interferometric and chromatic aberration method, are compared. It is shown that within the experimental accuracy the stress values determined using both these method are identical. Thus, it is shown that the chromatic aberration method is suitable for measuring the mechanical stresses inside the thin solid films and it is the competitive method for the other optical methods utilized for this purpose so far.
In this paper the quantitative dependence of the mechanical stress inside diamond-like carbon films containing Si and O atoms on a flow rate ratio of methane CH4 and hexamethyldisiloxane C6H18Si2O in the deposition mixture is determined. For this purpose the modified Stoney's formula is employed. The important quantities taking place in this formula, i.e. the radius of curvature of the spherical surface of a deformed silicon substrate because of the film stress and the film thickness, are determined using the combined optical method based on two-beam interferometry, variable angle spectroscopic ellipsometry and near-normal spectroscopic reflectometry. It is shown that the influence of the flow rate ratio on the values of the mechanical stresses taking place inside these films is negligible within the experimental accuracy achieved for determining these stresses if the total flow rate of gases used to be constant in the deposition mixture. A discussion of this fact is also performed. The film studied were prepared using the plasma enhanced chemical vapor deposition.
In this paper, a new optical method for characterizing nonuniform thin films is employed. For applying this method the special experimental arrangement containing CCD camera as a detector is used. Using this experimental arrangement the spectral dependencies of the local reflectances are obtained. After treating these experimental data of the distributions of the values of the local thicknesses and local refractive index along a large areas of the substrates of the nonuniform films are found. Moreover, it is shown that this method can be used to determine strong nonuniformities in both the optical parameters. The method is illustrated through the optical characterization of a nonuniform ZnSe epitaxial thin film deposited onto gallium arsenide single-crystal substrate and nonuniform film formed by the mixture of CNx and SiOy deposited onto silicon single-crystal substrate.
In this paper the optical method based on multisample modification variable angle spectroscopic ellipsometry (VASE) is used to characterize thin films of ZnSe prepared by molecular beam epitaxy onto GaAs single crystal substrates. It is found that this method can be employed for determining the spectral dependences of the optical constants and values of the thicknesses of the films mentioned. Moreover, it is shown that using this method the RMS values of the heights and the values of the correlation length characterizing roughness irregularities of the upper boundaries of the films can be determined as well. The application of the method is illustrated by means of characterizing six samples of the ZnSe-films exhibiting different values of the thicknesses.
In this contribution, a new mathematical procedure enabling us to calculate the optical quantities of the inhomogeneous thin films such as reflectance, transmittance and ellipsometric parameters will be described. This procedure is based on combining the known matrix formalism and Drude approximation. The inhomogeneous thin films is replaced by a multilayer system containing the thin films with a linear profiles of the dielectric function and different thicknesses. Every individual film of the multilayer system is described by the matrix corresponding to the Drude approximation. Using this procedure one can construct an efficient algorithm allowing to calculate the values of the optical quantities of the inhomogeneous thin films exhibiting great gradients of the refractive index profiles.
In this contribution examples of the optical characterization of multilayer systems with randomly rough boundaries are presented. The method based on measuring and interpreting the spectral dependences of the coherent reflectance is used to determine the values of the optical and statistical parameters of samples of three-layer and thirteen-layer systems exhibiting the rough boundaries. The systems mentioned are formed by thin films of SiO2 and TiO2.
In this review paper a survey of the most significant optical methods usable for characterizing solid surfaces is performed. Examples allowing to show practical features of applying these methods at investigating the surfaces mentioned are presented too. By means of these examples both a reliability and accuracy of the method are namely demonstrated.
The values of the basic characteristics of surface roughness measured by means of optical and non-optical methods often differ mutually. So far a systematic comparison of the results obtained by those methods has not been done. The results we have achieved comparing optical and non-optical methods of the surface roughness measurement for selected samples of rough surfaces and for selected methods are presented.
In this paper a method of shearing interferometry enabling us to perform a characterization of the basic statistical properties of non-gaussian randomly rough surfaces of solids will be described. This method is based on a statistical analysis of the form of dark fringe centers taking place in interferograms obtained by using a suitable interference microscope. By means of the method the root-mean-square values of heights and slopes, the values of autocorrelation lengths, autocorrelation coefficients of the heights and autocorrelation coefficient of the slopes of surface irregularities of glass diffusers will be determined.
Optical analysis of rough single and double layers is performed by interpreting the spectral dependences of the measured coherent reflectance. Formulas for the coherent reflectance of these systems derived within the scalar theory of diffraction of light are used for this interpretation. Possibilities and limitations of the method utilized are illustrated using several concrete samples of both the rough single and double layers represented by models corresponding to fully correlated (identical), partially correlated, and fully uncorrelated boundaries. It is shown that the values of the optical parameters, the root-mean-square (rms) values of the heights of the boundary irregularities and the values of the cross-correlation coefficients of the boundaries characterizing the layered systems mentioned can be determined within the method described.
Characterization of rough single and double layers is performed by interpreting spectral dependences of the coherent reflectance measured for these layers. Possibilities and limitations of the method are illustrated by means of several concrete samples of both the rough single and double layers represented by models corresponding to fully correlated (identical), partially correlated and fully uncorrelated boundaries.
In this contribution new approximate formulae for calculating the
specular reflectance R, the transmittance T and the scatter losses 5(5 = = l-R-T) of nonabsorbing multilayer systems, the rough boundaries of which
are generated by normal stochastic processes, are presented. The formulae
are derived within the scalar theory of diffraction under assumptions that
the boundaries are mutually independent from the statistical point of view
and the standard deviations of the height irregularities are relatively
small compared with wavelengths of incident light. Moreover, it is assumed
that slopes of the irregularities on all the boundaries of the system considered
are small enough (the standard deviations of angles coresponding to
the slopes are much smaller that unity) and that conditions of the Fraunhofer
approximation are fulfilled when light is detected by a detector.
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