Bruggeman Effective Medium Approximation Research Articles

Deposition of micro crystalline silicon films using microwave plasma enhanced chemical vapor deposition

A microwave plasma enhanced chemical vapor deposition (microwave PECVD) process has been investigated to deposit micro crystalline silicon films with a high growth rate from silane (SiH4). A three-layer Bruggeman-Effective-Medium-Approximation (BEMA) model was developed to describe the complex structure of the grown films. The model was confirmed by Raman and spectroscopic ellipsometry measurements. In addition the surface evolution was characterized by AFM (Atomic Force Microscopy) and spectroscopic ellipsometry data. Particular emphasis is given to the correlation between the structural film properties and the deposition parameters. Besides chemical reactions, it is shown that ion bombardment plays an important role for the crystallinity of the grown silicon films. In the presence of ions, hydrogen radicals are able to etch silicon, which significantly improves the crystallinity of the deposited films. If just radicals are present, the deposited films become amorphous.

High performance TiO2 nanotubes antireflection coating

The present study analyzes the use of TiO2 layer as antireflection coating. TiO2 thin films were prepared on silicon substrate by electrochemical anodization process with thicknesses of 130 and 170nm. The films exhibit a uniform nanotubular structure. The ellipsometry measurement data were analyzed using a multi-layer model, the bottom layer is a dense layer of TiO2 and the top layers are porous; they are formed by a mixture of TiO2 and void. The values of refractive index are obtained by the Bruggeman effective medium approximation. The refractive indexes of the bottom and top TiO2 sublayers were about 2.3 and 1.6, respectively. The lower values of reflectance are obtained with the thinnest film. For these samples the reflectance decreases about 90% compared to silicon and in some cases the reflectivity is less than 5%. The thickness influences of TiO2 thin films and their synthesis parameters on the optical constants are discussed.

Structural analysis of amorphous carbon films by BEMA theory based on spectroscopic ellipsometry measurement

The structural analysis of amorphous carbon films is imperative for the application of their unique properties into industrial fields. Density is one of the most fundamental properties of amorphous carbon films, and directly related to their structures. In the present study, thirteen amorphous carbon film samples with different sp3/(sp3+sp2) ratios and hydrogen contents were deposited by various physical and chemical vapor deposition techniques. All these films were analyzed by spectroscopic ellipsometry and simulated using Bruggeman effective medium approximation (BEMA) theory. In this simulation analysis, ten types of optical models were proposed based on the selected five kinds of standard materials (diamond, highly oriented pyrolytic graphite, glassy carbon, polyethylene, and void) with considering a feasibility of each model. The comparisons of the X-ray reflectivity density and BEMA calculated density, as well as those of the sp3/(sp3+sp2) ratios obtained from BEMA simulation and the near-edge X-ray absorption fine-structure analysis were carried out for the individual samples. Thus, using BEMA theory, it was established that the suitable optical models should be applied to make a detailed structural analysis of the individual types of amorphous carbon films.

Optical properties of anisotropic 3D nanoparticles arrays(a)(a)Contribution to the Focus Issue Self-assemblies of Inorganic and Organic Nanomaterials edited by Marie-Paule Pileni.

The optical properties of 3D periodic arrays of spheroidal Au nanoparticles are calculated using a Bruggeman effective medium approximation. The optical response of the supra-crystal depends on the volume fraction of the nanoparticles and their aspect or size ratio (major/minor axis). All the nanoparticles have the same orientation, and this defines an anisotropic dielectric function of the crystal. As a function of the filling fraction, while keeping the size ratio fixed, the maximum in the extinction spectra along the major and minor axes does not show a significant change. However, for a fixed filling fraction, varying the aspect ratio of the particles induces a shift of several hundred of nanometers in the maximum of the extinction spectra along the major axis and almost no changes along the minor axis. Depending on the aspect ratio and the filling fraction, we show that the supra-crystal has three regimes with different values of an effective plasma frequency.

Rapid thermal annealing effect on the microstructural and optical properties of nc-Si embedded in porous anodic alumina

Abstract In this work, nanocrystalline silicon (nc-Si) are deposited in a porous anodic alumina (PAA) matrix by a radio frequency plasma enhanced chemical vapor deposition (RF-PECVD) method. The rapid thermal annealing (RTA) effect on morphological and microstructural properties of nc-Si/PAA structure is investigated by SEM, EDX, XRD technique and Raman spectroscopy. Crystallization of the amorphous silicon is obtained after annealing at was 550 °C during a time ranging from 10 to 120 min. The effect of thermal annealing on the optical properties of nc-Si/PAA structure was studied by Spectroscopic Ellipsometry (SE) in the spectral range 0.3–0.8 μm. The Ellipsometric analysis demonstrated the formation of two separate layers during the annealing process. A silicon/alumina alloy as the upper layer and a polysilicon film at the bottom and in contact with the alumina barrier layer. The optical constants, thickness and the composition of each film have been estimated from the SE data using Bruggeman effective medium approximation (BEMA). PL spectroscopy was used to investigate the bandgap energy of nc-Si embedded within the PAA matrix, the origin of emission PL spectra as well as the observed red-shift have been discussed.

Study of the optical properties of silver nanoparticle layers and Si‐based nanostructure layers

Ellipsometric spectra (λ = 250–900 nm) of surface layers were for the first time obtained in three stages of the catalytic etching of silicon, used to fabricate wire‐like nanostructures. Self‐assembled silver particles deposited with chemical method on the silicon surface form a discontinuous layer with its own complex dielectric function ϵ, which is independent of the radiation incidence angle (at 50–70 degrees relative to the normal to the surface) and differs from ϵ of the bulk silver structure. The variation of the imaginary part of the pseudodielectric function, ϵ2, of the layer of silicon nanowire (SiNW) sprouts was studied. At the minimum catalytic etching duration, the thickness of the rough SiNW layer being formed is comparable with the thickness of the layer of preliminarily deposited silver. With increasing etching duration, a low‐refractive SiNW layer is formed with a thickness of 111 nm and void fraction of 33–78%, found in Bruggeman's effective medium approximation. The experimental data obtained with a spectroscopic ellipsometry and their interpretation made it possible to determine specific features of nanostructures at the earliest interval silicon etching time.

Mechanism of ultra-low reflectance for nanocrystalline Si/crystalline Si structure formed by surface structure chemical transfer method

By contact of platinum catalyst with Si wafers immersed in H2O2 plus HF solutions, ultra-low reflectance Si surfaces can be produced. The ultra-low reflectance results from the formation of a nanocrystalline Si (nc-Si) layer with ∼300 nm thickness. A porosity-graded optical model consisting of 19 sublayers for the nc-Si layer, which is determined from SEM and TEM observations, and the fitting of ellipsometric spectra, is found to well explain the optical properties. The dielectric function of each sublayer is calculated from the Bruggeman effective medium approximation using porosity and the dielectric functions of Si and ∼5 nm Si nanocrystals. The reflectance calculated from the optical model shows a good agreement with the experimental result in the wide wavelength region between 300 and 800 nm. This good agreement demonstrates that the ultra-low reflectance of the nc-Si/Si structure results from the refractive index monotonically increasing with the depth.

Ellipsometric porosimetry on pore-controlled TiO2 layers

The practical performance of surface coatings in applications like catalysis, water splitting or batteries depends critically on the coating materials’ porosity. Determining the porosity in a fast and non-destructive way is still an unsolved problem for industrial thin-films technology. As a contribution to calibrated, non-destructive, optical layer characterisation, we present a multi-method comparison study on porous TiO2 films deposited by sol-gel synthesis on Si wafers. The ellipsometric data were collected on a range of samples with different TiO2 layer thickness and different porosity values. These samples were produced by templated sol-gel synthesis resulting in layers with a well-defined pore size and pore density. The ellipsometry measurement data were analysed by means of a Bruggeman effective medium approximation (BEMA), with the aim to determine the mixture ratio of void and matrix material by a multi-sample analysis strategy. This analysis yielded porosities and layer thicknesses for all samples as well as the dielectric function for the matrix material. Following the idea of multi-method techniques in metrology, the data was referenced to imaging by electron microscopy (SEM) and to a new EPMA (electron probe microanalysis) porosity approach for thin film analysis. This work might lead to a better metrological understanding of optical porosimetry and also to better-qualified characterisation methods for nano-porous layer systems.

Safe and simple detection of sparse hydrogen by Pd-Au alloy/air based 1D photonic crystal sensor

A simple integrated hydrogen sensor using Pd-Au alloy/air based one dimensional photonic crystal with an air defect layer is theoretically modeled. Structural parameters of the photonic crystal are delicately scaled to generate photonic band gap frequencies in a visible spectral regime. An optimized defect thickness permits a localized defect mode operating at a frequency within the photonic band gap region. Hydrogen absorption causes modification in the band gap characteristics due to variation of refractive index and lattice parameters of the alloy. As a result, the transmission peak appeared due to the resonant defect state gets shifted. This peak shifting is utilized to detect sparse amount of hydrogen present in the surrounding environment. A theoretical framework is built to calculate the refractive index profile of hydrogen loaded alloy using density functional theory and Bruggeman's effective medium approximation. The calculated refractive index variation of Pd3Au alloy film due to hydrogen loading is verified experimentally by measuring the reflectance characteristics. Lattice expansion properties of the alloy are studied through X-ray diffraction analyses. The proposed structure shows about 3 nm red shift of the transmission peak for a rise of 1% atomic hydrogen concentration in the alloy.

Optical and structural properties of cobalt-permalloy slanted columnar heterostructure thin films

Optical and structural properties of sequential Co-column–NiFe-column slanted columnar heterostructure thin films with an Al2O3 passivation coating are reported. Electron-beam evaporated glancing angle deposition is utilized to deposit the sequential multiple-material slanted columnar heterostructure thin films. Mueller matrix generalized spectroscopic ellipsometry data is analyzed with a best-match model approach employing the anisotropic Bruggeman effective medium approximation formalism to determine bulk-like and anisotropic optical and structural properties of the individual Co and NiFe slanted columnar material sub-layers. Scanning electron microscopy is applied to image the Co-NiFe sequential growth properties and to verify the results of the ellipsometric analysis. Comparisons to single-material slanted columnar thin films and optically bulk solid thin films are presented and discussed. We find that the optical and structural properties of each material sub-layer of the sequential slanted columnar heterostructure film are distinct from each other and resemble those of their respective single-material counterparts.

Determination of optical constants including surface characteristics of optically thick nanostructured Ti films: analyzed by spectroscopic ellipsometry.

In the present work, optically thick nanostructured titanium (Ti) films of thickness ranging from ∼100 to 900 nm were deposited on a glass substrate by DC magnetron sputtering at room temperature. Microstructural and surface properties of the samples were studied by x-ray diffraction and x-ray photoelectron spectroscopy (XPS). The morphological results revealed a systematic normal grain growth mechanism with increasing thickness analyzed by a scanning electron microscope. The influence of thickness on film surface roughness has been investigated by atomic force microscopy (AFM). The optical dispersion behavior was examined by spectroscopic ellipsometry (SE) over the long wavelength range of 246-1688 nm. The experimentally observed SE parameters were theoretically fitted with Drude-Lorentz and Bruggeman effective medium approximation theory. The surface properties of the Ti film measured by XPS and AFM were further accounted for in the optical model to determine optical constants (n and k) and the obtained results are expected to be the best available for bulk Ti metal.

Improvements on effective permittivity measurements of powdered alumina: Implications for bulk permittivity properties of asteroid regoliths

Accurate measurements of the dielectric properties of materials are essential in constraining interpretations of radar observations of planetary bodies. For bodies whose surfaces are comprised of regolith this requires an understanding of the behaviour of the bulk permittivity of powders. In this research we measure the effective permittivity of powdered aluminium oxide (or alumina, Al2O3) in a 7mm and 14mm (diameter) coaxial airline at 7.5GHz for multiple samples with varying grain size. The dielectric constant of alumina is extracted from these measurements using the Bruggeman (Effective Medium Approximation) mixing equation. We develop a model to account for heterogeneity within the airline, specifically in regards to local variation in porosity. The results of the model show good correlation to experimental data and effectively correct for grain size effects on the measured bulk permittivity. We show that particle shape can have a significant impact on the output of the model and can be accounted for by modelling particles as ellipsoids rather than perfect spheres, where the depolarization factor must be measured and averaged for a specific sample batch.

Optical characteristics of wet-thermally oxidized bulk and nanoporous GaN

Gallium nitride (GaN) films deposited on sapphire substrates by metal organic chemical vapor deposition were successfully transformed into bulk and nanoporous gallium oxide (Ga2O3) using a wet thermal oxidation technique. Oxidation depth measurements confirmed that the oxide growth appeared to be faster in the case of nanoporous GaN than that of bulk GaN. Spectroscopic ellipsometry was used to evaluate and compare the optical properties of nanoporous and bulk Ga2O3 films, such as refractive index and extinction coefficient, which revealed improved optical properties for nanoporous Ga2O3 compared to the bulk. The simulations conducted on the ellipsometric spectra for bulk and nanoporous Ga2O3 using the Forouhi-Bloomer model and the Bruggeman effective medium approximation revealed the best fit with a low mean square error value. In the case of nanoporous Ga2O3, zero absorption was observed in the wavelength range of 300 nm to 840 nm, supporting the use of this material as a transparent coating in optoelectronic devices.

Effective-medium approximation for lattice random walks with long-range jumps.

We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.

Structural, Morphological and Optical Properties of Sn3Sb2S6 Thin Films Synthesized by Oblique Angle Deposition

The oblique angle deposition technique has attracted a lot attention in many different applications due to its unique advantage of programmable nanocolumns. In this work we use this technique to investigate the physical properties of obliquely thermal evaporated Sn3Sb2S6 thin films deposited onto unheated glass and silicon substrates, inclined from the flux vapor source at the deposition angles 0°, 40°, 60°, 75° and 85°. X-ray diffraction (XRD) and UV–Visible and near infrared (UV–Vis-IFR) analysis were used respectively to characterize the structural and optical properties of the layers. The influence of flux angle on the surface morphology and the microstructure was investigated by using scanning electron microscopy. The optical constants were obtained from analysis of the experimental recorded transmission and reflectance spectral data over the wavelength range 300 nm to 1800 nm. The band gaps of the synthesized thin films were found to be direct allowed transitions and increased from 1.44 eV to 1.66 eV with increasing γ from 0° to 85°, respectively. The absorption coefficients of the films are in the range of 105 cm−1 to 106 cm−1. The refractive indexes were evaluated in the transparent region in terms of the envelope method suggested by the Swanepoel model. It has been found that the refractive index decreases from 2.66 to 2.06 with increasing deposition angle from 0° to 85°, respectively. The relationship between the flux incident angles γ and the column angle β was also explored. The oblique angle deposition films showed an inclined columnar structure, with columns tilting in the direction of the incident flux. The effective packing densities of the synthesized Sn3Sb2S6 thin films were calculated using Bruggeman effective medium approximation.

Optical properties and surface damage studies of crystalline silicon caused by swift iron ions

p-Type silicon samples irradiated with 70MeV 56Fe5+ ions for various fluences varying between 5×1012 and 4×1014ionscm−2 have been studied using spectroscopic ellipsometry and Fourier transform infrared spectroscopy. The microstructure of the irradiated samples was modeled from ellipsometric data, using a multilayer optical model and Bruggeman effective medium approximation. The values of pseudodielectric function, absorption coefficient and Penn gap energy were determined with respect to ion fluence. The effective medium analysis suggests that the superficial silicon layer can be explained as a mixture of crystalline and damaged silicon. The thickness of the damaged layer and percentage of voids present in the layer were found to increase with increase in the ion fluence. The effect of disorder on the interband optical spectra, especially on the critical point E1 at 3.4eV was found to vary with ion fluence. A red shift in the critical point E1 with increasing ion fluence was observed. FTIR study showed of silicon samples irradiated with 70MeV 56Fe5+ ions produced the oscillations in the spectral region 1000–400cm−1. As irradiated sample showed more pronounced fringes, while contrast of the fringes and amplitude both were found to decrease with increase in depth.

Optical properties of a nanostructured glass-based film using spectroscopic ellipsometry

Nanostructured glass films, which are fabricated using spinodally phase-separated low-alkali glasses, have several interesting and useful characteristics, including being robust, non-wetting and antireflective. Spectroscopic ellipsometry measurements have been performed on one such film and its optical properties were analyzed using a 5-layer structural model of the near-surface region. Since the glass and the film are transparent over the spectral region of the measurement, the Sellmeier model is used to parameterize the dispersion in the refractive index. To simulate the variation of the optical properties of the film over the spot size of the ellipsometer (~3 × 5mm), the Sellmeier amplitude is convoluted using a Gaussian distribution. The transition layers between the ambient and the film and between the film and the substrate are modeled as graded layers, where the refractive index varies as a function of depth. These layers are modeled using a two-component Bruggeman effective medium approximation where the two components are the layer above and the layer below. The fraction is continuous through the transition layer and is modelled using the incomplete beta function.

High‐Permittivity Composites Thin Films for High‐Energy Storage Capacitor Application Using the Nonvacuum Method

ABSTRACTTo investigate a new embedded capacitor material with high capacitance value, the high dielectric constant (Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 ceramic was ground into nanoscale powder (nano‐BSTZ, the average particle size was approximately 73 nm). Different nano‐BSTZ contents were mixed with polyvinylidene fluoride (PVDF) to form the PVDF/nano‐BSTZ composites. The PVDF/nano‐BSTZ composite films were formed by using the nonvacuum screen printing method on indium tin oxide (ITO) glass, and their thickness was approximately 2 μm. As the nano‐BSTZ content increased from 10 to 50 wt%, the specific capacitance of the PVDF/nano‐BSTZ composite films really increased. Three different mixing rules were used to predict the effective dielectric constants of the PVDF/nano‐BSTZ composite films, and the Bruggeman's effective medium approximation and the Lichtenecker logarithmic mixing rules fitted the measured results. For the printed PVDF/nano‐BSTZ composite films, the dielectric constants also decreased with increasing measured frequency and the loss tangents were all less than 5%.

Spectroscopic Ellipsometry Characterization of Pd Thin Film Grown by Atomic Layer Deposition

Pd thin films grown by atomic layer deposition have been studied through spectroscopic ellipsometer with Bruggeman effective medium approximation (B-EMA) model to evaluate the optical properties, thickness and Pd coverage of the films. For the fitting results of thickness, mean square error increases with the gain of ALD cycles. At smaller Pd ALD cycles less than 400, the better fitting results of Pd coverage were obtained compared with Maxwell-Garnett effective medium approximation. It verifies the B-EMA is better for fitting samples with smaller filling fractions. Our study can be extended to characterize other thin films.

Correlation between microstructural and optical properties of silicon thin films grown onto porous alumina by plasma–enhanced CVD method

The silicon nanocrystals (Si NCs) are fabricated on a porous alumina (PAl) matrix by PECVD technique at different deposition time (dt) in order to produce PAlSi thin films with a high crystallinity. In this work, we report a correlation between microstructural and optical characterizations of PAlSi alloy in term of volumic Si NCs fraction and mainly the Si NCs sizes. The morphology and structure of the samples were characterized using scanning electron microscopy (SEM), atomic force microscopy (AFM), energy dispersive X–ray spectroscopy (EDX), X–Ray Diffraction (XRD) technique, and Raman spectroscopy. Optical properties of the microstructure were studied using spectroscopic ellipsometry (SE) data. Based on the SE data, an appropriate optical model is used to describe the PAlSi content with various volumic fraction of Si NCs. Bruggeman effective medium approximation and Forouhi-Bloomer models are used to analyze the effects of the volumic crystalline Si fraction on the optical properties of PAlSi, such as the refractive index (n), extinction coefficient (k) and energy band gap (Eg), as well as the dielectric functions. We show that the crystallization process is strongly dependent on the degree or the volumetric fractions of Si NCs embedded in a PAl matrix.