Optical properties of scandium films in the far and the extreme ultraviolet

The optical properties of thin Sc films deposited in ultrahigh-vacuum conditions have been investigated in the 6.7-174.4-nm spectral range. We measured transmittance and multiangle reflectance in situ in the 53.6-174.4 nm spectral range and used these measurements to obtain the complex refractive index of a Sc film at every individual wavelength investigated. Transmittance measurements were made of Sc samples that were deposited over grids coated with a support C film. The transmittance and the extinction coefficient of Sc films at wavelengths shorter than 30 nm were measured ex situ. The ex situ samples were protected with an additional top C film before their removal from vacuum. To our knowledge, these are the first optical measurements of Sc films reported in the spectral ranges cited.     

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.     

Reflectance optimization of inhomogeneous coatings with continuous variation of the complex refractive index

A model is derived for the reflectance optimization of an inhomogeneous coating made of absorbing materials. The model is applicable mainly for spectral regions where no transparent materials are available, such as in the extreme ultraviolet. The complex refractive index is assumed to take values within a given continuous domain and in a given sequence. The coating design is generated through a series of layer elements with a small refractive-index contrast across interfaces; the thickness of the element is calculated in terms of the refractive-index increment at the interface. The coating is optimized element by element starting from the substrate. When the refractive index varies both continuously and smoothly, the thickness element is of first order in the refractive-index increment. Suggestions are given on how to optimize a more general coating that alternates continuous and smooth refractive-index domains along with discrete indices, which results in a succession of inhomogeneous coatings and finite layers. An example is given to illustrate the model. A new material selection rule is obtained to discriminate whether the addition of a material on top of a partly grown coating will increase or decrease the reflectance of the coating. As a consequence, the model, which is highlighted toward the maximization of reflectance, can be used analogously for reflectance minimization such as for anti-reflection coatings.     

Ellipsometry on sputter-deposited tin oxide films: optical constants versus stoichiometry, hydrogen content, and amount of electrochemically intercalated lithium

Tin oxide thin films were deposited by reactive radio-frequency magnetron sputtering onto In(2)O(3):Sn-coated and bare glass substrates. Optical constants in the 3002500-nm wavelength range were determined by a combination of variable-angle spectroscopic ellipsometry and spectrophotometric transmittance measurements. Surface roughness was modeled from optical measurements and compared with atomic-force microscopy. The two techniques gave consistent results. The fit between experimental optical data and model results could be significantly improved when it was assumed that the refractive index of the Sn oxide varied across the film thickness. Varying the oxygen partial pressure during deposition made it possible to obtain films whose complex refractive index changed at the transition from SnO to SnO(2). An addition of hydrogen gas during sputtering led to lower optical constants in the full spectral range in connection with a blueshift of the bandgap. Electrochemical intercalation of lithium ions into the Sn oxide films raised their refractive index and enhanced their refractive-index gradient.     

Complete optical analysis of a non-absorbing thin film on an absorbing substrate by a new method of immersion spectroscopic reflectometry

A new method for determining the thickness and the spectral dependence of the refractive index characterizing a non-absorbing thin film placed on an absorbing substrate is described in this paper. Within this method two spectral dependences of the reflectance corresponding to the system immersed into two different non- absorbing ambients are employed. The main advantage of the method is that the values of the thickness and the refractive index can be determined by means of explicit formulae. The second important advantage is the fact that non-absorbing thin films with relatively small thicknesses can be analysed. The method is applied to amorphous SiO₂ thin films placed on silicon single-crystal wafers.     

Directional and angle-resolved optical scattering of high-performance translucent polymer sheets for energy-efficient lighting and skylights

Transparent refractive-index matched micro (TRIMM) particles have proved to be an excellent scattering component for use in translucent sheets. Measurements of hemispheric transmittance and reflectance versus angle of incidence, as well as angle-resolved studies of such translucent sheets, have been carried out to complement earlier published hemispheric reflectance and transmittance spectral measurements carried out at normal angle of incidence. Hemispheric values relative to angle of incidence are of interest for daylighting applications and building simulations, and angle-resolved measurements are vital for verifying that our modeling tools are reliable. Ray-tracing simulations based on Mie scattering for the individual TRIMM particles and angle-resolved measurements are in good agreement, indicating that the simulation method used is practical for the design of new scattering profiles by varying particle concentration or refractive index.     

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.     

A method for the determination of the optical constants ( n and k ) of thin films with large optical inhomogeneities

The existing methods for determining the optical constants of inhomogeneous thin films deal with non-absorbing films or at the most with films that have very small absorption (k?<?0.02). In this work, a method is presented for the determination of the optical constants of inhomogeneous thin films with large optical inhomogeneities. The optical constants are derived from normal-incidence measurements of reflectance and transmittance. The refractive index was modelled by quadratic variation. However, the absorption index was replaced by its mean value. The accuracy of this assumption was tested and its range of validity was determined. Subsequently, the method was applied to the determination of the optical constants of cerium oxide thin films.     

Optical properties of a slightly absorbing film for oblique incidence

Approximate equations are derived for calculating the transmittance and reflectance of a slightly absorbing film when radiation is incident at an arbitrary angle. These formulas are compared with those derived from wave optics. Examination of the real and the imaginary parts of the complex phase change and the complex angle of refraction shows the simple equations to be consistent with the wave-optics formulation under the assumption that the imaginary part of the refractive index of the film is much smaller than its real counterpart.     

Hemispherical and diffuse reflectance and transmittance of a slightly inhomogeneous film bounded by rough, unparallel interfaces

The optical reflectance and transmittance of an ideal thin film are calculated in a well-known way. As far as a non-ideal thin film is concerned - i.e., a slightly inhomogeneous thin film bounded by rough, unparallel interfaces - three categories of spectral coefficients can be defined, i.e.: specular reflectance and direct transmittance (light intensity flux along the optical axis), hemispherical reflectance and transmittance (light intensity flux integrated over the solid half angle π), and diffuse reflectance and transmittance (light intensity flux scattered around the optical axis) coefficients. In this paper a model recently introduced for the specular and direct coefficients is generalized to calculate also the hemispherical and diffuse coefficients of a non-ideal film.     

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.     

Correlation between optical path modulations and transmittance spectra of a-Si:H thin films

The optical constants of plasma-enhanced chemical-vapor-deposited amorphous silicon (a-Si:H) thin film upon a transparent substrate are determined within the UV-visible region by measurement of the transmittance spectrum. Apart from thickness irregularities, the effects of vertical film inhomogeneities (refractive-index distribution) on the spectrum are discussed. In this respect, although consideration of any possible variation in thickness of the film within the area illuminated by the probe beam is sufficient for correcting the modulation of the extrema of interference fringes, including in the model the thin transitional regions at substrate-film and film-air interfaces might be an alternative method for understanding the overall optical behavior of the spectrum.     

Some Observations on Absorbing Multilayers

Three aspects of absorbing optical thin films are discussed. First, the reflectance of a multilayer necessary to maximize the potential transmittance of a single metal film is obtained explicitly in terms of the thickness and refractive index of the film. Second, the form of the standing wave in a metal film at maximum potential transmittance is determined. Third, a technique for the design of an asymmetric mirror is presented. A numerical example is included.     

Comparison of near-forward light scattering on oceanic turbulence and particles

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.     

Single-layer model for surface roughness

Random roughness of an optical surface reduces its specular reflectance and transmittance by the scattering of light. The reduction in reflectance can be modeled by a homogeneous layer on the surface if the refractive index of the layer is intermediate to the indices of the media on either side of the surface. Such a layer predicts an increase in the transmittance of the surface and therefore does not provide a valid model for the effects of scatter on the transmittance. Adding a small amount of absorption to the layer provides a model that predicts a reduction in both reflectance and transmittance. The absorbing layer model agrees with the predictions of a scalar scattering theory for a layer with a thickness that is twice the rms roughness of the surface. The extinction coefficient k for the layer is proportional to the thickness of the layer.     

Estimation of the thickness and the optical parameters of several stacked thin films using optimization

The reverse engineering problem addressed in the present research consists of estimating the thicknesses and the optical constants of two thin films deposited on a transparent substrate using only transmittance data through the whole stack. No functional dispersion relation assumptions are made on the complex refractive index. Instead, minimal physical constraints are employed, as in previous works of some of the authors where only one film was considered in the retrieval algorithm. To our knowledge this is the first report on the retrieval of the optical constants and the thickness of multiple film structures using only transmittance data that does not make use of dispersion relations. The same methodology may be used if the available data correspond to normal reflectance. The software used in this work is freely available through the PUMA Project web page (http://www.ime.usp.br/~egbirgin/puma/).     

Universal antireflection coatings for substrates for the visible spectral region

It is possible to design normal-incidence antireflection coatings that reduce the reflectance of any substrate with a refractive index that lies in the range of 1.48 to 1.75. The performance of such coatings depends on the width of the spectral region over which the reflectance is to be suppressed, on the coating materials used for their construction, and on the overall optical thickness of the layer system. For example, the calculated average spectral reflectance of a set of six different substrates with refractive indices 1.48, 1.55, 1.60, 1.65, 1.70, and 1.75, when coated with a 0.56-μm-thick, eight-layer antireflection coating designed for the 0.40-0.80-μm spectral region, was 0.34%. This is higher than the average reflectance that is attainable with a conventional antireflection coating of similar optical thicknesses designed for a particular refractive index. However, it is an acceptable value for most applications. With the universal type of antireflection coating described, it is thus possible to coat a number of different refractive-index substrates in one deposition run, and this can result in considerable cost and time savings.     

Spatial spectral evolution in pulsed laser deposited lead-germanate thin films by micro-infrared spectroscopy

Lead-germanate thin films were developed on silicon substrates by pulsed laser deposition from bulk glassy targets of composition 0.4PbO-0.6GeO₂, and micro-infrared transmittance measurements were performed to assess the state of the grown films. Measurements across the radius of films revealed surprisingly large spectral changes, reminiscent of lead-oxide variations in corresponding bulk glasses. To search for the origin of this effect, the infrared spectra were simulated by employing the rigorous expression for the transmittance of a bilayer system to take into full account multiple internal reflections in both thin film and substrate. The results showed that the profiles of the experimental spectra can be accurately described by using as input the complex refractive index of the target glassy material and by considering film thickness variations from the center to the edges of the film. This work demonstrates the strong influence of optical effects on the infrared spectra of thin films, and manifests also the effectiveness of infrared spectroscopy when coupled with rigorous calculations to characterize the structure of thin films.     

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.