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Resolving lateral and vertical structures by ellipsometry using wavelength range scan
Abstract
For most thin film structures, by changing the wavelength range to fit ellipsometric spectra, the values of the fitted parameters also change to a certain extent. The reason is that compared with the ellipsometric sensitivity many thin films are vertically non-uniform. In absorbing films with significant dispersion in the used wavelength range, the penetration depth of probing light can show large variations depending on the wavelength. Consequently, the value of a fitted parameter for a certain wavelength range is a weighted sum of structural information over different depth ranges corresponding to the different wavelengths. By changing the wavelength range, the range of penetration depths can be adjusted, and the fitted values can be plotted as a function of the probed depth range calculated directly from the determined or tabulated extinction coefficients. We demonstrate the results on deposited polycrystalline thin films. The advantage of this approach over the parameterization of structural properties as a function of depth is that the wavelength scan approach requires no parameterized depth distribution model for the vertical dependence of a layer property. The difference of the wavelength scan method and the vertical parameterization method is similar to the difference between the point-by-point and the parameterized dielectric function methods over the used wavelength range. The lateral structures strongly influence the ellipsometric response, as well. One of the most remarkable effects is when the lateral feature sizes approach the wavelength of the probing light. In this case the effective medium method is not valid any more, since scattering and depolarization occurs. By scanning the wavelength range, the limit wavelength of the onset of scattering can be found, and used for the determination of the corresponding critical lateral period length.
... This discrepancy is accentuated by the sustained low uncertainty observed at a wavelength of 450 nm. Despite the optical penetration depth (OPD) predicting an approximate value of 240,000 nm, the measured layer thickness is around 2,000,000 nm [82][83][84][85][86]. This incongruity underscores the intricate interplay between optical properties and layer characteristics, emphasizing the imperative need for a nuanced understanding of the material's behavior under varying photon energies. ...
In this comprehensive study, we synthesized Co0.6Zn0.4Fe2O4 cubic spinel via the sol–gel method and characterized its structural, thermal, and optical properties. X-ray diffraction (XRD) verified the crystallization within the cubic Fd-3 m space group, and a detailed analysis determined a crystallite size ranging from 47 to 58 nm. Notably, the calculated crystallite size of 49.4 nm revealed inherent limitations in Scherer’s formula, which does not account for intrinsic strain effects from crystal defects, grain boundaries, and stacking. Optical investigations, utilizing UV–Vis absorption spectroscopy, unveiled a direct optical band gap of 1.26 eV, suggesting semiconductor behavior. The material’s thermal conductivity was found to be highly temperature sensitive, reaching its maximum value for both spin orientations at 900 K, with a quantified value of ke/τ = 4 × 1014 W/(mKs). This thermal behavior, along with the observed disorder (Eu value of 1.41 eV) and higher Urbach energy, offers valuable insights into the material’s response under varying temperature conditions, essential for applications in diverse technological domains.
... In earlier manual SE analyses, the variation of an analyzed energy range (or a wavelength range) was also adopted to determine a fine-structured dielectric function in an infrared region 13 or light-penetration-depth-dependent thin film structures. 14,15 In particular, for the infrared SE analysis, the analyzed region was expanded toward a lower energy (i.e., longer wavelengths) to resolve sharp absorption features observed in the infrared region. 13 In our method, established to analyze the SE spectra in the visible/ultraviolet region, the ε 2 spectrum of samples is modeled as a sum of several TL peaks, 3,12 ...
In spectroscopic ellipsometry, the optical properties of materials are obtained indirectly by generally assuming dielectric function and optical models. This ellipsometry analysis, which typically requires numerous model parameters, has essentially been performed by a trial-and-error approach, making this method as a rather time-consuming characterization technique. Here, we propose a fully automated spectroscopic ellipsometry analysis method, which can be applied to obtain dielectric functions of light absorbing materials in a full measured energy range without any prior knowledge of model parameters. The developed method consists of a multiple-step grid search and the following non-linear regression analysis. Specifically, in our approach, the analyzed spectral region is gradually expanded toward a higher energy, while incorporating an additional optical transition peak whenever the root mean square error of the fitting analysis exceeds a critical value. In particular, we have established a unique algorithm that could be employed for the ellipsometry analyses of different types of optical materials. The proposed scheme has been applied successfully for the analyses of MoOx transparent oxides and the complex dielectric function of a MoOx layer that exhibits dual optical transitions due to band-edge and deep-level absorptions has been determined. The developed method can drastically reduce a time necessary for an ellipsometry analysis, eliminating a serious drawback of a traditional spectroscopic ellipsometry analysis method.
... Figure 6 shows the ellipsometric modeling of Si nanowires with different lengths. It is shown that the wavelength range used for the fit is not only required to be adapted to the length of the nanowires, but the characteristic feature sizes can also be determined based on the used wavelength range [38,39]. This work also shows how different kinds of anisotropies can be distinguised based on the fit results using different models and assumptions. ...
Optical methods have been used for the sensitive characterization of surfaces and thin films for more than a century. The first ellipsometric measurement was conducted on metal surfaces by Paul Drude in 1889. The word 'ellipsometer' was first used by Rothen in a study of antigen-antibody interactions on polished metal surfaces in 1945. The 'bible' of ellipsometry has been published in the second half of the '70s. The publications in the topic of ellipsometry started to increase rapidly by the end of the '80s, together with concepts like surface plasmon resonance, later new topics like photonic crystals emerged. These techniques find applications in many fields, including sensorics or photovoltaics. In optical sensorics, the highest sensitivities were achieved by waveguide interferometry and plasmon resonance configurations. The instrumentation of ellipsometry is also being developed intensively towards higher sensitivity and performance by combinations with plasmonics, scatterometry, imaging or waveguide methods, utilizing the high sensitivity, high speed, non-destructive nature and mapping capabilities. Not only the instrumentation but also the methods of evaluation show a significant development, which leads to the characterization of structures with increasing complexity, including photonic, porous or metal surfaces. This article discusses a selection of interesting applications of photonics in the Centre for Energy Research of the Hungarian Academy of Sciences.
... OPD is also shown for pure SiO 2 in the middle graph in Fig. 4. These values could be higher by several factors in a mixed EML, and ellipsometric depth sensitivity is typically three times larger than OPD (see Fig. 4 in Ref. [29]). Depth profiling (SiO 2 vertical inhomogeneity characterization) remains difficult, because of the narrow SiO 2 sensitive part of the spectra that can probe the entire layer. ...
This paper suggests the evaluation of morphological parameters of porous silicon layers (PSL) using spectroscopic ellipsometry from UV to mid-infrared optical range. PSL were prepared by electrochemical etching of monocrystalline silicon wafers in hydrofluoric acid-based electrolyte. Measuring with an optical and an infrared ellipsometer with a wide spectral range permits an accurate characterization of PSL properties from the top surface to the bottom of the layer with thicknesses from several hundred nanometers up to a few tens of micrometers. Several different optical models for ellipsometric evaluations were developed to determine the thickness, the average porosity, the in-depth porosity gradient, the oxidation level and the surface roughness of the PSL. Porosity was modeled with multiple effective medium layers by varying ratio of crystalline silicon, void and oxidized silicon wherever needed. Thin PSL (<5 μm) shows no impact of current density on porosity and thickness. However, evaluation of thick PSL (20 - 50 μm) highlights the in-depth porosity gradient. Thickness values were also cross-checked with electron microscopy confirming the proposed ellipsometric models. Additionally, different oxidation techniques have also been compared in terms of oxidation level and void content. Volume expansion during PSL oxidation follows exactly the same behavior as that during the oxidation of planar silicon wafers.
... If no a priori information is available about the depth profile, the strong wavelength dependence of the penetration depth of light in silicon † at standard wavelengths (250-800 nm) can be utilized for making a "depth scan" when systematically changing the wavelength range used for the fit. 17 The capabilities of ellipsometry for measuring ultra-thin surface 18,19 or even embedded layers 20 have also been revealed for numerous materials and layer structures. Using spectroscopic optical characterizations, not only layer thicknesses and multi-layer structures but also material properties like elemental composition, 4, 21 phase (even in situ 22, 23 ) or crystallinity 3, 24 can be determined (see Fig. 1.1 of Ref. 13). ...
Optical techniques have been intensively developed for many decades in terms of both experimental and modeling capabilities. In spectroscopy and scatterometry material structures can be measured and modeled from the atomic (binding configurations, electronic band structure) through nanometer (nanocrystals, long range order) to micron scales (photonic structures, gratings, critical dimension measurements). Using optical techniques, atomic scale structures, morphology, crystallinity, doping and a range of other properties that can be related to the changes of the electronic band structure can most sensitively be measured for materials having interband transition energies in the optical photon energy range. This will be demonstrated by different models for the dielectric function of ZnO, a key material in optoelectronics and in numerous other fields. Using polarimetry such as spectroscopic ellipsometry, sub-nanometer precision has long been revealed for the thickness of optical quality layers. The lateral resolution of spectroscopic ellipsometry is limited (> 50 μm) by the use of incoherent light sources, but using single-wavelength imaging ellipsometry, a sub-micron lateral resolution can be reached. In case of sub-wavelength structures, the morphology (of e.g. porous or nanocrystalline materials) can be characterized using the effective medium theory. For structure sizes comparable to the wavelength, scatterometry is applied in a broad versatility of configurations from specular to angle resolved, from coherent to incoherent, from monochromatic to spectroscopic, from reectometric to polarimetric. In this work, we also present an application of coherent Fourier scatterometry for the characterization of periodic lateral structures.
Electrochemical migration is a critical factor contributing to failures in electronics due to humidity. When moisture accumulates on conductor-dielectric-conductor systems under bias voltage, electrochemical processes can be triggered, leading to the growth of metallic dendrites that may ultimately result in system failure. Despite its significance, many aspects of electrochemical migration remain unresolved, particularly regarding the physical characteristics of liquid buildup that facilitate dendrite growth and short circuit currents. While there are a few techniques that can measure water adsorption on the nanoscale, most conventional methods focus on water droplets within the size range of visible light wavelengths. In this study, we implemented a combined electrical-optical-ellipsometric measurement on FR-4 printed circuit boards featuring Sn surface finishes. Our experimental setup allowed for the measurement of water condensation across a wide range of thicknesses, while simultaneously monitoring the solder mask and metal electrodes during cooling. The ambient temperature of 25 ∘C and a relative humidity of 60% were constant during the measurement. By employing this approach, we elucidated the mechanisms of dendrite formation and short circuit currents, demonstrating that the water film remains continuous between droplets on the solder mask surface. Compared to Sn the nucleation was delayed on the solder mask with a larger surface coverage at smaller thicknesses. This comprehensive methodology provides crucial insights into the electrochemical migration process, enhancing our understanding of the underlying phenomena that contribute to electronic failures due to humidity. Our work highlighted the complementary nature of ellipsometry and optical imaging.
The morphological evolution of Ge layers growing on the SiO 2 /Si(100) substrate by photo-excited chemical vapor deposition was traced through an analysis of pseudodielectric functions measured by real-time spectroscopic ellipsometry. Simulation and fitting were carried out on multiple samples with various Ge film thicknesses as well as on sequential optical spectra from a sample with an incremental buildup of Ge atoms on one substrate. Single- and two-layer models involving crystalline Ge ( c-Ge), amorphous Ge ( a-Ge), and void components were employed under the Bruggeman effective medium approximation to represent wetting of the SiO 2 surface, nucleation of Ge seeds for the subsequent dot/island formation, and steady-state dot/island growth. A combination of c-Ge and a-Ge represents intermediate crystallinity, and void represents vacant space between dots/islands. A single-layer model with a mixture of c-Ge, a-Ge, and void components was used for crude estimation of the composition from which the time evolution of the volume fraction of the components was derived. However, fitting in the early growth stage resulted in an unrealistic structure, indicating that the dielectric function of the thin hydrogenated Ge network layer was very different from those of c-Ge and a-Ge. The optical spectra of dots/islands at the intermediate growth stage could be reproduced by a two-layer model consisting of a ( a-Ge + void) layer overlaid on a ( c-Ge + void) base layer. The real-time Ψ–Δ trajectories of ellipsometric angles monitored at a photon energy of 3.4 eV consisted of three branches. They could be reproduced by assuming the growth of an outer layer with an appropriate composition. After wetting on SiO 2 (branch 1), the Ge seed layer nucleates while the volume fraction of Ge rapidly decreases from 70% to 25% with proceeding growth (branch 2). Then, the volume fraction of Ge continuously increases up to 65%, eventually reaching steady-state dots/island growth (branch 3)
Oxide-based materials and structures are becoming increasingly important in a wide range of practical fields including microelectronics, photonics, spintronics, power harvesting, and energy storage in addition to having environmental applications. This book provides readers with a review of the latest research and an overview of cutting-edge patents received in the field.
It covers a wide range of materials, techniques, and approaches that will be of interest to both established and early-career scientists in nanoscience and nanotechnology, surface and material science, and bioscience and bioengineering in addition to graduate students in these areas.
Features:
Contains the latest research and developments in this exciting and emerging field
Explores both the fundamentals and applications of the research
Covers a wide range of materials, techniques, and approaches.
https://www.taylorfrancis.com/books/oxide-based-materials-structures-rada-savkina-larysa-khomenkova/e/10.1201/9780429286728
We develop and test a spectral ellipsometric method of nondestructive testing of the phase compositions of multilayer films and metal-oxide structures in the course of their growth on the surfaces of metals and alloys. The method is based on the preliminary thermodynamic and spectral analyses of the phase compositions of inhomogeneous surface oxides. The permanent monitoring of the spectra of ellipsometric parameters makes it possible to trace the distribution of phase composition of nanosized metal-oxide structures over the volume of inhomogeneous surface oxide (film) in the process of its growth. The proposed spectral-ellipsometric method can be useful for the nondestructive testing and, especially, for the in-situ automated investigations with subsequent classification of the structures, compositions, and types of multilayer metal-oxide structures in the course of their growth.
The research on solar cells based on photonic, plasmonic and various nanostructured materials has been increasing in the recent years. A wide range of nanomaterial approaches are applied from photonic crystals to plasmonics, to trap light and enhance the absorption as well as the efficiency of solar cells. The first part of this chapter presents examples on applications that utilize nanostructured materials for photovoltaics. In the second part, ellipsometry related metrology issues are discussed briefly, dividing the topic in two major parts: effective medium and scatterometry approaches.
Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of the system, and to fit the parameters in order to minimize the difference between the calculated and measured values. The most common problem of optical modeling is that the measured structures and materials turn out to be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically relevant, (2) improve the fit quality, (3) don't correlate with other parameters. The sensitivity of the parameters can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and porosity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in situ or in line capabilities of the optical methods will be demonstrated by different applications.
Porous silicon layers were prepared by electrochemical etching of p-type single-crystal Si (c-Si) of varying dopant concentration resulting in gradually changing morphology and nanocrystal (wall) sizes in the range of 2-25 nm. We used the model dielectric function (MDF) of Adachi to characterize these porous silicon thin films of systematically changing nanocrystal size. In the optical model both the surface and interface roughnesses have to be taken into account, and the E0, E1, and E2 critical point (CP) features are all described by a combination of several lineshapes (two-dimensional CP, excitonic, damped harmonic oscillator). This results in using numerous parameters, so the number of fitted parameters were reduced by parameter coupling and neglecting insensitive parameters. Because of the large number of fitted parameters, cross correlations have to be investigated thoroughly. The broadening parameters of the interband transitions in the measured photon energy range correlate with the long-range order in the crystal. The advantage of this method over the robust and simple effective medium approximation (EMA) using a composition of voids and c-Si with a nanocrystalline Si reference [Petrik et al., Appl. Surf. Sci. 253, 200 (2006)] is that the combined EMA+MDF multilayer method of this work provides a more detailed description of the material and layer structure.
Polysilicon layers with thicknesses between 8 and 600 nm deposited by low-pressure chemical vapor deposition at temperatures ranging from 560 to 640 °C were characterized by spectroscopic ellipsometry (SE) to determine the layer thicknesses and compositions using multilayer optical models and the Bruggeman effective-medium approximation. The dependence of the structural parameters on the layer thickness and deposition temperature have been investigated. A better characterization of the polysilicon layer is achieved by using the reference data of fine-grained polysilicon in the optical model. The amount of voids in the polysilicon layer was independently measured by Rutherford backscattering spectrometry (RBS). The SE and RBS results show a good correlation. The comparison of the surface roughness measured by SE and atomic force microscopy (AFM) shows that independently of the AFM window sizes, a good correlation of the roughness determined by SE and AFM was obtained. © 2000 American Institute of Physics.
Damage created by ion implantation into single crystalline silicon was characterized with an optical model based on the coupled half-Gaussian model developed by Fried et al [J. Appl. Phys. 71, 2835 (1992)]. In the improved optical model the damage profile was described by sublayers with thicknesses inversely proportional to the slope of the profile. This method allows a better resolution at the quickly changing parts of the profile, and a better approximation of the Gaussian profile with the same number of sublayers. A fitting procedure, which we call “multipoint random search,” was applied to minimize the probability of getting in a local minimum. The capabilities of our method were demonstrated for amorphizing doses using different ions and energies. The improved fit quality and the correlation with results of backscattering spectrometry basically supported the optical model. © 2003 American Institute of Physics.
Polysilicon layers prepared by low pressure chemical vapor deposition (LP-CVD) on oxidized silicon were measured by spectroscopic ellipsometry (SE), atomic force microscopy (AFM), and transmission electron microscopy (TEM). SE was used to determine layer thicknesses and compositions using multi-layer optical models. The measured spectra were simulated and fitted using a linear regression algorithm (LRA). The dielectric function of composite materials was calculated by the Bruggeman effective medium approximation (B-EMA). The dependence of the surface roughness and layer structure on the deposition temperature was studied. The interface layer between the buried oxide and the polysilicon layer, which represents the initial phase of growth, was modeled with a thin layer having polycrystalline silicon and voids. The precision of the SE layer thickness measurements was determined by a comparison with AFM and TEM results taking into account the 95% confidence limits of the LRA. The root mean square (RMS) roughness values measured by AFM using different scan sizes were compared to the thicknesses of the top layer in the SE model simulating the surface roughness. It was shown that the correlation between the SE and the AFM surface roughness results are affected by the scan size of AFM and the surface characteristics.
We report wavelength- (λ-) and size-dependent measurements of the dielectric functions (ε) of macroscopically uniform samples pressed from Al2O3 powders of different particle sizes. The data agree with effective medium (mean-field) theories for particle diameters less than about 0.25λ. For particle diameters larger than about 0.5λ, measured values of ε exceed allowable quasistatic limits for known volume fractions, and finite-wavelength effects must be considered. We show that finite-wavelength theories are more sensitive to microstructural parameters than quasistatic theories, which suggests that finite-wavelength models should be useful for microstructural or materials characterization and could also have predictive value. Finally, we show that the recent perturbation model of Bosi, Girouard, and Truong, that includes dynamic terms as additions to a quasistatic theory, predicts rates of increase of ε with particle size that greatly exceed those of experiment or other model calculations. Thus dynamic terms cannot in general be incorporated as additions to quasistatic theories but must be included in the initial formulation of the effective-medium problem.
The application of spectroscopic ellipsometry (SE) to obtain accurate depth profiles of ion-implanted silicon substrates is discussed. Details on the interpretation of SE spectra are given, explaining why such a complex analysis is possible. The power of SE to nondestructively obtain depth profiles of ion implantation damage is illustrated for hydrogen-implanted silicon and on low-dose implanted SIMOX (Separation by IMplanted OXygen) material. The obtained SE results are verified by cross-sectional transmission electron microscopy and by other analytical techniques.
A several‐parameter fitting of spectroscopic ellipsometry data is developed to characterize near‐surface layers in semiconductors damaged by implantation. The damage depth profiles are described by either rectangular, trapezoid‐type, or coupled half‐Gaussian (realistic) optical models. The rectangular model has three parameters: the average damage level, the effective thickness of the implanted layer, and the thickness of the native oxide. The trapezoid‐type model is enhanced with a fourth parameter, the width of the amorphous/crystalline interface. The realistic optical model consists of a stack of layers with fixed and equal thicknesses. The damage levels are determined by a depth profile function (presently coupled half‐Gaussians). Five parameters are used: the position of the maximum, the height, and two standard deviations of the profile, plus the thickness of the native oxide. The complex refractive index of each layer is calculated from the actual damage level by the Bruggeman effective medium approximation. The optical models were tested on Ge‐implanted silicon samples and cross checked with high‐depth‐resolution Rutherford backscattering spectrometry and channeling.
We investigated different optical models (one-layer, multilayer, parametric multilayer, and statistical parametric) for the ellipsometric characterization of thin films made of silica spheres in the diameter (D) range of 90-450 nm prepared by the Langmuir-Blodgett (LB) technique. As a continuation of a previous work (Nagy, N., et al. Langmuir 2006, 22, 8416) in terms of threshold wavelength determination and optical models, we investigated the wavelength range of the quasistatic limit (requirement for the effective medium approximation) depending onD.We compared the above models in the aspect of fit quality, stability, uncertainty of parameters, and the amount of information that can be obtained from the evaluation. Besides fundamental properties like diameter, coverage, or packing density, using sophisticated models we can also determine the size distribution of the particles. The ellipsometric results were compared with the results of dynamic light scattering and of scanning electron microscopy.
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