Interference suppression of light backscattering through oblique deposition of high-reflectivity multilayers: a theoretical analysis.

We demonstrate a theoretical approach whereby light backscattering toward the incident beam can be suppressed entirely for a high-reflectivity, rough-surfaced multilayer mirror fabricated using oblique deposition, such that the interface relief is replicated at a certain angle ß to the sample normal. The mirror comprises two parts: a main (lower) multilayer consisting of N identical bi-layers growing at the angle ßML to the mirror normal, and an additional bi- or tri-layer forming the topmost section of the mirror, which grows at another angle ßBL. We show that choosing appropriate growth angles ßML and ßBL results in a disappearance of backscattering toward the incident beam due to the destructive interference of waves scattered from the main multilayer and uppermost bi- or tri-layer. The conditions for the scattering suppression are formulated, and the suitability of different mirror materials is discussed.

Theoretical analysis and optimization of highly efficient multilayer-coated blazed gratings with high fix-focus constant for the tender X-ray region.

The problem of X-ray diffraction from multilayer-coated blazed diffraction gratings is analyzed. Invalidity of the conventional condition of maximal diffraction efficiency observed in previous experiments is explained theoretically. This is attributed to two factors: contribution of anti-blaze facets to diffraction efficiency and effect of strongly asymmetric diffraction. We demonstrate that a proper choice of the multilayer d-spacing allows to design grating with the diffraction efficiency close to the maximal possible one throughout the tender X-ray range (E∼1-5 keV). An optimization procedure is suggested for the first time to choose the optimal grating parameters and the operation diffraction order to obtain a high fix-focus constant and high diffraction efficiency simultaneously in a wide spectral range.

Interference suppression of light backscattering through oblique deposition of a layered reflecting coating: bi-layer on a substrate.

We theoretically demonstrate the possibility of entirely suppressing light backscattering towards the incident beam from a rough bilayer fabricated by deposition at an oblique angle, such that the substrate relief is replicated at a certain angle to the substrate surface. The necessary conditions of the scattering suppression were formulated. Interference suppression was observed experimentally (633 nm wavelength, 45° incidence angle, -35° scattering angle) with a set of SiO2-on-Ta2O5 bi-layers fabricated at different deposition angles. We detected a suppression of the scattering from the bi-layer fabricated at the deposition angle of 7.7° by a factor of about 30 compared with that from the sample deposited at normal incidence. The observed value of the scattering suppression was limited by the background noise of the measurements.

Optimized highly efficient multilayer-coated blazed gratings for the tender X-ray region.

The optimized design of multilayer-coated blazed gratings (MLBG) for high-flux tender X-ray monochromators was systematically studied by numerical simulations. The resulting correlation between the multilayer d-spacing and grating blaze angle significantly deviated from the one predicted by conventional equations. Three high line density gratings with different blaze angles were fabricated and coated by the same Cr/C multilayer. The MLBG with an optimal blaze angle of 1.0° showed a record efficiency reaching 60% at 3.1 keV and 4.1 keV. The measured efficiencies of all three gratings were consistent with calculated results proving the validity of the numerical simulation and indicating a more rigorous way to design the optimal MLBG structure.

Effect of the surface roughness on X-ray absorption by mirrors operating at extremely small grazing angles.

This study theoretically analyzes an increase in X-ray absorption by a grazing incidence mirror due to its surface roughness. We demonstrate that the increase in absorption can be several hundred times larger than predicted by the Nevot-Croce formula. As a result, absorption enhances by several times compared to a perfectly smooth mirror despite the extremely small grazing angle of an incident X-ray beam (a fraction of the critical angle of the total external reflection) and the high quality of the reflecting surface (the roughness height was 0.5 nm in modeling). The main contribution to the absorption increase was dictated by the mid-scale roughness (waviness) of the virgin substrate surface, whose quality thus defines an absorption enhancement. The approach was applied to the analysis of two real mirrors used in a synchrotron (BESSY-I) and a European X-ray free-electron laser (XFEL) beamline. The modern surface finishing technology of elastic emission machining provides extremely low substrate waviness, guaranteeing the negligible effect of the surface roughness on the absorption increase.

Nitridated Ru/B4C multilayer mirrors with improved interface structure, zero stress, and enhanced hard X-ray reflectance.

Ru/B4C multilayer mirrors are used for hard X-ray monochromators with moderate spectral resolution and high integral flux. To overcome the problem of large compressive stress inherent in Ru/B4C multilayers, a reactive sputtering technique using a mixture working gas of argon and nitrogen with different partial pressures was tested, and the fabricated multilayers had a period of 3 nm. The intrinsic stress was essentially reduced after nitridation and relaxed to zero value at approximately 15% partial pressure of nitrogen in the working gas. Interface roughness was slightly increased which can be caused by the polycrystalline structure inside the nitridated samples. More importantly, the nitridated multilayers showed an enhanced reflectance (67% at 8.04 keV photon energy) as compared with the one fabricated with pure Ar (54%). The structure analysis with transmission electron microscopy and X-ray photoelectron spectroscopy demonstrated that nitrogen incorporated into a multilayer structure was mostly located in the B4C layers forming BN compounds, which suppressed the diffusion of boron, stabilized the interfaces and enhanced the reflectance.

Design of a multilayer-based collimated plane-grating monochromator for tender X-ray range.

Collimated plane-grating monochromators (cPGMs), consisting of a plane mirror and plane diffraction grating, are essential optics in synchrotron radiation sources for their remarkable flexibility and good optical characteristics in the soft X-ray region. However, the poor energy transport efficiency of a conventional cPGM (single-layer-coated) degrades the source intensity and leaves reduced flux at the sample, especially for the tender X-ray range (1-4 keV) that covers a large number of K- and L-edges of medium-Z elements, and M-edges of high-Z elements. To overcome this limitation, the use of a multilayer-based cPGM is proposed, combining a multilayer-coated plane mirror with blazed multilayer gratings. With this combination, the effective efficiency of cPGMs can be increased by an order of magnitude compared with the conventional single-layer cPGMs. In addition, higher resolving power can be achieved with improved efficiency by increasing the blaze angle and working at higher diffraction order.

Analytic theory of alternate multilayer gratings operating in single-order regime.

Using the coupled wave approach (CWA), we introduce the analytical theory for alternate multilayer grating (AMG) operating in the single-order regime, in which only one diffraction order is excited. Differing from previous study analogizing AMG to crystals, we conclude that symmetrical structure, or equal thickness of the two multilayer materials, is not the optimal design for AMG and may result in significant reduction in diffraction efficiency. The peculiarities of AMG compared with other multilayer gratings are analyzed. An influence of multilayer structure materials on diffraction efficiency is considered. The validity conditions of analytical theory are also discussed.

Nitridated Pd/B4C multilayer mirrors for soft X-ray region: internal structure and aging effects.

Reactive sputtering with a mixture of argon and nitrogen (N2 partial pressure of 4%, 8%, and 15%) as the working gas is used to develop the high reflectance Pd/B4C multilayers for soft X-ray region application. Compared to the pure Ar fabricated sample, the interface roughness of the nitridated multilayer is slightly increased while the compressive stress is essentially relaxed from -623 MPa (pure Ar) to -85 MPa (15% N2). A maximum reflectance of 32% is measured at the wavelength of 9.5 nm for the multilayer fabricated with 15% N2. After storing the multilayers in an air environment for 6-17 months, a distinct aging effect is observed on the nitridated samples. The transmission electron microscopy results indicate that a large part of the top layers of the nitridated samples is deteriorated with severe interdiffusion, essential decrease in d-spacing, and compacted multilayer structure. The deterioration is less pronounced for the multilayers fabricated with a higher ratio of N2. Energy dispersive X-ray spectroscopy reveals that the concentration of nitrogen and boron in the degraded area is much reduced compared to the intact layers. A primitive model of upward diffusion of nitrogen and boron is proposed to explain the aging effects of the nitridated structure.

Wideband multilayer gratings for the 17-25 nm spectral region.

An approach to designing wideband blazed multilayer gratings is introduced and applied to gratings operating at 17-25 nm. We demonstrate single-order operation of broadband multilayer gratings, despite their very wide spectral and angular bandpass, when only one diffraction wave is excited and the diffraction efficiency reaches the reflectivity of a conventional depth-graded multilayer mirror, eliminating overlapping of different-order diffraction waves. The selection principles for the geometrical parameters of gratings are discussed. We formulate a "law of similarity" for wideband gratings that allows us to design gratings with different geometrical parameters but practically the same spectral dependence of the diffraction efficiency.

Improvement of interface structure and polarization performance of Co/C multilayers by incorporation of nitrogen.

Short-period (~3.5 nm) Co/C multilayer mirrors are fabricated by the direct current magnetron sputtering technique through the addition of a small proportion of nitrogen (4-15% partial pressure) to the working gas (Ar). The addition of nitrogen has been demonstrated to significantly suppress the interdiffusion of neighboring materials due to the nitridation of carbon layers as compared with the Co/C multilayer fabricated with the use of pure Ar. The optimal partial pressure of nitrogen was found to be 6%. At this pressure, nitrogen provides abrupt interfaces and the maximal peak value (19%) of the s-polarized radiation reflectivity at the 251-eV photon energy and 45° angle of incidence. The p-polarized radiation reflectivity proved to be less than 0.3%, demonstrating high potentialities of the nitridated Co/C multilayers as Bragg polarizers in the 4.5-6.5-nm spectral range.

Reflection of X-rays from a rough surface at extremely small grazing angles.

Peculiarities of X-ray diffraction from a rough surface at an extremely small grazing angle of an incident beam are theoretically studied. The interrelation of four diffraction channels (coherent reflectance, coherent transmittance, diffuse scattering in vacuum, and scattering into the matter depth) is analyzed for different limiting cases (large and small correlation length of roughness and large and extremely small grazing angle of incident radiation). Both the Debye-Waller and the Nevot-Croce factors are demonstrated to describe improperly the features of X-ray diffraction at extremely small grazing angles. More appropriate simple analytic expressions for the specular reflectivity and total integrated scattering in vacuum are obtained instead. Transformation of one limiting diffraction regime into another one with variation in the correlation length of roughness is discussed.

Enhancement of soft X-ray reflectivity and interface stability in nitridated Pd/Y multilayer mirrors.

Pd/Y multilayer mirrors operating in the soft X-ray region are characterized by a high theoretical reflectance, reaching 65% at normal incidence in the 8-12 nm wavelength range. However, a severe intermixing of neighboring Pd and Y layers results in an almost total disappearance of the interfaces inside the multilayer structures fabricated by direct current magnetron sputtering and thus a dramatic reflectivity decrease. Based on grazing incidence X-ray reflectometry and X-ray photoelectron spectroscopy, we demonstrate that the stability of the interfaces in Pd/Y multilayer structures can be essentially improved by adding a small amount of nitrogen (4-8%) to the working gas (Ar). High resolution transmission electron microscopy shows that the interlayer width is only 0.9 nm and 0.6 nm for Y(N)-on-Pd(N) and Pd(N)-on-Y(N) interfaces, respectively. A well-defined crystalline texture of YN (200) is observed on the electron diffraction pattern. As a result, the measured reflectance of the Pd(N)/Y(N) multilayer achieves 30% at λ = 9.3 nm. The peak reflectivity value is limited by the remaining interlayers and the formation of the YN compound inside the yttrium layers, resulting in an increased absorption.

Soft x-ray reflectometry, hard x-ray photoelectron spectroscopy and transmission electron microscopy investigations of the internal structure of TiO2(Ti)/SiO2/Si stacks.

We developed a mathematical analysis method of reflectometry data and used it to characterize the internal structure of TiO2/SiO2/Si and Ti/SiO2/Si stacks. Atomic concentration profiles of all the chemical elements composing the samples were reconstructed from the analysis of the reflectivity curves measured versus the incidence angle at different soft x-ray reflection (SXR) photon energies. The results were confirmed by the conventional techniques of hard x-ray photoelectron spectroscopy (HXPES) and high-resolution transmission electron microscopy (HRTEM). The depth variation of the chemical composition, thicknesses and densities of individual layers extracted from SXR and HXPES measurements are in close agreement and correlate well with the HRTEM images.

Evolution of the Internal Structure of Short-Period Cr/V Multilayers with Different Vanadium Layers Thicknesses.

Cr/V multilayer mirrors are suitable for applications in the "water window" spectral ranges. To study factors influencing the internal microstructure of Cr/V multilayers, multilayers with different vanadium layers thicknesses varying from 0.6 nm to 4.0 nm, and a fixed thickness (1.3 nm) of chromium layers, were fabricated and characterized with a set of experimental techniques. The average interface width characterizing a cumulative effect of different structure irregularities was demonstrated to exhibit non-monotonous dependence on the V layer thickness and achieve a minimal value of 0.31 nm when the thickness of the V layers was 1.2 nm. The discontinuous growth of very thin V films increased in roughness as the thickness of V layers decreased. The columnar growth of the polycrystalline grains in both materials became more pronounced with increasing thickness, resulting in a continuous increase in the interface width to a maximum of 0.9 nm for a 4 nm thickness of the V layer.