Cauchy Dispersion Model Research Articles

Pseudo-dielectric function spectra of the near surface layer of GaAs implanted with various fluence of Xe+ ions

Monocrystalline (100) semi-insulating gallium arsenide (GaAs) samples were irradiated with a 250-keV Xe+ ion beam at room temperature. To investigate the effect of ion irradiation on GaAs samples, the ion fluence was varied from 1 × 1012 to 3 × 1016 ions/cm2. The spectroscopic ellipsometry (SE) method and the Rutherford backscattering spectrometry (RBS) with nuclear reaction (NR) method were used to determine the properties of the virgin and implanted samples. The SE approach reveals that the pseudo-dielectric function of implanted GaAs samples varies with ion fluence. The RBS approach, which exposes the depth-profile of As, Ga, and Xe in the implanted samples, allows us to correlate changes in the pseudo-dielectric function with structural modifications caused by the ion irradiation. The NR approach points out the existence of an oxygen-enriched layer on the surface of implanted GaAs samples. Lastly, the optical study involving the Cauchy and Urbach dispersion model measures the refractive index n and extinction coefficient k of the native oxide layer on the surface of GaAs samples.

A Study on the Effect of Oxygen Flow Rate on Optical Properties of RF Sputtered a-GaOx Thin Films on Corning Glass Substrate

Transparent amorphous thin films of ultra-wide band gap (Eg ≈ 4.5–5.3 eV) gallium oxide (a-GaOx) were deposited on Corning glass substrates by radio frequency (RF) magnetron reactive sputtering under different oxygen flow rates. Amorphous nature of the deposited films was confirmed using X-ray diffraction method. Surface properties of the films were obtained from field emission scanning electron and atomic force microscopic images. Compositional and surface chemistry analyses were done using energy-dispersive X-ray and X-ray photoelectron spectroscopic techniques respectively. Optical characteristics of the films deposited under varying oxygen flow rates were investigated. UV-visible transmittance spectra showed excellent transparency in the visible region for all the films. Optical band gap values were found to increase with the increase of oxygen flow rates. Thickness of the films and refractive index dispersion relation were studied using spectroscopic ellipsometry by utilizing a Cauchy dispersion model. Refractive index dispersion parameters were obtained using Wemple-DiDomenico model. The results indicate that the presence of oxygen in the sputtering environment significantly alter the deposition rate and thereby optical properties of the films.

High-frequency and below bandgap anisotropic dielectric constants in α-(AlxGa1−x)2O3 (≤x≤1)

A Mueller matrix spectroscopic ellipsometry approach was used to investigate the anisotropic dielectric constants of corundum α-(AlxGa1−x)2O3 thin films in their below bandgap spectral regions. The sample set was epitaxially grown using plasma-assisted molecular beam epitaxy on m-plane sapphire. The spectroscopic ellipsometry measurements were performed at multiple azimuthal angles to resolve the uniaxial dielectric properties. A Cauchy dispersion model was applied, and high-frequency dielectric constants are determined for polarization perpendicular (ε∞,⊥) and parallel (ε∞,∥) to the thin film c-axis. The optical birefringence is negative throughout the composition range, and the overall index of refraction substantially decreases upon incorporation of Al. We find small bowing parameters of the high-frequency dielectric constants with b⊥=0.386 and b∥=0.307.

The measurement of chromatic dispersion of liquids based on rainbow technology with empirical mode decomposition

An acquisition system is designed to collect the rainbow signals at two different wavelengths simultaneously. The empirical mode decomposition (EMD) method was used to decompose and reconstruct the first-order rainbow signal. Airy, ripple and noise signal components were completely separated from the signal of the first-order rainbow by the EMD, and the refractive index of the droplet can be obtained by analyzing the separated airy structures. In our experiments, the rainbows from droplets of water, NaCl and C6H12O6 aqueous solutions were collected and the rainbow signals were analyzed by EMD. Based on the Cauchy dispersion model, the coefficients and the dispersion relation of water, NaCl and C6H12O6 aqueous solutions at different concentrations were obtained by measuring the refractive index at the wavelengths of 632.8 and 473 nm. We demonstrate an EMD-rainbow method to detect the chromatic dispersion of liquids.

Artificial bee colony algorithm: a novel strategy for optical constants and thin film thickness extraction using only optical transmittance spectra for photovoltaic applications

An effective approach to determine thin film thickness (d) and optical constants (n,k,α) from transmittance spectrum with interference fringes is proposed. The developed strategy is based on applying the artificial bee colony (ABC) algorithm and Cauchy dispersion model. The accuracy test of this method has been assessed by using simulated and real tests. Simulated test is used to check the ability of ABC algorithm to determine the parameters of simulated transmittance spectra. Real test deals with the investigation of the determination approach on experimental measured transmittance spectra. Those spectra were measured from six elaborated samples of amorphous hydrogenated silicon (a-Si:H) thin films with different thicknesses, which will be used as an eco-friendly layer for solar cell applications. The obtained results noticeably show the high effectiveness of the developed strategy to accurately determine the thin film thickness and optical constants.

Evaluation of optical parameters and characterization of few layer sputtered MoS2 film by spectroscopic ellipsometry

The study involves spectroscopic ellipsometry analysis of sputter deposited few layer MoS2 grown on three different substrates (ITO coated glass, n-silicon and p-silicon) for diverse deposition time. We have investigated optical parameters such as refractive index, extinction coefficient and dielectric constant of MoS2 layers in the visible region of electromagnetic spectrum. For such purpose of investigation we have involved Cauchy dispersion model (for the film deposited on n-silicon and p-silicon) and hybrid of Lorentz and Drude model (for the film deposited on ITO coated glass). Furthermore, comparative analysis at the diverse growth time of 5, 10, 15 and 20 min has been performed on the basis of optical parameters and surface morphology.

Raman spectroscopy and optical properties of GAZO thin films deposited at various substrate temperatures

We report the Raman study and optical properties of gallium and aluminium co-doped ZnO (GAZO) thin films deposited at various substrate temperatures by sputtering. The films exhibited Raman peaks at 99 cm-1, 437 cm-1 and 575 cm-1 which were assigned to the ZnO $ E_{2}$ (low), $ E_{2}$ (high) and $ {\rm A}_{1}$ (LO) modes, respectively. The wavelength dependence of the refractive index and the extinction coefficient were described by the Cauchy dispersion model, through theoretical modelling of the transmittance data. The refractive index showed an increasing trend while the extinction coefficient decreased with increasing substrate temperature in the visible region. This was attributed to the relative decrease in transmittance observed at higher substrate temperatures. The dielectric constant ( $ \varepsilon$ ) , dissipation factor $ (\tan\delta)$ and optical conductivity ( $ \sigma$ ) values were associated with the films’ high transparency. The Wemple and Didomenico single oscillator dispersion energies ( $ E_{o}$ and $ E_{d}$ increased with substrate temperature which was attributed to the reduction in residual stress, improvement in microstructural order and crystallinity. The static refractive index $ (n_0)$ , optical band gap $ (E_{g})$ , long wavelength dielectric constant ( $ \varepsilon_0$ , the $ M_{-1}$ and $ M_{-3}$ moments of the optical spectra and the non-linear refractive index ( $ n_2$ were determined. Optimum optical properties were obtained in films deposited on heated substrates (75 and $ 100 {}^{\circ}$ C).

Determination of refractive index and thickness of YbF3 thin films deposited at different bias voltages of APS ion source from spectrophotometric methods

Abstract Ytterbium fluoride (YbF3) single thin films were prepared on sapphire and monocrystalline silicon substrates through conventional thermal evaporation and ion beam-assisted deposition (IAD), at bias voltages ranging from 50 to 160 V of the Leybold advanced plasma source (APS). By using the Cauchy dispersion model, the refractive index and thickness of the YbF3 thin films were obtained by fitting the 400–2500 nm transmittance of the monolayer YbF3 thin films on the sapphire substrate. At the same time, the refractive index and thickness of the YbF3 thin films on the monocrystalline silicon substrates were also measured using the VASE ellipsometer at wavelength from 400 to 2200 nm. The results showed that the refractive index deviation of the YbF3 thin films between the fitted values by the transmittance spectra and the measured values by the VASE ellipsometer was <0.02 and the relative deviation of the thickness was <1%. Furthermore, the refractive index of the YbF3 thin films increased with increasing APS bias voltage. The conventional YbF3 thin films and the IAD thin films deposited at low bias voltage revealed a negative inhomogeneity, and a higher bias voltage is beneficial for improving the homogeneity of YbF3 thin films.

A complete parameterisation of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles

Abstract. Calculations of aerosol radiative forcing require knowledge of wavelength-dependent aerosol optical properties, such as single-scattering albedo. These aerosol optical properties can be calculated using Mie theory from knowledge of the key microphysical properties of particle size and refractive index, assuming that atmospheric particles are well-approximated to be spherical and homogeneous. We provide refractive index determinations for aqueous aerosol particles containing the key atmospherically relevant inorganic solutes of NaCl, NaNO3, (NH4)2SO4, NH4HSO4 and Na2SO4, reporting the refractive index variation with both wavelength (400–650 nm) and relative humidity (from 100 % to the efflorescence value of the salt). The accurate and precise retrieval of refractive index is performed using single-particle cavity ring-down spectroscopy. This approach involves probing a single aerosol particle confined in a Bessel laser beam optical trap through a combination of extinction measurements using cavity ring-down spectroscopy and elastic light-scattering measurements. Further, we assess the accuracy of these refractive index measurements, comparing our data with previously reported data sets from different measurement techniques but at a single wavelength. Finally, we provide a Cauchy dispersion model that parameterises refractive index measurements in terms of both wavelength and relative humidity. Our parameterisations should provide useful information to researchers requiring an accurate and comprehensive treatment of the wavelength and relative humidity dependence of refractive index for the inorganic component of atmospheric aerosol.

Temperature dependent optical constants for SiO2 film on Si substrate by ellipsometry

In situ ellipsometry measurements in the spectra range from 246 to 1000 nm were performed on a SiO2/Si system at temperatures varying from 25 to 600 °C. By using Cauchy dispersion model to describe SiO2 layer and B-spline to parameterize Si substrate, the temperature dependent optical constants of SiO2 film and Si substrate were precisely determined and analyzed which is helpful to understand the temperature effect of substrate for ellipsometry measurement. The temperature coefficient of refractive index of SiO2 at elevated temperature was obtained by ellipsometry. The results indicate that the temperature coefficient increases with increasing wavelength and decreasing temperature.

Controlling the optical properties of sputtered-deposited LixV2O5 films

This study examines the influence of lithium intercalation on the optical properties of vanadium pentoxide films. The films with a thickness between 400 and 1000 nm were prepared by DC magnetron sputter deposition. Cyclic voltammetry and chronopotentiometry were used to set a well defined lithiation state of the LixV2O5 films between x = 0 and x = 1. The optical properties of these films were measured by optical reflectometry in the wavelength range between 500 and 1700 nm. From the reflectance data, the refractive index and the extinction coefficient of the films were finally calculated as a function of the wavelength using Cauchy's dispersion model. The results confirm that the optical behavior of LixV2O5 films varies significantly upon lithium insertion. It is demonstrated that the changes produced in the optical properties are completely reversible within the limits of permanent structure changes.

Morphological and optical comparison of the Si doped GaN thin film deposited onto the transparent substrates

The aim of this paper is to expand the body of knowledge about the silicon doped gallium nitride thin films deposited on different substrates. The physical properties of the Si doped GaN thin films deposited on the glass and polyethylene terephthalate substrates by thermionic vacuum arc which is plasma production technique were investigated. Thermionic vacuum arc method is a method of producing pure material plasma. The Si doped GaN thin films were analyzed using the following methods and the devices: atomic force microscopy, x-ray diffraction device, spectroscopic ellipsometer and energy dispersive x-ray spectroscopy detector. The produced Si doped GaN thin films are in the (113) orientation. The thicknesses and refractive index were determined by using Cauchy dispersion model. Surface morphologies of produced thin films are homogenous and low roughness. Our analysis showed that the thermionic vacuum arc method present important advantages for optical and industrial applications.

Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization

The wavelength-selective properties of optical thin films offer a sensible solution to the problems of effective wavelength-selective use of solar energy. However, the design of the optical constants of these optical thin films is crucial to the study of the film’s optical properties. To address this problem, we introduced stochastic particle swarm optimization (SPSO) to an inverse model of the optical constants and thicknesses of optical thin films in this paper. Initially, we discussed the anti-error capacity of the Cauchy dispersion model, and we then discussed the importance of the parameters used in the Forouhi–Bloomer dispersion model, before modifying the Forouhi–Bloomer dispersion model on this basis. We also discussed the influence of the measured error on the inversion effects of each parameter in the modified model. Finally, we inverted the measured transmittance data using the Cauchy dispersion model, the Forouhi–Bloomer dispersion model and a modified Forouhi–Bloomer dispersion model, and the effectiveness and the feasibility of SPSO when applied to the determination of optical constants is verified.

The structure and optical properties of lead-free transparent KNLTN-La0.01 ceramics prepared by conventional sintering technique

Abstract (Na0.52K0.44Li0.04)0.97La0.01Ta0.20Nb0.80O3 (KNLTN-La0.01) lead-free subtransparent ceramics was prepared by a conventional sintering technique. The structure and the optical properties of the ceramics were investigated. The room temperature crystallographic indexing revealed the ABO3 perovskite type, tetragonal phase and P4mm point group in the ceramics. The surface and fractured surface SEM micrographs showed a dense microstructure with few micropores in KNLTN-La0.01 ceramics, which was obviously better than for the pure KNLTN ceramics. The refractive indexes of the films were investigated by an ellipsometer and the results show that the KNLTN-La0.01 subtransparent ceramics reveals significant wavelength dependent dispersion. The refractive index ranges from 2.14 to 2.06 with the wavelength increase from 380 nm to 900 nm. The dispersive behavior was analyzed by three parameters of Cauchy dispersion model and the values of the parameters A, B and C are 2.0610±0.0005, 0.0054±0.0003 and 0.00069±0.00004, respectively.

Thermo-optical properties of 1H[3,4-b] quinoline films used in electroluminescent devices

Electroluminescence cells with H[3,4-b] quinoline layers are promising devices for a blue light emitting EL diode. This work measured the optical reflectance as a function of temperature in copolymers PAQ layers deposited on Si crystalline substrate. Using the extended Cauchy dispersion model of the film refractive index we determined the thermo-optical coefficients for quinoline layers in the temperature range of 76–333K from combined ellipsometric and spectrofotometric studies. The obtained values of thermo-optical coefficients of thin PAQ film, were negative and ranged in 5–10×10−4 [1/K].

Optical Mueller matrix modeling of chiral AlxIn1 − xN nanospirals

Metamaterials in the form of chiral nanostructures have shown great potential for applications such as chemical and biochemical sensors and broadband or wavelength tunable circular polarizers. Here we demonstrate a method to produce tailored transparent chiral nanostructures with the wide-bandgap semiconductor AlxIn1−xN. A series of anisotropic and transparent films of AlxIn1−xN were produced using curved-lattice epitaxial growth on metallic buffer layers. By controlling the sample orientation during dual magnetron sputter deposition, nanospirals with right-handed or left-handed chirality were produced. Using a dual rotating compensator ellipsometer in reflection mode, the full Mueller matrix was measured in the spectral range 245–1700nm at multiple angles of incidence. The samples were rotated one full turn around their normal during measurements to provide a complete description of the polarization properties in all directions. For certain wavelengths, unpolarized light reflected off these films becomes highly polarized with a polarization state close to circular. Nanostructured films with right- and left-handed chirality produce reflections with right- and left-handed near-circularly polarized light, respectively. A model with a biaxial layer in which the optical axes are rotated from bottom to top was fitted to the Mueller-matrix data. Hence we can perform non-destructive structural analysis of the complex thin layers and confirm the tailored structure. In addition, the refractive index, modeled with a biaxial Cauchy dispersion model, is obtained for the AlxIn1−xN films.

Growth of β-Ga2O3 nanowires and their photocatalytic and optical properties using Pt as a catalyst

Growth of Ga2O3 nanowires (NWs) was carried out by vapor–liquid–solid (VLS) on silicon substrates using Pt as a catalyst. Structural analysis revealed that the Ga2O3 NWs are single phase nature with monoclinic β-Ga2O3 crystal structure. The optical functions of β-Ga2O3 NWs films have been determined by ellipsometry investigations from 300–2100nm. A two layer model employing the Cauchy dispersion model for the main layer and Bruggeman effective medium approximation (BEMA) for the surface layer was found to be sufficient and reasonable. Low refractive index values comparable to those of bulk material, which may ascribed to the low packing density for the films obtained by the used VLS growth method, are obtained. A direct optical band gap value of 3.58eV was observed. The photocatalytic activity of β-Ga2O3 NWs was evaluated by the degradation of methylene blue. The β-Ga2O3 NWs showed enhanced photocatalytic activity.

自适应模拟退火遗传算法在薄膜厚度及光学常数反演中的应用

It is very important to measure thickness and optical constants accurately for film fabrication,research and applicatiom.With Cauchy dispersion model,the optical constants and thickness of thin film are inversed by fitting the curve of transmission spectrum using whole optical spectrum fitting based on adaptive simulated annealing genetic algorithm.The results of TiO2 and SiO2/TiO2 thin films deposited by electron beam evaporation respectively are in good agreement with the measuring.The experimental result shows that the calculated transmittance of the film is consistent with the measured value.The thickness error is less than 2nm,and the refractive index error at 560nm is less than 0.03.

Effect of oxygen atmosphere on the structure and refractive index dispersive behavior of KTa0.5Nb0.5O3 thin films prepared by PLD on Si(0 0 1) substrates

KTa0.5Nb0.5O3 thin films were deposited on Si(001) substrates by pulsed laser deposition (PLD) with different oxygen pressures (10Pa, 15Pa, 20Pa, 25Pa and 30Pa). The effect of oxygen atmosphere on the structure and refractive indices of the films were studied. It is found that the phase structure, the scale of the grains, the surface roughness and the optical properties of the films are sensitive to oxygen atmosphere variation. The refractive indices of the films were investigated by ellipsometer and the dispersive behavior was analyzed by Cauchy dispersion model. The films grown with 15Pa oxygen pressure show the pure perovskite structure and the dispersion behaviors possess the normal dispersion shape; and other influence on the quality and properties of KTa0.5Nb0.5O3/Si(001) films were discussed.

Spectroscopic ellipsometry measurements on an anisotropic crystal: 6H-SiC

In spectroscopic ellipsometry (SE) measurement, accuracy of optic axis orientation is very important requirement. To reduce the error arising from the uncertainty in optic axis orientation, we applied multiple angles SE measurement performed on 6H-SiC with the optical axis perpendicular to the sample (0001) surface in the 300–800nm wavelength range at room temperature. The refractive indices and extinction coefficients for ordinary and extraordinary were both fitted by Cauchy dispersion model. The obtained results were of great agreement with literatures.