Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data

Artificial neural networks and the Levenberg–Marquardt algorithm are combined to calculate the thickness and refractive index of thin films from spectroscopic reflectometry data. Two examples will be discussed, the first is a measurement of thickness and index of transparent films on silicon, and the second is a measurement of three thicknesses and index of poly-silicon in a rough poly-silicon on oxide stack. A neural network is a set of simple, highly interconnected processing elements imitating the activity of the brain, which are capable of learning information presented to them. Reflectometry has been used by the semiconductor industry to measure thin film thickness for decades. Modeling the optical constants of a film in the visible region with a Cauchy dispersion model allows the determination of both thickness and refractive index of most transparent thin films from reflectance data. The use of an alloy interpolation model for the optical constants of poly-silicon allows the determination of thicknesses and poly optical constants. In this work artificial neural networks are used to obtain good initial estimates for thickness and dispersion model parameters, these estimates are then used as the starting point for the Levenberg–Marquardt algorithm which converges to the final solution in a few iterations. These measurement programs were implemented on a Nanometrics NanoSpec 8000XSE.     

Tailoring the structural,electrical, and optical features of Erbium(III)-Tris(8-hydroxyquinolinato) nanostructured films for optical applications: effect of film thickness

This paper elaborates on the thickness-dependent structural, optical, and electrical properties of Erbium(III)-Tris-8-hydroxyquinolinato (ErQ3) films. The surface morphology reveals the grains that consolidate to make denser films with increasing film thickness. The ErQ3 grain sizes increased from 80 to 187 nm as the thickness increased from 80 to 190 nm. From XRD analysis, the ErQ3 films are partially crystallized with only one peak at 2θ?=?9.80° and a plateau in the range of 20–40°. Electrical measurement of ErQ3 films showed that the electrical conductivity had a strong dependence on film thickness. Transmittance and reflectance measurements showed that the films exhibited a 2.60 eV bandgap, and it does not depend on the thickness of the film. Also, the dispersion of the refractive index was analyzed to determine the essential parameters. The nonlinear optical parameters such as nonlinear refractive index and third-order nonlinear optical susceptibility were calculated by Miller's principles.

     

Thickness dependence of structural and optical properties of indium tin oxide nanofiber thin films prepared by electron beam evaporation onto quartz substrates

Indium tin oxide (ITO) thin films, produced by electron beam evaporation technique onto quartz substrates maintained at room temperature, are grown as nanofibers. The dependence of structural and optical properties of ITO thin films on the film thickness (99-662 nm) has been reported. The crystal structure and morphology of the films are investigated by X-ray diffraction and scanning electron microscope techniques, respectively. The particle size is found to increase with increasing film thickness without changing the preferred orientation along (2 2 2) direction. The optical properties of the films are investigated in terms of the measurements of the transmittance and reflectance determined at the normal incidence of the light in the wavelength range (250-2500 nm). The absorption coefficient and refractive index are calculated and the related optical parameters are evaluated. The optical band gap is found to decrease with the increase of the film thickness, whereas the refractive index is found to increase. The optical dielectric constant and the ratio of the free carrier concentration to its effective mass are estimated for the films.     

Determination of the optical constants (n and k) of inhomogeneous thin films with linear index profiles

A new method for the determination of optical constants of absorbing inhomogeneous thin films is proposed. It requires measurements at normal incidence of the reflectance and transmittance of the film. In an inhomogeneous thin film, the optical constants vary along the thickness of the film. It has been reported in the literature that only the spatial integral value of the absorption index needs to be considered if its value is small. Therefore, in the proposed method, the mean value of the absorption index was used. The validity of this assumption was tested. On the other hand, the variation in the refractive index along the thickness of the film was taken into account. The method is discussed along with the nature of the solutions obtained and the effects of various parameters and assumptions. The method is applied successfully to inhomogeneous thin films of zirconium oxide.     

Optical constants of aluminum films in the extreme ultraviolet interval of 82-77 nm

Measurements of the extreme ultraviolet (EUV) reflectance of unoxidized aluminum films versus the angle of incidence in the interval of 82-77 nm, just below the aluminum plasma wavelength (83 nm), are presented. The continuum of helium was used as a radiation source for the first time in EUV reflectometry, to our knowledge. The surface roughness of substrates and samples was characterized by atomic force microscopy. The complex refractive index of unoxidized aluminum was obtained from reflectance measurements at each wavelength for the first time in this spectral range. Data on the refractive index, the dielectric constant, and the energy loss function in the above interval are shown together with our previous data obtained in an interval of 82.6-113.5 nm. Current results on the refractive index show a good match with the data in the literature calculated through the Kramers-Kronig analysis, the largest differences being in the imaginary part of the refractive index at the shortest wavelengths.     

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.     

Far-infrared laser measurement of the refractive index of polypropylene

The refractive index of polypropylene in the far infrared (FIR) is measured by means of a suitably modified laser of a FIR spectrometer. When thin polypropylene films of 12.7-microm nominal thickness are introduced in the optical cavity of a laser at the Brewster angle, the radiation ceases because of the change in the optical path of the laser beam. This change is measured from the displacement of one of the laser mirrors, which is necessary to restore the laser resonance. The refractive index of polypropylene is deduced from this measurement and from the film thickness, as obtained from an independent measurement based in pycnometry. The value obtained for the refractive index is 1.492(15) for the wavelengths between 118.834 and 251.140 microm, for a polypropylene film of 12.71(2)-microm thickness and 0.9049(7) g/cm3 density.     

Reflectance spectra and refractive index of a Nd:YAG laser-oxidized Si surface

The reflectance spectra and refractive index of Nd:YAG laser-oxidized SiO₂ layers with thicknesses from 15 to 75 nm have been investigated with respect to the laser beam energy density and substrate temperature. Thickness and refractive index of films have been determined from reflectance measurements at normal light incidence in the spectral range 300–800 nm. It was found that the oxide-growth conditions at higher substrate temperatures and laser powers greater than 3.36 J cm⁻² provides a better film quality in terms of both optical thickness and refractive index. However, the refractive indices of the films are smaller in the whole spectral range studied as compared to that of conventional thermally grown SiO₂. This might be due to the porous structure formed during the laser-assisted oxidation. The results suggest the need of post-oxidation annealing to improve the refractive indices of the films, suitable for Si-device applications.     

Simple Method for Determining Slowly Varying Refractive-Index Profiles from in situ Spectrophotometric Measurements

Reliable control of the deposition process of optical films and coatings frequently requires monitoring the refractive-index profile throughout the layer. In the present research a simple in situ approach is proposed that uses a WKBJ matrix representation of the optical transfer function of a single thin film on a substrate. Mathematical expressions are developed that represent the minima and the maxima envelopes of the curves transmittance versus time and reflectance versus time. The refractive index and the extinction coefficient depth profiles of different films are calculated from simulated spectra as well as from experimental data obtained during the PECVD (plasma-enhanced chemical vapor deposition) of silicon-compound films. Variation in the deposition rate with time is also evaluated from the position of the spectra extrema as a function of time. The physical and mathematical limitations of the method are discussed.     

Optical properties of SiO2-TiO2 sol-gel thin films

The optical properties of thin SiO₂-TiO₂ sol-gel composite films were investigated using exact optical models and the Forouhi-Bloomer model, (Phys. Rev. B34, 7018 (1986)), which describes the optical dispersion of amorphous dielectrics. Films deposited on glass and silicon substrates, were characterized by optical transmission and reflection measurements. Theoretical spectra have been generated and fitted to the experimental ones via standard regression analysis techniques. The (five) adjustable Forouhi-Bloomer parameters describing the dispersion of the complex refractive index, as well as the film thickness were determined. The refractive index and absorption coefficient of the films were found to depend on the molar contents of the component oxides.     

Metallized thiazolylazo dyes as optical recording materials

A series of metallized thiazolylazo dyes have been designed and synthesized. Smooth films on optical glass and single-crystal silicon were prepared using the spin-coated method. The UV-Vis absorption spectra of the dyes were measured in solution and in films. The optical constant (complex refractive index N=n+ik) of the films on single-crystal silicon has been determined using a scanning ellipsometer. The variation of the complex refractive index, N, with wavelength, λ, was obtained. From the value of n, k and the thickness of the dye films, the variation of the reflectance vs dye film thickness was then calculated. Thermogravimetric analysis (TGA) and differential thermal analysis (DTA) of the nickel thiazolylazo dye showed a clear threshold of thermal decomposition with a sharp exothermic park. Static optical recording tests were carried out. The results show that the nickel thiazolylazo dye is more suitable for use in short-wavelength diode-laser optical recording.     

A study of silicon oxynitride film prepared by ion beam assisted deposition

A SOI-based optoelectronic device needs a high-quality antireflection coating on both faces of the device to minimize the optical reflectance from the face. In this work amorphous silicon oxynitride films were deposited on silicon substrates by ion beam assisted deposition (IBAD). The main purpose was to use silicon oxynitride film as single layer anti-reflection coating for SOI-based optoelectronic devices. This application is primarily based on the ability to tune the silicon oxynitride optical functions to the optimal values by changing deposition parameters. The chemical information was measured by X-ray photoelectron spectroscopy (XPS). Spectroscopic ellipsometry (SE) was applied to measure the refractive index and thickness. Single-side polished silicon substrate that was coated with silicon oxynitride film exhibited low reflectance. Double-side polished silicon substrate that was coated with silicon oxynitride film exhibited high transmittance. In addition, the Fresnel losses could be reduced to 0.08 dB by depositing silicon oxynitride films onto double-side polished silicon substrates. The results suggested silicon oxynitride film was a very attractive single layer anti-reflection coating for SOI-based optoelectronic device.     

Structural and optical properties of layer-by-layer solution deposited Cu2SnS3 films

Cu₂SnS₃ (CTS) is a simple and potential material for low-cost thin film solar cells. The present work incorporates the study of changes in structural and optical properties of layer-by-layer solution deposited CTS films with annealing. Raman spectroscopy is used to ascertain structural modification upon annealing. Increase in annealing temperature leads to a structural transition from tetragonal to cubic phase. Effect of annealing on optical properties of the films is evaluated in the wavelength range of 400–2,400 nm. It is proposed that layer-by-layer growth method fundamentally defines the optical behaviour of these films. Optical constants and parameters such as refractive indices, dielectric constants and electron energy loss function are calculated from transmittance and reflectance data. The refractive indices, n and k are determined to be in ranges of 1.8–2.2 and 0.18–1.2, respectively. The real and imaginary dielectric constants vary from 1.5 to 4.6 and 0.7 to 5, respectively. Dispersion of refractive index is analyzed using two different theoretical models of Wemple–diDomenico and Spitzer–Fan.     

Optical properties of PZT thin films deposited on a ZnO buffer layer

The optical properties of lead zirconate titanate (PZT) thin films deposited on ZnO were studied by m-lines spectroscopy. In order to retrieve the refractive index and the thickness of both layers from the m-lines spectra, we develop a numerical algorithm for the case of a two-layer system and show its robustness in the presence of noise. The sensitivity of the algorithm of the two-layer model allows us to relate the observed changes in the PZT refractive index to the PZT structural change due to the ZnO interface of the PZT/ZnO optical waveguide.     

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.     

Physical properties of thermally evaporated silicon films nitrided at different rf plasma-processing time

Nitrided surfaces and composition gradients in thin films exhibit interesting mechanical, electrical, and optical properties. Therefore, amorphous hydrogen-free silicon (a-Si) thin films were deposited by electron beam evaporation and subsequently nitrided by an inductively coupled rf plasma. The effects of successive plasma-processing cyclic time on structural and optical properties as well as electrical resistivity were examined by different characterization techniques. It was found that the rf plasma treatment has a massive effect on the physical properties of the Si films. The Si thin films were transformed gradually into nitrides compound and the amount of nitrogen in the film increased with increasing the rf plasma-processing time. The Si nitrided films showed structural, optical, and electrical properties dependent on the plasma-nitriding time. Increasing the rf plasma-processing time reduced the thickness, increased transmittance, increased resistivity, and decreased the reflectance of the nitrided Si films. The electrical resistivity increased to about nine orders of magnitude when the film was nitrided at a plasma-processing time of 25 min. The optical band gap increased from 2.42 to 3.52 eV with increasing the plasma-processing time from 10 to 35 min. The decrease in the refractive index with the increase in the plasma-processing time is attributed to the possible change in the bucking density as well as to the increase in the band gap.     

Thermal stability of sputtered zirconium oxide films

In this work, the effect of post-growth annealing on the structural and optical properties of sputtered zirconium oxide films has been investigated. The temperature dependence of structure, density, and optical constants has been systematically studied by X-ray diffraction, X-ray reflectometry, atomic force microscopy (AFM) and optical spectroscopy. X-ray diffraction studies show no variation in the crystalline phase upon annealing except grain growth. X-ray reflectivity measurements determine a density increase of approximately 11% and a simultaneous thickness reduction of 10% upon annealing. The surface roughness of the films increases upon annealing as determined by XRR and confirmed by AFM measurements. Optical spectroscopy measurements confirm that the refractive index n of the films decreases with increasing annealing temperature. At the same time the optical band gap E_g of the films increases from 4.58 to 4.97 eV annealing at 900°C. The surprising decrease of refractive index upon annealing is attributed to both the intermixing of Si with ZrO₂ and the increasing surface roughness of the films.     

A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence

A method is proposed for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence over an extended wavelength interval. A necessary condition for the applicability of the method is the existence of maxima and minima in the reflectance due to interference effects. The problem of multiple solutions is analysed and the optical thicknesses at the extrema are used for choosing the correct solutions. For absorbing films two alternative procedures are described. One procedure requires an approximate value of the film thickness to start with and refines it during the calculation. The other procedure does not depend on a previous knowledge of the thickness but gives it as a result together with n(λ) and k(λ). A separate procedure is proposed for transparent and almost transparent films. An application of the method is carried out in which excellent agreement is obtained between calculated and experimental results.     

Advanced key technologies for magnetron sputtering and PECVD of inorganic and hybrid transparent coatings

Besides classical multilayer systems with alternating low and high refractive indices, reactive pulse magnetron sputtering processes offer various possibilities of depositing gradient films with continuously varying refractive index. Using nanoscale film growth control it is possible to achieve optical filter systems with a defined dependency of refractive index on film thickness, e.g. by sputtering a silicon target in a time variant mixture of oxygen and nitrogen. Also reactive co-sputtering of different target materials such as silicon and tantalum in oxygen is suitable as well. Rugate filters made from SiO_xN_y or Si_xTa_yO_z gradient refractive index profiles find their application in spectroscopy, laser optics and solar concentrator systems.Furthermore polymer substrates are increasingly relevant for the application of optical coatings due to their mechanical and economical advantages. Magnetron PECVD (magPECVD) using HMDSO as precursor allows to deposit carbon containing films with polymer-like properties. Results show the suitability of these coatings as hard coatings or matching layers. Multifunctional coatings with antireflective and scratch-resistant properties were deposited on polymer substrates using a combined magPECVD and sputter deposition process.     

Analytical solutions for determining the optical constants of very thin films

A method for determining the refractive index (n), extinction coefficient (k), and physical thickness (d) of very thin films is presented. After limited development of the film characteristic matrix elements to the third order in (d/λ) (λ is wavelength), we derive simple analytical expressions for n, k, and d in terms of the film front reflectance, back reflectance and transmittance. The main advantages of the method are that the equations for n, k, and d are simpler, have a lower order and allow calculation of the optical constants with lower uncertainties than in the case of similar methods described in the literature.