Direct measurement of the extinction coefficient by differential transmittance.

A new procedure to measure the extinction coefficient k of film materials that are relatively transparent is presented. This procedure does not require the use of an optical-constant model or the knowledge of extra physical properties of the material, such as the specific heat capacity. It involves preparing a sample with two areas, at least one of them coated with the film, whereas the other may remain uncoated or may be coated with a different thickness of the same material. The differential transmittance between the two sample areas is shown to be proportional to k of the film material in the following measurement conditions: the incident light is p polarized and it impinges at the film material Brewster angle. The differential transmittance is obtained with a single measurement by making the light beam or the sample to oscillate with respect to one another and by using a lock-in amplifier; for normalization purposes, the transmittance in one of the sample areas is also measured. The proportionality factor between the normalized differential transmittance and k only involves the wavelength, the film thickness, and the Brewster angle. The knowledge of the film Brewster angle requires that the film refractive index (n) is measured beforehand; this can be performed with standard procedures, such as ellipsometry, since such techniques are efficient at measuring n of a transparent material, but are inefficient at measuring a small k. The procedure is exemplified with the calculation of k in the far ultraviolet of AlF3 films deposited by evaporation. The dependence of the uncertainty of k obtained with this procedure is analyzed in terms of the uncertainty of the film n, of wavelength, and of the degree of polarization of the incident beam. The selection of a substrate with similar n to the film material is also discussed. The uncertainties involved with the present procedure were analyzed for a specific example and an uncertainty of 2 × 10-5 in k calculation is considered feasible.

Far UV narrowband mirrors tuned at H Lyman α.

Imaging at H Ly-α (121.6 nm), among other spectral lines in the short far UV (FUV), is of high interest for astrophysics, solar, and atmosphere physics, since this spectral line is ubiquitously present in space observations. However, the lack of efficient narrowband coatings has mostly prevented such observations. Present and future space observatories like GLIDE and the IR/O/UV NASA concept, among other applications, can benefit from the development of efficient narrowband coatings at Ly-α. The current state of the art of narrowband FUV coatings lacks performance and stability for coatings that peak at wavelengths shorter than ∼135 nm. We report highly reflective AlF3/LaF3 narrowband mirrors at Ly-α prepared by thermal evaporation, with, to our knowledge, the highest reflectance (over 80%) of a narrowband multilayer at such a short wavelength obtained so far. We also report a remarkable reflectance after several months of storage in different environments, including relative humidity levels above 50%. For astrophysics targets in which Ly-α may mask a close spectral line, such as in the search for biomarkers, we present the first coating in the short FUV for imaging at the OI doublet (130.4 and 135.6 nm), with the additional requirement of rejecting the intense Ly-α, which might mask the OI observations. Additionally, we present coatings with the symmetric design, aimed to observe at Ly-α, and reject the strong OI geocoronal emission, that could be of interest for atmosphere observations.

Optical constants and absorption properties of Te and TeO thin films in the 13-14†nm spectral range.

Undesired mask-induced effects caused by thick absorber layers in EUV photomasks reduce the quality of the projected patterns at the wafer stage in EUV photolithography scanners. New materials with better absorption properties than the state-of-the-art absorbers, TaN and TaBN, are required to mitigate these effects. In this work, we investigated the optical properties (δ and k) of Te and TeO films in the 13-14 nm range, and the absorption properties of these two materials at 13.5 nm. δ and k are obtained through fitting experimental values of reflectivity versus angle of incidence in the EUV range. We follow a methodology which combines different characterization techniques (X-ray reflectivity, EUV reflectivity, and X-ray photoemission spectroscopy) to reduce the number of free parameters in models and hence, increase the reliability of the optical constants obtained. At 13.5 nm, we obtain δ=0.03120, k = 0.07338 for Te, and δ=0.04099, k = 0.06555 for TeO. To experimentally verify the absorption properties of these materials, different thicknesses of Te and TeO films are cast on top of a state-of-the-art mask-quality EUV multilayer with 66.7% reflectivity at 13.5 nm. We found that a reflectivity of ∼0.7% can be attained with either 32.4 nm of Te, or 34.7 nm of TeO, greatly surpassing the absorption properties of TaN and TaBN. The morphology and surface roughness of the Te and TeO films deposited on the multilayer are also investigated.

Why is the Adachi procedure successful to avoid divergences in optical models?

Adachi proposed a procedure to avoid divergences in optical-constant models by slightly shifting photon energies to complex numbers on the real part of the complex dielectric function, ε1. The imaginary part, ε2, was ignored in that shift and, despite this, the shifted function would also provide ε2 (in addition to ε1) in the limit of real energies. The procedure has been successful to model many materials and material groups, even though it has been applied phenomenologically, i.e., it has not been demonstrated. This research presents a demonstration of the Adachi procedure. The demonstration is based on that ε2 is a piecewise function (i.e., it has more than one functionality), which results in a branch cut in the dielectric function at the real photon energies where ε2 is not null. The Adachi procedure is seen to be equivalent to a recent procedure developed to turn optical models into analytic by integrating the dielectric function with a Lorentzian function. Such equivalence is exemplified on models used by Adachi and on popular piecewise optical models: Tauc-Lorentz and Cody-Lorentz-Urbach models.

Window functions for self-consistency evaluation of optical constants.

Optical-constant data of a material typically come from various sources, which may result in inconsistent data. Sum rules are tests to evaluate the self-consistency of optical constant data sets. Standard sum rules provide collective self-consistency evaluation of an optical-constant set in the full electromagnetic spectrum, but they give no information on the specific spectral range originating the inconsistency. Spectrally-resolved self-consistency information can be obtained with the use of window functions (WFs). Window functions can give more weight to the desired spectral range in the calculation of the sum rule. A previously developed WF was successfully used to evaluate self-consistency over the spectrum, but since it involves steep transition at the window edges and center, it has a trend to turn unstable in the calculation of sum-rule integrals for a fast decaying WF outside the window band. Two new WFs have been developed to reduce such instability. They use weight functions that smoothly cancel at the two window edges and center. The two new WFs use a weight function with three straight lines or with two 4-degree polynomials. The new WFs have been tested on exact optical constants with a coarse sampling, and they provide a strong instability reduction in self-consistency evaluation compared with the old WF. The new WFs have been also tested on experimental data sets of Al and Au reported in the literature, which unveils ranges of inconsistency. The large stability of the new WFs compared with the old one helps decide that the inconsistency calculated with the new WFs on experimental data must be attributed to inconsistency of the data sets, and not to poor sampling rate. A WF that has been used in the literature in the calculations of the dielectric function at imaginary energies for the thermal Casimir effect is also analyzed in terms of self-consistency when it is applied to sum rules involving optical constant at real (not imaginary) energies.

Analytic optical-constant model derived from Tauc-Lorentz and Urbach tail.

Tauc-Lorentz model is commonly used to describe the dielectric constant of amorphous semiconductors as a function of few parameters. However, this model is not fully analytic and presents other mathematical shortcomings. A modified self-consistent model based on the integration of [E'-(E + ia)]-1 functions using Tauc-Lorentz`s ε2 expression as a weight function is presented. This new model is analytic and meets all other mathematical requirements of optical constants. The main difference with TL model stands at photon energies close to or smaller than the bandgap energy. The new model has been satisfactorily tested on SiC optical constants. Additionally, an analytic extension of the new model has been also developed to include the Urbach tail. The complete model has been tested with Si3N4 optical constants, and it enables to extend the optical-constant characterization of materials down to zero energy.