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.     

Laser reflectometry in situ measurement of lead zirconate titanate film growth

A convenient method is described for optical characterization of thin films during growth. The method has been demonstrated on lead zirconate titanate (PZT) films deposited by pulsed laser ablation for various temperatures. The optical constants of the PZT films as well as the film growth rate were determined in situ by fitting (with three free parameters) the calculated reflectance as a function of film thickness to the experimental reflectance curve as a function of deposition time, as obtained by unpolarized laser reflectometry. The fitted parameters are the uniform complex PZT refractive index and the layer thickness (assumed proportional to time), with the complex refractive index of the platinum substrate being measured previously. These results compare well with the subsequent ellipsometric measurements made to assess the precision of the reflectometry technique.     

Thickness measurements on transparent substrates based on reflection ellipsometry. I. Optical effects of high-refractive-index additional layers

Theoretical studies were conducted for thickness measurements using transparent substrates on the external and internal reflection configurations. For three-phase systems consisting of ambient, film, and substrate, the refractive index of the substrate could be optimized to obtain the high sensitivity of an ellipsometric quantity delta to the film thickness and the small susceptibility of delta to errors in the incident angle. It was shown that the combination of an ordinary glass substrate and an additional dielectric layer with an appropriate layer thickness works as a synthetic high-index single substrate (SHIS). The optical effect of the combination was approximately described by use of the effective refractive index of SHIS. A method to select the refractive index of the additional layer was also given.     

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 ?.     

Optical analysis of absorbing double layers by combined reflection and transmission ellipsometry

A method known as combined ellipsometry, which utilizes the simultaneous interpretation of the ellipsometric parameters determined for light reflected and transmitted by the air side and by the substrate side of thin films, was used to obtain an optical analysis of absorbing double layers deposited onto a non-absorbing substrate. It is shown that the use of this method enables the evaluation of all the optical parameters characterizing absorbing double layers consisting of a non- absorbing and an absorbing thin film. Combined ellipsometry can be used for analysing the double layers formed by two highly absorbing thin films in a reasonable way if this method is complemented by a precise auxiliary method, e.g. the Fizeau method. These conclusions are demonstrated by experimental results obtained for samples of the following double layers: MgF₂/Al, Al/MgF₂, TiO/Au and Au/Ni. The ellipsometric parameters were measured at a wavelength λ of 632.8 nm.     

Unambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry

We present a spectroscopic method of determining both thickness and dielectric functions of thin films on previously characterized substrates. The method requires that spectroscopic ellipsometric data be taken over an energy range where the substrate has a sharp optical structure, e.g. a critical point. These data are used to determine a “pseudodielectric” function for the film, which necessarily depends on the assumed film thickness. We develop a general first-order theory which shows that the correct thickness and dielectric function of the film are those for which the substrate feature vanishes in the calculated pseudodielectric function. The theory is also used to investigate sensitivity and applicability. We show that sensitivity can be enhanced by differentiating the pseudodielectric function with respect to energy. The method is demonstrated with several numerical and experimental examples, which illustrate that monolayer thickness accuracy can be achieved.     

Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film

Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission deltar, deltat are found to be identical, and the associated ellipsometric parameters psir, psit are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the p and s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.     

Determination of film thickness and refractive index in one measurement of phase-modulated ellipsometry

Ellipsometry is often used to determine the refractive index and/or the thickness of a polymer layer on a substrate. However, simultaneous determination of these parameters from a single-wavelength single-angle measurement is not always possible. The present study determines the sensitivity of the method to errors of measurement for the case of phase modulated ellipsometry and identifies conditions for decoupling film thickness and refractive index. For a specific range of film thickness, both the thickness and the refractive index can be determined from a single measurement with high precision. This optimal range of the film thickness is determined for organic thin films, and the analysis is tested on hydrogel-like polymer films in air and in water.     

Variable wavelength,variable angle ellipsometry including a sensitivities correlation test

Combining simultaneously both variable wavelength and variable angle of incidence to assess solutions of the optical parameters of a system, a procedure is developed which provides more information on the optical parameters than methods where either the wavelength or the angle of incidence is held constant. This results in a reduction in the interdependence of the optical parameters, and provides for more acceptable solutions. For a film on a substrate structure, if one knows the substrate optical parameters, the thickness and optical properties of the film can be characterized at each wavelength without the need for (a) a dispersion equation, (b) an independent measurement of the thickness or (c) any special requirements on the substrate optical properties. For a nearly transparent film on an absorbing substrate, all four parameters of the three-medium model (the substrate and film refractive indices, substrate extinction coefficient and film thickness) can be determined. If in addition one uses a dispersion relation for the refractive index in a very weakly absorbing film, the optical properties of an absorbing substrate and the film can be determined unambiguously.As a second major feature of this paper we show that the sensitivity correlation matrix, as well as the traditional parameter correlation matrix, should be calculated if one is to determine the independence of ellipsometric parameter solutions. An SiO₂ film on silicon is used for illustration, but of course the analysis is recommended for more complicated materials systems.     

Tilted bilayer membranes as simple transmission quarter-wave retardation plates

A tilted bilayer membrane, which consists of two thin films of transparent optically isotropic materials of different refractive indices, can function as a transmission quarter-wave retarder (QWR) at a high angle of incidence. A specific design using a cryolite-Si membrane in the infrared is presented, and its tolerances to small shifts of wavelength, incidence angle, and film thickness errors are discussed. Some designs provide a dual QWR in transmission and reflection. Such devices provide simple linear-to-circular (and circular-to-linear) polarization transformers. Bilayer eighth-wave retarders without diattenuation are also introduced.     

Optical properties of CeO<Subscript>2</Subscript> thin films

Cerium oxide (CeO₂) thin films have been prepared by electron beam evaporation technique onto glass substrate at a pressure of about 6 × 10⁻⁶ Torr. The thickness of CeO₂ films ranges from 140–180 nm. The optical properties of cerium oxide films are studied in the wavelength range of 200–850 nm. The film is highly transparent in the visible region. It is also observed that the film has low reflectance in the ultra-violet region. The optical band gap of the film is determined and is found to decrease with the increase of film thickness. The values of absorption coefficient, extinction coefficient, refractive index, dielectric constant, phase angle and loss angle have been calculated from the optical measurements. The X-ray diffraction of the film showed that the film is crystalline in nature. The crystallite size of CeO₂ films have been evaluated and found to be small. The experimental d-values of the film agreed closely with the standard values.     

Influence of incoherent superposition of light on ellipsometric coefficients

Reflections from the back surface of a transparent substrate influence the evaluation of optical constants of thin films from ellipsometric measurements. If the thickness of the substrate is large compared with the coherence length of the light, the relative phase between the p and s mode, which commonly is measured by ellipsometry, cannot be defined properly. We show how the reflections from the back surface of the substrate are taken into account in ellipsometric measurements by calculating the intensities of reflections for arbitrary angles of polarization. Applications of the new method, such as transmittance ellipsometry, ellipsometry at the back surface of the substrate, and the determination of the optical constants at the substrate-layer interface, are compared with measurements.     

介质薄膜的透射光谱测量及其光学参数的分析

介绍介质薄膜透射光谱的测量以及基于分析薄膜透射光谱的计算薄膜光学参数的方法。对制备在玻璃基板上的二氧化钛、二氧化硅和氧化锌薄膜进行了可见光谱区的透射比测量，并用包络线方法和最优化方法对这些透明薄膜的光学参数进行了计算和分析。着重讨论了最优化方法在分析薄膜光学参数中的应用及其误差分析。此外，还对包络线方法和最优化方法进行了比较。     

Determination of optical constants of thin films and multilayer stacks by use of concurrent reflectance, transmittance, and ellipsometric measurements

Using measurements of reflectance, transmittance, and the ellipsometric parameter D, we have determined the thickness, refractive index, and the absorption coefficient of various thin films and thin-film stacks. (D, the relative phase between the p- and s-polarized components, is measured for both reflected and transmitted light.) These optical measurements are performed with a specially designed system at the fixed wavelength of lambda = 633 nm over the 10 degrees -75 degrees range of angles of incidence. The examined samples, prepared by means of sputtering on fused-silica substrates, consist of monolayers and trilayers of various materials of differing thickness and optical constants. These samples, which are representative of the media of rewritable phase-change optical disks, include a dielectric mixture of ZnS and SiO(2), an amorphous film of the Ge(2)Sb(2.3)Te(5) alloy, and an aluminum chromium alloy film. To avoid complications arising from reflection and transmission losses at the air-substrate interface, the samples are immersed in an index-matching fluid that eliminates the contributions of the substrate to reflected and transmitted light. A computer program estimates the unknown parameters of the film(s) by matching the experimental data to theoretically calculated values. Although our system can be used for measurements over a broad range of wavelengths, we describe only the results obtained at lambda = 633 nm.     

Spectroscopic ellipsometry characterization of SiNx antireflection films on textured multicrystalline and monocrystalline silicon solar cells

We present a spectroscopic ellipsometry study of silicon nitride based antireflection films deposited on chemically textured multi- and monocrystalline silicon wafers. The ellipsometric parameters were measured from the near infrared to the ultra violet spectral region. We report the effective thickness and complex index of refraction parameters of the antireflection films from all studied surfaces, regardless of their microscopic morphology. We report on a method to make ellipsometric measurements of the effective optical constants and thickness parameters of thin films deposited on alkaline etched (100)-oriented monocrystalline silicon. The effect of the texture on the complex index of refraction can be described within an effective medium approximation approach. The optical properties are consistent with those obtained from a series of reference films deposited on flat silicon surfaces.     

Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry

Analytic expressions for the eigenvalues for the four-wave components at an oblique angle of light incidence inside a randomly oriented anisotropic magneto-optic dielectric medium are reported explicitly. In particular, these solutions are valid as long as the dielectric function tensor consists of a symmetric and an antisymmetric part. The normalized Jones reflection and transmission coefficients, i.e., the generalized ellipsometric parameters of homogeneously layered systems having nonsymmetric dielectric properties, are obtained immediately from a recently reviewed 4 x 4 matrix approach. Our explicit solutions allow a future analysis of the generalized ellipsometric data of multilayered magneto-optic media regardless of the orientation of the material magnetization and crystalline axes and the angle of light incidence. Possible experimental thin-film situations are discussed in terms of generalized ellipsometric parameters and illustrated for birefringent free-carrier effects in heavily doped semiconductor thin films and for oblique magnetization directions in magneto-optic multilayer systems.     

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.     

Shadow-angle method for anisotropic and weakly absorbing films

A method for determining the optical properties of a film on an isotropic substrate is proposed. The method is based on the existence of two specific incidence angles in the angular interference pattern of the p-polarized light where oscillations of the reflection coefficient cease. The first of these angles, theta(B1), is the well-known Abelès angle, i.e., the ambient-film Brewster angle, and the second angle theta(B2) is the film-substrate Brewster angle. In the conventional planar geometry and in a vacuum ambient there is a rigorous constraint epsilon(1) + epsilon > epsilon(1)epsilon on the film and the substrate dielectric permittivities epsilon(1) and epsilon, respectively, for the existence of the second angle theta(B2.) The limitation may be removed in an experiment by use of a cylindrical lens as an ambient with epsilon(0) > 1, so that both angles become observable. This, contrary to general belief, allows one to adopt the conventional Abelès method not only for films with epsilon(1) close to the substrate's value epsilon but also for any value of epsilon(1). The method, when applied to a wedge-shaped film or to any film of unknown variable thickness, permits one to determine (i) the refractive index of a film on an unknown substrate, (ii) the vertical and the horizontal optical anisotropies of a film on an isotropic substrate, (iii) the weak absorption of a moderately thick film on a transparent or an absorbing isotropic substrate.     

Spectrographic ellipsometry study of a liquid crystal display substrate consisting of thin films of SiO2, polyimide and indium tin oxide on glass

Variable angle spectrometric ellipsometry at room temperature is used to determine thin film parameters of substrates used in liquid crystal displays. These substrates consist of sequential thin films of polyimide (PI), on indium tin oxide (ITO),on SiO₂ deposited on a glass backing approximately 1.1 mm thick. These films were studied by sequentially examining more complex systems of films (SiO₂, SiO₂-ITO, SiO₂-ITO-PI). The SiO₂ layer appears to be optically uniform and flat. The ITO film is difficult to characterize. When this surface film's lower surface is SiO₂ and upper surface is an air-ITO-interface it is found that including surface roughness and variation of the optical properties with ITO thickness in the model improved the fit; suggesting that both phenomena exist in the ITO films. However, the surface roughness and graded nature of optical properties could be not determinable by ellipsometry when the ITO is coated with a polyimide film. The PI films are ellipsometrically flat and over the wavelength range from 500 to 1400 nm the real refractive index of polyimide films varying in thickness between 25 and 80 nm is well modeled by a two-term Cauchy model with no absorption. The ellipsometric thickness of the ITO layer is the same as the profilometric thickness; however, the ellipsometric thickness of the polyimide layers is roughly 10 nm larger than that obtained from the profilometer. These final observations are consistent with the literature.