Determination of thickness, refractive index, and thickness irregularity for semiconductor thin films from transmission spectra

A simplified theoretical model has been proposed to predict optical parameters such as thickness, thickness irregularity, refractive index, and extinction coefficient from transmission spectra. The proposed formula has been solved for thickness and thickness irregularity in the transparent region, and then the refractive index is calculated for the entire spectral region by use of the interference fringes order. The extinction coefficient is then calculated with the exact formula in the transparent region, and an appropriate model for the refractive index is used to solve for the extinction coefficient in the absorption region (where the interference fringes disappear). The proposed model is tested with the theoretical predicted data as well as experimental data. The calculation shows that the approximations used for solving a multiparameter nonlinear equation result in no significant errors.     

Simulation and fabrication of attenuated phase-shifting masks: CrF(x)

To acquire the required resolution for 248- and 193-nm lithography, a study of attenuated phase-shifting mask (Att-PSM) technology is in progress. We performed a simulation study using a matrix method to calculate relative transmittance and the amount of phase shift of light through the PSM. However, we found that the average film composition changed with deposition time. Accordingly, optical constants were found to be a strong function of film thickness. Therefore we rearranged the relationship between deposition parameters (e.g., deposition time or gas flow rate ratio) and optical constants (e.g., refractive index and extinction coefficient) to extract the empirical formula for the optical constants with respect to film composition. To verify our simulation study, we fabricated a phase shifter based on our simulation result, which was found to have a transmittance of 8.3% and a phase shift of 179.5 degrees . Consequently, we obtained a reliable optimum condition for the deep-ultraviolet Att-PSM.     

Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements

Spectrally resolved white-light phase-shifting interference microscopy can be used for rapid and accurate measurements of the thickness profile of transparent thin-film layers deposited upon patterned structures exhibiting steps and discontinuities. We examine the sensitivity of this technique and show that it depends on the thickness of the thin-film layer as well as its refractive index. The results of this analysis are also valid for any other method based on measurements of the spectral phase such as wavelength scanning or white-light interferometry.     

浮法玻璃表面光学常数分析

本文通过光谱椭偏仪测量浮法玻璃空气面和锡面的偏振信息,利用Cauchy光学模型分析得到浮法玻璃两表面的布鲁斯特角和光学常数,分析结果表明浮法玻璃空气面、锡面、理想玻璃界面的布鲁斯特角分别为56.7°、57°和56.8°,空气面形成疏松的表面层,厚度为2.75nm,折射率小于玻璃本底,锡面形成锡扩散表面层,厚度为81.29nm,折射率大于玻璃本底折射率,并且随厚度呈现出非线性梯度变化,结合透光率数据分析得到玻璃消光系数在10-6量级。由于浮法玻璃空气面和锡面的折射率明显不同,需要在后续玻璃镀膜光学设计时区别对待。     

Determination of the parameters of surface layers on glasses by p-polarized reflectances

The relationship between the incidence angle of a p-polarized beam and the reflectance ratio on both sides of glass or other transparent material is very sensitive to surface layer parameters such as refractive index, extinction coefficient, and thickness, especially when the refractive indexes of the surface layers and the flat host are nearly the same. We provide some primary experimental results and the numerical simulation on the basis of the theory of thin-film optics. By data fitting, we determine the parameters of the glass surface layer with this method, which has the advantages of simplicity of both equipment and understanding.     

Determination of properties of wedged, nonuniformly thick, and absorbing thin films by using a new numerical method

Nonuniformity in the thickness of thin films can severely distort their transmission spectra as compared with those of flat, smooth films. Methods that extract properties such as refractive index, thickness, and extinction coefficient of such films can suffer inaccuracies when they are applied to wedged or nonuniformly thick films. To accurately extract optical properties of nonuniform films, we have developed a novel numerical method and efficient constitutive relations that can determine film properties from just the transmission spectrum for films that are locally smooth with negligible scattering loss. This optimum parameter extraction (OPE) method can accommodate films with two-dimensional thickness variation that would result in significant errors in the values of refractive index and film thickness if not considered. We show that for carefully chosen test cases and for actual pulsed-laser-deposition AlN thin films, properties such as refractive index, extinction coefficient, and film thickness were very accurately determined by using our OPE method. These results are compared with previous techniques to determine the properties of thin films, and the accuracy of and applicable conditions for all these methods are discussed.     

Porous silica xerogel films as antireflective coatings – Fabrication and characterization

The paper presents a simple fabrication method of porous silica xerogel films. By adding a surface active agent Triton X-100™ to the starting solution, we can considerably reduce the surface tension, which, in turn, allows to fabricate silica films of high porosity. The paper presents the influence of surfactant content and the influence of heating temperature on the refractive index and thickness of the fabricated films. We fabricated silica films of the minimum refractive index below 1.3 and corresponding porosity ∼50%. Due to low refractive index, the elaborated porous silica xerogel films can be applied to reduce the light reflection coefficient in optical systems. In this work the spectral characteristics of the refractive index, extinction coefficients, the reflection and transmission coefficients and also depolarization factor are presented. The paper also provides results of surface morphology of produced layers, obtained using an atomic force microscope.     

Titanium oxide film for the bottom antireflective layer in deep ultraviolet lithography

Titanium oxide thin film, fabricated with tetraisopropyltitanate and oxygen by electron cyclotron resonance-plasma-enhanced chemical vapor deposition, is investigated as a potential candidate for the antireflective layer in KrF excimer laser (248-nm) lithography. The oxygen flow-rate dependence of the optical properties such as the refractive index (n) and the extinction coefficient (k) of the film at the 248-nm wavelength has been characterized, and the films with the expected combinations of n and k values for the antireflective layer have been deposited. Simulation results indicate that reflectance values of less than 4% and as low as 1.2% can be reached at the interface between the photoresist and the film postulating the structures of the photoresist/300-A TiO(x) film/c-Si substrate and the W-Si substrate, respectively, by selected proper combinations of n and k values. Moreover the reflectance can be further reduced to almost zero by changing the film thickness. Thus it is found that titanium oxide thin films can be used as the bottom antireflective layer in KrF excimer laser lithography.     

Development of thickness measurement program for transparent conducting oxide thin films

The gallium doped zinc oxide has been one of the candidates for the transparent conducting oxide thin film electrode. It is not suitable to use a conventional light interference method to measure the thickness of the gallium doped zinc oxide thin film because the refractive index and extinction coefficient of the thin film is unknown during the optimization of the deposition conditions. In this paper, we report on the details of the film thickness program which uses the measured optical and electric properties and relationship between the plasma frequency and the optical constant of the film. The obtained film thickness of the prepared gallium doped zinc oxide thin film using the program was comparable with thicknesses measured by a cross-sectional analysis of the atomic force microscopy and the surface profiler. Moreover, the optical constant of refractive index and extinction coefficient of the film could also be estimated.     

Optical and microstructural characterization of sol/gel derived cerium-doped PZT thin films

Optical properties of cerium-doped PZT thin films on sapphire prepared by a sol-gel technique are investigated using both transmission and reflection spectra in the wavelength range 200 to 900 nm. The refractive index, extinction coefficient and thickness of the film are determined from the measured transmission spectra. The packing density of the film is calculated from its refractive index using the effective medium approximation (EMA), and average oscillator strength and wavelength are estimated using a Sellmeir-type dispersion equation. Absorption coefficient (α) and the band gap energy (E_g) of each film composition are also calculated. Possible correlations of microstructure and phase formation behaviour with changes in band gap energy and other optical properties are discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Modeling of the refractive index and extinction coefficient of binary composite films

Southwell's analysis of optical multilayers within the limits of very thin films has been extended to include absorption in the multilayer for predicting the effective values of the refractive index n(e) and extinction coefficient k(e) of mixed-composition binary homogeneous films over a wide spectral region, including the high-absorption (k > 10(-2)) region. It has been found that n(e) in general is a complicated function of the optical parameters (n(1), k(1), n(2), k(2)) and volume fractions (f(1), f(2)) of the component materials in a homogeneous layer, and the expression for n(e) becomes the same as that predicted by the Drude model in the spectral region where the layers are transparent. Moreover, according to the present analysis, the volume fractions of the product of the refractive index and the extinction coefficient of the component materials of a binary composite film are additive and the sum equals the product of the effective refractive index and extinction coefficient of the composite film.     

Antireflecting coating from Ta<Subscript>2</Subscript>O<Subscript>5</Subscript> and SiO<Subscript>2</Subscript> multilayer films

Sol-gel method is important for depositing antireflective coating that allows control over thickness as well as the index of refraction. Antireflective coatings which are produced from Ta₂O₅ and SiO₂ multi-layer thin films using sol-gel spin coating method are presented. The refractive index and the thickness are controlled by the composition and the concentration of the solution respectively. The thickness, refractive index and extinction coefficient of the films were calculated through transmission and reflection measurement by an NKD analyser. Mechanical properties of the films were checked by the cross tape test and dry sun test at 760 W/m². The result shows that the sample heat treated at 450^∘C for 15 min approaches a reflectance with less than 0.5% at around 840 nm.     

Determination of the refractive index and thickness of holographic silver halide materials by use of polarized reflectances

A method to determine the refractive index and thickness of silver halide emulsions used in holography is presented. The emulsions are in the form of a layer of film deposited on a thick glass plate. The experimental reflectances of p-polarized light are measured as a function of the incident angles, and the values of refractive index, thickness, and extinction coefficient of the emulsion are obtained by using the theoretical equation for reflectance. As examples, five commercial holographic silver halide emulsions are analyzed. The procedure to obtain the measurements and the numerical analysis of the experimental data are simple, and agreement of the calculated reflectances, by use of the thickness and refractive index obtained, with the measured reflectances is satisfactory.     

Low temperature silicon nitride by hot wire chemical vapour deposition for the use in impermeable thin film encapsulation on flexible substrates

High quality non porous silicon nitride layers were deposited by hot wire chemical vapour deposition at substrate temperatures lower than 110 degrees C. The layer properties were investigated using FTIR, reflection/transmission measurements and 1:6 buffered HF etching rate. A Si-H peak position of 2180 cm(-1) in the Fourier transform infrared absorption spectrum indicates a N/Si ratio around 1.2. Together with a refractive index of 1.97 at a wavelength of 632 nm and an extinction coefficient of 0.002 at 400 nm, this suggests that a transparent high density silicon nitride material has been made below 110 degrees C, which is compatible with polymer films and is expected to have a high impermeability. To confirm the compatibility with polymer films a silicon nitride layer was deposited on poly(glycidyl methacrylate) made by initiated chemical vapour deposition, resulting in a highly transparent double layer.     

Interference Effects in Time-resolved Reflectivity Measurements in Thin Semiconductor Films

The study of non-equilibrium charge carriers in semiconductor films by time-resolved reflectivity measurements is greatly simplified if the change in reflectivity change varies linearly with the photoinduced change in refractive index. In the present work it is shown that interference effects in the transparent layer influence this dependence significantly. The sample reflectivity can either increase or decrease, depending on the film thickness. If the reciprocal absorption coefficient of the semiconductor is smaller than the film thickness, a refractive index profile is created inside the layer. The reflection at this profile diminishes the influence of the beams reflected at the semiconductor-substrate interface. The changes in reflectivity then vary linearly with the changes in refractive index, independently of the film thickness. Numerical calculations were performed to help interpret time-resolved reflectivity measurements on amorphous silicon films.     

Gold nanorods as nanotransducers to monitor the growth and swelling of ultrathin polymer films

In this work, we demonstrate that plasmonic nanostructures can be employed as nanoscale transducers to monitor the growth and phase transitions in ultrathin polymer films. In particular, gold nanorods with high refractive index sensitivity (~150 nm/refractive index unit (RIU)) were employed to probe the growth and swelling of polyelectrolyte multilayers (PEM). By comparing the wavelength shift and extinction intensity increase of the localized surface plasmon resonance (LSPR) of the gold nanorods coated with PEM in air and water, the swelling of PEM was estimated to be 26% ± 6%. The swelling was quantitatively confirmed with independent thickness measurement of PEM in dry and swollen states using AFM. The deployment of shape-controlled metal nanostructures with high refractive index sensitivity represents a novel and facile approach for monitoring the phase transition in polymers with nanoscale resolution.     

Substrate-dependent optical absorption characteristics of titanium dioxide thin films

We used the electron-beam evaporation method in various oxygen partial pressure environments to deposit TiO(2) thin films on various glass substrates at 300 degrees C. We found the threshold oxygen partial pressures above which the film is transparent are different for films on various substrates. Below the threshold oxygen partial pressure, the refractive index and the extinction coefficient of the films varied from substrate to substrate. The films on substrates with higher threshold oxygen partial pressure were associated with a higher extinction coefficient and a higher growth rate. These phenomena are correlated with the appearance of rutile phase in the anatase phase, which is also correlated with variations in the Al(2)O(3) and Na(2)O content in the substrates. The Al(2)O(3) content in the substrate tends to enhance the formation of rutile phase in the film and to give a higher extinction coefficient for the film, while the Na(2)O content in the substrate tends to retard the rutile formation in the film and to give a lower extinction coefficient for the film.     

Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation

A method is described for the simultaneous measurement of the refractive index and thickness of a transparent film. The method is based on the rotational shift of the interference pattern caused by the change of the light incidence angle. The refractive index is evaluated without any prior information about film thickness or about the substrate and its refractive index. In addition, the roughness of the interfaces and/or the presence of an unidentified thin layer are not important. In two experimental examples, the refractive index and thickness are measured for a GaN thin film and a cling-film.     

Determination of the Dill parameters of thick positive resist for use in modeling applications

The determination of Dill parameters of thick resist is very important to improve simulation models of resist exposure and real world processes. A new extraction technique of Dill parameters based on spectroscopic ellipsometry in combination with an advanced resist exposure model is proposed for thick resist analysis. The complex refractive index of the resist is related to the relative concentration of the photoactive compound in the resist in order to describe the vertical distribution of the refractive index and the extinction coefficient. Moreover, Dill parameters are extracted by directly fitting the bleaching curves to the measured ellipsometry data. The new approach was investigated experimentally by spectroscopic ellipsometry measurements on AZ5214E resist with two moderate layer thickness values in order to verify the accuracy of the new method. Dill parameters were extracted by using this new technique and by applying resist samples subjected to different exposure doses. Possible reasons for the variation of Dill parameters depending on resist thickness are explained. Furthermore, advantages, limitations and potential improvements of the model are discussed. Finally, the impact of Dill parameter variation on image formation in the resist is demonstrated by applying the spectroscopic ellipsometer analysis results as input parameters to the lithography simulator Dr.LiTHO.     

Dielectric Metalens by Multilayer Nanoimprint Lithography and Solution Phase Epitaxy

Metasurfaces have ushered in a huge development for their superior ability in manipulating light properties including phase, amplitude, and polarization, which show great potential as alternatives for the refractive optical devices. Recently, many applications of metasurface including metalens have been proposed and investigated, aiming at substituting their refractive counterparts. However, the commonly used fabrication approaches employ electron-beam lithography (EBL) followed by dry etching or atomic layer deposition (ALD) of dielectric materials, which are expensive and inefficient. Besides, dry etching of dielectric materials at sub-100 nm scale with a high aspect ratio is challenging. Herein, a new approach for dielectric metalens fabrication is presented, which combines multilayer nanoimprint lithography and solution phase epitaxy. High aspect ratio ZnO nanopillars with a height-to-diameter ratio of over 7:1 are demonstrated. By using the multilayer nanoimprint lithography, increased aspect ratio nanostructures from shallow imprinting molds are obtained. The highly anisotropic growth characteristic enables nanopillars to grow at a height that exceeds the resist thickness. With this ability, ZnO metalenses are fabricated where the height of nanopillar reaches 1.1 μm, achieving a focusing efficiency of 50%. The process is cost-effective with a high throughput, which can be widely used for many optical applications.