Analysis Of Spectroscopic Ellipsometry Data Research Articles

Performance of machine learning algorithms in spectroscopic ellipsometry data analysis of ZnTiO3 nanocomposite

In this research, the optical properties of the PVP: ZnTiO3 nanocomposite are studied using the spectroscopic ellipsometry technique. The preparation procedure of the ZnTiO3 nanocomposite is explained in detail. The absorbance/transmittance, surface morphology, structural information, chemical identification, and surface topography of the ZnTiO3 nanocomposite is studied using UV–Vis spectroscopy, field-emission scanning electron microscopy, Raman spectroscopy, Fourier transform infra-red, and atomic force microscopy, respectively. The ellipsometry method is used to obtain the spectra of the real and imaginary parts of the dielectric function and refractive index in the photon energy range of 0.59–4.59 eV. Moreover, using two machine learning algorithms, namely artificial neural network and support vector regression methods, the ellipsometric parameters ψ and Δ are analyzed and compared with non-linear regression. The error and accuracy of each three methods, as well as the time required for their execution, are calculated to compare their suitability in the ellipsometric data analysis. Also, the absorption coefficient was used to determine the band gap energy of the ZnTiO3 nanocomposite, which is found to be 3.83 eV. The second-energy derivative of the dielectric function is utilized to identify six critical point energies of the prepared sample. Finally, the spectral-dependent optical loss function and optical conductivity of the ZnTiO3 nanocomposite are investigated.

The spectroscopic ellipsometry measurement of non-polar freestanding GaN: comparison between isotropic and anisotropic models

For anisotropic materials, the pseudo-dielectric function (DF) from isotropic model is often applied in spectroscopic ellipsometry data analysis instead of the DF from anisotropic model because of its simplicity. Whether this approximation is applicable depends on the discrepancy between the pseudo-DF and the DF, which we find to be related to the illumination configuration greatly. For the ellipsometry spectra obtained from a non-polar freestanding GaN in two configurations with the c-axis perpendicular and parallel to the incident plane respectively, both anisotropic model and isotropic model are used to compare the difference between the fitted absorption coefficient and pseudo-absorption coefficient. As a consequence, the discrepancy between the two coefficients is less than 10 even at the absorption edge when electric field is perpendicular to the c-axis, while the discrepancy exceeds 40 at the absorption edge when electric field is parallel to the c-axis. These results indicate that the approximation of using isotropic model instead of anisotropic model is reasonable in the former configuration, while it is not applicable in the latter configuration and will render an overestimation of bandgap. The above two different discrepancies could be explained by the first-order term approximation of pseudodielectric function. We further demonstrate the necessity for anisotropic model by comparing the deviations of the crystal-field splitting obtained from anisotropic and isotropic model with the theoretical value respectively.

Optical properties investigation of reactively sputtered tantalum oxynitride films

The coalescent behavior of metal oxide and metal nitride in metal oxynitride (MON) is making the material more conspicuous. Along with tunable optical properties, enhances mechanical properties, better chemical stability can be derived for MONs, which are of prime importance in the fields, such as photovoltaic, photo-chromatics, photocatalytic, protective and aesthetic coatings. In this paper, the optical properties of tantalum oxynitride thin film deposited through a reactive magnetron sputtering method were explored. Pure tantalum target was sputtered with argon gas in the presence of an optimized O2/N2 gas ratio. The chemical and physical properties of the film were investigated by X-ray diffraction technique, Scanning Electron Microscopy and AFM. Optical properties were explored with UV–visible spectroscopy and Spectroscopic Ellipsometry (SE). Transmittance and reflectance of the films show that the optical properties of the films have transparency (70–90%) and an absorption edge near 350 nm. For the analysis of SE data, the Tauc-Lorentz optical model with an additional Lorentz oscillator for semiconductor or insulator material were used. Here, the Ellipsometry technique has provided detailed optical nature of the film in terms of refractive index (n) ranging from 1.82 to 2.62, Energy Bandgap (Eg) 3.6 eV along with film thickness (∼200 nm) and surface roughness (∼6 nm).All these optical properties make the material a suitable candidate for antireflective coating, preparation of optical filters, photocatalytic agent, transparent coating for optical devices.

Deep Learning for Rapid Analysis of Spectroscopic Ellipsometry Data

High‐throughput experimental approaches to rapidly develop new materials require high‐throughput data analysis methods to match. Spectroscopic ellipsometry is a powerful method of optical properties characterization, but for unknown materials and/or layer structures the data analysis using traditional methods of nonlinear regression is too slow for autonomous, closed‐loop, high‐throughput experimentation. Herein, three methods (termed spectral, piecewise, and pointwise) of spectroscopic ellipsometry data analysis based on deep learning are introduced and studied. After initial training, the incremental time for inferring optical properties can be a thousand times faster than traditional methods. Results for multilayer sample structures with optically isotropic materials are presented, appropriate for high‐throughput studies of thin films of phase‐change materials such as GeSbTe (GST) alloys. Results for studies on highly birefringent layered materials are also presented, exemplified by the transition metal dichalcogenide MoS2. How the materials under test and the experimental objectives may guide the choice of analysis methods are discussed. The utility of our approach is demonstrated by analyzing data measured on a composition spread of GeSbTe phase‐change alloys containing 177 distinct compositions, and identifying the composition with optimal phase‐change figure of merit in only 1.4 s of analysis time.

On the optimization of knot allocation for B-spline parameterization of the dielectric function in spectroscopic ellipsometry data analysis

Dielectric function representation by B-splines became quite popular and widely used in the context of spectroscopic ellipsometry data interpretation. B-splines are defined by a polynomial degree and a sequence of knots (i.e., the number and positions of knots). Defining the knot sequence is non-trivial, and this task has a significant effect on the actual effectiveness of the B-spline parameterization in spectroscopic ellipsometry data analysis. In this paper, we propose a simple, practical, and systematic knot placement scheme that improves ordinary trial-and-error technique in establishing the knot spacing. The approach suggested here is based on an integral span, a measure introduced in this work. The proposed procedure provides a possibility to determine the knot locations automatically (or, at least, semi-automatically) and excludes widespread modeling ambiguities associated with uncertain knot vector. Moreover, our approach guarantees the absence of non-monotonic behavior of the mean-squared-error function and thereby improves the accuracy of our analysis. The performance of the proposed method has been tested for several real cases of the study.

Direct observation and evolution of electronic coupling between organic semiconductors

The electronic wave functions of an atom or molecule are affected by its interactions with its environment. These interactions dictate electronic and optical processes at interfaces, and is especially relevant in the case of thin film optoelectronic devices such as organic solar cells. In these devices, charge transport and interfaces between multiple layers occur along the thickness or vertical direction, and thus such electronic interactions between different molecules---same or different---are crucial in determining the device properties. Here, we introduce an in situ spectroscopic ellipsometry data analysis method called differential analysis in real time (DART) with the ability to directly probe electronic coupling due to intermolecular interactions along the thickness direction using vacuum-deposited organic semiconductor thin films as a model system. The analysis, which does not require any model fitting, reveals direct observations of electronic coupling between frontier orbitals under optical excitations leading to delocalization of the corresponding electronic wave functions with thickness or, equivalently, number of molecules away from the interface in C60 and MeO-TPD deposited on an insulating substrate $(\mathrm{Si}{\mathrm{O}}_{2})$. Applying the same methodology for C60 deposited on phthalocyanine thin films, the analyses shows strong, anomalous features---in comparison to C60 deposited on $\mathrm{Si}{\mathrm{O}}_{2}$---of the electronic wave functions corresponding to specific excitation energies in C60 and phthalocyanines. Translation of such interactions in terms of dielectric constants reveals plasmonic type resonance absorptions resulting from oscillations of the excited state wave functions between the two materials across the interface. Finally, reproducibility, angstrom-level sensitivity, and simplicity of the method are highlighted showcasing its applicability for studying electronic coupling between any vapor-deposited material systems where real-time measurements during thin film growth are possible.

Spectroscopic ellipsometry study of Cu2ZnSn(SxSe1-x)4 bulk polycrystals

The pseudo dielectric function of Cu2ZnSn(SxSe1-x)4 [x = 0.35, 0.62, 0.81] bulk polycrystals is determined over the range 1.1–4.6 eV at room temperature from the analysis of spectroscopic ellipsometry data using the Adachi model. From the analysis, the lowest E0 transition and high energy E1A and E1B transitions are clearly identified, and used to follow the evolution of the pseudo dielectric function as a function of the composition. It is shown that the fundamental E0 and high energy E1A transitions can be tuned by increasing the sulfur content over a range of 0.3 eV. These results show the potential of the kesterite compounds for the design of efficient tailored photovoltaic solar cells.

Anisotropic optical properties of a-axis AlN films: a spectroscopic ellipsometry study

We report the uniaxial anisotropic optical constants of wurtzite-type a-axis oriented AlN films deposited on Si (100) using DC reactive magnetron sputtering as a function of growth temperature (Ts, 35 to 600 °C) using the spectroscopic ellipsometry (SE) technique. The thickness and roughness of these films are determined from the regression analysis of SE data, which are corroborated using TEM and AFM techniques. Highly oriented a-axis AlN film grown at 400 °C, exhibits high n and low k at 210 nm (deep-UV region) with small birefringence (−0.01) and dichroism (0.03) near the band edge. All these AlN films exhibit transparent nature from near-infrared (NIR) to 354 nm, where optical band gap energies vary between 5.7 to 6.1 eV.

Tuning the excitonic properties of ZnO:Sn thin films

The effects of Sn doping, deposition temperature, and post-annealing treatment on the excitonic behavior of ZnO:Sn (SZO) thin films deposited by dc-unbalanced magnetron sputtering have been studied. Sn doping induces the decrease of grain size and promotes the formation of oxygen vacancy-related trap states as indicated by A1 LO mode in Raman spectra and green emission in photoluminescence spectra. Using a critical point analysis of the dielectric functions from spectroscopic ellipsometry data analysis, Sn doping blueshifts the excitonic absorption and decreases the exciton lifetime via screening the electron-hole Coulomb interaction. By varying the deposition temperature from room temperature up to 300 °C (SZO-3), there is no change in excitonic absorption. Then, annealing of SZO-3 at 600 °C under oxygen environment (SZO-6) strongly improves the excitonic absorption as well as its lifetime. Critical point analysis on SZO-6 sample clearly reveals the excitonic transition at 3.38 eV and exciton-phonon complexes at 3.66 eV. Thus, the result is important to improve the functionality of doped ZnO with strong excitonic absorption for optoelectronic applications.

Spectroscopic ellipsometry data analysis using penalized splines representation for the dielectric function

Accuracy of the spectroscopic ellipsometry data analysis strongly depends on appropriate modeling of the complex dielectric function ε (or the complex index of refraction N) over required spectral range. In this paper, we outline penalized B-spline (P-spline) formulation for an arbitrary dielectric function ε modeling in spectroscopic ellipsometry data analysis. The main idea is to first use a generous number of equally-spaced knots (up to the number of spectral points) to describe even highly complicated structure in the imaginary part ε2 of the dielectric function and then provide a certain penalty on the coefficients of adjacent B-splines to tune the smoothness of the ε curve. Two real-data applications have been provided to evaluate the practical performance and effectiveness of the proposed penalized formulation for dielectric function representation. A comparison of obtained results with the findings of our previous studies without penalization demonstrates a good agreement between the proposed method and ordinary B-spline representation in an equally-spaced fashion with optimal number of knots.

Optical simulation of external quantum efficiency spectra of CuIn1−xGaxSe2 solar cells from spectroscopic ellipsometry inputs

Applications of in-situ and ex-situ spectroscopic ellipsometry (SE) are presented for the development of parametric expressions that define the real and imaginary parts (ε1, ε2) of the complex dielectric function spectra of thin film solar cell components. These spectra can then be utilized to analyze the structure of complete thin film solar cells. Optical and structural/compositional models of complete solar cells developed through least squares regression analysis of the SE data acquired for the complete cells enable simulations of external quantum efficiency (EQE) without the need for variable parameters. Such simulations can be compared directly with EQE measurements. From these comparisons, it becomes possible to understand in detail the origins of optical and electronic gains and losses in thin film photovoltaics (PV) technologies and, as a result, the underlying performance limitations. In fact, optical losses that occur when above-bandgap photons are not absorbed in the active layers can be distinguished from electronic losses when electron-hole pairs generated in the active layers are not collected. This overall methodology has been applied to copper indium-gallium diselenide (CuIn1−xGaxSe2; CIGS) solar cells, a key commercialized thin film PV technology. CIGS solar cells with both standard thickness (>2 μm) and thin (<1 μm) absorber layers are studied by applying SE to obtain inputs for EQE simulations and enabling comparisons of simulated and measured EQE spectra. SE data analysis is challenging for CIGS material components and solar cells because of the need to develop an appropriate (ε1, ε2) database for the CIGS alloys and to extract absorber layer Ga profiles for accurate structural/compositional models. For cells with standard thickness absorbers, excellent agreement is found between the simulated and measured EQE, the latter under the assumption of 100% collection from the active layers, which include the CIGS bulk and CIGS/CdS heterojunction interface layers. For cells with thin absorbers, however, an observed difference between the simulated and measured EQE can be attributed to losses via carrier recombination within a ∼0.15 μm thickness of CIGS adjacent to the Mo back contact. By introducing a carrier collection probability profile into the simulation, much closer agreement is obtained between the simulated and measured EQE. In addition to the single spot capability demonstrated in this study, ex-situ SE can be applied as well to generate high resolution maps of thin film multilayer structure, component layer properties and their profiles, as well as short-circuit current density predictions. Such mapping is possible due to the high measurement speed of <1 s per (ψ, Δ) spectra achievable by the multichannel ellipsometer.

Selecting the right number of knots for B-spline parameterization of the dielectric functions in spectroscopic ellipsometry data analysis

B-spline representation of the dielectric functions provides many theoretical and practical benefits for material modeling in spectroscopic ellipsometry. However, the number of knots (and their locations, in general) defines actual performance of B-splines in ellipsometric data analysis. On the one hand, too large number of knots can result in serious overfitting of the experimental data. On the other hand, this number should be sufficient to fit all essential spectral features. Selection of the right number of knots is, in practice, a very subjective and empirically-driven task. In this paper, we discuss the choice of the number of knots utilizing three well-established versions of statistical information criteria in form of Akaike, corrected Akaike and Bayesian Information Criteria (AIC, AICc and BIC, respectively). The criteria establish a compromise between over- and underfitting of experimental data and allow formalized selection of the right number of knots. Effectiveness of the proposed methodology is illustrated using a few real-data examples.

Convergence and precision characteristics of finite difference time domain method for the analysis of spectroscopic ellipsometry data at oblique incidence

The finite difference time domain (FDTD) method presents attractive advantages for analysis of the spectroscopic ellipsometry (SE) response of complex, non-planar samples including generality and suitability to address complex structures as well as non-linear effects and/or non-periodic morphologies. However, it is imperative to advance our understanding, and more importantly, to design strategies to improve the computational time of FDTD method calculations. In a previous report we show the ability to simulate the SE response of prototypical samples based on far-field projections of near-field simulation based on the FDTD method with accuracy equivalent to ∼0.5 monolayer precision in film thickness up to 70° angle of incidence (AoI). In this contribution, we provide a refined strategy that results in ∼3 orders of magnitude improvement in the determination of the SE data as estimated by the χ2 figure of merit for modeling of SE data at angles as large as 80° AoI with respect to the standard solution. Significantly the proposed strategy also provides improvement in the computation time that speeds up by a factor ∼4× at 70° AoI but that can be as large as ∼20× for 40° AoI.

Model selection in spectroscopic ellipsometry data analysis: Combining an information criteria approach with screening sensitivity analysis

In the field of optical metrology, the selection of the best model to fit experimental data is absolutely nontrivial problem. In practice, this is a very subjective and formidable task which highly depends on metrology expert opinion. In this paper, we propose a systematic approach to model selection in ellipsometric data analysis. We apply two well-established statistical methods for model selection, namely, the Akaike (AIC) and Bayesian (BIC) Information Criteria, to compare different dispersion models with various complexities and objectively determine the “best” one from a set of candidate models. The information criteria suggest the most optimal way to quantify the balance between goodness of fit and model complexity. In combination with screening-type parametric sensitivity analysis based on so-called “elementary effects” (the Morris method) this approach allows to compare and rate various models, identify key model parameters and significantly enhance process of ellipsometric measurements evaluation.

Effects of 200 keV Ar-ions irradiation on the structural and optical properties of reactively sputtered CrN films

Modification in structural and optical properties of chromium-nitride (CrN) films induced by argon ion irradiation and thermal annealings were investigated using various experimental techniques. CrN films deposited by d. c. reactive sputtering on Si substrate were implanted with 200 keV argon ions, at fluences of 5–20 × 1015 ions/cm2. As-implanted samples were then annealed in vacuum, for 2 h at 700 °C. Rutherford backscattering spectrometry, X-ray diffraction, cross-sectional (high-resolution) transmission electron microscopy and spectroscopic ellipsometry (SE) measurements were carried out in order to study structural and optical properties of the layers. After irradiation with 200 keV Ar ions a damaged surface layer of nanocrystalline structure was generated, which extended beyond the implantation profile, but left an undamaged bottom zone. Partial loss of columnar structure observed in implanted samples was recovered after annealing at 700 °C and CrN started to decompose to Cr2N. This layer geometry determined from transmission electron microscopy was inferred in the analysis of SE data using the combined Drude and Tauc-Lorentz model, and the variation of the optical bandgap was deduced. The results are discussed on the basis of the changes induced in the microstructure. It was found that the optical properties of the layers are strongly dependent on the defects' concentration of CrN.

Designing optical metamaterial with hyperbolic dispersion based on an Al:ZnO/ZnO nano-layered structure using the atomic layer deposition technique

Nano-layered Al:ZnO/ZnO hyperbolic dispersion metamaterial with a large number of layers was fabricated using the atomic layer deposition (ALD) technique. Experimental dielectric functions for Al:ZnO/ZnO structures are obtained by an ellipsometry technique in the visible and near-infrared spectral ranges. The theoretical modeling of the Al:ZnO/ZnO dielectric permittivity is done using effective medium approximation. A method for analysis of spectroscopic ellipsometry data is demonstrated to extract the optical permittivity for this highly anisotropic nano-layered metamaterial. The results of the ellipsometry analysis show that Al:ZnO/ZnO structures with a 1:9 ALD cycle ratio exhibit hyperbolic dispersion transition change near 1.8 μm wavelength.

Through-the-glass spectroscopic ellipsometry for analysis of the optical structure of CdTe thin-film solar cells in the superstrate configuration.

The polycrystalline CdS/CdTe thin-film solar cell in the superstrate configuration has been studied by spectroscopic ellipsometry (SE) using glass side illumination whereby the reflection from the glass/film-stack interface is collected whereas that from the ambient/glass interface is rejected. The SE data analysis applies dielectric functions ( ) for solar cell component materials obtained by variable-angle and in-situ SE. In the SE analysis of the complete cell, a step-wise procedure ranks the free parameters, including thicknesses and those defining the spectra in , according to their ability to reduce the root-mean-square deviation between simulated and measured SE spectra, and the best-fit results compare well with electron microscopy. Combining all SE results, the solar cell quantum efficiency (QE) can be simulated without free parameters, and comparisons with QE measurements enable identification of losses. The capabilities have wide applications in photovoltaic module mapping and in-line monitoring.

Effect of ion bombardment on the structural and optical properties of TiO2 thin films deposited from oxygen/titanium tetraisopropoxide inductively coupled plasma

Titanium dioxide films were deposited on silicon substrates from oxygen/titanium tetraisopropoxide inductively coupled radiofrequency plasmas in a helicon reactor operated at low temperature (<150°C) and low pressure (0.4Pa). The effect of the ion energy (Ei), varied in the 15–175eV range, on the morphology, microstructure and optical properties of the films is investigated. Scanning electron microscopy (SEM) shows that at low energy (Ei=15eV), the film exhibits a columnar morphology consisting of a bottom dense layer, an intermediate gradient layer and a top roughness layer. Increasing the ion energy results in more homogeneous films along the growth direction as confirmed by the in-situ kinetic ellipsometry measurements and post deposition spectroscopic ellipsometry data analysis. In addition, the atomic force microscopy (AFM) measurements reveal that the film top surface becomes smoother as Ei is increased. X-ray diffraction (XRD) diagrams show that only anatase is identified in the film deposited at 15eV, whereas the complete phase transformation from anatase to rutile occurs at Ei=75eV. These results are in good agreement with the Fourier transform infrared spectroscopy (FTIR) spectra which also show that the hydroxyl groups absorbed in the films deposited at 15eV, are greatly decreased for Ei≥45eV. Suitable structural models combined with the Tauc–Lorentz dispersion law have been found to accurately fit the spectroscopic ellipsometry experimental data. The results in good agreement with SEM and AFM measurements are also consistent with the structural properties evidenced by XRD and FTIR. The refractive index (n) can be increased significantly by increasing the ion energy from 15eV to 75eV, reaching a value of 2.49 at 1.96eV. Upon increasing the ion energy above 75eV n is shown to decrease due to micropores which are formed in the films.

Extracting the complex optical conductivity of mono- and bilayer graphene by ellipsometry

A method for analysis of spectroscopic ellipsometry data is demonstrated to extract the optical conductivity of mono- and bilayer chemical-vapor-deposited graphene. We model graphene as a truly two-dimensional (2D) material with a sheet conductivity, rather than a phenomenological effective refractive index as has been used in the literature. This technique measures both the real and imaginary part of the optical conductivity, which is important for graphene optoelectronics and metamaterials. Using this method, we obtain broadband measurements of the complex optical conductivity for mono- and bilayer graphene from ultraviolet to mid-infrared wavelengths. We also study how chemical doping with nitric acid modifies the complex optical conductivity.

Bandgap Engineering and Optical Constants of YxAl1-xN Alloys

We study wurtzite YxAl1-xN (0≤x ≤0.22) films with (0001) orientation deposited by magnetron sputtering epitaxy on Si(100) substrates and we determine the alloys band gap energies and optical constants. Room temperature spectroscopic ellipsometry (SE) is employed in the energy range from 1 to 6.3 eV, and data modeling based on the standard dielectric function model is used. As a result of the SE data analysis the YxAl1-xN refractive index and extinction coefficient are determined. The band gap of YxAl1-xN is found to decrease linearly from 6.2 eV (x = 0) down to 4.5 eV (x = 0.22). We further observe an increase of the refractive index with increasing Y content; from 1.93 to 2.20 (at 2 eV) for x = 0 and 0.22, respectively, reflecting the increase in material density.