Ellipsometric Parameters Research Articles

Broadband ellipso-polarimetric camera utilizing tunable liquid crystal achromatic waveplate with improved field of view.

An ellipso-polarimetric camera integrated with improved field of view tunable achromatic waveplate (AWP) over wide spectral band based on nematic liquid crystal retarders is presented. The AWP operates as half, quarter and full waveplate over a wide range of 430-780nm and wide field of view. The proposed analysis proved that capturing images at these modes is sufficient to extract the ellipsometric parameters: sin(2ψ), cos(Δ) and the Stokes parameters S1 and S3, besides showing the relations in between. Transmission and reflection modes setups are demonstrated in addition to an ellipso-polarimetric smartphone camera. The results show for the first time superiority of cos(Δ) images in which prominent contrast and fine details appear even with scattering objects and higher immunity to device errors. Biometric, remote sensing and archeological improved imaging applications are demonstrated.

Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model

A multiple-beam interference model is used to derive approximate formulae for the reflection and transmission coefficients of inhomogeneous thin films exhibiting large gradients of refractive index profiles. It is shown that these formulae are constituted by series containing the Wentzel-Kramers-Brillouin-Jeffreys term and correction terms with increasing order corresponding to number of considered internal reflections inside the films. A numerical analysis enabling us to show the influence of a degree of inhomogeneity on spectral dependencies of reflectance and ellipsometric parameters of inhomogeneous films is performed. Advantages and disadvantages of our approach compared with other approximate approaches are discussed. The optical characterization of a selected non-stoichiometric silicon nitride film prepared by reactive magnetron sputtering onto silicon single crystal substrate is performed for illustration of using our formulae in practice.

Data mining to predict the average outer diameter of vertically aligned TiO2 nanotubes

Nowadays, the development of new technology is strongly based on nanomaterials studies, such as vertically aligned TiO2 nanotubes (TONTs), which are widely used in different fields of industry. Physical properties of these materials depend on their size (inner and outer diameters) and shape, for this reason they must be measured accurately. Inner and outer diameter measurement is performed manually on images obtained by means of scanning electron microscopy. Time-consuming image analysis, subjective and low-representative readings are some disadvantages found in this process. This paper proposes a model to predict the average outer diameter of TONTs using Data Mining and Ellipsometry, because they have the potential to overcome disadvantages mentioned above. The diameter with measurements of light reflection intensity and ellipsometric parameters is modelled using different techniques. A model that shows a very low prediction error using linear support vector machines for regression is reported.

Physical properties enhancement of porous silicon treated with In2O3 as a antireflective coating

Abstract In this work, we investigate the effect of Indium Oxide (In2O3) on the microstructural, optical, optoelectrical, and electrical properties of Porous Silicon (PS) layer. PS film was prepared by electrochemical anodization technique. In2O3 thin film was coated onto PS layer by using simple chemical immersion method. The investigation showed a significant enhancement in the optoelectronic property of PS coated with In2O3. The In2O3/PS layer was thermally annealed to improve the efficiency of the photovoltaic cells. Surface morphology and chemical composition modification of In2O3/PS were analyzed by atomic force microscopy (AFM) and Fourier transfer infrared (FTIR) spectroscopy. Optical reflectivity of sample In2O3/PS decreases significantly from 30% to 2.4% owing to an improvement in the light absorption. The optical parameters such as refractive index (n) and extinction coefficient (k), real and imaginary dielectric constants (e1 & e2), as well as the components percentage and thickness of samples were determined by analyzing the TanΨ and CosΔ ellipsometric parameters. Photoluminescence (PL) analysis of PS layer treated with In2O3 before and after annealing indicated a bleu emission shifts due to the quantum confinement effect of the oxidized silicon nanocrystals. Annealed PS coated In2O3 resulted a significant improvement in the minority carrier lifetime (τeff) from 2 to 16.4 μs. The optoelectronic and electronic quality of the treated PS layer with In2O3 was enhanced noticeably compared to the untreated porous layer, making it an ideal candidate for the solar cell applications.

The dependence of ellipsometric parameters Δ and Ψ on refractive index of superficial film

The ellipsometrical analysis of external specular reflection of light on non-absorbing superficial films allows us to know factors which influence the ellipsometric measurement of the analyzed system. For optical non-absorbing superficial films the curves Δ = f(Ψ) are closed, the curves Δ = f(df) and Ψ = f(df) are periodical, while the curves Δ = f(nf) and Ψ = f(nf) are pseudo-periodic. Observations on the dependence of the ellipsometric parameters Δ and Ψ on nf are presented.

Calibration of a simple heterodyne interferometric ellipsometer

In this study, we develop a simple heterodyne interferometric ellipsometer, which is a heterodyne interferometer based on a dual-frequency, linearly polarized laser that is integrated with a common-path interferometric configuration. This device can measure ellipsometric parameters with high accuracy because it incorporates a method to calibrate the polarization effect of the beam splitter and the nonidentical characteristics of the photodetectors. The measured deviation in the ellipsometric parameters of a quarter-wave plate was less than 0.9%. The measurement results for a thin gold film deposited on silicon substrate were compared with those obtained by a commercial ellipsometer.

Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

We demonstrate that the ellipsometric parameters of the isotropic samples can be measured by a partial polarimeter with only eight intensity measurements. Under the Gaussian and Poisson noises, we propose the optimal measurement matrices for the polarization state generator and the polarization state analyzer that minimize the total estimation variance of eight nonzero Mueller elements related to the ellipsometric parameters. In addition, since considering only four of the eight elements, the estimation variance can be further reduced, and we also introduce two proper criteria to find the optimal measurement matrices that robustly minimize the total estimation variance for these four Mueller elements. Compared with the existing measurement matrices based on 16 intensity measurements, our proposed matrices can effectively decrease the total estimation variance and, thus, improve the measurement precision of the Mueller matrix and ellipsometric parameters with only eight measurements. Furthermore, the proposed optimal measurement matrices do not depend on the Mueller elements of samples and thus not on the ellipsometric measurements.

Определение профиля состава квантовых ям HgTe/Cd-=SUB=-x-=/SUB=-Hg-=SUB=-1-x-=/SUB=-Te методом одноволновой эллипсометрии

An ellipsometric method for reconstruction of the composition profile throughout the thickness in thin mercury-cadmium-telluride nanostructures grown by MBE has been developed. The method is based on ellipsometric data, measured during structure growth and following solution of the inverse ellipsometric problem. For this, a replacement of a part of the inhomogeneous layer by a homogeneous substrate with specially chosen optical constants has been done. Numerical simulation showed the correctness of such replacement and the efficiency of the developed algorithm. Using this method, the active region of the heterostructure consisting of five HgTe quantum wells separated by wide-band CdHgTe spacers has been studied. Using the results of continuous measurements of ellipsometric parameters obtained in situ during structure growth, the composition profiles for all five sequentially grown quantum wells was determined. A high repeatability of the composition distribution through the thickness is shown.

Ellipsometric Method of Substrate Temperature Measurement in Low-Temperature Processes of Epitaxy of InSb Layers

The present study is aimed at solving the problem of in situ thermometry of lowtemperature processes of molecular beam epitaxy of indium antimonide. A spectral ellipsometric method for measuring the temperature of InSb epitaxial layers is proposed. The method is based on the temperature dependence of the energy positions of the critical points. The spectra of ellipsometric parameters of the material in the temperature range from 25 to 270 °C are measured. The analysis of these spectra shows that the most temperature-sensitive parameters are the spectral positions of the peaks of the ellipsometric parameter, which are manifested near the critical points E1 and E1 + Δ1. It is found that the dependences of the peak positions on temperature in the above-mentioned temperature range are linear functions with the slope factors of 0.21 and 0.10 nm/°C, respectively. These factors determine the sensitivity of the method and ensure the temperature measurement accuracy within 2–3 °C.

Ellipsometric Method for Measuring the CdTe Buffer-Layer Temperature in the Molecular-Beam Epitaxy of CdHgTe

An ellipsometric procedure developed for noncontact in situ measurement of the CdTe buffer-layer temperature is presented. The procedure is based on the temperature dependence of the energy position of CdTe critical points and is intended for determining the initial temperature of the growth surface before epitaxy of the cadmium–mercury–telluride compound. An express method for determining the position of critical points by the spectra of ellipsometric parameter Ψ is proposed. A series of calibrated experiments is performed. They result in determination of the temperature dependences of the position of critical points. Estimations and the experiment show that the temperature-measurement accuracy is ±3°C.

Эллипсометрический метод измерения температуры буферных слоев CdTe в технологии молекулярно-лучевой эпитаксии CdHgTe

AbstractAn ellipsometric procedure developed for noncontact in situ measurement of the CdTe buffer-layer temperature is presented. The procedure is based on the temperature dependence of the energy position of CdTe critical points and is intended for determining the initial temperature of the growth surface before epitaxy of the cadmium–mercury–telluride compound. An express method for determining the position of critical points by the spectra of ellipsometric parameter Ψ is proposed. A series of calibrated experiments is performed. They result in determination of the temperature dependences of the position of critical points. Estimations and the experiment show that the temperature-measurement accuracy is ±3°C.

Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise.

The two ellipsometric parameters of an isotropic sample can be measured with simplified polarimetry setups that acquire at least four intensity measurements. However, these measurements are perturbed by noise and the measurement strategy has to be optimized, in order to limit noise propagation. We determine two different measurement strategies that are optimal for both white Gaussian additive noise and Poisson shot noise. The first one involves a polarization state generator (PSG) with a single state of polarization and a polarization state analyzer (PSA) with four states. The second one involves both PSG and PSA having two states. The total estimation variances obtained with both strategies are demonstrated to be minimal, of equal values, and independent of the ellipsometric parameters to be measured. They are based on simple optical elements and could simplify and accelerate ellipsometric measurements.

Optical constants of restored and etched reduced graphene oxide: a spectroscopic ellipsometry study

Structural and defective information in graphene are usually detected by Raman spectroscopy and electrical techniques; however, less attention has been paid to a spectroscopic ellipsometry investigation on graphene. Here, optical responses of graphene grown by chemical vapor deposition (G), reduced graphene oxide (RGO), restored RGO, and etched RGO are characterized by spectroscopic ellipsometry. The Lorentz oscillator model is used to fit the ellipsometric parameters. The resulting optical constants, refractive index and extinction coefficient are higher in less defective graphene, i.e. G and restored RGO. The results can be correlated with the Raman spectroscopic observation – fewer defects leading to higher density and more optical absorption. Our investigation opens a new angle of view to probe the structural information in the defective graphene and thus favors the production of high-quality graphene.

Three-step phase-shifting imaging ellipsometry to measure nanofilm thickness profiles

Three-step phase-shifting imaging ellipsometry is proposed for the dynamic measurement of a nanofilm's thickness profile in two dimensions. The designed apparatus consists of an ellipsometric optical configuration and an image-processing unit to perform phase-shifting imaging ellipsometry measurements, a key technique used to achieve dynamic and two-dimensional measurements. The uncertainties of the ellipsometric parameters ψ and Δ were evaluated based on the developed optical system and the proposed three-step phase-shifting technique. The thickness profile of a SiO2 nanofilm on a silicon substrate was measured to calibrate the proposed apparatus; results were comparable to those obtained by a commercial spectroscopic ellipsometer. The measured thickness profiles are almost flat over the area of 1.10 mm × 2.21 mm with the spatial resolutions of 1.58 and 4.62 μm in the horizontal and vertical directions, respectively. The differences of average thickness between the proposed apparatus and a commercial spectroscopic ellipsometer were less than 3 nm. Furthermore, measurement precision was validated by obtaining a standard deviation of less than 2.5 nm.

Vacuum ultraviolet quarter wave plates based on SnTe/Al bilayer: Design, fabrication, optical and ellipsometric characterization

Vacuum ultraviolet and extreme ultraviolet polarized light plays a significant role in many applications from materials science and solar physics investigations to optical components development. In this paper, we study the optical performances and the quarter wave retarder properties of aluminum coating capped with SnTe/Al thin film. The measurements have been performed by using a reflectometer properly improved for ellipsometric characterizations. The specimen has been fully characterized at hydrogen Lyman–alpha line (121.6 nm) by deriving the reflectance and the ellipsometric parameters, i.e. the ratio r and the phase difference δ. We found that the SnTe/Al bilayer behaves as phase retarder, although the performances differ from the ideal case. In fact, the polarimetric analysis combined with the optical test at different wavelengths allowed to identify carbon contamination on the top layer and a mild oxidation of the aluminum coating that affect the optical throughput.

Spectroscopic Ellipsometry and Optical Dispersion Analysis of Nanocrystalline CdS Thin Films

This study reports on spectroscopic ellipsometry (SE) and optical dispersion analysis of chemically deposited CdS thin films. The CdS thin films were prepared using chemical bath deposition and annealed in N2 atmosphere at temperatures of 100, 200, 300, and 500 °C for 60 min. The optical constants of nanocrystalline CdS thin films were investigated with SE. The ellipsometric parameters of the CdS thin films were measured with SE in the photon energy range from 1.24 to 6.48 eV. To investigate the dispersion parameters, the dispersion of the refractive index of the thin films was analyzed using the Wemple–DiDomenico single-oscillator model (W–D model) and the Sellmeier model. The optical dispersion parameters of the oscillator energy, the dispersion energy, the average oscillator strength, and the average oscillator wavelength of CdS thin films were investigated. In addition, dispersion parameters of CdS thin films were investigated as a function of the annealing temperature. The dispersion parameters of CdS thin films by the W–D model and Sellmeier model change with annealing temperature, which causes the transformation of the crystal structure.

Optical quantities of multi-layer systems with randomly rough boundaries calculated using the exact approach of the Rayleigh–Rice theory

In this paper, the exact approach of the Rayleigh–Rice theory enabling us to calculate optical quantities of multi-layer systems with boundaries exhibiting slight random roughness is presented. This approach is exact in the sense that it takes into account the propagation of perturbed electromagnetic fields (waves) among randomly rough boundaries including all cross-correlation and auto-correlation effects. The restriction to the second order of perturbation, which is the lowest order that gives nonzero corrections to coherent waves (obeying the Snell’s law), represents the only approximation used in our calculations. It is assumed that the layers and the substrates are formed by optically homogeneous and isotropic materials. The formulae obtained in the theoretical part are used to investigate the influence of layer thicknesses and roughness parameters on reflectances and associated ellipsometric parameters of the selected numerical examples of a three-layer system. The presented approach represents the generalization of the exact approach for single-layer systems and the improvement of the approximate approach for multi-layer systems published earlier. The exact approach of the RRT has a substantial importance for the optical characterization of multi-layer systems occurring in applied research and optics industry applications.

Ellipsometry-based conductivity extraction in case of phosphorus doped polysilicon

In this work, we investigated a new method for thin films electrical conductivity extraction based on spectroscopic ellipsometry. This has been enabled through the correlation between the films conductivity and their ellipsometric properties. Indeed, it has been demonstrated that numerous ellipsometric fitting-based approaches can provide, in an indirect way, the electrical characteristics of thin films. The study was focused on electrical conductivity, but doping level or carriers’ mobility can also be extrapolated from ellipsometric measurements. Among various possibilities leading to electrical properties extraction, we can cite the extremal values of Ψ and Δ ellipsometric angles, their associated wavelengths, the mean square error and the maximal and minimal reflectivities ratio. Otherwise, the correlation between extrinsic conductivity and ellipsometric parameters evolution has been confirmed in case of low doping levels with particular behavior after annealing. This contactless method has been successfully applied to polycrystalline silicon films deposited on oxidized, p-type monocrystalline substrates, by low pressure chemical vapor deposition technique, and lightly or heavily phosphorus doped by diffusion. The feasibility of the method has been proven in this case, but also in other cases like implanted polysilicon layers or silicon-on-insulator (not included here).

New generation of α-MnO2 nanowires @PDMS composite as a hydrogen gas sensor

New hydrogen gas sensor has been prepared by α-MnO2 nanowires in polydimethylsiloxane matrix. For this purpose, the high aspect ratio α-MnO2 nanowires has been prepared by the aid of hydrothermal method and then dispersed into poly-dimethyl siloxane polymer media. For gas sensing, the samples have been exposed under different gas concentrations from 0 to 5%. The sensor responses have been examined by normalized ellipsometric parameter with respect to the chamber filled with N2 Gas. Our results indicate linear behavior of resonance wavelength in ellipsometric parameter as a function of gas concentrations which can open a new insight for the sample’s capability to hydrogen gas sensing applications.

Optimal configuration of partial Mueller matrix polarimeter for measuring the ellipsometric parameters in the presence of Poisson shot noise and Gaussian noise

We address the optimal configuration of a partial Mueller matrix polarimeter used to determine the ellipsometric parameters in the presence of additive Gaussian noise and signal-dependent shot noise. The numerical results show that, for the PSG/PSA consisting of a variable retarder and a fixed polarizer, the detection process immune to these two types of noise can be optimally composed by 121.2° retardation with a pair of azimuths ±71.34° and a 144.48° retardation with a pair of azimuths ±31.56° for four Mueller matrix elements measurement. Compared with the existing configurations, the configuration presented in this paper can effectively decrease the measurement variance and thus statistically improve the measurement precision of the ellipsometric parameters.