Experimental determination of optical constants in the vacuum ultra violet wavelength region between 80 and 140 nm: A reflectance versus thickness method and its application to ZnSe

The 80-120 nm spectral range is a key domain for solar physics. Below 105 nm solids do not transmit light and the reflectance of available mirrors is particularly low which makes optical measurements specifically difficult. Optical constants of the materials may consequently be unavailable or unreliable.We present here a two media reflectance method at normal incidence suited to this VUV range, in which the variable is not the incidence angle but the thickness of the top layer made of the material to be analyzed. The real (n) and imaginary (k) parts of the complex index are directly and graphically determined in the (n, k) plane as the common intersection point of isoreflectance curves corresponding to samples different only in the thickness of the top layer.The method is tested and illustrated with ZnSe films evaporated on Al covered float glass substrates. In the literature, the reflectance magnitudes measured on ZnSe crystals differ strongly from an author to the other, leading to discrepant data for ZnSe in the VUV domain.We obtain precise and reliable values of (n, k), which fit the experimental values determined on freshly cleaved ZnSe crystals by J.L. Freeouf and the theoretical values calculated from the electronic band structure of ZnSe by John P. Walter and Marvin L. Cohen, but strongly differ from the optical constants selected by E.D. Palik in his tables.     

Optical properties of MnAl films

The optical properties of MnAl films of different compositions, deposited at different substrate temperatures and in the thickness range 25 to 90 nm, are reported. The reflectance and transmittance are measured in the wavelength range 320–900 nm for near normal incidence of light. These measurements are used to calculate the optical constants namely, refractive index (n) and extinction coefficient (k). The wavelength and thickness dependence of these optical constants are reported. The optical measurements for films with higher Mn content and grown at higher substrate temperature reveal that n and k values are constant over a wide wavelength range (500–900 nm) showing high reflectance in the visible and near infrared region.     

Optical properties of nanostructured InSe thin films

Thin films of InSe were prepared by thermal evaporation technique. The as-deposited films have nano-scale crystalline nature and the annealing enhanced the degree of crystallinity. The optical properties of nanocrystalline thin films of InSe were studied using spectrophotometric measurements of transmittance, T, and reflectance, R, at normal incidence of light in the wavelength range 200–2500 nm. The optical constants (refractive index, n, and absorption index, k) were calculated using a computer program based on Murmann's exact equations. The calculated optical constants are independent of the film thickness. The optical dispersion parameters have been analysed by single oscillator model. The type of transition in InSe films is indirect allowed with a value of energy gap equals to 1.10 eV, which increased to 1.23 eV upon annealing.     

Optical constants of nanosized films of metal titanium

A new ellipsometric technique for optical measurements of the refraction and extinction indices and thickness of nanosized metal-titanium films in air is proposed and implemented. It is shown that the determination of optical constants of titanium films by measuring the ellipsometric parameters Ψ and Δ for a light beam incident upon the metal/substrate interface through the substrate of fused silica allows one to obtain optical constants of the metal, which correlate well with the results of the most reliable measurements performed in vacuum chambers. In this case, one can additionally determine the thickness and refractive index of the natural oxide film on the titanium surface. The obtained values of the optical constants of titanium, n ₂ = 3.42 ± 0.05 and k ₂ = 3.75 ± 0.05 (λ = 632.8 nm), agree well with the results of the measurements made in vacuum. The proposed technique makes it possible to measure the thicknesses of titanium films within the range 7–30 nm with an accuracy of 0.7 nm. The technique is tested on titanium films deposited onto fused silica substrates obtained by vacuum thermal evaporation. The possible error of determining the thickness due to various additional factors is estimated. The results of ellipsometric measurements of the thickness are compared with the data obtained from parallel measurements of electric resistance of the films.     

椭偏光谱法研究溶胶-凝胶TiO2薄膜的光学常数

以钛酸丁酯为前驱体,采用溶胶-凝胶工艺成功制备了TiO₂薄膜.利用反射式椭圆偏振光谱仪测量了薄膜的椭偏参量Ψ和Δ,并用Cauchy模型对椭偏参数进行数据拟合,得到了薄膜的厚度和光学常数在380—800 nm的色散关系.用分光光度计测量了薄膜的反射率,并用干涉法计算薄膜的厚度;使用原子力显微镜观测了薄膜的表面微结构,分析讨论了不同退火温度处理的薄膜微结构与光学常数之间的关系.研究结果表明,Cauchy模型能较好地符合溶胶-凝胶TiO₂薄 关键词： 光学常数 2薄膜')" href="#">TiO₂薄膜 溶胶-凝胶 椭圆偏振     

Optical characterization of thin thermal oxide films on copper by ellipsometry

A complete optical characterization in the visible region of thin copper oxide films has been performed by ellipsometry. Copper oxide films of various thicknesses were grown on thick copper films by low temperature thermal oxidation at 125 °C in air for different time intervals. The thickness and optical constants of the copper oxide films were determined in the visible region by ellipsometric measurements. It was found that a linear time law is valid for the oxide growth in air at 125 °C. The spectral behaviour of the optical constants and the value of the band gap in the oxide films determined by ellipsometry in this study are in agreement with the behaviour of those of Cu₂O, which have been obtained elsewhere through reflectance and transmittance methods. The band gap of copper oxide, determined from the spectral behaviour of the absorption coefficient was about 2 eV, which is the generally accepted value for Cu₂O. It was therefore concluded that the oxide composition of the surface film grown on copper is in the form of Cu₂O (cuprous oxide). It was also shown that the reflectance spectra of the copper oxide–copper structures exhibit behaviour expected from a single layer antireflection coating of Cu₂O on Cu. Received: 19 July 2001 / Accepted: 27 July 2001 / Published online: 17 October 2001     

Accuracy of determining the optical constants of semiconductors from their infrared transmittance

The accuracy of determining the optical constants of semiconductors in the infrared range on the basis of absolute and relative transmittances of layers of varions thicknesses is analyzed graphically. The analysis showed that measurement of absolute transmittances for thickness ratios not smaller than three yields sufficiently accurate absorptance and reflectance values. Measurement of relative transmittances with allowance for multiple reflection is a highly accurate means of determining absorptance but is useless for determining reflectance. The curves appearing in the paper make possible practical error estimates for various specimen thickness ratios and surface reflectances.     

Experimental determination of optical constants of MgF2 and AlF3 thin films in the vacuum ultra-violet wavelength region (60-124 nm), and its application to optical designs

The investigation of some solar radiations of interest for astrophysicists requires optics in the 80-130 nm vacuum ultra-violet spectral range (VUV). In this domain, where both transmittance and reflectance of most materials are very low, the measurement of optical constants is specifically difficult, and optical data are consequently often either inexistent or uncertain. Reliable modelling of optical components for VUV, like polarizing multi-layered mirrors, necessitates prior measurement of complex indices of the thin films involved in the coating. Fluorides like MgF₂ or AlF₃ are among the rare materials capable to contribute to multi-layer mirrors in the VUV.We have determined optical constants of thin films of these two materials by using a two media reflectance method at normal incidence and a graphical determination particularly suited to this VUV region, which we presented in a previous paper. Optical constants are determined in the range 60-124 nm with 2 nm step, and are compared to existing data. On the basis of these measured indices, polarizing mirrors for λ₁ = 121.6 nm or λ₂ = 103.2 nm have been modelled and fabricated. Their reflectance measured versus incidence angle by using monochromatized synchrotron radiation at the above wavelengths is found in agreement with the calculated predictions.     

Optical constants of thin oxide films on titanium

Thin oxide films on titanium formed by heating were studied by the ellipsometric method. To obtain the complex refractive index and film thicknesses, the ellipsometric measurements were performed by means of the immersing method: each sample was measured first in air and then in a liquid of known refractive index (in our case CCl₄). The optical constants and the oxide film thickness were computed by means of a computer from two pairs of ellipsometric values. To state the optical constants of clean titanium surface the graphic-computational method was proposed and applied. The measurements were carried out at two wavelengths on oxide films grown in air and dry oxygen by thermal oxidation at temperatures from 150 to 700 °C. It has been shown that when increasing the film thickness the refractive index of the film decreases, whereas the absorption coefficient is independent on the film thickness. Optical constants of oxide films growing in dry oxygen are smaller than those growing in air.     

Determination of thickness and optical constants of metal films from an extended ATR spectrum by using a statistical method

Sudden changes in reflectivity within a small angle or wavelength range are very sensitive to both the metal film thickness and optical constants. Metal films such as silver or gold display two sudden changes in their reflectance curve ? the first occurring at the critical angle, which is then followed by a sharp surface plasmon resonance (SPR) dip at an incident angle that is a few degrees greater than the critical angle. In this report, we describe a method involving the optimization of the sum of squared difference (SSQ) to produce good fitting amongst the reflectivity data points from a function curve derived from theory. The standard errors on each output parameter for the best curve fit are determined from the covariant matrix eigenvalues.     

Method of envelopes for studying a two-film system on a reflecting substrate

For determining the optical constants and the thickness of thin films (including strongly absorbing films) by the spectrophotometric method, we propose to deposit them on intermediate films formed on strongly reflecting substrates. Due to this, an interference pattern depending on the optical constants and the thickness of the film under study will be observed in the reflectance spectrum. The method of envelopes of the extrema in the reflectance spectrum that is based on the iterative approach is developed for studying two-film systems.     

Sur la determination des constantes optiques du calcium a partir de couches epaisses

We investigate how it is possible to determine the best the optical constants of calcium from measurements of the transmittance T and reflectance at the interfaces metal-vacuum R and metal substrate R′ on thin films, using a method of successive approximations. We compare the results obtained using the experimental values of (R, R′, T) or (R, T) or (R′, T), for two films of different thicknesses. We show that a satisfactory result is obtained with the values of (R′, T). We determine, in this manner, the optical constants of calcium in the energy range 2 –5.6 eV, and we compare the results obtained with those determined by other authors.     

气溶胶垂直非均一分布对天空背景亮度的影响

对白天天空背景亮度进行了数值实验;模拟了不同标高下的气溶胶垂直分布对天空背景亮度的影响;比较了不同垂直分层和整层均匀气溶胶分布下,天空背景亮度的相对偏差,并分析了天空背景亮度对地表反射率的敏感性。结果表明:给定气溶胶光学厚度下,不同标高的垂直分布得到的天空背景亮度差别很大;天空背景亮度对地表反射率和气溶胶总光学厚度都比较敏感,敏感程度受太阳-观测几何的影响。     

Optical properties of gold electrode surfaces covered with metal monolayers

The relative reflectivity changes ΔR/R of a gold electrode surface caused by the deposition of monolayers of thallium, copper and lead from electrolytic solutions at underpotentials have been studied in situ in the photon energy range between 1.8 and 5.2 eV. The optical constants of the surface layer giving rise to this measured reflectivity change have been calculated and compared to the results of the electroreflectance effect on bare gold surfaces. It is shown that the reflectance change observed during the monolayer deposition is to first order due to a change in the gold electrode surface layer and not to absorption processes in the monolayer itself. The latter ones cause a fine structure superimposed to the substrate spectrum. The relatively strong change in the gold surface optical constants upon metal monolayer deposition is explained in terms of an enhanced electroreflectance effect due to the partially ionic character of the metal adatoms, which alters the free electron concentration in the substrate surface layer. Electroreflectance spectra obtained on gold surfaces covered with a monolayer of thallium compare favourably with dielectric loss functions computed for charged gold surfaces. This supports the assumption that the reflectivity changes observed upon metal monolayer deposition are mostly due to changes in the optical properties of the substrate metal surface.     

Proprietes optiques de couches de Be evaporees et etudiees sous ultra-vide dans L'u.v. De 2,5–25 eV

Optical constants of thin films of Be are obtained from reflectance measurements between 2 and 25 eV. These films are obtained by evaporation in ultra-high vacuum and studied in situ. The optical conductivity σ and real part ?₁ of the dielectric constant are compared with previous theoretical and experimental results. The agreement is good, particularly for the important structure of σ at 4.8 eV. The volume plasmon is situated at 19.2 ± 0.4 eV and the surface plasmon at 13.6 eV.     

Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers

We present a method using attenuated total reflection (ATR) with excitation of surface plasma waves at different wavelengths and angles of incidence, which allows an accurate determination of the thickness and optical constants of absorbing surface layers from optical measurements only. This method is applied to the case of very thin Au surface layers on (111)Ag, and the results are discussed.     

软X射线（60—900eV）超薄膜的光学常数

用反射率方法测定了软X射线波段(60～900eV)超薄膜的光学常数.反射率测量在同步辐射光束线上完成.对测量数据做非线性最小二乘曲线拟合得出光学常数,同时还精密确定了超薄膜的膜厚与薄膜与基板表面粗度的均方根值.文中介绍了样品制备、反射率测量、数据解析及误差分析的方法,并给出了C、Au、Pt超薄膜的相应结果.     

Optical constants of titanium and silicon dioxide films

In this paper a study of optical constants of titanium and silicon dioxide films prepared in Balzers BAK 600 and BA 510 conventional high-vacuum apparatus is described. Both the dispersion and the geometrical thickness were determined from normal reflectance spectrum by adapted general algorithm of the statistical interpretation of measured data. The dependence of optical constants on oxygen pressure for both materials and the evaporation rate dependence for titanium dioxide were obtained. The time changes of these constants were also measured.     

银薄膜对光学基底表面粗糙度及光散射的影响

为了研究金属银薄膜与光学基底表面粗糙度和光散射的关系,提出了通过对光学薄膜矢量散射公式积分来获得界面粗糙度完全相关模型和完全非相关模型下其表面的总反射散射的方法.理论计算了光学基底上两种模型在不同厚度银膜下的总反射散射和双向反射分布函数.结果表明,当沉积在光学基底上的银薄膜的厚度大于80 nm后,两种模型下计算的银薄膜的表面总反射散射都等于基底的总积分散射,银薄膜能较好地复现出基底的粗糙度轮廓.实验研究表明为了复现基底的粗糙度,银薄膜的最佳厚度应在80~160 nm之间.     

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

This paper presents a parametric study of the time-resolved hemispherical reflectance of a plane-parallel slab of homogeneous, cold, absorbing, and isotropically scattering medium exposed to a collimated Gaussian pulse. The front surface of the slab is transparent while the back surface is assumed to be cold and black. The 1-D time-dependent radiation transfer equation is solved using the modified method of characteristics. The parameters explored include (1) the optical thickness, (2) the single scattering albedo of the medium, and (3) the incident pulse width. The study pays particular attention to the maximum transient hemispherical reflectance and identifies optically thin and thick regimes. It shows that the maximum reflectance is independent of the optical thickness in the optically thick regime. In the optically thin regime, however, the maximum hemispherical reflectance depends on all three parameters explored. The transition between the optically thick and thin regimes occurs when the optical thickness is approximately equal to the dimensionless pulse width. Finally, correlations relating the maximum of the hemispherical reflectance as a function of the optical thickness, the single scattering albedo of the materials, and the incident pulse width have been developed. These correlations could be used to retrieve radiation characteristics or serve as initial guesses for more complex inversion schemes accounting for anisotropic scattering.