Effective area is one of the most important parameters of x-ray telescopes. It can be increased by enlarging the entrance aperture or maximizing the reflectivity through the proper designing and optimization of the reflecting coating. A method to increase the reflectivity of grazing incidence x-ray mirrors in the 0.5- to 8-keV energy region is analyzed. The idea consists in the use of a trilayer reflecting coating instead of single-layer one (e.g., C/Ni/Pt mirror instead of Pt one). Deposition of low-absorbing medium-Z and low-Z layers onto the top of strongly absorbing high-Z material results in essential increase in the reflectivity while keeping the same width of the reflectivity plateau. In particular, C/Ni/Pt trilayer mirror demonstrates enhancement of the double reflection coefficient by a factor achieving 1.5 to 3.5 compared to that of Pt-coated mirror. The effective area of a telescope is also considerably increased. The experimental results are in a very good agreement with the theoretical predictions. In addition, the C/Ni/Pt trilayer mirror exhibits a reasonable thermal stability and a relatively low compressive stress of about −550 MPa.
The low efficiency of conventional single layer gratings at the tender X-ray region (E=1~5 keV) significantly limits the photon flux of the beamline and the development of related imaging and spectroscopy experiments in this region. To overcome this issue, multilayer coated gratings have been proposed and developed. The diffraction behavior of a multilayer grating is more complex than a single layer grating. To understand the diffraction behavior and exert the maximum potential of this new optics, we have built an analytical theory based on coupled wave theory. A high efficiency single order diffraction regime was first identified which means only one diffraction order will be excited with a certain incidence angle and structure parameters. This is applicable to blazed multilayer gratings (BMGs). To achieve maximum efficiency, the optimum grating and multilayer structures were analyzed. The highest theoretical efficiency of a BMG can reach the same value of the coated multilayer reflectance. Moreover, blazed multilayer gratings exhibit the advantage of high harmonics suppression. For the BMG, the conventional condition of maximal diffraction efficiency, Dsinα = nd, where D and d is the grating period and multilayer period, respectively, α is blaze angle, n is diffraction order, has been proved invalid. This is due to the contribution of anti-blaze facets to diffraction and effect of strongly asymmetric diffraction. Based on these, a Cr/C BMG was fabricated in collaboration with the Department for Nanometer Optics and Technology in BESSY-II. Maximum efficiency of up to 60% was demonstrated at 3 keV which is close to the theoretical prediction.
Simple analytic equation is deduced to explain new physical phenomenon detected experimentally: growth of nano-dots (40–55 nm diameter, 8–13 nm height, 9.4 dots/μm2 surface density) on the grazing incidence mirror surface under the three years irradiation by the free electron laser FLASH (5–45 nm wavelength, 3 degrees grazing incidence angle). The growth model is based on the assumption that the growth of nano-dots is caused by polymerization of incoming hydrocarbon molecules under the action of incident photons directly or photoelectrons knocked out from a mirror surface. The key feature of our approach consists in that we take into account the radiation intensity variation nearby a mirror surface in an explicit form, because the polymerization probability is proportional to it. We demonstrate that the simple analytic approach allows to explain all phenomena observed in experiment and to predict new effects. In particular, we show that the nano-dots growth depends crucially on the grazing angle of incoming beam and its intensity: growth of nano-dots is observed in the limited from above and below intervals of the grazing angle and the radiation intensity. Decrease in the grazing angle by 1 degree only (from 3 to 2 degree) may result in a strong suppression of nanodots growth and their total disappearing. Similarly, decrease in the radiation intensity by several times (replacement of free electron laser by synchrotron) results also in disappearing of nano-dots growth.
Multilayer mirrors (MLM) with narrow spectral bandwidth are important for X-ray spectroscopy and imaging
experiments in order to improve the spectral resolution. To overcome the bandwidth limit of conventional
multilayers, single order lamellar multilayer grating (LMG) is one of the most promising methods. Driven by the
high resolution spectroscopy for the plasma diagnosis at E=~1keV, single order LMG based on MoSi2/Si multilayer
is developed. The multilayer period is 5.0 nm, with the Si thickness ratio of 0.6. An LMG with 600 nm grating
period and 1:2 line-to-space ratio is designed. As it works at the single order diffraction regime, the 0th order peak
reflectance (in theory) of the LMG is 45.4% at E=1.2 keV, which is the same as the multilayer mirror. The
bandwidth can be reduced by 3 times compared to the planar multilayer. To demonstrate this LMG structure,
MoSi2/Si multilayers have been deposited using direct current magnetron sputtering. Deep reactive ion etching
technique is under optimization in order to produce the multilayer grating structure with a high aspect-ratio of
around 5.
The high resolution extreme ultraviolet spectroscopy mission based on the normal-incidence multilayered diffraction grating technology, which provides high effective area and spectral resolution, can carry out a survey of local Galactic stellar and white dwarf targets. Compared to grazing-incidence systems, this approach allows previous observatory-class science to be delivered in a low-cost package. The instrument has already been proven in two sub-orbital space flights. However, the multilayer used before is periodic one and the working band-pass is limited. In this paper, the spectroscopic properties of a normal-incidence multilayered diffraction grating were simulated with three kinds multilayers for the wavelength range between 17.5nm and 25.0nm, which includes lines of Fe VIII to XIII that will be strongest in the cooler (solar like) coronae, plus some weaker lines of O, Si, S and Ar. The highest efficiency at central wavelength of band-pass can be obtained if the periodic multilayer is adopted. The most flat response efficiency can be achieved if we utilized a non-periodic multilayer. The simulation results demonstrated that the choice of the multilayer is dependent on the requirement to the spectroscopy mission and should be considered carefully.
We present a short review of our activities carried out in Tongji University (Shanghai, China) in the field of theory and technology of soft X-ray multilayer diffraction gratings. Diffraction gratings are widely used to study the structure and dynamics of a matter in laboratory and space by spectral analysis techniques. Combining multilayer and grating structures into a single unit allows to increase essentially both the spectral resolution and the efficiency of the diffraction optics. The unified analytical theory of soft X-ray diffraction from multilayer gratings operating in the single-order regime is briefly discussed. The single-order regime occurs when incident wave excites the only diffraction order and it is characterized by ultimately high diffraction efficiency tending to the reflectivity of conventional multilayer mirror. Our first experiments in fabrication of the blazed multilayer gratings by anisotropic etching of a silicon crystal with small roughness of the facet surfaces are described.
In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL.
In the early 1990’s [App. Opt. 32(19), 3344-531 (1993)], Church and Takacs pointed out that the specification of surface
figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. In the present
work, we demonstrate the limitations of specification, characterization, and performance evaluation based on the totally
statistical approach, including root-mean-square (rms) roughness and residual slope variation, evaluated over the spatial
frequency bandwidths that are system specific, and a more refined statistical description of the surface morphology
based on the power spectral density (PSD) distribution. We show that the limitations are fatal, especially, in the case of
highly collimated coherent x-ray beams, like beams from X-ray Free Electron Lasers (XFELs). The limitations arise due
to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of
the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the
problem, we treat a method, suggested in [Opt. Eng. 51(4), 046501, 2012] and based on an autoregressive moving
average (ARMA) modeling of the slope measurements with a limited number of parameters. The effectiveness of the
approach is demonstrated with an example peculiar to the x-ray optical systems under design at the European XFEL.
R. van der Meer, B. Krishnan, I. Kozhevnikov, M. De Boer, B. Vratzov, H. M. Bastiaens, J. Huskens, W. van der Wiel, P. Hegeman, G. C. Brons, K.-J. Boller, F. Bijkerk
Lamellar Multilayer Gratings (LMG) offer improved resolution for soft-x-ray (SXR) monochromatization, while
maintaining a high reflection efficiency in comparison to conventional multilayer mirrors (MM). We previously used a
Coupled-Waves Approach (CWA) to calculate SXR diffraction by LMGs and identified a single-order regime in which
the incident wave only excites a single diffraction order. We showed that in this regime the angular width of the zeroth-order
diffraction peak simply scales linearly with Γ (lamel-to-period ratio) without loss of peak reflectivity. However,
the number of bi-layers must then be increased by a factor of 1/Γ. Optimal LMG resolution and reflectivity is obtained in
this single-order regime, requiring grating periods of only a few hundred nm, lamel widths < 100nm and lamel
heights > 1μm [1]. For the fabrication of LMGs with these dimensions, we use a novel process based on UV-NanoImprint
Lithography (UV-NIL) and Bosch-type Deep Reactive Ion Etching (DRIE). Successful fabrication of
LMGs with periods down to 200nm, line widths of 60nm and multilayer stack heights of 1μm is demonstrated. SXR
reflectivity measurements were performed on these LMGs at the PTB beamline at the BESSYII synchrotron facility. The
measurements demonstrate an improvement in resolution by a factor 3,5 compared to conventional MMs. Further
analysis of the SXR reflectivity measurements is currently being performed.
Recent progress in the design and the manufacturing of wide bandpass x-ray multilayers has opened up new possibilities in hard x-ray optics, particularly in astrophysics and synchrotron x-ray applications.
In contrast to previous design based on semi-empirical laws or extensive computer calculation, the recent development of an analytical expression has greatly improved the design of aperiodic multilayer mirrors, allowing to generate any given spectral dependence of the reflectivity. In practice, an approximate differential equation is used to derive an in-depth multilayer composition profile whose reflectivity response approaches the desired one. Based on this asymptotic solution, usually sufficiently close to the final solution, the optimum multilayer composition profile is calculated numerically using a classical downhill algorithm.
We have studied the intrinsic characteristics of depth-graded multilayers using the procedure described above, with an emphasis put on the important case of a flat reflectivity response over a large but limited spectral range. The performance of depth-graded multilayer mirrors manufactured at ESRF and characterized at the BM5 beamline are presented. The necessity to account at the design level for deposition process parameters, such as chemical composition and thickness errors, and for the effective optical constants is highlighted.
The analysis of the roughness of B4C films of different thickness as well as W/B4C multilayer mirrors of different periods is performed basing on AFM and x-ray scattering (XRS) measurements. It is demonstrated that the linear model of a film growth is able to describe the whole set of experimental data including films at initial island stage of growth, if suppose the relaxation processes of a film surface to depend on the film thickness. New approach to the inverse problem of x-ray reflectometry consisting in inferring the dielectric constant profile from the reflectivity data is shortly discussed.
The potentialities of the x-ray scattering methods (XRS) for quantitative testing of supersmooth surfaces, thin films, and multilayer structures are discussed. The results of the surface roughness study with the use of XRS technique in hard and sort x-ray spectral regions are compared with independent measurements of the roughness by atomic force microscopy (AFM). It is demonstrated that the results obtained by XRS and AFM are in a very good agreement in spite of different physical principles and underlying the methods. XRS technique is applied for the roughness study of thin films which are used in applications for x-ray and UV optics. The XRS method is demonstrated to enable quantitative evaluation of PSD functions of both the film interfaces and the correlation between the substrate and film roughnesses. X-ray investigations of the correlation of the roughnesses of short-period multilayer structures are discussed as well. The use of the whispering gallery effect is demonstrated to extend the XRS method to control of the concave surface roughness.
Oleg Gilev, Victor Asadchikov, Angela Duparre, Nikolai Havronin, Igor Kozhevnikov, Yury Krivonosov, Sergey Kuznetsov, Vitaly Mikerov, Vladimir Ostashev, Vladimir Tukarev
It is demonstrated that the simplest model of a surface, assuming step-like variation of the dielectric permeability at a vacuum-matter interface, does not permit the quantitative description of all the features of x-rays reflection and scattering observed in experiment, even though the effects of the surface roughness are taken into consideration accurately. These features are much more pronounced for metals having a large number of the conductivity electrons which are bound slightly with individual atoms. Evidently, the wave function of the electron gas of a metal cannot abrupt sharply at a surface but decreases gradually into vacuum at a distance of several angstroms. To validate or disprove the hypothesis for the presence of a near surface transition layer of the electron density in metals, a set of experiments is performed. Reflection and scattering of hard and soft x-rays, and cold neutrons (which are sensitive to nuclear density distribution and insensitive to the electron one) from metal samples are measured. The independent measurements of the surface micro-topography are performed with the use of atomic force microscopy. The results obtained demonstrate the presence of a near surface layer, which is caused by gradual change of electron density, with a thickness of several angstroms.
This film roughness and its correlation with the substrate microtopography are studied using x-ray scattering at (lambda) equals 0.154 nm. The approach is applied for the investigation of superthin films of several nanometers thickness, when both interfaces are responsible for x-ray scattering, and consists in the direct determination of PSD functions from a set of x-ray scattering diagrams measured at different grazing angles of the probe beam. X-ray scattering methods are demonstrated to enable the quantitative evaluation of PSD functions of external film surfaces as well as the correlation between the substrate and film roughnesses. Results of measurements of thin films of materials widely used in the fabrication of short-period multilayer mirrors are discussed. The result of the x-ray scattering measurements are compared with independent investigations of the external film surface by atomic force microscopy.
The surface roughness of polished glass substrates as well as metal an dielectric coatings is studied using atomic force microscopy, hard and soft x-ray scattering at the wavelength (lambda) equals 0.154 nm and 4.47 nm, and light scattering (LS) at (lambda) equals 325 nm. It is demonstrated that all the methods, permitting the determination of PSD functions in partly overlapping, partly different ranges of spatial frequency, are in a good agreement in spite of different physical principles underlying the methods. The possible reasons for some differences in the PSD functions determined form different measurements are discussed. The main of them are a more difficult interpretation of LS data when dielectric coatings are present and a limitation on the angular range of hard x-ray scattering measurements imposed by the applicability of the perturbation theory used for experimental data processing.
We propose to extend x-ray scattering method to the investigation of concave surface roughness. Our approach is based on the use of the whispering gallery effect, which consists in that an x-ray beam falling tangentially on to a concave surface slides along a surface due to successive total external reflections. During its propagation the beam gradually broadens because the scattering transfers some part of radiation to the range of larger glancing angles. Fitting of a simulated angular distribution of outgoing beam to a measure done enables the determination of statistical parameters of concave surface roughness. Possible experimental schemes are analyzed by using ray-tracing technique, radiation scattering by surface roughness being modeled by the Monte Carlo method. Results of experiments in x-ray spectral region are discussed. Carbon-coated cylindrical surfaces with the radius of curvature of 6 cm and the arc angle of 45 and 60 degrees are studied with soft x-rays. The measured angular distributions of outgoing radiation are shown to agree quantitatively with the theoretical calculations when the scattering of x-rays by the surface roughness are taken into account. The rms roughness and the correlation length of the studied surface are found to be about 1.2 nm and 0.3 micrometers , respectively. The possibility of the study of concave surface roughness with the use of hard x-rays is also discussed.
A new approach is proposed for the design of wide band-pass multilayer optical elements for the hard x-ray spectral region. The method, based on the combination of analytical and numerical methods, solves the inverse problem consisting of inferring the composition profile of a depth-graded multilayer coating. First, assuming the multilayer d-spacing profile to be a monotone function of the depth and the d- spacing gradient to be large enough, we derived the differential equation that describes the change of period necessary to guarantee a given spectral reflectivity profile. Then, a computer code using an algorithm of steepest descent was used to refine numerically the multilayer period profile, each layer thickness being treated as an independent variable. When using the solution to the differential equation as a starting point of the direct problem, a many-fold decrease of computer time could be obtained. At each step, the spectral dependence of reflectivity was accurately computed using a standard matrix method. Simulations of the particular case of constant reflectivity and maximum integrated reflectivity over a wide spectral range are presented. The best choice of material pairs for comprising a depth-graded multilayer structure is discussed from the viewpoint of maximum achievable reflectivity and least number of bi-layers. Features of depth-graded multilayer mirrors, which are distinctive from conventional periodic mirrors, are examined.
Recent progress in the manufacturing of X-ray multilayers has opened up new possibilities in the field of hard x-ray optics allowing to produce wide bandpass optical elements through the design of depth-graded multilayer coatings. However, the inverse problem consisting of inferring the composition profile of the multilayer has only been addressed in a semi- empirical way, which encouraged us to develop a new (theoretical) approach. Our method is composed of three steps. First, we use an approximate analytical expression to describe the x-ray reflectivity spectral dependence of any arbitrary graded-multilayer structure. Such an approximation is obtained by assuming the multilayer d-spacing profile to be a monotone function of the depth. The d-spacing gradient is also assumed to be large enough, so that the reflection condition for each given energy is fulfilled in a depth zone that is small compared to the thickness of the multilayer stack. On this basis we could derive the differential equation that describes the change of period necessary to guarantee a given spectral reflectivity profile. Then, a computer code, written for solving the inverse problem, lead us to the desired multilayer period profile. Finally, the effective spectral dependence of reflectivity was accurately computed using a standard matrix method. Simulations of the particular case of constant reflectivity over a wide spectral range are presented. Possible applications of wide bandpass multilayers in synchrotron and astrophysics hard x-ray optics are discussed.
Flat and spherical Os - Si multilayer mirrors were synthesized and studied. Measured normal incidence reflectivity was 20% at the wavelength lambda equals 380 angstrom. The effect of impurities in silicon layers on the multilayer reflectivity in the ultrasoft x-ray region is discussed.
Basic properties of whispering gallery mirrors in soft X-ray region are considered. The following applications of whispering gallery optics are discussed: increasing of utilization efficiency of point source radiation, deflection of synchrotron radiation beam to vertical plane and its transportation to another horizontal level, resonators for soft X-ray lasers and the use of whispering gallery effect for investigation of roughness of concave surfaces.
Applications of the whispering gallery (WhG) optics for the steering of the synchrotron radiation (SR) are considered. The general principles of operation of the vertical SR beamline for proximity X-ray lithography are discussed. The possibilities of the WhG optics for the transportation of the SR beam to the second floor and for the steering of the hard X-ray radiation are analyzed.
The problem of multilayer mirrors which are capable to reflect X-ray radiation at two given wavelengths is discussed. Three kinds of two- period multilayers are considered and comparison of their properties in the soft X-ray region is presented. The scheme of soft X-ray scanning microscope on the basis of Schwarzschild objective with two-period multilayer coating is proposed for chemical microanalysis of biological samples.
Igor Kozhevnikov, L. Balakireva, I. Lyakhovskaya, A. Parobets, V. Kondratenko, Yurii Pershin, A. Ponomarenko, Anatoli Fedorenko, Vladimir Levashov, Spartak Sagitov, O. Tolstikhin, V. Chirkov, L. Babaeva, Tatjana Ivanova, Alexander Vinogradov
Optical constants of Si, C, Mo, and Nb thin films as well as of fused quartz and float glass substrates have been determined experimentally in the (lambda) approximately equals 80 - 190 angstrom wavelength range. The dependence of optical constants on film thickness and film production technology is demonstrated. The factors influencing substance permittivity in the soft x-ray range are discussed. It is discovered that the main of them is the presence of impurities introduced into the film during its deposition. The chemical composition of multilayer Mo-Si x-ray mirrors is studied. It is shown that if O, N, and Ar impurities in Si films are taken into account, the available experimental data on the reflectivity and resolution of Mo-Si mirrors in the soft x-ray range can be described quantitatively.
The expression for X-ray scattering diagram by thin film roughness is obtained and analyzed in the perturbation theory approximation. Specific features of X-ray scattering are discussed which have no analogs in X- ray scattering from a single surface and are caused by the interference effects. These are: oscillations of X-ray scattering diagram, the lack of X-ray scattering from external film surface, and interference suppression (up to some orders) of X-ray scattering intensity.
The influence of smooth (not step-like) variation of the dielectric function near a surface on reflectivity and scattering of X-rays is investigated theoretically. It is shown than the presence of the transition layer can essentially change the shape of differential scattering intensity diagram, especially when the incidence angle of X- ray beam is more than critical angle of the total external reflection. The application of model involved allows one to describe the Yoneda effect quantitatively (whereas it is impossible in the frames of a step- like model of the dielectric function).
The possibilities of X-ray scattering methods are demonstrated for the quantitative study of supersmooth surface microgeometry. It is shown that the model of a surface which takes into account layered inhomogeneities near a surface enables one to obtain better agreement between theory and experiment in comparison with the step-like model of a surface which widely used elsewhere.
The possibilities of X-ray scattering methods are demonstrated for the quantitative study of supersmooth surface microgeometry. It is shown that the model of a surface which takes into account layered inhomogeneities near a surface enables one to obtain better agreement between theory and experiment in comparison with the step-like model of a surface which widely used elsewhere.
The influence of smooth (not step-like) variation of the dielectric function near a surface on reflectivity and scattering of X-rays is investigated theoretically. It is shown that the presence of the transition layer can essentially change the shape of differential scattering intensity diagram, especially when the incidence angle of X-ray beam is more than critical angle of the total external reflection. The application of model involved allows one to describe the Yoneda effect quantitatively (whereas it is impossible in the frames of a step-like model of the dielectric function).
Problems of short period multilayer mirrors fabrication are discussed. Results of synthesis of multilayer structures with nanometer period are presented. The shortest period observed is 13 angstroms for W - Si and W - B4C sputtered multilayers. Measurements of near normal incidence reflectivity at (lambda) equals 31 - 32 angstroms are described for W - Sc multilayers with period about 16 angstroms. Measured reflectivity achieves 3.3% and is in good agreement with theoretical model.
The ray tracing code SURF for x-ray optics simulation is presented. The code can be applied to x-ray imaging problems, and steering and concentration of x-ray beams. The results of the simulation of x-ray laser beam focusing with figured multilayer optics and pattern imaging with Schwartschild objective are given.
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