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.

Multilayer beamsplitter polarizers for key UV-FUV spectral lines of solar polarimetry.

Multilayer beamsplitter polarizers have been developed for improved solar polarimetry at key spectral lines. The advantage of beamsplitter polarizers is that a single device separates s from p polarization; this helps minimize attenuation and enables a more compact and lighter polarimeter, which is important for space instruments. Polarizers based on Al/AlF3 multilayers were prepared for both C IV (155 nm) and Mg II (280 nm) lines, and based on Al/MgF2 multilayers for H Lyman α line (121.6 nm). Polarizers were designed to mainly reflect (transmit) s (p) polarization. Beamsplitter performance and throughput are shown to compare advantageously with polarizers in the literature. Beamsplitter polarizers kept a valuable performance after several years of ageing.

Far UV-enhanced Al mirrors with a Ti seed film.

A Ti seed film is investigated towards improving the far UV reflectance of Al/MgF2 mirrors. Samples were initially coated with a Ti film in half of the area and they were later coated in the full area with an Al film and protected with MgF2. All materials were deposited by evaporation. Samples were prepared with the MgF2 layer deposited either at room temperature (RT) or at 225°C. A 3-nm thick Ti seed film was seen to significantly increase the reflectance of Al/MgF2 mirrors at the well-known reflectance dip centered at ∼160 nm; this was attributed to a reduction of short-range surface roughness at the Al/MgF2 interface, which is responsible for radiation absorption through surface-plasmon (SP) coupling. SP absorption was more efficiently reduced with a Ti seed film on samples fully deposited at RT. A Ti seed film as thin as 1 nm provided the largest SP absorption reduction, and the SP dip was almost completely removed.

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.

Optical constants at complex energies: local deconvolution.

Causality implies that the optical constants of any material continue in the upper complex plane of photon energies or wavelengths as an analytic function. This is the basis for Kramers-Kronig dispersion relations to obtain ɛ1 from ɛ2, or n from k. However, there have not been attempts to explore this continuation. This research focuses on such continuation and on applications thereof. An interesting property has been found: optical constants progressively smoothen when entering the upper complex plane. The continuation to complex energies is found to result in an average of the optical constants with a Lorentzian weight function. This optical-constant smoothening originated in a shift to the upper complex plane is naturally produced in optical constants that have been obtained by means of an optical instrument with a Lorentzian slit function. This smoothening results in reduced resolution through convolution with the slit function. A procedure that takes advantage of optical constants at complex energies is developed for optical-constant deconvolution. Deconvolution is performed locally, i.e., with no integration, and it consists of shifting the energy of the optical constants by an imaginary amount by means of a Taylor series expansion. The first correction term involves the derivative of the other optical constant. Even though deconvolution of optical constants measured with a Gaussian slit cannot be directly performed with the present method, an approach based on powers of the Lorentz function is also proposed. This procedure could be implemented as an analysis tool of a spectrophotometer or an ellipsometer; this tool would enable one to measure optical constants with a modest resolution and to improve it by post-processing them with the present scheme.

Lyman-ß narrowband coatings with strong Lyman-α rejection.

Novel narrowband multilayer coatings efficient at a wavelength as short as 100 mn are presented, which pushes shortwards the existing limit of reported narrowband multilayers. Such limit had been established at ~120 nm, close to the MgF2 cutoff wavelength. The new multilayers combine layers of Al, LiF, and SiC, in an Al/LiF/SiC/LiF multilayer design (four layers, starting with the innermost layer). Among these materials, Al and LiF are deposited by evaporation and SiC by ion-beam-sputtering. In addition to a high, narrow peak close to H Lyman ß (102.6 nm), these multilayers simultaneously provide a very small reflectance at H Lyman α (121.6 nm). This combined performance is demanded in space instrumentation for astrophysics and solar physics observations among others, where imaging the sky at the important diagnostic spectral line of Lyman ß line requires rejecting the frequently much more intense background at Lyman α line. Such is the case for solar corona observations at Lyman ß, which is masked by the strong Lyman α line. The multilayer peak is placed close to another important diagnostic tool: the OVI doublet at 103.2 and 103.8 nm. The target of small reflectance at 121.6 nm was seen to be the most critical. The best strategy in multilayer preparation was to prepare it with such minimum reflectance at slightly shorter wavelengths so that the coating evolved to shift it longwards over time. Multilayers kept a remarkable 102.6 nm/121.6 nm reflectance ratio over time in spite of some performance degradation. Hence, a multilayer coating aged of 4 years kept a reflectance of 43% at 102.6 nm and 0.2% at 121.6 nm.

Optimization of MgF2-deposition temperature for far UV Al mirrors.

Progress towards far UV (FUV) coatings with enhanced reflectance is invaluable for future space missions, such as LUVOIR. This research starts with the procedure developed to enhance MgF2-protected Al reflectance through depositing MgF2 on a heated aluminized substrate [Quijada et al., Proc. SPIE 8450, 84502H (2012)] and it establishes the optimum deposition temperature of the MgF2 protective film for Al mirrors with a reflectance as high as ~90% at 121.6 nm. Al films were deposited at room temperature and protected with a MgF2 film deposited at various temperatures ranging from room temperature to 350°C. It has been found that mirror reflectance in the short FUV range continuously increases with MgF2 deposition temperature up to 250°C, whereas reflectance decreases at temperatures of 300°C and up. The short-FUV reflectance of mirrors deposited at 250°C only slightly decreased over time by less than 1%, compared to a larger decay for standard coatings prepared at room temperature. Al mirrors protected with MgF2 deposited at room temperature that were later annealed displayed a similar reflectance enhancement that mirrors protected at high temperatures. MgF2 and Al roughness as well as MgF2 density were analyzed by x-ray grazing incidence reflectometry. A noticeable reduction in both Al and MgF2 roughness, as well as an increase of MgF2 density, were measured for films deposited at high temperatures. On the other hand, it was found a strong correlation between the protective-layer deposition temperature (or post-deposition annealing temperature) and the pinhole open area in Al films, which could be prevented with a somewhat thicker Al film.

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.

Transmittance and optical constants of Ca films in the 4-1000 eV spectral range.

The low expected absorption of Ca in the extreme ultraviolet (EUV) makes it an attractive material for multilayers and filters because most materials in nature strongly absorb the EUV. Few optical constant data had been reported for Ca. In this research, Ca films of various thicknesses were deposited on grid-supported C films and their transmittance measured in situ from the visible to the soft x-rays. The measurement range contains M2,3 and L2,3 absorption edges. Transmittance measurements were used to obtain the Ca extinction coefficient k. A minimum k of 0.017 was obtained at ∼23 eV, which makes Ca a promising low-absorption material for EUV coatings. A second spectral range of interest for its low absorption is below the Ca L3 edge at ∼343 eV. Measured k data and extrapolations were used to calculate the refractive index n using Kramers-Krönig relations. This is the first self-consistent data set on Ca covering a wide spectral range including the EUV.

Triple-wavelength, narrowband Mg/SiC multilayers with corrosion barriers and high peak reflectance in the 25-80 nm wavelength region.

We have developed new, Mg/SiC multilayer coatings with corrosion barriers which can be used to efficiently and simultaneously reflect extreme ultraviolet (EUV) radiation in single or multiple narrow bands centered at wavelengths in the spectral region from 25 to 80 nm. Corrosion mitigation was attempted through the use of Al-Mg or Al thin layers. Three different multilayer design concepts were developed and deposited by magnetron sputtering and the reflectance was measured at near-normal incidence in a broad spectral range. Standard Mg/SiC multilayers were also deposited and measured for comparison. They were shown to efficiently reflect radiation at a wavelength of 76.9 nm with a peak reflectance of 40.6% at near-normal incidence, the highest experimental reflectance reported at this wavelength for a narrowband coating. The demonstration of multilayer coatings with corrosion resistance and multiple-wavelength EUV performance is of great interest in the development of mirrors for space-borne solar physics telescopes and other applications requiring long-lasting coatings with narrowband response in multiple emission lines across the EUV range.

Self-consistent optical constants of sputter-deposited B4C thin films.

The optical constants of ion-beam-sputtered B4C films have been measured by ellipsometry in the 190-950 nm range. The set of data has been extended toward both shorter and longer wavelengths with data in the literature, along with interpolations and extrapolations, in order to obtain a self-consistent set of data by means of Kramers-Krönig analysis. All data correspond to films that were deposited by sputtering on nonheated substrates, and hence they are expected to be amorphous. The B4C bandgap was calculated as a fitting parameter of Tauc equations for indirect transitions using the present optical constants. Good global accuracy of the data was estimated through the use of various sum rules. The consistent data set includes the visible to the extreme UV (EUV); this large spectrum of characterization will enable the design of multilayer coatings that combine a relatively high reflectance in parts of the EUV with a desired performance at a secondary range, such as the visible.

Self-consistent optical constants of SiC thin films.

The optical constants of ion-beam-sputtered SiC films have been measured by ellipsometry in the 190 to 950 nm range. The set of data has been extended both toward shorter and longer wavelengths with data in the literature, along with inter- and extrapolations, in order to obtain a self-consistent set of data by means of Kramers-Krönig analysis. All data correspond to films that were deposited by sputtering on nonheated substrates, and hence they are expected to be amorphous. A bandgap of 1.9 eV for the films was fitted from the obtained optical constants. A good global accuracy of the data was estimated through the use of various sum rules. The consistent dataset includes the visible to the extreme ultraviolet (EUV); this large spectrum of characterization will enable the design of multilayer coatings that combine a high reflectance in parts of the EUV with desired performance at a secondary range, such as the visible. To our knowledge, this paper provides the first compilation of the optical constants of amorphous SiC films.

Transmittance and optical constants of erbium films in the 3.25-1580 eV spectral range.

The optical constants of erbium (Er) films were obtained in the 3.25-1580 eV range from transmittance measurements performed at room temperature. Thin films of Er were deposited by evaporation in ultra high vacuum conditions and their transmittance was measured in situ. Substrates consisted of a thin C film supported on a grid. Transmittance measurements were used to obtain the extinction coefficient k of the Er films. The refractive index n of Er was calculated using the Kramers-Krönig analysis. k data were extrapolated both on the high- and low-energy parts of the spectrum by using experimental data and calculated k values available in the literature. Er, similar to other lanthanides, has a low-absorption band below the O(2,3) edge onset; the smallest absorption was measured at ~22.5 eV. Therefore, Er is a promising material for filters and multilayer coatings in the energy range below the O(2,3) edge, in which materials typically have an absorption stronger than at other energies. Good consistency of the data resulted from the application of f and inertial sum rules.

Graphite to diamond transition induced by photoelectric absorption of ultraviolet photons.

The phase transition from graphite to diamond is an appealing object of study because of many fundamental and also, practical reasons. The out-of-plane distortions required for the transition are a good tool to understand the collective behaviour of layered materials (graphene, graphite) and the van der Waals forces. As today, two basic processes have been successfully tested to drive this transition: strong shocks and high energy femtolaser excitation. They induce it by increasing either pressure or temperature on graphite. In this work, we report a third method consisting in the irradiation of graphite with ultraviolet photons of energies above 4.4 eV. We show high resolution electron microscopy images of pyrolytic carbon evidencing the dislocation of the superficial graphitic layers after irradiation and the formation of crystallite islands within them. Electron energy loss spectroscopy of the islands show that the sp2 to sp3 hybridation transition is a surface effect. High sensitivity X-ray diffraction experiments and Raman spectroscopy confirm the formation of diamond within the islands.

Narrowband multilayer coatings for the extreme ultraviolet range of 50-92 nm.

A new type of multilayer coatings with narrowband reflection properties and peaked in the approximately 50- 92 nm spectral range has been developed. Multilayers are based on Yb, Al, and SiO films and they have been prepared by thermal evaporation. Efficient multilayers based on Yb and Al, with an SiO protective layer were prepared, but they developed a dendrite structure, which was attributed to the reactivity between Al and Yb. Multilayers based on Yb and Al, with both SiO protective and barrier layers, resulted in efficient reflective filters, with no observable dendrite growth. The peak reflectance of aged multilayers was of the order of approximately 0.20, with bandwidths in the range of 12 to 22 nm FWHM.

In situ reflectance and optical constants of ion-beam-sputtered SiC films in the 58.4 to 149.2 nm region.

The reflectance of freshly deposited SiC thin films is measured in situ for what we believe is the first time. SiC was deposited by means of ion-beam sputtering. Reflectance was measured as a function of the incidence angle in the far and extreme ultraviolet wavelengths from 58.4 to 149.2 nm. In situ measurements allowed obtaining the intrinsic reflectance of SiC films, which is somewhat larger than what had been measured for samples exposed to the atmosphere. Reflectance measurements were used to determine the optical constants of the material in the same spectral range. We compare our data to those of the literature corresponding to SiC films deposited by different techniques and exposed to the atmosphere. In situ determined optical constants will allow a more accurate design of multilayers containing ion-beam-sputtered SiC layers.

Removal of a protective coating on Al by ion etching for high reflectance in the far ultraviolet.

The effect of ion etching on the reflectance of Al coatings in the far ultraviolet is investigated. Ion etching of an overlayer grown on Al was performed by applying 100-300 eV Ar(+) ions using an ion gun. Ion etching was employed to remove the oxide naturally grown on an Al film that had been in contact with atmosphere. Ion etching was also used to remove part or all of the protective MgF(2) film on Al. The reflectance at 121.6 nm, H Lyman alpha line of the overlayer-removed Al surface was monitored after protecting it with a MgF(2) layer. Ion etching on both types of coatings resulted in an excellent reflectance value at 121.6 nm, whereas a reflectance loss was observed at longer wavelengths.

Electron-beam deposited boron coatings for the extreme ultraviolet.

Boron films deposited by evaporation with an electron-beam were found to have a relatively high reflectance in the extreme ultraviolet with values similar to those of ion-beam-sputtered (IBS) SiC and IBS B(4)C. The largest reflectance was measured for an 11 nm thick boron film. Some reflectance degradation was observed for boron films stored in a desiccator. Reflectance degradation varied from sample to sample and was found to be either similar to that of IBS SiC and IBS B(4)C or larger.