Analytic theory of soft x-ray diffraction by lamellar multilayer gratings

Кожевников, И. В.; Meer, Robert van der; Bastiaens, Hubertus M.J.; Boller, Klaus-J.; Bijkerk, Frederik

doi:10.1364/oe.19.009172

Cited by 19 publications

(49 citation statements)

References 9 publications

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“…143,144 Kozhevnikov et al then identified the single-order operating regime for the multilayer grating. 146,147 In this scheme, only one diffraction order will be excited and the reflected power is concentrated in this single order, if the angular width of the zeroth or higher order peak is much smaller than the angular distance between the adjacent orders. Thus, an SLMG can achieve the same maximum reflectance as a standard multilayer mirror, while the bandwidth is reduced by a factor of C, with C being the lamella-to-period ratio of the grating, assuming that the number of bilayers is increased by a factor 1/C.…”

Section: Single Order Lamellar Multilayer Gratingmentioning

confidence: 99%

“…Thus, an SLMG can achieve the same maximum reflectance as a standard multilayer mirror, while the bandwidth is reduced by a factor of C, with C being the lamella-to-period ratio of the grating, assuming that the number of bilayers is increased by a factor 1/C. 147 This is a unique advantage compared to other methods to reduce the bandwidth of a ML, like using a small d-spacing with low contrast materials or using higher Bragg orders as discussed in Section II C.…”

Section: Single Order Lamellar Multilayer Gratingmentioning

confidence: 99%

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Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics

Huang

Медведев

Kruijs

et al. 2017

Applied Physics Reviews

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Extreme ultraviolet and soft X-ray (XUV) multilayer optics have experienced significant development over the past few years, particularly on controlling the spectral characteristics of light for advanced applications like EUV photolithography, space observation, and accelerator- or lab-based XUV experiments. Both planar and three dimensional multilayer structures have been developed to tailor the spectral response in a wide wavelength range. For the planar multilayer optics, different layered schemes are explored. Stacks of periodic multilayers and capping layers are demonstrated to achieve multi-channel reflection or suppression of the reflective properties. Aperiodic multilayer structures enable broadband reflection both in angles and wavelengths, with the possibility of polarization control. The broad wavelength band multilayer is also used to shape attosecond pulses for the study of ultrafast phenomena. Narrowband multilayer monochromators are delivered to bridge the resolution gap between crystals and regular multilayers. High spectral purity multilayers with innovated anti-reflection structures are shown to select spectrally clean XUV radiation from broadband X-ray sources, especially the plasma sources for EUV lithography. Significant progress is also made in the three dimensional multilayer optics, i.e., combining micro- and nanostructures with multilayers, in order to provide new freedom to tune the spectral response. Several kinds of multilayer gratings, including multilayer coated gratings, sliced multilayer gratings, and lamellar multilayer gratings are being pursued for high resolution and high efficiency XUV spectrometers/monochromators, with their advantages and disadvantages, respectively. Multilayer diffraction optics are also developed for spectral purity enhancement. New structures like gratings, zone plates, and pyramids that obtain full suppression of the unwanted radiation and high XUV reflectance are reviewed. Based on the present achievement of the spectral tailoring multilayer optics, the remaining challenges and opportunities for future researches are discussed.

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Section: Single Order Lamellar Multilayer Gratingmentioning

confidence: 99%

Section: Single Order Lamellar Multilayer Gratingmentioning

confidence: 99%

Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics

Huang

Медведев

Kruijs

et al. 2017

Applied Physics Reviews

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“…(36) it is possible to find useful formula (such a generalized Bragg law for laminar multilayer grating) and optimization criteria; the reader can refer to the paper by Kozhevnikov et al [16] for further information. It is interesting to note that the above formalism is similar to the one of the CMT of optical waveguide couplers, so that one gets some insights in the physics of the laminar multilayer grating in single-order regime from studies about coupled waveguides in contra-directional coupling [18,19].…”

Section: Eigenstate Solutions Of the CM Equationsmentioning

confidence: 99%

“…The level of difficulty is increasing as soon as the profile of the pattern is not lamellar, that is when the profile of the multilayer pitch varies with the depth. To overcome these problems, it has been recently proposed to appeal to the well-know coupled-waves approach; this one has been successfully performed for the lamellar MGs [16]. In this paper we adopt this approach for two different scopes:…”

Section: Introductionmentioning

confidence: 99%

Analysis by Coupled-Mode Theory of X-ray Multilayer Gratings

André

Jonnard

Guen

2013

UVX 2012 - 11e Colloque Sur Les Sources Cohérentes Et Incohérentes UV, VUV Et X ; Applications Et Développements Récents

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Abstract. Multilayer gratings developed since the end of the ninethies are now used for various purposes in x-uv optics: polychromator, narrow bandpass monochromators. . . We have implemented the Coupled-Mode Theory (CMT) to calculate the performances of these devices (efficiencies, bandwidths. . . ) especially for quasi-lamellar gratings with different shapes of the multilayer pitch. We have fabricated such gratings and compared CMT calculations with measurements obtained at the BEAR beamline of ELETTRA.

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“…at energies between roughly 100 and 1500 eV. Unfortunately, the spectral resolution of ML mirrors in this regime is inherently limited by absorption of the fluorescent x-rays that need to be analyzed [4][5][6][7]. Although the natural line widths of fluorescent x-rays are typically E/ΔE ≈ 1000 [8], closely spaced lines could often not be distinguished due to the limited resolution of the analyzing optical element.…”

Section: Motivationmentioning

confidence: 99%

Single-order lamellar multilayer gratings

Meer¹

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Cover: 3D artist impression of a Lamellar Multilayer Grating (LMG). A Transmission Electron Microscope image of an actual LMG is shown on the rear. The grating was etched into a 400 bi-layer W/Si multilayer mirror with a total stack height H of 1 μm and a tungsten layer thickness of only 3 atoms. The grating had a period D of 300 nm and a lamel width ΓD of 75 nm. In comparison to the TEM image on the rear, the red and green layers in the artist impression correspond to tungsten and silicon, respectively. The bi-layer period in the artist impression is overestimated by a factor of 10 for visibility. SummaryA major challenge in the soft x-ray (SXR) and eXtreme UltraViolet (XUV) spectral ranges is the ability to manipulate the incident radiation using optical elements. By patterning conventional multilayer mirrors with nanoscale structures, novel optical elements with a variety of optical properties can be obtained. In this work, the design, fabrication and characterization of Lamellar Multilayer Gratings (LMG) was investigated. Such LMGs are a particular form of the general class of Bragg-Fresnel optics which combine Fresnel optics with Bragg reflection to provide unique dispersive and focusing optics. In particular, LMGs can be used to improve the spectral resolution of x-ray fluorescence techniques.A Coupled Waves Approach (CWA) was derived to simulate the optical performance, in terms of resolution and reflectivity, of LMGs. This CWA allowed to study the physical principles behind LMGs and resulted in the identification of an optimal LMG operating regime. In this regime, the incident beam is reflected in a single diffraction order and is hence referred to as the singleorder regime. Such single-order LMGs were fabricated using UV-NanoImprint Lithography and Bosch Deep Reactive Ion Etching, a process chosen to enable rapid practical development. Single-order operation was experimentally demonstrated and showed an improvement in spectral resolution of a factor of 3.8 with regard to conventional multilayer mirrors. Singe-order excitation of higher diffraction orders was also measured and analyzed.Single-order operation often requires multilayer stacks and grating structures that cannot be fabricated with sufficient accuracy using current technologies. As this invalidates the semi-infinite multilayer approximation, we investigated the optical performance of LMGs with finite multilayer stacks. We determined the ratio between the absorber thickness and bi-layer period of the multilayer stack can be used to further tailor LMG optical performance to maximize bandwidth reduction or minimize peak reflectivity loss. We also investigated various degradation processes that could limit the lifetime of LMGs, which is important for the applicability of such elements. Oxidation of tungsten and silicon as well as changes to the sidewall composition were clearly seen. However, SXR reflectivity remained stable to within measurement accuracy for an extended storage period of 18 months in a 1 atm air environment. The possibility of ...

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Analytic theory of soft x-ray diffraction by lamellar multilayer gratings

Cited by 19 publications

References 9 publications

Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics

Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics

Analysis by Coupled-Mode Theory of X-ray Multilayer Gratings

Single-order lamellar multilayer gratings

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