Effective Medium Approximation Model Research Articles

Computational design of isotropic and anisotropic ultralow thermal conductivity polymer foams

Current state-of-the-art commercial polymer thermal insulation foam exhibits a thermal conductivity of 24 mW⸳m−1⸳K−1 (equivalently thermal resistivity of R-6/in.), similar to that of static air. To further optimize building energy efficiency, achieving even lower thermal conductivity is needed, which is, however, highly challenging. This paper presents computational evidence that demonstrates the feasibility of achieving an ultra-low thermal conductivity of less than 14.4 mW⸳m−1⸳K−1 (equivalently R-10/in.) using isotropic and anisotropic foam cell designs. For the isotropic design, we have identified analytical effective medium approximation (EMA) models within the accuracy of ±5% as finite element analysis (FEA) in predicting the effective thermal conductivity of foams with various porosities and filler gases. For the anisotropic design, we have developed and validated new EMA models against FEA in predicting the effective thermal conductivity of general anisotropic cuboids and Voronoi foams. For both isotropic and anisotropic designs, the design spaces for 18, 16, and 14.4 mW⸳m−1⸳K−1 (equivalently R-8, R-9 and R-10/in.) using various filler gases are obtained. It is found that polymer foams can be improved to achieve ultralow thermal conductivity by reducing CO2 concentration, reducing radiation, increasing porosity, and using anisotropic pore geometry. These findings contribute to the development of highly efficient thermal insulation materials, enhancing building energy efficiency and promoting sustainable construction practices.

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry.

In this work, we discuss the precision of the effective medium approximation (EMA) model in the data analysis of spectroscopic ellipsometry (SE) for solid materials with micro-rough surfaces by drawing the regime map. The SE parameters ψ (amplitude ratio) and Δ (phase difference) of the EMA model were solved by rigorous coupled-wave analysis. The electromagnetic response of the actual surfaces with micro roughness was simulated by the finite-difference time-domain method, which was validated by the experimental results. The regime maps associated with the SE parameters and optical constants n (refractive index) and k (extinction coefficient) of the EMA model were drawn by a comparison of the actual values with the model values. We find that using EMA to model micro-rough surfaces with high absorption can result in a higher precision of the amplitude ratio and extinction coefficient. The precisions of ψ, Δ, n and k increase as the relative roughness σ/λ (σ: the root mean square roughness, λ: the incident wavelength) decreases. The precision of ψ has an influence on the precision of k and the precision of Δ affects the precision of n. Changing σ alone has little effect on the regime maps of the relative errors of SE parameters and optical constants. A superior advantage of drawing the regime map is that it enables the clear determination as to whether EMA is able to model the rough surfaces or not.

Effect of temperature and fluid on rock microstructure based on an effective-medium theory

Abstract Temperature and pressure variations during the geologic diagenesis process can lead to complex pore structures in tight rocks. The effective-medium theory, based on the stress–strain relationship in combination with pore structure parameters, can be used to describe the elastic-wave responses of rocks. In this work, the differential effective medium (DEM) and self-consistent approximation (SCA) models are combined to invert the pore-crack spectrum. The Voigt–Reuss–Hill average is used to estimate the elastic moduli of the minerals. Then, based on SCA, the pore structures are incorporated into the rock matrix to create a new host phase. Subsequently, the DEM theory is used to add cracks with different volume fractions and aspect ratios to the host phase. To predict the structure of pores and cracks (crack density and aspect ratio), an objective function is defined as the sum of variances between experimentally measured and predicted wave velocities. The results show that the modeling predictions of P- and S-wave velocities at different temperatures and pressure ratios agree well with the experimental measurements. Variations in pore structure are determined at a zero effective pressure and different temperatures. We analyze the characteristics of how cracks change with variations in temperature and confining pressure, providing a theoretical basis for characterizing the structure of tight rocks.

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.

Manipulating the Thermal Conductivity of the Graphene/Poly(vinyl alcohol) Composite via Surface Functionalization: A Multiscale Simulation.

The reverse non-equilibrium molecular dynamics simulation is used to investigate the influence of functional groups (FGs) on the thermal conductivity of a graphene/poly(vinyl alcohol) (PVA) composite, which considers non-polar (methyl) and polar (hydroxyl, amino, and carboxyl) groups. First, the polar groups can be more effective to improve the interfacial thermal conductivity than the non-polar group. This can be explained well by characterizing the interfacial Coulombic energy, number and lifetime of hydrogen bonds, vibrational density of states, and integrated autocorrelation of the interfacial heat power. Moreover, the hydroxyl group can improve the interfacial thermal conductivity more than the other groups, which can be rationalized by analyzing the surface roughness of graphene and the radial distribution function of FGs and the PVA chains. However, the introduction of FGs destroys the graphene structure, which consequently reduces the intrinsic thermal conductivity. Furthermore, by adopting the effective medium approximation model and finite element method, there exists a critical graphene length where the overall thermal conductivities are equal for the functionalized and pristine graphene. Finally, the distribution state of graphene is emphasized to be more vital in determining the overall thermal conductivity than the generally accepted interfacial thermal conductivity.

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.

Thermal Conductivity and Mechanical Properties of Polymer Composites with Hexagonal Boron Nitride—A Comparison of Three Processing Methods: Injection Moulding, Powder Bed Fusion and Casting

Materials providing heat dissipation and electrical insulation are required for many electronic and medical devices. Polymer composites with hexagonal boron nitride (hBN) may fulfil such requirements. The focus of this study is to compare composites with hBN fabricated by injection moulding (IM), powder bed fusion (PBF) and casting. The specimens were characterised by measuring thermal conductivity, tensile properties, hardness and hBN particle orientation. A thermoplastic polyurethane (TPU) was selected as the matrix for IM and PBF, and an epoxy was the matrix for casting. The maximum filler weight fractions were 65%, 55% and 40% for IM, casting and PBF, respectively. The highest thermal conductivity (2.1 W/m∙K) was measured for an IM specimen with 65 wt% hBN. However, cast specimens had the highest thermal conductivity for a given hBN fraction. The orientation of hBN platelets in the specimens was characterised by X-ray diffraction and compared with numerical simulations. The measured thermal conductivities were discussed by comparing them with four models from the literature (the effective medium approximation model, the Ordóñez-Miranda model, the Sun model, and the Lewis-Nielsen model). These models predicted quite different thermal conductivities vs. filler fraction. Adding hBN increased the hardness and tensile modulus, and the tensile strength at high hBN fractions. The strength had a minimum as the function of filler fraction, while the strain at break decreased. These trends can be explained by two mechanisms which occur when adding hBN: reinforcement and embrittlement.

Role of Electrode Thickness in NiFe Nanogranular Films for Oxygen Evolution Reaction

Nanostructured materials may provide a route to overcome the electrode-limiting performance in water splitting, the oxygen evolution reaction (OER), within the framework of low-cost catalysts search. However, for alloyed NiFe nanostructures, the relationship among the OER efficiency and the electrode physical characteristics (morphology, porosity, size, thickness, or mass loading) is largely unknown. This work introduces a new type of alloyed NiFe (90/10% at) nanogranular electrodes obtained by supersonic cluster beam deposition and investigates the dependence of their catalytic activity toward the OER on the film morphological and stoichiometric properties. The synthesized alloyed NiFe nanoparticles with 0.3–3.8 nm size assemble from the gas phase to form ultrathin film electrodes with thickness in the 15–88 nm range, corresponding to 5–30 μg/cm2 mass loading. The fitting of the optical spectroscopic data by an effective medium approximation model suggests that, independent of the thickness, the films have a 20% porosity and are completely hydroxydated. The resulting catalytic efficiency is independent on the film thickness, while the turnover frequency decreases with increasing electrode loading. These data suggest that an excess of catalyst mass with respect to the OER active sites is deposited in the case of thicker electrodes and sets the 15 nm film as an upper loading limit to maximize the electrocatalyst efficiency. This study represents a crucial step toward thickness optimization of NiFe electrodes to fabricate low-cost OER catalysts.

Optical Properties and Ultrafast Near‐Infrared Localized Surface Plasmon Dynamics in Naturally p‐Type Digenite Films

AbstractCopper chalcogenides are materials characterized by intrinsic doping properties, allowing them to display high carrier concentrations due to their defect‐heavy structures, independent of the preparation method. Such high doping enables these materials to display plasmonic resonances, tunable by varying their stoichiometry. Here, plasmonic dynamics is studied in drop‐cast Cu9S5 (digenite) nanocrystals (NCs) film using ultrafast pump–probe spectroscopy. The NCs are synthesized by thermal annealing of copper foil using chemical vapor deposition (CVD), followed by sonication and drop‐casting of the isolated few‐layered flakes on different substrates. The samples display a broad localized surface plasmon resonance (LSPR) in the near‐infrared (NIR), peaking at 2100 nm. The free carrier response is further confirmed by fitting the linear absorption with a Drude–Lorentz effective medium approximation model. The high temporal resolution allows to measure the relaxation dynamics of the photo‐excited holes, which are dominated by a fast decay (τ1 = 360 ± 20 fs) and correspond to hole–phonon scattering processes, followed by a long‐lived (τ2 > 1 ns) signal associated with phonon–phonon scattering relaxation. These results confirm the possibility of fabricating Cu9S5 films retaining the plasmonic properties of individual NCs, anticipating integrating these films into heterojunctions with suitable hole acceptor materials to build hot‐hole‐transfer‐based optoelectronic devices.

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.

The dual role of interlayer crosslinks leads to an abnormal behavior of interlayer thermal resistance in multilayer graphene

Understanding and controlling the interlayer thermal resistance (ITR) are crucial to the cross-plane thermal transport in multilayer graphene (MLG). Using non-equilibrium molecular dynamics simulations, we show that the ITR of MLG can be effectively tuned by in-plane defects, sp2 and sp3 C–C bond crosslinks. Specifically, with the increase of the in-plane defect density, the ITR initially increases sharply and then almost saturates; while with the increase of the crosslink density, the ITR initially also increases sharply, then peaks and subsequently decreases rapidly to a level that can be even lower than that of pristine MLG. The underlying mechanism for this unexpected variation of ITR with crosslink density is explored through the analyses of the phonon density of states (DOS) and spectral transmission function. It was found that the crosslinks play a dual role: the crosslink-generated in-plane defect enhances phonon scattering and leads to an increase in the ITR, while the interlayer bonding gives rise to a fast phonon transmission pathway and decreases the ITR. An effective medium approximation (EMA) model was proposed to describe the dual role of the crosslinks. This work provides new insight into the thermal transport behavior of crosslinks, which is useful for modulating the cross-plane thermal transport of MLG for the thermal management of MLG-based nanodevices.

Influence of Surface Defects on the Thermal Conductivity of Hexagonal Boron Nitride/Poly(dimethylsiloxane) Nanocomposites: A Molecular Dynamics Simulation.

In this simulation, the reverse nonequilibrium molecular dynamics simulation is employed to explore how the surface defects in hexagonal boron nitride (h-BN) influence the thermal conductivity of poly(dimethylsiloxane) (PDMS)-based composites. First, the interfacial thermal conductivity and the intrinsic thermal conductivity of h-BN are obtained by tuning the defect density, the inhomogeneity of the defect distribution, and the number of h-BN layers. The defects enhance the interfacial thermal conductivity, especially for h-BNs with high inhomogeneity of the defect distribution and multilayer. However, the intrinsic thermal conductivity of h-BN is declined significantly by the defects. They can be explained well by the vibrational density of states of PDMS and h-BNs and their overlap. Then, by combining the effective medium approximation model with the simulation, the overall thermal conductivity of composites is obtained. It exhibits a gradual decrease with increasing defect density or reducing the inhomogeneity of the defect distribution. Meanwhile, the enhancement extent of the overall thermal conductivity by improving the concentration and size of h-BNs depends on the defect density and the defect distribution. Finally, the comparison between the simulation and experiment is discussed. In summary, our work provides some valuable insights into how the defect density, the defect distribution, and the number of layers influence the thermal conductivity of the PDMS-based composite.

Tailoring the microstructure of an oriented graphite flake/Al composite produced by powder metallurgy for achieving high thermal conductivity

An Al matrix composite reinforced with 40 vol% graphite flake (Gf) was developed by powder metallurgy as a promising candidate for thermal management applications. Thermal conductivity (TC) along the orientation direction of the composite sintered at 640 °C was measured to be 452 W/m K, which is approximate to the highest TC value theoretically predicted by effective medium approximation model. The three underlying mechanisms responsible for such TC enhancement were clarified in terms of microstructure characterization. First, heat treatment of as-received Gf under Ar + H2 atmosphere resulted in reduction of defects on the edge contributing to improvement of interface thermal exchange efficiency between Al and Gf. Second, image analysis quantitatively confirmed that a step-by-step die filling process using the spherical powder ensures the perfect orientation of Gf in the Al matrix. Third, it was found that the TC of the composite increases with the sintering temperature from 580 to 640 °C. The formation of a small amount of fine platelet-like Al4C3 at the interface between the side surface of Gf and Al matrix indicates the desirable bonding state for minimizing interfacial thermal resistance, beneficial for the overall TC enhancement. Besides, the relevant coefficient of thermal expansion and bending strength were discussed.

Effective medium approximation based interpretation for Mueller matrix spectra of polydimethylsiloxane gratings

Dielectric corrugated gratings are of considerable interest due to their applications in acousto-optics, quantum electronics, integrated optics, spectroscopy, and holography integrated optics. Rigorous coupled-wave analysis has been widely used for the analysis of dielectric gratings. However, this approach is not only time-consuming and computer intensive but it also does not really promote the physical understanding of the origin of the observed optical behavior. Here, we use Mueller matrix (MM) spectroscopic ellipsometry to systematically study the sinusoidal polydimethylsiloxane grating. We correlate the observed polarization mixing in the Mueller matrix to the underlying physical origin using the physics-based approach. The calculated MM contour plots obtained from a biaxial Bruggemann effective medium approximation model are completed by the presence of Rayleigh-Woods anomalies. The roles of optical interference, geometric anisotropy, and diffraction orders are respectively identified by their different dispersion behavior, with their interactions and couplings highlighted. Such a straightforward procedure provides a new method for analyzing dielectric gratings, which requires considerably less computer power and is directly linked to the physical interpretations.

Optical properties of electrochemically etched N-type silicon wafers for solar cell applications

Abstract The presented experiments and studies are intended for photovoltaic applications of crystalline silicon. This work deals with chemical treatment of the surface of n-type silicon wafers with different resistivity to reduce their reflectivity. Chemical surface treatment of silicon is an alternative method to using the antireflection layer. Optical losses caused by the reflection of light from the surface of the solar cells significantly reduce their efficiency. The investigated samples were prepared by the electrochemical etching method in the solution based on hydrofluoric acid and ethanol. The analysis of the prepared samples is divided into two parts, namely experimental measurements, and theoretical modeling. Experimental measurements are performed using UV-VIS spectroscopy, spectroscopic ellipsometry and SEM microscopy. Theoretical modeling is based on the construction and optimization of theoretical model of optical response (reflectivity and ellipsometric parameters) to determine the effective refractive index and thickness of formed structure. Effective refractive index of studied samples in theoretical model of optical response is based on Looyenga effective medium approximation and Tauc-Lorentz dispersion model.

Facile and scalable fabrication of highly thermal conductive polyethylene/graphene nanocomposites by combining solid-state shear milling and FDM 3D-printing aligning methods

Polymer-based thermal conductive composites (PTCs) with both excellent thermal and mechanical properties are highly desirable in the thermal management of modern microelectronic industry. However, the enhancement efficiency for fillers loaded polymer composite is actually lower than the theoretically predicted value. The significant reasons could be due to the restriction of interfacial thermal resistance at filler-polymer matrix interfaces as well as the thermal conductive orientation dependence of anisotropic fillers. In the present study, solid-state shear milling (S3M) strategy and FDM 3D-printing aligning technology were combined to synergistically improve thermal conductivity of linear low-density polyethylene (LLDPE)/graphene nanoplatelet (GNPs) nanocomposites. The fabricated FDM 3D-printed parts exhibit a significantly enhanced through-plane thermal conductivity up to 3.43 W m−1 K−1 along printing direction compared to that of neat LLDPE (0.40 W m−1 K−1) and also that of traditionally melt-compounded LLDPE/GNPs composites (1.98 W m−1 K−1) at the same GNPs loading of 15.0 vol%. The enhanced thermal conductivity is attributed to the long-range aligned bridge-connected network structure of GNPs constructed in the PE matrix along printing direction due to the shear-inducing effect of FDM 3D-printing. Simultaneously, the S3M technology we adopted also reduces the interfacial thermal resistance and thus increases the thermal conductivity of the obtained nanocomposite, which was further demonstrated by the way of theoretical effective medium approximation (EMA) models we applied. The achieved high thermal conductivity and mechanical properties of the FDM 3D-printed LLDPE/GNPs thermal conductive parts suggest promising applications in the heat diffusion of some advanced electronic devices.

Enhanced thermal conductivity by constructing 3D-networks in poly(vinylidene fluoride) composites via positively charged hexagonal boron nitride and silica coated carbon nanotubes

Thermal-conductive yet electrical-insulating polymer composites with outstanding mechanical properties have attracted increasing attention in the electronic field. Herein, three-dimensional (3D) thermal-conductive networks were built in PVDF matrix via electrostatic repulsion of positively charged hexagonal boron nitride (m-hBN) and bridging of silica-coated carbon nanotubes (MWCNTs-SiO2). The results indicated that 25 wt% m-hBN/MWCNTs-SiO2/PVDF presented fascinating characteristics: a high thermal conductivity of 1.51 W/(m·K) and an excellent tensile strength of 55.02 MPa, with the enhancements of 586% and 25% respectively compared to pure PVDF; besides, superior dielectric properties and electrical insulation were obtained, with dielectric constant of 4.95, dielectric loss tangent of 0.14 at 1 MHz, and volume resistivity of 3.45 × 1012 Ω·cm. The Effective Medium Approximation (EMA) model revealed that the formation of 3D-networks could significantly decrease thermal resistance and promote phonon transmission. The outstanding heat dissipation capability of m-hBN/MWCNTs-SiO2/PVDF was verified by infrared imaging test, indicating its potential applications for thermal management.

Ab initio Investigation of Interfacial Thermal Transport for HMX‐PVDF Interface

AbstractThe theoretical investigation of heat dissipation for polymer‐bonded explosives (PBXs) is in high demand in explosive design in terms of safety and realibility, particularly as lack of effective experimental measurements. Here, we investigate the fundamental understanding of thermal transport across the heterogeneous interface between HMX and PVDF, by using the diffuse mismatch model and anharmonic inelastic model. This work explores the interfacial thermal conductance via ab initio calculation and derived phonon dispersions, phonon group velocities. For HMX‐PVDF interface, it is shown that low‐frequency phonon modes (especially lower than 10 THz) and two‐phonon elastic processes play dominant roles in the interface thermal transport. Furthermore, we present the calculated interfacial thermal conductance as a function of temperature. The thermal conductivity of mixture HMX‐PVDF system is analyzed with an effective medium approximation model. From these calculations, we give the thermal transport properties predictions of PBX for thermal conductivity enhancement and provides fundamental microscopic insights into phonon transport physics in PBX.

Tunable Nanoporous Anodic Alumina Photonic Crystals by Gaussian Pulse Anodization.

This study presents a Gaussian pulse anodization approach to generate nanoporous photonic crystals with highly tunable and controllable optical properties across the visible-NIR spectrum. Nanoporous anodic alumina Gaussian photonic crystals (NAA-GPCs) are fabricated in oxalic acid electrolyte by Gaussian pulse anodization, a novel form of pulse-like anodization. The effect of the Gaussian pulse width in the anodization profile on the optical properties of these photonic crystals is assessed by systematically varying this fabrication parameter from 5 to 60 s. The optical features of the characteristic photonic stopband (PSB) of NAA-GPCs-the position of the central wavelength, full width at half-maximum, and intensity-are found to be highly dependent on the Gaussian pulse width, the angle of incidence of incoming photons, and the nanopore diameter of NAA-GPCs. The effective medium of NAA-GPCs is assessed by monitoring spectral shifts in their characteristic PSB upon infiltration of their nanoporous structure with analytical solutions of d-glucose of varying concentration (0.0125-1 M). Experimental results are validated and mechanistically described by theoretical simulations, using the Looyenga-Landau-Lifshitz effective medium approximation model. Our findings demonstrate that Gaussian pulse anodization is an effective nanofabrication approach to producing highly sensitive NAA-based PC structures with versatile and tunable PSBs across the spectral regions. The findings provide new exiting opportunities to integrate these unique PC structures into photonic sensors and other platform materials for light-based technologies.

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.