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Abstract
Broadband Mo/Be multilayer structures were designed for maximum uniform normal-incidence reflectivity in a broad range of 111–138 Å, which lies near and beyond the L2,3 absorption edge of Si. A comparison was made of the capabilities of two classes of aperiodic structures and of so-called “stack” structures, which are composed of several periodic structures with different periods stacked one over the other. Six-stack Mo/Be 80-layer structures were synthesized on concave (R = 1 m) superpolished fused silica substrates. Their absolute reflectivity was measured at 13% – 14% in the 111–138 Å optimization range using a laboratory reflectometer with a laser-plasma radiation source. The normal-incidence reflection spectra of the mirrors were recorded in the configuration of a transmission-grating spectrograph using the slowly varying quasicontinuum of a laser-driven tungsten plasma. Comparing the reflectivity data with the reflection spectra recorded with a CCD permitted estimating a decrease in the detector responsivity beyond the Si L-edge. The broadband normal-incidence multilayer mirrors facilitate the development of a high-resolution imaging spectrograph covering a usable range about the Si L-edge to characterize, for instance, the L-edge fine structures and chemical states. These mirrors will also find use in imaging solar instruments with a high spectral resolution operating aboard a spacecraft and in laboratory instruments for plasma diagnostics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
For a long period of time, the main emphasis in the development of normal-incidence multilayer mirrors (MMs) for the soft X-ray spectral range was placed on periodic MMs with a narrow spectral width and as-high-as-possible peak reflectance coefficient. Furthermore, the MMs were designed on the basis of Mo/Si multilayer structure, which is fairly good for 135 Å XUV lithography [1], but at the same time exhibit rather poor reflectivity at wavelengths shorter than 125 Å, where the L2,3 absorption edge of Si lies. In the current work, we report on the design and reflectivity measurements of Be-based aperiodic MMs with plateau reflectivity in the 111 –138 Å spectral range.
The idea of making broadband normal-incidence MMs for the soft X-ray/XUV range was conceived by Meekins et al. in the 1980s [2], bearing in mind, in particular, their application in soft X-ray/XUV astronomy. Vernon et al. [3] synthesized Mo/Si structures with a weak “chirp” of neighboring bilayer thicknesses with structure depth in order to somewhat broaden the width of the reflection peak and increase the integral reflection coefficient at the expense of a slight lowering of the peak reflectivity. More recently, van Loevezijn et al. [4] addressed the task of making broadband normal-incidence MMs. Two formulations of the problem appeared in Refs. [2,4]: to design a binary multilayer structure optimized either for maximum uniform reflectivity or maximum integral reflectivity in a specified wavelength interval at normal incidence, the thicknesses of all individual layers being considered as independent variables (optimization parameters). In Ref. [4] other optimization criteria were also considered: in particular, maximum integral reflectivity in a specified interval of incidence angles at a fixed wavelength.
A numerical algorithm was developed in Refs. [5,6] for the solution of different optimization problems, with all individual layer thicknesses treated as independent optimization parameters. Wang and Michette [7] also considered all Mo and Si layer thicknesses as the optimization parameters in the design of broadband normal-incidence Mo/Si MMs. Designed and synthesized on a concave substrate in Ref. [8] was a Mo/Si multilayer structure optimized for maximum uniform reflectivity in a range of 125–250 Å with the inclusion of MoSi2 transition layers (12 Å for Mo-on-Si and 6 Å for Si-on-Mo transition layers [9]). A free-standing transmission grating spectrograph, in which the MM served as the focusing element, was employed to obtain quasicontinuous (target: tungsten) and line (target: LiF) spectra of laser-produced plasma in a range λ ∼ 125–250 Å [8]. Subsequently these mirrors were repeatedly used in experiments (see, for instance, Refs. [10–15] and review Ref. [16]). Recently, a broadband (125–300 Å) high-resolution stigmatic (imaging) spectrograph was implemented, which makes use of an aperiodic normal-incidence Mo/Si MM as the focusing element and a plane grazing-incidence VLS grating [17]. The capabilities of the spectrograph for space-resolved spectroscopy/diagnostics of laboratory plasma were experimentally demonstrated.
In Ref. [11] it was shown that it is possible to make broadband normal-incidence MMs also in other subranges of the XUV. Specifically, simulations of Mo/Be and Rh/Be aperiodic multilayer structures without the inclusion of transition layers suggested the feasibility of making mirrors with a uniform reflectivity at a level of ∼20% in a range of 111–135 Å [11].
Mention should also be made of successful endeavors to make broadband reflective polarizers based on aperiodic Mo/Si structures [18] for a 30-Å wide band centered at a wavelength of 142.5 Å and broadband reflective polarizers for shorter-wavelength bands [19–21].
Supposedly the shortest-wavelength broadband normal-incidence aperiodic mirrors were reported by Windt and Gullikson [22], who designed, fabricated and studied Pd-bearing multilayer structures for the ranges 89–112 and 89–140 Å. For some samples (e.g., Pd/B4C/Y/B4C), the measured reflectivity band extended even a few Angstroms below the nominal short-wavelength bound of 89 Å. Also designed and synthesized were broadband aperiodic Sb/B4C multilayers for ranges of 90–100, 95–105, and 100–120 Å [23].
The densities of materials in nanometer-thick layers, generally speaking, depend on the layer thickness. For instance, the density of Mo increases from 0.77 to 0.97 of the tabular value with increase in layer thickness from ∼14 to 55 Å [24]. As a result, the layer thicknesses of a synthesized aperiodic structure differ from the designed ones. With this circumstance in mind, Kozhevnikov et al. [25] improved the approach in which all layer thicknesses are treated as optimization parameters. They modified the optimization criterion in such a way as to lessen the thickness variations of the neighboring layers of the same material and thereby make more predictable the result of synthesis. This is achieved at the expense of an insignificant lowering of integral reflection coefficient and a slight impairment of reflectivity uniformity. Kozhevnikov et al. [25] dealt with the design of an aperiodic Mo/Si structure with a uniform reflectivity in the range of incidence angles of 0°–18° at an EUV lithography wavelength of 135 Å.
An alternative approach to the design of broadband MMs implies a superposition of several periodic structures with different periods stacked one above the other (the so-called stack MM). In the XUV, this approach was first introduced, as far as we know, by Kuhlmann et al. [26], who designed a three-stack Mo/Si structure which provided a fairly uniform reflectivity (45%–50%) in a range of incidence angles of 0°–20° at a wavelength of 130 Å. Recently a comparison was made of the aperiodic and stack structures with plateau in a spectral range of 170–210 Å intended for solar astronomy [27]. The authors arrived at the conclusion that stack structures are preferable from the standpoint of synthesis, but the achievable plateau level is somewhat lower.
Using Be in lieu of Si permits shifting the short-wavelength bound of the plateau reflectivity to 111 Å, the K-edge of Be. Periodic Mo/Be coating has been studied experimentally since 1995 [28], and a peak reflectivity of 68.7% at a wavelength of 113Å was reported for a 70-bilayer periodic MM [28]. The width (FWHM) of the reflectivity peak was about 2.7 Å.
Recently, comprehensive work on Be-containing aperiodic MMs for the wavelength ranges 16.5–21 nm and 28–33 nm was reported in Ref. [29]. The mirrors are intended for operation in a solar spectroheliograph, which comprises a plane grazing-incidence grating and a normal-incidence focusing multilayer mirror [30], aboard the International Space Station in the framework of the KORTES Project [31]. The aperiodic MMs were optimized for uniform reflectivity in the specified bands using a genetic algorithm. The characteristics of traditional Mo/Si MMs and beryllium-containing Mo/Be, Mo/Be/Si, Al/Be, and Mg/Be aperiodic systems were compared. The Mo/Be/Si MMs were shown to be preferable in the 16.5–21 nm range, while aperiodic Mg/Be MMs with a protective aluminum capping layer were preferable in the 28–33 nm range, being two and a half times superior in reflectivity to the corresponding aperiodic Mo/Si MMs (26% vs 10% in the 28–33 nm range).
In the present work we set ourselves the task of making normal-incidence mirrors based on Mo/Be multilayer structures with a uniform reflectivity in the 111–138 Å range. Broadband normal-incidence XUV mirrors broaden the capabilities of high-resolution stigmatic spectral imaging. They are intended for solar astronomy as well as for spectroscopy/diagnostics of laboratory plasmas and other XUV radiation sources with high spectral and spatial/angular resolution. The 111–138 Å plateau range of the Mo/Be multilayers, in particular, covers the Balmer series domain of hydrogen-like C VI ions: Hβ (135 Å), Hγ (120 Å), Hδ (114 Å). These lines are perfectly suited to space-resolved plasma density measurements from their Stark broadening, which may be accomplished using stigmatic spectrometers of the type described in Ref. [17]. The broadband normal-incidence multilayer mirrors also favor the development of a high-resolution imaging spectrograph covering a usable range about the Si L-edge to characterize, for instance, the L-edge fine structures and chemical states. The normal-incidence 111–138 Å Mo/Be multilayers reported in this work are well suited for recording, for instance, the lines of carbon-like FeXXI (113.31 Å) and nitrogen-like FeXX (113.34, 121.83, and 121.87 Å) excited in solar flares.
Calculations were made both of aperiodic structures and of stack ones optimized for maximum uniform reflectivity in this range. In the former case, the ideas of Kozhevnikov et al. [25] were extended to the case of uniform spectral reflectivity for a fixed angle of incidence.
At the stage of fabrication of MMs, we decided in favor of the stack structure considering the simplicity of its synthesis. Based on the same designed six-stack structure, three stack Mo/Be multilayers (Mirrors No. 1–3) were synthesized on concave superpolished substrates, and their reflectivity was measured with a reflectometer with a laser-plasma radiation source [32,33]. Furthermore, the reflection spectra of the mirrors were recorded in the configuration of a normal-incidence transmission-grating spectrograph, the laser plasma of a tungsten target serving as the source of quasicontinuum. Also recorded was the line spectrum of a LiF laser target. The reflectivity data were compared with the reflection spectra observed with the laser plasma source, which permitted estimating the CCD detector responsivity variation about the Si L-edge.
When performing simulations, advantage was taken of the optical constants values for Mo and Be, which were experimentally determined in Refs. [34,35] and borrowed from the website of the Center for X-Ray Optics in Berkeley [36].
2. Design of aperiodic and stack structures
In the design of an aperiodic structure that satisfies some optimization criterion (for instance, maximum uniform reflectivity in a predefined wavelength range), which is referred to as the inverse problem of multilayer optics, the mathematical problem involves minimizing the corresponding functional. In this case, all layer thicknesses are treated as optimization parameters (independent variables). In this work, the program code for calculating aperiodic structures with plateau reflectivity reported in Refs. [5,6] was modified so as to endow it with the capability to control the difference between the thicknesses of neighboring layers (not necessarily of the same material). To this end, the functional under minimization was given the following form:
The first (Fig. 1(a)) version provides a plateau level of about 16.4% and a sufficiently high uniformity: $\sigma = 3.4\%$. Introducing p = 10−9 Å-1, Δn = 2 has the effect that the plateau level becomes slightly lower (15.9%, Fig. 1(c)). In this case, the layer-to-layer thickness jumps are appreciably smoothed out (Fig. 1(d)). This is achieved at the expense of some lowering of the plateau and an increase in the rms departure of the reflectivity (1.38%, or $\sigma = 8.7\%$ in relative units) from the plateau level. The six-stack structure provides a somewhat lower plateau level (14.5%) and a somewhat higher rms departure of 1.29% of the absolute reflection coefficient, or about 9% in relative units.
Fig. 1. At the left: calculated spectral reflectivities of two aperiodic structures (a, c) and of a six-stack structure (e) optimized for maximum uniform reflectivity at 5° off normal in the 111–138 Å range. At the right: layer thicknesses of the corresponding structures. Coefficient p of formula (1) is equal to zero (a, b) and 10−9 Å-1 (c, d, Δn = 2). The aperiodic structures consist of 82 layers, while the six-stack structure consists of 40 bi-layers. The layers are numbered from the top to the bottom of the stack.
Interestingly, the spread in thickness of Mo layers for the simulated aperiodic structures is smaller than for the simulated six-stack structure.
Unexpectedly, for p = 5·10−11 Å-1 and Δn = 1 (bringing closer the neighboring layer thicknesses) the spread (39–27 Å) of Mo-layer thicknesses can be quite small without any appreciable loss in plateau level and uniformity [38].
3. Synthesis and characterization of the six-stack structures
To synthesize the first broadband Mo/Be mirrors, we decided in favor of the six-stack structure in view of its greater simplicity of implementation and better diagnozability from the reflection of X-rays (1.54 Å) at grazing incidence [27,39]: a smaller number of parameters makes it possible to solve the inverse problem and carry out efficient correction of the deposition procedure.
Multilayer mirrors were deposited by dc-magnetron sputtering. The synthesis process was carried out on a magnetron sputtering system with four planar magnetrons. Deposition was carried out in argon environment with a 99.998% purity at a pressure of 0.11 Pa, while the background pressure was lower than 5·10−4 Pa. The electric power on the magnetrons was 250 W for Be and 156 W for Mo. In this case, the growth rate of the films was 0.1 nm/s for Be and 0.16 nm/s for Mo.
During the deposition process, the substrate rotates simultaneously around its own axis and around the axis of the vacuum chamber. An additional factor that ensures the uniformity of the film thicknesses is the curved diaphragm installed between the magnetron and the substrate. In this paper, the uniformity of the MMs periods on substrate was about 0.5%. The thickness of the deposited layers was controlled by the choice of the speed for the passage over a particular magnetron.
The reflectivity measurements were performed using a reflectometer with a laser-plasma radiation source operating at a pulse-repetition rate of 10 Hz [32,33]. The spectral resolution experimentally measured at the Be K-edge (111 Å) was 0.32 Å. The probing beam measured (FWHM) 0.135 mm vertically and 0.32 mm horizontally. For each spectral point, an exposure time of 5 s was used (50 laser shots). To suppress the reflectivity data fluctuations arising in part from the source intensity fluctuations, the data were normalized to the X-ray monitor signal. Figures 2(a)–2(d) show the measured spectral reflectivities of three Mo/Be mirrors deposited on superpolished spherical (R = 1000 mm) substrates of fused silica KU-1. The measured reflectivities amount to about 13%–14% in the 111–138 Å range for a satisfactory uniformity of the reflectivity over the spectral range and a perfect uniformity over the aperture. Figure 2(a), in particular, serves to illustrate the reproducibility of reflectivity measurements: the measurements for the central point averaged over three runs are shown in black, and one of these measurement runs is shown in red. The difference in absolute reflectivity is typically under 1%.
Fig. 2. Measured spectral 5°-off-normal reflectivities of the three six-stack Mo/Be structures deposited on concave spherical (R = 1000 mm) superpolished substrates of fused silica (a – d). (a) Reflectivity measurements for mirror No.2. Measurements for the central point averaged over three runs (black). One of these measurements (red). Measurements for points 10 mm (blue) and 20 mm (green) away from the center.
4. Operation of the mirrors in a transmission grating spectrometer
A stigmatic normal-incidence XUV spectrometer was assembled using the Mo/Be MMs, which fulfilled the function of the focusing element. The radiation was dispersed with a free-standing transmission grating (TG) with a nominal line density $p = 1000$ mm-1 and an aperture of ∼5 cm2. The detector was made around a backside-illuminated e2v CCD array with 13 × 13 μm (2048 × 1060) pixels (Fig. 3). The source of quasicontinuum XUV radiation was the plasma of a tungsten target excited by Nd:YAG laser pulses (0.5 J, 8 ns, 1.064 μm). For the central ray, the angle of incidence on the mirror was 5°.
Fig. 3. Configuration of the stigmatic normal-incidence transmission-grating spectrometer comprising laser-produced plasma (LP), the entrance slit, a focusing Mo/Be mirror under study ($R = 1000$ mm), a large-aperture free-standing transmission grating (TG), and a CCD detector.
Shown in Fig. 4(a) is the measured reflectivity (orange line) of mirror No. 3 (the same as in Fig. 2(d)), and the reflection spectrum of the tungsten plasma recorded in one laser pulse using the CCD detector (blue histogram, “raw” data) in the configuration of the normal-incidence TG spectrometer schematized in Fig. 3. The spectrum of the tungsten plasma is scaled to match the reflectivity curve at wavelengths longer than 125 Å (the Si L-edge). The difference in the domain λ < 125 Å is attributable to the effect of the L2,3 absorption edge of Si in the CCD detector.
Fig. 4. Six-stack mirror No. 3. Reflection spectrum recorded with the TG spectrometer from tungsten plasma (blue histogram, “raw” data) and reflectivity measured with a reflectometer (orange line). The recorded reflection spectrum is normalized to coincide with the measured spectral reflectivity in the domain λ > 125 Å (above the L2,3 edge of Si) (a). Measured reflectivity (orange line), simulated reflectivity (black), and recorded reflection spectrum corrected with the inclusion of the spectral transmittance of the conventional “dead” 54 nm thick Si layer. The simulated reflectivity is not scaled and coincides with the plot in Fig. 1(e). The histogram was obtained by 1 × 30 binning the CCD counts in the direction perpendicular to the dispersion direction (b).
Shown in Fig. 4(b), along with the measured reflectivity of mirror No. 3 (orange line), is the simulated reflectivity (not scaled, the same as in Fig. 1(e),) of mirror No. 3 design structure (black line). Notice that the simulated reflectivity is in excellent agreement with the measured one. The small difference between the orange and black lines (i.e., between the performance of the synthesized multilayer structure and the designed structure) testifies to the predictability and precision of the synthesis procedure.
Also shown in Fig. 4(b) is the recorded reflection spectrum (blue histogram) corrected with the inclusion of the spectral transmission coefficient of the (“conventional dead”) silicon layer of thickness (54 ± 1) nm in the detector. In the correction, account was taken of the reflectivities and recorded reflection spectra for the three mirrors as well as of the rectangular instrument function of the spectrometer defined by the entrance slit (30 μm). The spectral attenuation coefficients of silicon, which were measured in Ref. [40], were determined from the atomic scattering factors available from the CXRO site [36]. The three plots in Fig. 4(b) agree nicely. The Si “conventional dead” layer thickness of 54 nm provided the best fit between the measured spectral reflectivities and the recorded reflection spectra for the three Mo/Be mirrors. We emphasize that we do not adhere to the simplest dead-layer model. The data given in this Section serve only to characterize the behavior of the CCD detector responsivity about the Si L-edge, which is important to experimenters. It varies approximately as exp(–σNdconv), where σ is the wavelength-dependent Si atomic absorption cross section, N is the atomic density, and dconv ≈54 nm.
Figure 5 shows the plasma spectrum recorded in the laser irradiation of a LiF target, and Fig. 6 is the histogram of its first-order diffraction spectrum. One can see the lines of the multiply charged ions FV–FVII. Recording the known spectrum of LiF plasma permitted the plate scale of the spectrometer to be defined more precisely.
Fig. 5. Plasma spectrum recorded with the TG spectrometer configuration in the irradiation of a LiF target (shown are ±1st and ±2nd orders of diffraction). The four strongest line groups of multiply charged ions are indicated.
Fig. 6. Histogram of the LiF plasma spectrum in the 1st diffraction order. The histogram was obtained by summing up (binning) the counts over 30 pixels in the perpendicular direction to the direction of dispersion.
Therefore, experimental data testify to the development of broadband (111–138 Å) normal-incidence Mo/Be MMs with a satisfactory uniformity of the spectral reflectivity in the spectral range of optimization.
5. Summary
We numerically designed aperiodic Mo/Be multilayer structures that provide uniform normal-incidence reflectivity of 16.4% in the range 111–138 Å, the rms departure from the plateau level being under 4% in relative units. The capabilities of two classes of aperiodic structures were compared. In this case, the ideas of Kozhevnikov et al. [25] were extended to the case of uniform reflectivity over a spectral range for a fixed angle of radiation incidence. Structures were designed with a smoothed variation of the thicknesses of neighboring layers of the same material at a sacrifice in plateau reflectivity (15.9%) and uniformity (rms departure: 8.6% in relative units). Interestingly, structures were designed with a smoothed variation of the thicknesses of all neighboring layers without a sacrifice in reflectivity (16.4%) and uniformity (under 4%). Six-stack Mo/Be structures were also designed to simplify the MMs synthesis process. They provide a lower plateau level (14.5%) and are reasonably uniform (9%).
Three six-stack Mo/Be MMs were synthesized on concave (R = 1 m) substrates, and their reflectivities were measured in the range 95–155 Å. Their plateau reflectivities were found to be equal to 13–14% in the 111–138 Å optimization range.
The reflection spectra of the mirrors were recorded in the configuration of a normal-incidence transmission grating spectrograph with a CCD detector. In this case, the source of quasicontinuum was the laser-produced plasma of a tungsten target. The reflectivity data were compared with the reflection spectra obtained with the quasicontinuum source. The difference between the spectral curves under the L2,3 absorption edge of Si (λ < 125 Å) permitted estimating the run of CCD detector responsivity about the Si L-edge.
Broadband normal-incidence XUV mirrors broaden the capabilities of high-resolution stigmatic spectral imaging. Broadband aperiodic Mo/Be MMs are intended for XUV astronomy, for high-resolution spectrographs for the study of the Si L-edge fine structure in material science, as well as for spectroscopy/diagnostics of laboratory plasmas and other XUV radiation sources with high spectral and spatial/angular resolution. As noted in the Introduction, the 111–138 Å plateau range of the Mo/Be multilayers covers the Balmer series domain of hydrogen-like C VI ions, which are perfectly suited to space-resolved plasma density measurements from their Stark broadening. This may be accomplished, for instance, using stigmatic spectrometers of the type described in Ref. [17].
Funding
Russian Science Foundation (20-62-46050); Japan Society for the Promotion of Science (JP19H00669).
Acknowledgements
A.S.P. was supported by JSPS KAKENHI; E.N.R. was supported by the Russian Science Foundation.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [36]. Part of the data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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