Automatic evaluation of optical constants and thickness of thin films: application to thin dielectric layers

Accurate computation of the Briot-Sellmeier and Briot-Cauchy chromatic dispersion coefficients from the transmittance spectrum of thin films of arbitrary absorptance

An exact formalism devoted to the determination of dispersion coefficients is described. The method takes into account two frequent experimental configurations: a solid thin layer on a substrate and a fluid, or solid, layer between a substrate and a superstrate. Introducing the concepts of reduction and reduced finesse, this method is based entirely on the fringes' spectral position of the maxima in the transmittance spectrum. It is found that the chromatic dispersion does not affect the spectral position of the minima in the same way as it does for the maxima. There is no need to get the refractive-index curve, n(lambda), to determine the dispersion coefficients nor to work at multiple incidence angles. Bringing together the possible nonrestrictive approximations, the method becomes easy and simple to implement from a spectrophotometer in tandem with a computer. In addition, the spectrometer does not require ordinate-axis calibration, and knowledge of the substrate's and superstrate's refractive index is not required. Alternatively, the method can be easily used to accurately determine the thickness of thin layers. A numerical example using a thin layer of 2-methyl-4-nitroaniline (MNA) is given.

Artificial anisotropy and polarizing filters

The calculated spectral transmittance of a multilayer laser mirror is used to determine the effective index of the single layer equivalent to the multilayer stack. We measure the artificial anisotropy of photoresist thin films whose structure is a one-dimensional, subwavelength grating obtained from interference fringes. The limitation of the theory of the first-order effective index homogenization is discussed. We designed normal-incidence, polarizing coating and a polarization rotator by embedding anisotropic films in simple multilayer structures.

Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry

Dielectric thin films often present microstructures that give rise to a variation of the refractive index with the distance from the substrate. We propose a method of analysis of ellipsometric data for homogeneous and slightly inhomogeneous films that are deposited on transparent substrates. Assuming a linear refractive-index gradient, we are able to determine not only the average index and the thickness but also the degree of inhomogeneity of the films by spectroscopic ellipsometry at variable angles of incidence. We apply this method to titanium dioxide films deposited on glass, which present different degrees of inhomogeneity depending on the preparation conditions.

Infrared optical constant determination of weakly absorbing dielectric thin films

Simple approximate relations are given for the reflectance of a weakly absorbing dielectric layer deposited as a quarter wave or a half-wave upon transparent and metallic substrates. These approximated relations are used in the infrared to calculate the optical constants n and k and the inhomogeneity partial differentialn of the index n of a material deposited as a thin film. A high degree of accuracy is sought for k. Two examples are given for ZnS and ThF(4) in the 3-11-microm spectral range.

Two-step regression procedure for the optical characterization of thin films

A diode array rapid scan spectrometer is used for measuring the intensity of polychromatic light in the 300-420-nm range reflected from a diamondlike carbon film as a function of wavelength. With a fixed grating setting, the wavelength range of 120 nm can be covered in 23 ms. From the reflected intensity, a new two-step regression procedure is utilized to determine refractive index, bandgap, slope of the absorption edge, and film thickness. The calculated parameters are independent of the starting set and the sequence of parameter estimation. The accuracy of the regression procedure is verified by comparison to the envelope method. It is shown using simulated data that, for strongly absorbing films, the new regression procedure is more accurate than the envelope method. The new regression method can handle very noisy reflectance spectra also.

Comparison of the properties of titanium dioxide films prepared by various techniques

Fourteen university, government, and industrial laboratories prepared a total of twenty pairs of single-layer titanium dioxide films. Several laboratories analyzed the coatings to determine their optical properties, thickness, surface roughness, absorption, wetting contact angle, and crystalline structure. Wide variations were found in the optical and physical properties of the films, even among films produced by nominally the same deposition techniques.

Determination of the optical constants of MgF(2) and ZnS from spectrophotometric measurements and the classical oscillator method

The values of the optical constants of magnesium fluoride (MgF(2)) and zinc sulfide (ZnS) thin films are obtained using a classical oscillator model and the experimental values of their spectral transmittance. Auger electron spectroscopy was performed on the samples to determine the chemical composition of the films. These materials are important in the design of filters, mirrors, and antireflection coatings for optical instrumentation. Unfortunately their properties strongly depend on evaporation conditions. The procedure described here allows direct measurement of the dispersive refractive index of the film after deposition.

Automatic determination of the optical constants of inhomogeneous thin films

The refractive index of a layer is a sensitive function of the preparation conditions. Normal incidence measurement of the optical properties can reveal possible inhomogeneity of index. We propose a method of automatic determination of the complex refractive index and thickness of a layer which includes systematic measurement of the degree of inhomogeneity which is represented by a simple model. The usefulness of the technique is demonstrated by examples that form part of an experimental study of a number of useful optical materials including Y(2)O(3), TiO(2), MgF(2), HfO(2), and SiO(2). The dispersions of the refractive index, the extinction coefficient, and of the inhomogeneity are represented by Cauchy formulas with accurately determined coefficients. The results can therefore be readily used in computing the optical properties of thin-film multilayers.

Inhomogeneity in films: limitation of the accuracy of optical monitoring of thin films

With present-day refinements, thin film multilayers can be designed theoretically to meet virtually any reasonable filtering requirements. Often, when the optical properties are specified over very wide spectral regions the thicknesses of the various layers are not related in any simple way. The manufacture of such multilayers presents many difficulties. The tolerances on layer thickness and refractive indices in some designs are often very narrow. We have developed an optical method for the accurate control of layer thickness that involves the measurement of transmittance over a wide spectral region (400-1000 mm). This measurement is performed continuously during deposition by a rapid scanning monochromator. The accuracy of such a system depends on a precise knowledge of the indices of refraction that are produced during the multilayer deposition. In addition the structure of many optical thin films used for hard coatings departs considerably from the simple method that is traditionally used in optical coating designs. In the method we have developed to compensate for such discrepancies, optical inhomogeneity is included by assuming a linear refractive-index profile, determined by analyzing experimental results. These results are in agreement with other studies of structure.

Coating Fabry-Perot interferometer plates with broadband multilayer dielectric mirrors

A number of broadband multilayer dielectric coatings with reflectances of ~0.9 are described. Techniques used to produce highly uniform coatings for airspaced Fabry-Perot interferometers are given in detail, with emphasis on a method of optically monitoring the layer thicknesses. The method results in reasonable agreement over the whole spectrum between the design specifications and those of the finished coating as well as in good reproducibility.

Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors

Many spectral filtering problems require assemblies of layers having thicknesses that bear no obvious relationship to one another. After a brief review of the optical methods used to monitor deposition of multilayers containing nonintegral thicknesses, we show that the performance of monitoring systems can be improved further by including the real-time calculation of any necessary layer thickness changes that may be required to compensate any errors that might still occur. The apparatus described consists of a minicomputer coupled to a rapid-scanning spectrometer. Such a procedure working in real time avoids the cumulative effects of successive errors. The technique is demonstrated in the production of a beam splitter.

Wideband optical monitoring of nonquarterwave multilayer filters

The construction of optical filters, which are required to have optical properties well defined over wide spectral regions, demands the use of multilayer designs in which there are no simple relationships between the thicknesses of the layers. There are considerable difficulties in the manufacture of such multilayers. First, we must be able to reproduce, sufficiently accurately, the indices of refraction that have been used in the theoretical design. Then we must be able to control the optical thicknesses of each layer, which necessitates measurement of the optical properties of the multilayer during deposition. The apparatus described consists of a minicomputer coupled to a rapid-scanning spectrometer that continuously measures the spectral profile during deposition of each layer. The precise measurement of the evolution of the optical properties during actual construction of a filter allows us to control layer thickness with very good accuracy. The technique is demonstrated in the monitoring of a beam splitter made of a few layers.

Optical thin film production with continuous reoptimization of layer thicknesses

For various reasons when optical multilayer systems are constructed the thicknesses of individual layers depart from the desired values. This often results in an unacceptable performance of the filter. In this paper a production method for nonabsorbing multilayer coatings is described, which is based on monochromatic transmittance monitoring and which, to a certain degree, compensates for these errors. After the deposition of each layer a computer program is provided with the actual monitoring data from which the layer thickness is deduced. The program then reoptimizes the performance of the system by changing the thicknesses of the remaining layers. A numerical and experimental study has been made of the production of a seven-layer neutral beam splitter on glass. Theoretical data are also given for an AR coating on glass.

Optical monitoring of nonquarterwave multilayer filters

Many spectral filtering problems require the use of assemblies of layers having thicknesses which bear no obvious relationship to each other. Successful production of these multilayers requires films with thicknesses approximating theoretical values. We show that the optical methods currently used in the production of film assemblies of quarterwave layer thicknesses, which are based on the use of just one single wavelength, are poorly adapted to monitoring the deposition of nonintegral thickness multilayers. In contrast we show that with an optical control system utilizing a broad spectral bandwidth, thickness errors can be reduced. Transmittance measurements with the precision necessary to achieve this improved thickness control are attainable with existing instrumentation. This result is established by a computer simulation of the construction of a specific multilayer and remains valid for other nonquarterwave multilayer filters.