Bruggeman Effective Medium Approximation Research Articles

A hybrid effective medium description for nanoporous gold films and thickness-mediated control of optical absorption.

With the increasing demand for sensing platforms operating across UV, visible, and near-infrared wavelengths, nanoporous gold has emerged as an ideal substrate for rapid, quantitative detection of analytes with excellent specificity and high sensitivity. This study investigates thickness-mediated compositional changes and their impact on scattering characteristics of thin nanoporous gold films fabricated using selective chemical etching. Specifically, we observe thickness-induced morphological and structural changes across different fabricated samples from 25 to 100 nm in thickness. Upon their optical characterization across UV-VIS-NIR spectral regime, we notice that the constitutional differences among samples manifest distinctively & deterministically in their total optical scattering response. In order to gain insights into these observed scattering responses and to fathom the subtle connections between structural properties of NPG films and their optical response, a hybrid theoretical model comprising Maxwell-Garnett & Bruggeman effective medium approximations has been adopted. Our approach not only allows to appropriately account for the inhomogeneous nature of these films, but also corroborates well with the atomic force microscopy characterizations of the fabricated samples. Furthermore, tracing such a theoretical model is important as it helps in systematically ascertaining additional loss terms emerging in the complex dielectric function of films due to their nanoscale porosity & roughness, permitting a good reproduction of measured optical spectra. We believe, our approach will not only facilitate accurate regulation of losses in NPG thin films but will also aid in deriving customized optical performance from them, thereby advancing their potential applications in sensing and beyond.

Optical properties of yttria-stabilized zirconia from spectroscopic ellipsometry

Complex dielectric function (ɛ = ɛ1 + iɛ2) spectra of a heat treated single crystal yttria-stabilized zirconia (YSZ) have been determined over a spectral range of 0.03–8.5 eV using spectroscopic ellipsometry. Spectra are collected using three instruments covering different parts of the measured spectrum. The YSZ sample is modeled as a semi-infinite bulk crystal covered by a surface layer described by a Bruggeman effective medium approximation of equal parts YSZ and void.

Dendritic Ag@c-Si structure for influenza A virus detection by SERS and machine learning

The combination of Surface-enhanced Raman Scattering (SERS) method and machine learning algorithms has been successfully demonstrated for the detection and differentiation of influenza A virus in buffer medium. Dendritic Ag nanostructures on single-crystal Si wafer have been proposed as SERS-active substrates, which are fabricated using a low-cost and reproducible AgNO3 reduction method. Depending on the time of Ag deposition, structures of different morphologies were obtained. These structures were studied by spectroscopic ellipsometry (SE). To analyze the spectra obtained by SE, we used the Bruggeman effective medium approximation to determine the volume fraction and height of the metal, the Drude model to describe free electrons, the Tauc-Lorentz model to describe the influence of interband transitions, as well as Lorentz model and Gauss model to describe localized surface plasmon resonance (LSPR). SERS was achieved through LSPR excitation and the presence of “hot spots” in the regions around the tips and in the spaces between close-packed dendritic Ag nanostructures. The sample with the most developed surface is the most promising for SERS, since the spectral position of the LSPR is at 658 nm, which is close to the excitation wavelength of the He–Ne laser. The SERS spectra of influenza A virus in buffer medium are difficult to distinguish, so a machine learning algorithms (principal component analysis and support vector machine) were used to directly classify them. For the sample with the most developed morphology, the detection accuracy of influenza A virus was 76.6 ± 4.2 % at a total protein concentration in the test analyte of 300 μg/ml (according to the Lowry method).

Tuning of the Effective Refractive Index of Crystalline Si Thin Films with Controlled Modification of Nanohole Dimensions By Dry-Etching

Silicon thin films with holes are composite materials with noteworthy optical properties that can be controllably fabricated by state-of-the-art Si process technologies. For light with wavelengths larger than the hole sizes and spacing, typically by a factor of 10, the perforated Si thin films behave like an effective (refractive index) medium. Under these conditions, the optical properties of the films can be modelled by the effective medium approximation (EMA). By manipulating the volumetric air fraction (holes) of such films, the refractive index can be modified accordingly. Such a property can be exploited to tune the index contrast in various photonic devices such as filters and waveguides.This work presents a novel scalable method that combines charged sphere colloidal lithography (CSCL) and dry-etching to pattern Si thin films. We demonstrate controlled tuning of the effective refractive index by controlled lateral dry-etching of the holes. The fabricated nanoholes are spatially disordered in a 220 nm thick crystalline Si film. CSCL is performed using polystyrene particles of 60 (P60) and 100 (P100) nm diameter. The CSCL step results in a disordered arrangement of the particles with average spatial separations of 2-4 times their diameter. Using Cr as a mask, cylindrical holes are etched into Si by inductively coupled plasma-reactive ion-etching (ICP-RIE) using a pseudo-Bosch process. An additional isotropic ICP-RIE dry-etch step is introduced to widen the holes in a controlled manner, utilizing CF4 and O2 gas mixture. Importantly, this hole-widening step is time-controlled to ensure that the holes do not overlap laterally. Finally, the Cr mask is removed by wet-etching.By analyzing scanning electron microscopic (SEM) images, we estimate the lateral etch rates for the P60 and P100 samples are approximately 0.76 nm/s and 0.52 nm/s, respectively. Using this process, the average hole diameter can be increased systematically up to circa 68-97%, compared to their original diameters, while avoiding overlap. The effective refractive index of the perforated Si thin films is determined using the optical air fill factor obtained from modelling the spectroscopic ellipsometry data with Bruggeman effective medium approximation. The determined optical air fill factor varies from circa 20% to 50% with hole widening. The ellipsometry data provides the true air fill factor of the samples directly; SEM analysis could also be used, however, it is complex and cannot determine the actual porosity of the films. The ellipsometry results show that the determined refractive index is constant in the 1500 - 4000 nm wavelength range. The refractive index decreases from 3.42 for unstructured Si film to 2.9 and 2.7 for the as-etched perforated Si films of P60 and P100 samples, respectively. With controlled lateral etching of the holes, the effective refractive index systematically decreases further to approximately 2.1 for the P60 and P100 samples, which is a 39% reduction compared to Si refractive index. The determined effective indices represent averaged values accounting for possible structural birefringence, which can be used as a guideline to design photonic devices such as filters.The presented findings indicate that the effective refractive index of perforated Si thin films can be engineered by controlling the lateral dimensions of holes. While this conclusion relates specifically to crystalline Si thin films, the same concept may also be applied to other perforated dielectric thin films. Figure 1

The Optical Properties of Thin Film Alloys of ZnO, TiO2 and ZrO2 with Al2O3 Synthesised Using Atomic Layer Deposition

In this work, the results of ellipsometric studies of thin films of broadband oxides (ZnO, TiO2, ZrO2) and broadband oxides doped with Al2O3 (Al2O3–ZnO, Al2O3–TiO2, Al2O3–ZrO2) are presented. All layers have been produced using the atomic layer deposition method. Ellipsometric studies were performed in the wavelength range of 193–1690 nm. Sellmeier and Cauchy models were used to describe the optical properties of the tested layers. Dispersion dependencies of refractive indices were determined for thin layers of broadband oxides on silicon substrates, and then for layers of Al2O3 admixture. The EDX investigations enabled estimation of the composition of the alloys. The Bruggeman effective medium approximation (EMA) model was used to determine the theoretical dependencies of the dispersion refractive indices of the studied alloys. The refractive index values determined using the Bruggeman EMA model are in good agreement with the values determined from the ellipsometric measurements. The doping of thin layers of ZnO, ZrO2 and TiO2 with Al2O3 enables the creation of anti-reflective layers and filters with a specific refractive index.

Influence of microstructure on dielectric function and plasmonic properties of silver nanoparticles grown by solid state dewetting: a spectroscopic ellipsometry study

This work reports the microstructure influence on dielectric function and plasmonic properties of silver nanoparticles (Ag NPs). Ag NPs with varying microstructures were grown on corning glass substrate by solid-state dewetting (SSD) of sputtered silver thin films deposited by varying RF power. Dielectric function and plasmonic properties of Ag NPs were investigated from spectroscopic ellipsometry (SE) data using a quite unique model in terms of the combination of different oscillators. Drude–Lorentz model along with two Gauss oscillators was used to account for intraband, interband transitions and different modes of localized surface plasmon resonance (LSPR) of Ag NPs. It was observed that peak of imaginary part of pseudo dielectric function, which is due to LSPR of Ag NPs, shifted towards the lower energy at higher RF power due to increase in thickness of precursor films which subsequently resulted in to increase in particle size. A shift in the LSPR peak in absorbance spectra in UV–Vis-NIR spectroscopy was also observed. No LSPR peak is observed in SE or UV–Vis absorbance spectra for thick films deposited at high RF power due to the presence of continuous silver film even after annealing. This change in microstructure from nanoparticle formation to continuous films is also reflected in the values of void fraction and surface roughness calculated from SE using Bruggeman Effective Medium Approximation (BEMA). Field Emission Electron Microscopy (FESEM), Atomic Force Microscopy (AFM), and X-ray diffraction (XRD) were used to probe the microstructure of Ag NPs. Root mean square (RMS) roughness evaluated from AFM matched well with surface roughness measured from SE.

Optical Properties of Reactive RF Magnetron Sputtered Polycrystalline Cu3N Thin Films Determined by UV/Visible/NIR Spectroscopic Ellipsometry: An Eco-Friendly Solar Light Absorber

Copper nitride (Cu3N), a metastable poly-crystalline semiconductor material with reasonably high stability at room temperature, is receiving much attention as a very promising next-generation, earth-abundant, thin film solar light absorber. Its non-toxicity, on the other hand, makes it a very attractive eco-friendly (greener from an environmental standpoint) semiconducting material. In the present investigation, Cu3N thin films were successfully grown by employing reactive radio-frequency magnetron sputtering at room temperature with an RF-power of 50 W, total working gas pressure of 0.5Pa, and partial nitrogen pressures of 0.8 and 1.0, respectively, onto glass substrates. We investigated how argon affected the optical properties of the thin films of Cu3N, with the aim of achieving a low-cost solar light absorber material with the essential characteristics that are needed to replace the more common silicon that is currently in present solar cells. Variable angle spectroscopic ellipsometry measurements were taken at three different angles, 50∘, 60∘, and 70∘, to determine the two ellipsometric parameters psi, ψ, and delta, Δ. The bulk planar Cu3N layer was characterized by a one-dimensional graded index model together with the combination of a Tauc–Lorentz oscillator, while a Bruggeman effective medium approximation model with a 50% air void was adopted in order to account for the existing surface roughness layer. In addition, the optical properties, such as the energy band gap, refractive index, extinction coefficient, and absorption coefficient, were all accurately found to highlight the true potential of this particular material as a solar light absorber within a photovoltaic device. The direct and indirect band gap energies were precisely computed, and it was found that they fell within the useful energy ranges of 2.14–2.25 eV and 1.45–1.71 eV, respectively. The atomic structure, morphology, and chemical composition of the Cu3N thin films were analyzed using X-ray diffraction, atomic force microscopy, and energy-dispersive X-ray spectroscopy, respectively. The Cu3N thin layer thickness, profile texture, and surface topography of the Cu3N material were characterized using scanning electron microscopy.

Investigation of Electrochromic, Combinatorial TiO2-SnO2 Mixed Layers by Spectroscopic Ellipsometry Using Different Optical Models.

We determined the optimal composition of reactive magnetron-sputtered mixed layers of Titanium oxide and Tin oxide (TiO2-SnO2) for electrochromic purposes. We determined and mapped the composition and optical parameters using Spectroscopic Ellipsometry (SE). Ti and Sn targets were put separately from each other, and the Si-wafers on a glass substrate (30 cm × 30 cm) were moved under the two separated targets (Ti and Sn) in a reactive Argon-Oxygen (Ar-O2) gas mixture. Different optical models, such as the Bruggeman Effective Medium Approximation (BEMA) or the 2-Tauc-Lorentz multiple oscillator model (2T-L), were used to obtain the thickness and composition maps of the sample. Scanning Electron Microscopy (SEM) with Energy-Dispersive X-ray Spectroscopy (EDS) has been used to check the SE results. The performance of diverse optical models has been compared. We show that in the case of molecular-level mixed layers, 2T-L is better than EMA. The electrochromic effectiveness (the change of light absorption for the same electric charge) of mixed metal oxides (TiO2-SnO2) that are deposited by reactive sputtering has been mapped too.

Implications of Electron Transport Layer and Back Metal Contact Variations in Tin–Lead Perovskite Solar Cells Assessed by Spectroscopic Ellipsometry and External Quantum Efficiency

The structural and optical properties of hybrid organic-inorganic metal halide perovskite solar cells are measured by spectroscopic ellipsometry to reveal an optically distinct interfacial layer among the back contact metal, charge transport, and absorber layers. Understanding how this interfacial layer impacts performance is essential for developing higher performing solar cells. This interfacial layer is modeled by Bruggeman effective medium approximations (EMAs) to contain perovskite, C60, BCP, and metal. External quantum efficiency (EQE) simulations that consider scattering, electronic losses, and the formation of nonparallel interfaces are created with input derived from ellipsometry structural-optical models and compared with experimental EQE to estimate optical losses. This nonplanar interface causes optical losses in short circuit current density (JSC) of up to 1.2 mA cm-2. A study of glass/C60/SnO2/Ag or Cu and glass/C60/BCP/Ag film stacks shows that C60 and BCP mix, but replacing BCP with SnO2 can prevent mixing between the ETLs to prevent contact between C60 and back contact metal and enable the formation of a planar interface between ETLs and back contact metals.

Free carrier plasma edge and plasmonic excitations in heavily doped surface grated n-type Si

Infrared spectroscopic ellipsometry (SE) in the MID IR region was applied at room temperature to heavily doped n++-Si to obtain information about the free carrier plasma edge and plasmonic excitations before and after the Si surface was grated with a period Λ of 294 nm to a nominal depth of 20 nm by using laser lithography. Besides, SE measurements were performed in the NIR-VIS-UV spectral range to validate the optical models for non-grated and grated Si. In the latter case a thin grated layer on silicon surface was alternatively modelled either within Bruggeman effective medium approximation (BEMA) or by treating this layer as an anisotropic thin film (ATF). A model that included SiO2 (2.1 nm), n++-Si substrate and a 24.5 nm-thick ATF for grated layer was found to be good enough to reproduce the obtained ellipsometric parameters in the accessed spectral range. Intraband optical transitions are shown to overwhelmingly contribute to the MID IR dielectric function (DF) below the free carrier plasma edge (FCPE) of non-grated n++-Si. The parameters obtained for conduction electrons from Drude fit to this function agree well with the relevant data reported for Si so far. FCPE of non-grated n++-Si is positioned at 1416 cm−1. For graded layer this value is preserved within determination accuracy. The life time of plasmonic excitations that appeared as a single peak with a perfect Lorentz line-shape in the dielectric energy loss function of non-grated Si and grated Si layer is about 70 fs. Shape induced optical anisotropy, along with presumably conical diffraction that identified itself through a distinct angle-dependent upturn in the reflection spectra of p-polarized light incident upon surface in the plane perpendicular to Λ is behind the whole set of ellipsometric data obtained for n++-Si with subwavelength grating on the surface.

Calculations of adsorption-dependent refractive indices of metal-organic frameworks for gas sensing applications.

Detection of volatile organic compounds (VOCs) is one of the most challenging tasks in modelling breath analyzers because of their low concentrations (parts-per-billion (ppb) to parts-per-million (ppm)) in breath and the high humidity levels in exhaled breaths. The refractive index is one of the crucial optical properties of metal-organic frameworks (MOFs), which is changeable via the variation of gas species and concentrations that can be utilized as gas detectors. Herein, for the first time, we used Lorentz-Lorentz, Maxwell-Ga, and Bruggeman effective medium approximation (EMA) equations to compute the percentage change in the index of refraction (Δn%) of ZIF-7, ZIF-8, ZIF-90, MIL-101(Cr) and HKUST-1 upon exposure to ethanol at various partial pressures. We also determined the enhancement factors of the mentioned MOFs to assess the storage capability of MOFs and the biosensors' selectivity through guest-host interactions, especially, at low guest concentrations.

Hard-Templated Porous Niobia Films for Optical Sensing Applications

Porous Nb2O5 films obtained by a modified hard-template method were studied and their optical and sensing properties were optimized in order to find applications in chemo-optical sensing. Porous films were prepared by following three steps: liquid mixing of niobium sol and SiO2 colloids in different volume fractions, thermal annealing of spin-coated films for formation of a rigid niobia matrix, and selective removal of silica phase by wet etching thus generating free volume in the films. The morphology and structure of the films were studied using transmission electron microscopy and selected area electron diffraction, while their optical and sensing properties were estimated using UV-VIS-NIR reflectance measurements in different ambiences such as air, argon and acetone vapors and nonlinear curve fitting of the measured reflectance spectra. Bruggeman effective medium approximation was applied for determination of the volume fraction of silica and air in the films, thus revealing the formation of porosity inside the films. For further characterization of composite films, their water contact angles were measured and finally conclusions about the impact of initial chemical composition and etching duration on properties of the films were drawn.

Spectro-ellipsometric probing of wetting, nucleation, and dot/island formation during photo-excited chemical vapor deposition of Ge on SiO2 substrate

The morphological evolution of Ge layers growing on the SiO2/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 SiO2 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 SiO2 (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)

Reflection Coefficient Calculation of a Structure Including a Porous Silicon Layer with Transfer Matrix Method and FDTD

Porous silicon is an important material for a variety of application area such as anti-reflective coating for solar cells. Today, solar cell market is mostly dominated by silicon based solar cells. Porous silicon thin films are easy to fabricate and it is compatible with silicon technology. Designing porous silicon anti-reflective coating layers is a critical issue to enhance silicon based solar cell performance. There are several methods to calculate reflection coefficient of porous silicon thin layers. In this study, transfer matrix method and finite-difference time-domain method are used to calculate reflection coefficient of porous silicon thin layers. Because finite-difference time-domain method gives more accurate results, the results obtained with finite-difference time-domain method are used to control the results obtained with transfer matrix method. In transfer matrix method, refractive indices of the porous silicon layers are calculated with Bruggeman effective medium approximation.

Characterization of amorphous carbon films from 5 nm to 200 nm on single-side polished a-plane sapphire substrates by spectroscopic ellipsometry

In this work, a series of amorphous carbon films were deposited on a-plane sapphire substrates by magnetron sputtering with deposition time from 15 min to 8 h, in order to investigate the thickness and optical properties in the process of growth in a non-destructive way. They were characterized by using Mueller matrix spectroscopic ellipsometry together with topography profilometry and Raman spectroscopy. Two models of a Bruggeman effective medium approximation model and a single Cody-Lorentz oscillator model have been proposed to fit films thickness and optical constants from Ultraviolet (UV) to visible (210 nm–800 nm), and Transmission Electron Microscope (TEM) has been used to verify the proposed model for thickness fitting results. The optical constants of the amorphous carbon film have been determined by fitting together all measurements in samples deposited for 2 h or more, with the film thickness being the only sample-independent parameter. The results show that the thickness from 5 nm to 200 nm can be characterized in a nondestructive way although there is a relatively large thickness error compared with the Transmission Electron Microscope results for thin films (d < 20 nm) when the deposition time is less than 2 h because of the nonuniform deposition in the beginning. The relative error between the TEM and Spectroscopic Ellipsometry results can be reduced to 1% after 4 h sample. That means spectroscopic ellipsometry can still provide an indicator for the trend of thickness growth.

Investigation of Combinatorial WO3-MoO3 Mixed Layers by Spectroscopic Ellipsometry Using Different Optical Models.

Reactive (Ar-O2 plasma) magnetron sputtered WO3-MoO3 (nanometer scaled) mixed layers were investigated and mapped by Spectroscopic Ellipsometry (SE). The W- and Mo-targets were placed separately, and 30 × 30 cm glass substrates were slowly moved under the two (W and Mo) separated targets. We used different (oscillator- and Effective Medium Approximation, EMA-based) optical models to obtain the thickness and composition maps of the sample layer relatively quickly and in a cost-effective and contactless way. In addition, we used Rutherford Backscattering Spectrometry to check the SE results. Herein, we compare the “goodness” of different optical models depending upon the sample preparation conditions, for instance, the speed and cycle number of the substrate motion. Finally, we can choose between appropriate optical models (2-Tauc-Lorentz oscillator model vs. the Bruggeman Effective Medium Approximation, BEMA) depending on the process parameters. If one has more than one “molecular layer” in the “sublayers”, BEMA can be used. If one has an atomic mixture, the multiple oscillator model is better (more precise) for this type of layer structure.

Multilevel effective material approximation for modeling ellipsometric measurements on complex porous thin films

Abstract Catalysts are important components in chemical processes because they lower the activation energy and thus determine the rate, efficiency and selectivity of a chemical reaction. This property plays an important role in many of today’s processes, including the electrochemical splitting of water. Due to the continuous development of catalyst materials, they are becoming more complex, which makes a reliable evaluation of physicochemical properties challenging even for modern analytical measurement techniques and industrial manufacturing. We present a fast, vacuum-free and non-destructive analytical approach using multi-sample spectroscopic ellipsometry to determine relevant material parameters such as film thickness, porosity and composition of mesoporous IrOx–TiOy films. Mesoporous IrOx–TiOy films were deposited on Si wafers by sol–gel synthesis, varying the composition of the mixed oxide films between 0 and 100 wt%Ir. The ellipsometric modeling is based on an anisotropic Bruggeman effective medium approximation (a-BEMA) to determine the film thickness and volume fraction of the material and pores. The volume fraction of the material was again modeled using a Bruggeman EMA to determine the chemical composition of the materials. The ellipsometric fitting results were compared with complementary methods, such as scanning electron microscopy (SEM), electron probe microanalysis (EPMA) as well as environmental ellipsometric porosimetry (EEP).

Effective Optical Properties of Laterally Coalescing Monolayer MoS2.

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) exhibit compelling dimension-dependent exciton-dominated optical behavior influenced by thickness and lateral quantum confinement effects. Thickness quantum confinement effects have been observed; however, experimental optical property assessment of nanoscale lateral dimension monolayer TMDCs is lacking. Here, we employ ex situ spectroscopic ellipsometry to evaluate laterally coalescing monolayer metalorganic chemical vapor deposited MoS2. A multisample analysis is used to constrain Bruggeman and Maxwell-Garnett effective medium approximations and the effective dielectric functions are derived for laterally coalesced and uncoalesced MoS2 films (∼10-94% surface coverage for ∼10-140 nm lateral grain sizes). This analysis demonstrates the ability to probe MoS2 optical exciton behavior at growth-relevant grain sizes in relation to chemical vapor nucleation density, ripening, and lateral growth conditions. Our analysis is pertinent toward expected in situ epitaxial 2D TMDC film growth metrology to enable the facile development of monolayer films with targeted process-dependent optical properties.

Revealing plasmon-phonon interaction in nanocrystalline MgFe2O4 spinels by far-infrared reflection spectroscopy

Room-temperature far-infrared reflectivity spectra of nanocrystalline, partially inverse MgFe2O4 were investigated. MgFe2O4 samples were prepared by sol-gel method and sintered at three different temperatures (400, 600 and 800 °C). Raman spectroscopy was employed to estimate the degree of inversion in the sintered samples. The degree of inversion was found to increase from 0.52 to 0.74 as the sintering temperature increased from 400 °C to 800 °C. The reflectivity spectra, besides the four infrared modes characteristic for spinels (ν1, ν2, ν3, ν4), revealed the presence of free carriers. Plasmon-longitudinal optical (LO) phonon interaction was analyzed using factorized coupled and decoupled plasmon-phonon models, combined with the Bruggeman effective medium approximation. From these models it was obtained that the ν1 and ν3 phonon modes are more strongly coupled with plasmons than the ν2 mode. A potential mechanism of plasmon-phonon interaction in inverse MgFe2O4 spinel has been discussed.

Spectroscopic Ellipsometry Study on Tuning the Electrical and Optical Properties of Zr-Doped ZnO Thin Films Grown by Atomic Layer Deposition.

This work reports the ellipsometry analysis of atomic layer deposition (ALD) films of ZnO doped with Zr to determine parameters like free carrier concentration and mobility. Thin films of zinc oxide (ZnO) and Zr-doped ZnO of thickness ∼100 nm were prepared by atomic layer deposition on sapphire, SiO2/Si(100), and Si(100) substrates. Variable-angle spectroscopic ellipsometry was used to study their optical properties in the 0.5–3.5 eV spectral range. The optical constants were accurately obtained using a model that combines Drude and Tauc–Lorentz oscillators with Bruggeman effective medium approximations, allowing the inclusion of a roughness layer in the optical model. The effect of Zr doping (ca. 1.9–4.4 atom %) was then investigated in both as-prepared samples and samples annealed in the temperature range of 100–300 °C. All of the films exhibited good optical transparency (ca. 70–90% in the visible region). For doping levels below 2.7 atom %, the real part of the dielectric permittivity reveals a semiconductor-to-metal transition in the near-infrared (NIR) region, as the permittivity goes from positive to negative. Besides, the plasma energy increases with increasing Zr concentration, and both resistivity and carrier concentration exhibit slightly parabolic behaviors, with a minimum of ∼1.5 × 10–3 Ω cm and a maximum of 2.4 × 1020 cm–3, respectively, at the same critical Zr concentration (2.7 atom %). In contrast, the carrier mobility decreases rapidly from 76.0 to 19.2 cm2/(V s) with increasing Zr content, while conductivities and carrier mobilities worsen when the annealing temperature increases, probably due to the segregation of ZnO crystals. Finally, the optical band gap is very stable, revealing its interesting independence of substrate composition and annealing temperature, as it collapses to a single master curve when band gap energy is plotted versus free carrier concentration, following the Burstein–Moss effect. Overall, the Zr-doped ZnO films studied here would be a highly desirable system for developing thermally stable transparent conductive oxides (TCOs).