Maxwell-Garnett Effective Medium Approximation Research Articles

Dependent scattering effects in aggregates with touching or overlapping non-absorbing spherical particles

This study evaluates the effect of dependent scattering and particle overlapping on the integral radiation characteristics of fractal aggregates of monodisperse and non-absorbing spherical particles for a wide range of particle and aggregate sizes. It also aims to identify a scattering approximation capable of rapidly predicting these radiation characteristics. The scattering cross-section and asymmetry factor of fractal aggregates with touching or overlapping spherical particles were computed using the T-matrix method or the discrete-dipole approximation, respectively. The simulated aggregates were composed of up to 30,000 spherical particles with size parameter xs varying from 0.03 to 5 for an aggregate size parameter χs of up to 23. The results established that dependent effects (i) were more significant in the scattering cross-section and asymmetry factor than in the absorption cross-sections and (ii) increased with decreasing particle size parameter xs. In addition, overlapping of particles was found to have a negligible effect on the integral radiation characteristics of the aggregates. Finally, the scattering cross section and asymmetry factor of any aggregates consisting of particles such that xs≤1 could be predicted by the so-called equivalent effective property (EEP) approximation treating the aggregates as equivalent homogeneous spheres with the same diameter and with effective refractive index given by the Maxwell–Garnett effective medium approximation.

Inferring iron oxides species content in atmospheric mineral dust from DSCOVR EPIC observations

Abstract. The iron-oxide content of dust in the atmosphere and most notably its apportionment between hematite (α-Fe2O3) and goethite (α-FeOOH) are key determinants in quantifying dust's light absorption, its top of atmosphere UV radiances used for dust monitoring, and ultimately shortwave dust direct radiative effects (DRE). Hematite and goethite column mass concentrations and iron-oxide mass fractions of total dust mass concentration were retrieved from the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) measurements in the ultraviolet–visible (UV–Vis) channels. The retrievals were performed for dust-identified aerosol plumes using aerosol optical depth (AOD) and spectral imaginary refractive index provided by the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm over six continental regions (North America, North Africa, West Asia, Central Asia, East Asia, and Australia). The dust particles are represented as an internal mixture of non-absorbing host and absorbing hematite and goethite. We use the Maxwell–Garnett effective medium approximation with carefully selected complex refractive indices of hematite and goethite that produce mass fractions of iron oxides species consistent with in situ values found in the literature to derive the hematite and goethite volumetric/mass concentrations from MAIAC EPIC products. We compared the retrieved hematite and goethite concentrations with in situ dust aerosol mineralogical content measurements, as well as with published data. Our data display variations within the published range of hematite, goethite, and iron-oxide mass fractions for pure mineral dust cases. A specific analysis is presented for 15 sites over the main dust source regions. Sites in the central Sahara, Sahel, and Middle East exhibit a greater temporal variability of iron oxides relative to other sites. Niger site (13.52° N, 2.63° E) is dominated by goethite over Harmattan season with median of ~2 weight percentage (wt.%) of iron-oxide. Saudi Arabia site (27.49° N, 41.98° E) over Middle East also exhibited surge of goethite content with the beginning of Shamal season. The Sahel dust is richer in iron-oxide than Saharan and northern China dust except in Summer. The Bodele Depression area shows a distinctively lower iron-oxide concentration (~1 wt. %) throughout the year. Finally, we show that EPIC data allow to constrain the hematite refractive index. Specifically, we select 5 out of 13 different number of hematite refractive indices widely variable in published laboratory studies by constraining the iron-oxide mass ratio to the known measured values. Provided climatology of hematite and goethite mass fractions across main dust regions of the Earth will be useful for dust shortwave DRE studies and climate modeling.

Validation of the aerosol optical property products derived by the GRASP/Component approach from multi-angular polarimetric observations

The multi-angle polarimetric satellite observations are helpful for improving the retrievals of aerosol parameters. However, practical applications of polarization technology are still limited because of complexity of measurement and interpretation of polarimetric observations. In this study, we analyze the performance of a new component approach developed in the frame of the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm. In addition to aerosol optical properties including particle size distribution, non-sphericity and index of refraction that are commonly derived from multi-angle radiance and polarization measurements, the GRASP/Component approach also provides some information about aerosol composition. Specifically, in this approach aerosol is modeled as an internal mixture of several components with distinctly different chemical compositions and known refractive indices. The approach is intended not only to provide additional insight on aerosol composition but also to improve retrieval of basic aerosol optical properties. This study presents comprehensive validation and evaluation of Aerosol Optical Depth (AOD), Ångström exponent (AE), fine mode AOD (AODF), coarse mode AOD (AODC), and single scattering albedo (SSA) as retrieved by the GRASP/Component approach. The GRASP/Component products include aerosol retrievals using two different aerosol component mixing rules, i.e., Maxwell-Garnett (MG) effective medium approximation and a simple Volume-Weighted averaging (VW). The differences between the results obtained using these two assumptions are also discussed. The obtained results show that the aerosol optical property products of GRASP/Component approach have good agreement with the ground-based AERONET measurements, which is comparable to other PARASOL/GRASP approaches. Specifically, the AOD retrieved by GRASP/Component approach show high correlation and nearly no bias both over land and ocean, as compared with AERONET. The more detailed aerosol properties such as AE, AODF, AODC and SSA also show one of the best comparisons with AERONET. These improvements can probably be attributed to the use of the additional physical constraints on spectral dependence of the complex refractive index and the reduction of total number of aerosol parameters directly retrieved in the GRASP/Component approach. In addition, the choice of mixing rules had no significant effect on optical retrievals. With the exception of SSA, the results obtained based on the MG mixing rule were found to be slightly better over those obtained using VW mixing rule, especially for bias.

Highly thermal conductivity and flame retardant flexible graphene/MXene paper based on an optimized interface and nacre laminated structure

Low thermal conductivity (TC) and poor flame retardancy of graphene oxide (GO) have limited its application in thermal management. Herein, a facile strategy is developed to fabricate flexible and free-standing graphene/MXene (GM) films by filtration of MXene and GO dispersions, followed by reduction and thermal welding. As results, interlamellar insertion of MXene into graphene has occurred and optimized interface was constructed between MXene and graphene. According to Y. Agari’s semi-empirical model and modified Maxwell-Garnett effective medium approximation, demonstrating that an optimized interface between MXene and graphene is conducive to heat conduction, and reduces the interface scattering. In-plane TC thus reached to 26.49 Wm−1K−1, and the thermal boundary resistance decreased to 8.81 × 10−10 from 1.54 × 10−8 m2KW−1. GM films also present excellent flame retardancy (peak heat release is ~10 Wg−1) and it still maintained initial shape after combustion. Using as-prepared GM films as heat dissipation, we demonstrate its potential usefulness in electronic device-cooling applications.

Thickness dependent native oxidation kinetics observation and prediction for Cu films using spectroscopic ellipsometry

Long-term native oxidation of polycrystalline Cu films with different thicknesses is investigated using spectroscopic ellipsometry. In order to more accurately determine the thickness of the oxide layer, a three-phase Maxwell-Garnett effective medium approximation model has been proposed to fit both the ellipsometric parameters and reflectance. X-ray photoelectron spectroscopy and transmission electron microscopy have been used to verify the rationality of the proposed model and measured results. The results demonstrate the Cabrera-Mott rule, and both the oxidation rate and the initial oxide thickness show significant dependencies on the thickness of Cu film. When thickness increases from 15 nm to 400 nm, the oxidation rate, defined as the slope in the inverse logarithmic correlation, decreases from 0.11/(nm·day) to 0.03/(nm·day) following an exponential function. Meanwhile, the initial oxide thickness, i.e. the intercept in the inverse logarithmic correlation, decreases from 0.73/nm to 0.3/nm in the light of a parabolic function. In the end, the oxidation evolution of a Cu film with arbitrary thickness is further predicted based on the obtained thickness-dependency, which is expected to provide a reference for better application of Cu films.

Active beam steering and afocal zooming by nematic liquid crystal-infiltrated graded index photonic structures

This study presents active beam steering and afocal zooming of light by incorporating liquid crystals (LCs) with graded index photonic crystals (GRIN PCs). The GRIN PC structures are composed of low refractive index polymer annular rods with holes of gradually varying radii. To actively manipulate incident light, the annular rods are infiltrated with nematic LCs. By applying an external voltage to the infiltrated LCs, the effective index profile of the low-index GRIN PC structure is modulated without introducing any mechanical movement. The incident beam deflection and corresponding focal distance modulation are tuned only by controlling the applied bias voltage. In the present work, the hyperbolic secant refractive index profile is chosen to design GRIN PC structures. To design a GRIN PC structure with annular PCs, the Maxwell–Garnett effective medium approximation is employed. We analytically express the relation between infiltrated LCs and the gradient parameter to show the physical background of the tuning ability of the proposed devices. Beam steering and afocal zooming devices are analytically investigated via geometrical optics, and numerically realized with the help of a finite-difference time-domain method. A beam deflection with an angle change of Δθout = 44° and a light magnification with maximum ×2.15 are obtained within operating frequencies of a/λ = [0.10–0.15] and a/λ = [0.15–0.25], respectively, where ‘a’ is the lattice constant and λ is the incident wavelength. The corresponding operating frequency bandwidths are calculated as 40% and 50% for the beam steering and afocal zooming applications, respectively. LCs are inexpensive materials and work under low voltage/power conditions. This feature can be used for designing an electro–optic GRIN PC device that has the potential for use in a wide variety of optical applications.

An ellipsometric analysis to model the order-disorder transition in Au-SiO2 nano-granular thin films induced by thermal annealing

We present an ellipsometric analysis to model the order-disorder transition in nano-granular gold embedded in a silica matrix (Au-SiO2). The optical measurements were performed by means of Reflection Spectroscopic Ellipsometry (RSE) over the spectral wavelength range 300–2500 nm. Upon thermal annealing of Au-SiO2 in the temperature range of 200 to 800 °C, a clear order-disorder textural transition in the film is exhibited. Analyzing the surface roughness by atomic force microscopy (AFM), the as-prepared film shows a narrow height distribution peak around ~3 nm, which reveals a good uniformity of the particles size. When the annealing temperature increases, the particles increasingly tend to coalesce into bigger sizes leading to non-homogeneous films showing increasingly larger surface roughness. We systematically determined the evolution of the film surface roughness parameters by using the AFM cumulative height distribution, which was introduced in RSE in order to evaluate the effective optical constants of the Au–SiO2 films, and to numerically fit the recorded Ψ, Δ and T spectra using a multiple Gaussian oscillators model. As a result, a reliable determination of the Au-SiO2 effective thicknesses and optical constants was achieved. Additionally, we fitted the experimental data to the Maxwell-Garnett (MG) effective medium approximation (EMA). It is shown that MG-EMA does not fit for the lower annealing temperature due to the particle self-organization. However, when the particles disorder takes place, as a consequence of the annealing temperature increase, the MG-EMA fit is increasingly improved. All in all, a clear evidence of the order-disorder transition in the Au-SiO2 nano-granular system induced by thermal annealing is provided.

Terahertz dielectric properties of multiwalled carbon nanotube/polyethylene composites

The terahertz dielectric properties of multiwalled carbon nanotube/polyethylene (MWCNT/PE) composites prepared in different ways and with various contents of carbon nanotubes have been measured by terahertz time-domain spectroscopy. The experimental dielectric susceptibilities were modeled within effective medium approximation. The MWCNTs with average diameter of 9 nm produced by ethylene decomposition over FeCo catalyst were used in the experiments. Two types of composites were prepared by various mechanical mixing of MWCNT and polyethylene powders. The other two types of composites were fabricated employing ethylene polymerization on the MWCNTs before mechanical mixing with polyethylene powder. The samples with MWCNT concentration of 0.1, 0.5, 1 and 4 wt. % were prepared for each composite type. The measured dielectric susceptibilities were higher for composites made of nanotubes with preliminary polymerization of ethylene as compared to the composites produced by just mechanical mixing at equal concentrations of MWCNTs. It was also found that the dielectric susceptibilities of the MWCNT/PE composites can be satisfactory described within Maxwell–Garnett effective medium approximation at sufficient levels (>0.5–1 wt. %) of MWCNT contents. The obtained results confirm the possibility to produce MWCNT/PE composite materials with desired dielectric properties in terahertz range.

Adapting Bobbert-Vlieger model to spectroscopic ellipsometry of gold nanoparticles with bio-organic shells.

We investigate spectroscopic imaging ellipsometry for monitoring biomolecules at surfaces of nanoparticles. For the modeling of polarimetric light scattering off surface-adsorbed core-shell nanoparticles, we employ an extension of the exact solution for the scattering by particles near a substrate presented by Bobbert and Vlieger, which offers insight beyond that of the Maxwell-Garnett effective medium approximation. Varying thickness and refractive index of a model bio-organic shell results in systematic and characteristic changes in spectroscopic parameters [Formula: see text] and [Formula: see text]. The salient features and trends in modeled spectra are in qualitative agreement with experimental data for antibody immobilization and fibronectin biorecognition at surfaces of gold nanoparticles on a silicon substrate, but achieving a full quantitative agreement will require including additional effects, such as nanoparticle-substrate interactions, into the model.

Optics of water microdroplets with soot inclusions: Exact versus approximate results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

Correlation between the free volume and thermal conductivity of porous poly(vinyl alcohol)/reduced graphene oxide composites studied by positron spectroscopy

Light-weight porous poly(vinyl alcohol) (PVA)/reduced graphene oxide (rGO) composites were prepared by freeze-drying method. The effects of doping rGO nanosheets on the free volume and the thermal conductivity were systematically investigated. Experimental results indicated that the free volume decreased after addition of rGO due to the interfacial interaction between rGO and PVA, such as hydrogen bond. The thermal conductivity increased nearly linearly with rGO content. In order to understand the mechanism of thermal conductivity enhancement, the thermal conductivity was calculated using different kinds of models, including parallel model, series model and Maxwell-Garnett effective medium approximation (EMA), which were then compared with experimental result. The difference value between the experimentally measured thermal conductivity and the EMA theoretically calculated result was closely associated with interfacial interaction, revealing that the better the dispersion of rGO, the stronger the interfacial interaction, and the larger the thermal resistance and the lower the relative thermal conductivity. A direct relationship between the fractional free volume and the thermal conductivity has been obtained, suggesting that the interfacial free volume plays an important role in determining phonon scattering and the thermal conductivity of composites.

Ellipsometry study on Pd thin film grown by atomic layer deposition with Maxwell–Garnett effective medium approximation model

Maxwell–Garnett effective medium approximation (MG-EMA) model is chosen to study Pd ultrathin film grown on Si substrate, as well as its growth on self-assembled monolayers (SAMs) modified substrate respectively. The general oscillator (GO) model with one Drude and two Lorentz oscillators is firstly applied to fix the optical constants of Pd. Compared with Pd bulk model, MG-EMA model with GO is more reliable to predict the film thickness verified by X-ray reflection test. The stable growth rate on Si substrate reveals our methods are feasible and the quartz crystal microbalance measurement confirms the stability of the ALD chamber. For Pd coverage, MG-EMA fitting result is similar to the statistical computation from scanning electron microscope when Pd ALD cycles are over 400, while large bias exists for cycles under 400, might be due to that air is not the proper filling medium between nanoparticles. Then we change the filling medium into SAMs as a comparison, better fitting performance is obtained. It is demonstrated that the filling medium between nanoparticles is important for the application of MG-EMA model.

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.

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

Ultrathin noble metal films have attracted lots of attentions in fuel cell catalysts, hydrogen storage, emission control, etc. Among many synthesis methods, atomic layer deposition (ALD) is a powerful one to fabricate ultrathin films with great precision [1]. The measurement of such noble metal films is quite important to both understand the initial growth behavior and guide the film fabrication process. Spectroscopic ellipsometry (SE) is a fast and non-destructive thin film characterization technique with atomic sensitivity [2]. The initial growth of noble metals, however, is in island growth mode and bulk metal model could not correlate with such structures. Similar structures have been reported by the Maxwell-Garnett Effective medium approximation (MG-EMA) model to study the optical properties of Au, Ag thin films [3-4]. In this paper, we choose the MG-EMA model with General oscillator (GO) to study the size and volume fraction. In this study, MG-EMA model has been chosen to study Pd ultrathin film grown on Si substrate, as well as its growth on self-assembled monolayers (SAMs) modified substrate respectively. The GO model with one Drude and two Lorentz oscillators is firstly applied to fix the optical constants of Pd. Compared with Pd bulk model, MG-EMA model with GO is more reliable to predict the film thickness verified by X-ray reflection test. The stable growth rate on Si substrate reveals our methods are feasible and is in accordance with the quartz crystal microbalance measurement. For Pd coverage, MG-EMA fitting result is similar with the statistical computation from scanning electron microscope when cycles of Pd ALD cycles are over 400, while large bias exists for cycles under 400, might be due to that air is not the proper filling medium between nanoparticles. Then we change the filling medium into SAMs as a comparison, better fitting performance is obtained. It is demonstrated that the filling medium between nanoparticles is important for the application of MG-EMA model.

Dielectric engineering of Ge nanocrystal/SiO2 nanocomposite thin films with Ge ion implantation: Modeling and measurement

Abstract Ge nanocrystal (nc-Ge) embedded SiO 2 nanocomposite thin films have been synthesized with the ion implantation technique. The distribution profile of nc-Ge in the SiO 2 matrix can be tailored by varying the implantation energy and dose in the Ge ion implantation process; thus the effective dielectric constant of the nc-Ge/SiO 2 nanocomposite thin films can be engineered. The effective metal–oxide-semiconductor (MOS) capacitance of the nanocomposite thin films has been calculated using the sub-layer model and the Maxwell–Garnett effective medium approximation, taking the reduced dielectric constant corresponding to the nanometer size of nc-Ge into account. On the other hand, capacitance–voltage measurements on the MOS structures based on the nc-Ge/SiO 2 thin films have been conducted to extract the capacitance experimentally. The modeling and measurement results have shown good agreement, suggesting that the nanocomposite dielectric engineering can be easily realized through the energy- and dose-controlled Ge + implantation technique.

Plasmonic Heavily-Doped Semiconductor Nanocrystal Dielectrics: Making Static Photonic Crystals Dynamic

In this work we introduce photonic devices with dynamically modifiable transmission properties through the combination of the transfer matrix method, the Drude model, and the Maxwell-Garnett effective medium approximation. Heavily doped semiconductor nanocrystal layers with tunable plasmonic near-infrared (NIR) properties are embedded as dielectrics into the otherwise invariable one-dimensional photonic crystals. A selective tuning of the localized surface plasmon resonance in the NIR modifies the refractive index contrast in the photonic structure, consequently affecting the intensity and position of the photonic band in the visible spectral range. The resulting possibility to dynamically modify the transmission properties in the visible and NIR highlights their application for sensing, tunable light filtering, or electrochromic devices.

Photothermal Characterization of Thermochromic Materials for Tunable Thermal Devices

A detailed infrared study of the semiconductor-to-metal transition (SMT) in a vanadium dioxide \((\hbox {VO}_{2})\) film deposited on a silicon wafer is presented. The \(\hbox {VO}_{2}\) phase transition is studied in the mid-infrared (MIR) region by analyzing the transmittance and the reflectance measurements, and the calculated emissivity. The temperature behavior of the emissivity during the SMT puts into evidence the phenomenon of the anomalous absorption in \(\hbox {VO}_{2}\) which has been explained by applying the Maxwell-Garnett effective medium approximation theory, together with a strong hysteresis phenomenon, both useful to design tunable thermal devices. Photothermal radiometry has been applied in order to study the changes in the modulated emissivity induced by a laser. Experimental results show how the use of these techniques represent a good tool for a quantitative measurement of the optothermal properties of vanadium dioxide-based structures.

Si nanocrystal-based triple-layer anti-reflection coating for Si solar cells

A triple-layer anti-reflection coating (TL-ARC) with Si nanocrystals (nc-Si)-dielectric nanocomposite thin film structure is proposed for Si solar cells. The TL-ARC has a graded refractive index (RI) profile of high RI, medium RI, and low RI. Such RI profile is achieved with the structure consisting of a Si3N4 layer embedded with high concentration of nc-Si and another Si3N4 layer embedded with low concentration of nc-Si and a SiO2 layer. The design of the TL-ARC is carried out with the calculation of the effective indices of the high-RI and medium-RI layers with the Maxwell-Garnett effective medium approximation model. Due to the photoluminescence properties of nc-Si embedded in Si3N4 matrix, the TL-ARC has the inherent capability of down-converting ultraviolet photons to low-energy photons that are useful to Si solar cells. The deposition of the TL-ARC on Si solar cell is fabricated with plasma enhanced chemical vapor deposition in a single process step. The performance enhancement of Si solar cells by the TL-ARC has been demonstrated by experiments.

Optical modeling of multilayered coatings based on SiC(N)H materials for their potential use as high-temperature solar selective absorbers

SiCH thin films grown from Ar/tetramethylsilane plasmas (PECVD) were evaluated as absorber layers in selective coatings for high-temperature solar receivers. SiCH coatings are used in thermomechanical applications because of their good thermal stability. A SiCH film with an absorption index k(430nm)=0.11 was taken as a reference for optical simulations of refractory metal–SiCH multilayer stacks and cermets. The transfer matrix method and Maxwell–Garnett effective medium approximation were used to calculate the spectral reflectance and transmittance of the selective absorbers. Their solar absorptance and thermal emittance were also deduced. A seven-layer stack with alternating metal and SiCH layers was found to present a simulated solar absorptance of 0.92 and thermal emittance of 0.08 at 500°C.

Temperature dependent optical properties of Si nanocrystals embedded in SiO2 matrix

The optical properties of Si nanocrystals (nc-Si) with different sizes (2∼5 nm) embedded in a SiO2 matrix synthesized by the SiOx/SiO2 superlattice approach were studied in a temperature range from room temperature to 600 K by spectroscopic ellipsometry. The Maxwell–Garnett effective medium approximation and Lorentz oscillator model were employed to extract the dielectric function of nc-Si. The results show that the temperature dependence of optical properties of nc-Si is sensitive to its size. An empirical expression of Varshni approximation was obtained to characterize the band-gap energy change of nc-Si at different temperatures.