Correlation-free reflection diagnostics of biaxially anisotropic nanoscale films on transparent isotropic materials

The possibilities of determining the parameters of biaxially anisotropic ultrathin dielectric films on transparent isotropic substrates by differential reflectance and ellipsometric measurements are analyzed. The analysis is based on analytical reflection formulas obtained in the framework of a long-wavelength approximation. It is shown that it is possible to simultaneously determine the thickness and all six parameters of anisotropy for such films. The accuracy of the obtained analytical formulas for determining the parameters of anisotropic ultrathin films is estimated by computer simulations where the reflection problem was solved numerically on the basis of the rigorous electromagnetic theory for anisotropic layered systems.     

Closed equation for the normal incidence reflectance of thin films on absorbing substrates

The optical constants of thin films can be obtained from inversion of spectrophotometric measurements by using minimization gradient methods. The computational approach of these minimization methods requires closed compact formulas for reflectance and/or transmittance. For normal incidence closed compact formulations for the direct transmittance, both for thin films on transparent or absorbing substrates, and for the reflectance of thin films on transparent substrates, are available in the literature. We report here a closed compact formula to evaluate reflectance spectra of thin films on absorbing substrates, and it is shown that for vanishing substrate absorption this new, to the best of our knowledge, approach gives the same results obtained from the formulation corresponding to thin films supported by transparent substrates.     

Ellipsometry of anisotropic (sub)nanometric dielectric films on absorbing materials

A new ellipsometric method was developed for determining optical parameters of ultrathin uniaxially anisotropic dielectric films. It is based on the phase conversion measurements of polarized reflected light at different incident angles. The elaborated technique possesses very high sensitivity and is successfully applicable even for sub-nanometric layers because the phase changes for such layers on absorbing substrates are generally markedly greater than the measurement error. Another interesting facet of this method lies in the fact that the traditional model-based regression analysis is not used for data handling. The inversion problem is resolved on the basis of an original analytical approach, which has no need of initial guesses for the desired parameters. The presented method is tested using a numerical simulation.     

Reflection of light in the vicinity of the Brewster angle from a multilayer system of ultrathin inhomogeneous dielectric films

An analysis of the influence of nanoscopically stratified dielectric overlayer on the reflection parameters of linearly polarized light from transparent substrates is carried out. The second-order formulas for characteristic Brewster angles are derived and their accuracy is estimated by using exact numerical methods for the solution of the inhomogeneous reflection problem. The possibilities are discussed for determining the parameters of nanometre-scale dielectric layers by means of characteristic reflection angles. A novel scanning angle differential reflectance method in the vicinity of the classical Brewster angle, whose sensitivity is in principle the same as that of ellipsometry, is developed.     

Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements

We propose a new and simple procedure to overcome the ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements. The basis for the proposed method is an error analysis with the help of an error simulation technique and an error variation technique. We show that in practice (owing to experimental errors) it is not possible to overcome the problem of ambiguity by normal-incidence spectroscopic measurements alone. At least one oblique-incidence measurement is necessary for unambiguously determining the optical constants of the film. We discuss the consequences of experimental errors of the measured transmittance and reflectance values for the determination of the optical constants.     

Optical constants of absorbing films

A new method for the determination of the optical constants of absorbing films supported on a transparent substrate using measured normal incidence R/T and R/T values is presented. Compared to the classical normal incidence photometric methods of deducing the optical constants from the measured R and T values the present method offers a time saving of 50% in experimental measurements and is able to give the optical constants and thickness of the films simultaneously to an accuracy of 2% and 0.5% respectively.     

Analytical method of determining optical constants of a weakly absorbing thin film

We propose an analytical method for determining the refractive index and the extinction coefficient of a weakly absorbing thin film. This method is based on measurements of the reflectance extreme and corresponding transmittance of the film at normal incidence. Simulations of the theoretical accuracy of the method are given. The effect of the errors of reflectance and transmittance measurements on determination of the optical constants is also analyzed. The method is successfully applied to calculate the optical constants of indium tin oxide films.     

IR spectroscopic determination of the refractive index and thickness of hydrogenated silicon layers

IR spectroscopic techniques widely used to determine the thickness and refractive index of layers and thin films of various materials are adapted for determining those of hydrogenated silicon layers. Based on a literature analysis, three formulas are chosen which enable the refractive index and thickness of such layers to be determined from reflection and transmission spectra. The formulas are applicable, with some restrictions, to other samples in the form of relatively transparent layers (films) on transparent substrates. Experimental data are presented that illustrate the use of the formulas.     

Simultaneous determination of the optical constants and thickness of very thin films by using soft-x-ray reflectance measurements

A nonlinear, least-squares curve-fitting method is described that simultaneously determines the optical constants and the thickness of a very thin (? 100-?) film from reflectance versus angle of incidence (R - θ) data measured in the soft-x-ray region. The method is applied to R - θ data obtained for very thin, sputtered films of carbon (65 ? thick) and gold (94 ? thick) at photon energies of 60-900 eV. The results show that the present method is capable of accurately determining the thickness of very thin films even for transparent materials, and that the obtained optical constants are in good agreement with values reported for films with a thickness of 1000 ?.     

Determination of the Optical Constants and Thickness of a Highly Absorbing Film Using the Attenuated Total Reflection Technique

Abstract

Theoretical analysis of the Kretschmann configuration for attenuated total reflection experiments shows that near the critical angle the reflectivity is strongly dependent upon the dielectric constants and thickness of a thin absorbing layer on the prism surface. Numerical calculations based on Fresnel's equations illustrate this clearly for thin absorbing films. Using this property of highly absorbing films it has then been possible to determine the optical constants of a thin film of phthalocyanine over the visible region of the spectrum.     

Diffuse reflectance and transmittance spectra of an interference layer. 2. Evaluation of tin oxide-coated glass

A model for the calculation of diffuse reflectance and transmittance of a single interference layer on a transparent substrate is applied to pyrolytically deposited tin oxide films on glass. Total as well as diffuse reflectance and transmittance spectra were measured in an integrating sphere, and scattering levels between 0.002 and 0.1 were recorded. The optical constants and the thickness of the films were determined from the total reflectance and transmittance spectra. The wavelength-dependent effective root-mean-square roughness of aluminum-coated tin oxide front surfaces was determined by the application of the scalar scattering theory. Surface roughness values between 5 and 25 nm were obtained. The obtained effective rms roughness values of the air-film interface were used together with the other film parameters to calculate the diffuse reflectance and transmittance spectra of the tin oxide-coated glass substrates. A comparison between calculated and experimental spectra showed good agreement for diffuse reflectance, diffuse transmittance, and total integrated scattering spectra.     

Monitoring the deposition of an interference film by differential reflection of light

The change in the reflection (differential reflection) of light from an interference film as a result of the deposition of an ultrathin layer on it is investigated. Formulas describing the differential reflection around the reflectivity minima and maxima of the film are obtained by a perturbation method. It is shown that these formulas and the corresponding differential measurements can be used for an easy and unambiguous determination of the thickness and refractive index not only of ultrathin surface layers but also of the interference films themselves. The proposed method is especially convenient for monitoring the deposition of thin-film structures. Pis’ma Zh. Tekh. Fiz. 24, 78–86 (October 26, 1998)     

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 characterization of sputtered semitransparent zirconium nitride films

Thin semi-transparent ZrN films have been prepared using reactive dc magnetron sputtering. The films had thickness from 11 to 43 nm and were grown on heated and room temperature glass substrates. The optical constants, N=n+ik, of the thin films have been determined with an RT inversion method in the wavelength interval 0.40 to 2.0 μm. The thickness of the films was determined from the photometric measurements. The optical properties of the thin films on glass were compared to opaque and thin ZrN films grown on single crystalline Si. The Drude parameters were calculated from the measured optical constants in the relaxation region of the thin films. The relaxation time, τ, of the thin films was found to increase with film thickness, substrate temperature and substrate crystallinity. The relaxation time is the mean free time for the electrons between collisions and a long relaxation time corresponds to a film with high optical quality. The observed decrease of τ with decreasing film thickness can be explained by the higher statistical probability of the electrons in a thin film to collide with the two surfaces of the film. Another explanation to the decrease of τ with film thickness is scattering from grain boundaries and lattice impurities. The higher optical quality of films grown on heated substrates is probably due to an increased grain size. The measured optical constants were compared with calculated optical constants, using the Drude model, and the optical behaviour of thin ZrN films was found to be well described by the screened free-electron model.     

Analysis of errors in thin-film optical parameters derived from spectrophotometric measurements at normal light incidence

A comparative analysis is made of the errors in deriving the optical parameters (n, refractive index; k, absorption coefficient; d, film thickness) of thin films from spectrophotometric measurements at normal light incidence. The errors in determining n, k, and d by the (TR(f)R(b)), (TR(f)R(m)), (TR(b)R(m)), (TR(f)), (TR(m)), and T(k = 0) methods are compared. It is shown that they are applicable to optical constants of thin films in the n > 1.5, k < 4.5, and d/lambda = (0.02-0.3) range, and their combinations make possible the determination of n and k to an accuracy of better than ?4%. To derive the optical constants in a wide spectral range with high accuracy and isolate the correct physical solutions reliably, one should apply all methods, using the relevant solutions with the lowest errors, as shown in this research, when determining the optical constants of As(2)S(3) and Sb(2)Se(3) films.     

The optical properties of thin cobalt films by a self-consistent photometric technique

The advantages, difficulties and limitations of photometric techniques for the determination of optical constants are discussed. An optimized self-consistent procedure is used to evaluate the optical constants of a series of cobalt films from simple relative reflectance measurements. The films are polycrystalline and range in thickness from 110 to 10 nm. In addition to possible interband structure a strong resonance peak was observed in their optical absorption spectrum at 1.1 eV. This is tentatively identified as “optical conduction resonance” which is a collective free-electron oscillation in the aggregated surface or structure of the films.     

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.     

Multiple-angle-of-incidence ellipsometry for GaAs\GaPAs superlattices

In this paper we present results of multiple-angle-of-incidence (MAI) ellipsometry for strained GaAs\GaP_xAs_1−x superlattices (SL) with the composition x ≈ 0.4 and with different layer thickness in the range of 8–80 nm. SLs have been grown on the GaAs (100) substrates by chemical vapour deposition. The geometrical parameters of SLs have been determined by X-ray diffraction patterns. From MAI measurements the thickness and optical constants of SL films have been calculated by solving inverse ellipsometric problem. The latter was solved by using Tichonov’s regularization algorithm. The anisotropic film model of SL and capping isotropic layer were taken into account at solving. The optical constants obtained together with the full thickness of SL have been related to the SL microstructure using an effective medium approximation. These results are compared with ones obtained by far-infrared reflection spectroscopy in the ‘‘reststrahlen’’ band region. The quality of SLs in connection with technology of thin films growth are discussed.     

Optical properties of gold island films—a spectroscopic ellipsometry study

Metal island films of noble metals are obtained by deposition on glass substrates during the first stage of evaporation process when supported metal nanoparticles are formed. These films show unique optical properties, owing to the localized surface plasmon resonance of free electrons in metal nanoparticles. In the present work we study the optical properties of gold metal island films deposited on glass substrates with different mass thicknesses at different substrate temperatures. The optical characterization is performed by spectroscopic ellipsometry at different angles of incidence and transmittance measurements at normal incidence in the same point of the sample. Fitting of the ellipsometric data allows determining the effective optical constants and thickness of the island film. A multiple oscillator approach was used to successfully represent the dispersion of the effective optical constants of the films.