1. Introduction

In recent decades, one-dimensional multilayer mirrors have proved to be key components for many applications in the EUV spectral range (wavelengths from ∼10 to 100 nm). The constructive interference between rays reflected by each layer enables high reflectance in near-normal incidence in this spectral region [1]. These multilayer structures usually consist of a periodic or aperiodic stack of thin films including two or three different materials deposited on an optical substrate [1–5]. The efficiency of such multilayer mirrors is affected by several parameters, e.g., the dielectric constants of the selected materials, the density and composition of the layers, the interfacial roughness, the presence of interdiffusion or interlayers. Several material combinations have been proposed with experimental EUV near-normal incidence reflectance higher than 50%, including Mo/Si [6] Mo/Be [7], Sc/Si [8], Mg/Sc/SiC [9], Al/Mo/SiC [5] and Al/Sc/SiC [10].

Despite these high efficiencies and a wide range of applications, one-dimensional multilayer structures suffer from a limited spectral resolution (typically λ/Δλ < 50 in the EUV). Two-dimensional multilayer gratings have been proposed as an alternative to reach higher spectral resolution [11,12]. By combining multilayer interference and grating diffraction, they enable very high spectral resolution (λ/Δλ > 1000) with good efficiency.

On one hand, lamellar gratings have been successfully developed to produce high-resolution EUV spectrometers. Two different periodic Mo/Si multilayer coatings have been modeled and deposited on lamellar gratings to diffract at near-normal incidence in the 17–21 nm and 25–29 nm wavelength bands, respectively, for the EUV spectrometer aboard the Solar-B mission [13]. The two multilayer designs achieved grating efficiency ranging between 8% to 12% at the central wavelength but do not allow to maintain a high efficiency on the wavelength band of interest because of the narrow bandpass of the multilayer reflectance spectra. Periodic Mo/Si multilayer gratings have also been used for a sounding rocket high-resolution spectrometer experiment [14]: the measured diffraction efficiency at the near-normal incidence was about 10% at 23 nm. Similar efficiencies have been reported around 13 nm for Mo/Si multilayer grating under a 45° incidence angle [15].

On the other hand, blazed gratings provide higher diffraction efficiencies, but they are extremely difficult to fabricate with high groove density on curved substrates (such as toroidal or ellipsoidal grating substrates), which are required for EUV spectro-imaging applications. In particular, Voronov et al. have achieved very high diffraction efficiencies with multilayer blazed gratings: almost 25% for the 1^st order with Al/Zr multilayer grating with groove density (10,000 l/mm) [16] and 52% for the 2^nd order with Mo/Si multilayer grating (2525 l/mm) [17]. Unfortunately, the technologies used to produce these blazed grating with high groove density (typically > 3000 l/mm) are either not compatible with a curved surface substrate [16,18] or complex and expensive [19].

Up to now, very few studies discuss the realization of EUV multilayer gratings with broadband efficiency. Aperiodic multilayer structures can provide efficient broadband reflectance in the EUV spectral range, as shown in previous works [20–22]. Yang et al [23] proposed a theoretical study of aperiodic multilayer designs on a blazed grating that operate in the spectral range of 17–25 nm. Their simulations with different multilayer material combinations showed that it is possible to optimize the diffraction efficiency on a broad spectral range by using aperiodic multilayer coatings. Another way to increase the bandpass of a multilayer coating is to use a periodic stack with a reduced number of periods. No experimental data have been reported until now however for multilayer gratings with a low number of periods or with aperiodic multilayers. It has been previously found that the initial lamellar grating surface profile takes a trapezoidal shape and that the angle of the trapezoidal slightly negatively affects the efficiency [24]. In addition, the deposition of the multilayer coating usually modifies the profile. In particular, a smoothening of the profile high frequencies as the number of periods increases has been reported in the case of blazed gratings [16,17]. Using multilayers with a low number of periods might reduce these smoothening effects, and thus provide a possible alternative solution for broadband efficiency gratings.

In this paper, we present an experimental study of high groove density lamellar gratings with a multilayer designed to maximize the efficiency at near-normal incidence in a broad spectral band with peak reflectance centered at 27 nm for spectro-imaging applications. In particular, this work contributes to the development of multilayer gratings for the Solar-C mission [25]. Such applications require high groove densities in order to maximize the spectral resolution of the instrument. Therefore, we choose a groove density of 3600 l/mm, similar to the groove density used in the Solar-B mission (4000 l/mm) [13]. Figure 1 shows the schematic diagram of a periodic Al/Mo/SiC multilayer deposited on a silica lamellar grating substrate. The incident EUV light falls perpendicular to the grooves of the grating (classical configuration) with an incident angle θ. Three diffraction orders are represented in this figure: −1^st, 0^th, and +1^st. The diffraction angle (Φ) is determined according to the grating law equation [26]:

 

Fig. 1. schematic diagram of a periodic multilayer deposited on a lamellar grating in the case N = 2.

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2. Simulation tools and experimental setup

2.1 Simulation tools

The IMD software (version 5.04) [27] is used to optimize periodic and aperiodic designs of Al/Mo/SiC over an a-SiO₂ flat substrate without considering interfacial roughness by employing a genetic algorithm and targeting maximum reflectance from 25 nm to 29 nm in normal incidence. Material optical constants used in simulations were taken from Ref. 28 . The densities used for Al, Mo, and SiC are 2.699 g/cm³, 10.22 g/cm³, and 3.217 g/cm³ respectively.

Figure 2(a) shows a schematic of the grating trapezoidal profile without multilayer: it has a grating depth (d), a trapeze angle (α), and top and bottom bases. The fill factor (ff) in the case of the trapezoidal grating is defined as the ratio of the FWHM base to the period (P). Multilayer gratings are simulated without considering interfacial roughness by a homemade MATLAB code based on RCWA and using Reticolo [29] to investigate the diffraction efficiency of multilayers over trapezoidal or lamellar (α=90°) gratings as represented in Fig. 2(b). The trapezoidal profile is approximated by dividing the depth into 10 layers of equal thickness, in agreement with previous literature [24]. Further, the width of each sub-layer is linearly diminished from the bottom to the top of the groove as shown in Fig. 2(b). This simulation model is based on a perfect replication of the initial grating profile after deposition of the multilayer. In particular, the model assumes that the α values are the same at the grating surface and at the multilayer surface, and that the deposited layers have the same thickness on the slope, top, and bottom parts of the grating.

 

Fig. 2. schematic diagram of (a) the trapezoidal grating profile before deposition and (b) the multilayer coating (N = 6) deposited on the trapezoidal grating.

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2.2 Grating sample parameters

3 fused silica grating samples with 3600 ± 1lines/mm were fabricated by Carl ZEISS Jena GmbH through the fabrication process of spin coating, holographic exposure, etching by ion beam etching (IBE), and cleaning in O₂-plasma. The silica substrate microroughness before groove etching was in the 0.2 nm range. Before the deposition, the grating samples were cleaned with N₂ gas flow. The dimension of each grating sample is 20 × 20 × 6 mm³. ZEISS reported that the gratings have a 21 ± 2 nm groove depth and a trapezoidal profile with an angle α=45°±5°.

2.3 Equipment

Al/Mo/SiC multilayers were deposited in an ISO6 cleanroom at Laboratoire Charles Fabry using a Plassys MP800 magnetron sputtering machine either on flat Si or on grating substrates. For flat Si substrates, we used 20 × 20 mm² Si wafer pieces with 1 mm thickness, (100) crystal orientation, and surface microroughness in the 0.3 nm range. 2 different multilayer coatings were deposited on the 2 halves of each grating sample by using a mask in front of the sample. The sputtering machine geometry and the deposition parameters have been described in previous papers [4], [5]. We used pure SiC and Mo targets (respectively 99.5% and 99.95% purity) and a Si-doped (1.5 wt.%) Al target (99.99% purity). The plasma discharge was established with a 2 mTorr Argon pressure [5]. We applied a DC-Current of 0.06 A and an RF power of 200 W and 150 W for the Mo, Al, and SiC targets, respectively.

For GIXR, we used a Discover D8 diffractometer from BRUKER company. The machine is equipped with a Cu Kα radiation source (λ=0.154 nm), a rotary absorber, Soller and divergence slits, a collimating Göbel mirror, and a scintillator. The reflectance curves were measured in specular configuration with grazing angles varying from 0 to 5 degrees by step of 0.01 degree. We analyzed the GIXR data by using IMD software [27].

The grating samples have been characterized by atomic force microscopy (AFM) before and after deposition in an ISO7 cleanroom at SOLEIL Synchrotron. We used an AFM NX 20 from Park System company in non-contact mode. The image sizes were 2 × 2 µm². The AFM data are analyzed by employing the software WSxM 5.0 [30] in order to determine the grating parameters: top and bottom roughness, groove depth (d), FWHM fill factor (ff), and the slope of the trapeze (α).

An Al/Mo/SiC periodic multilayer deposited on a flat Si wafer has been analyzed by Transmission electron microscopy (TEM). The cross-section sample has been prepared by using an FEI ThermoFisher Helios Nanolab 660. A platinum layer (Pt) is deposited on top of the multilayer in order to protect the sample during the ion beam etching process. Energy dispersive x-ray spectrometry (EDX) was performed in scanning TEM (STEM) mode by using an FEI ThermoFisher Titan3 G2 80-300 microscopy operating at 300 kV and equipped with a Cs probe corrector as well as a Super X EDX detector.

Additionally, the multilayer-coated Si samples and gratings were characterized by soft x-ray reflectometry (SXR) at the Metrology and Tests beamline, SOLEIL synchrotron. The experimental conditions are the same as in Ref. 31 except that we use the 75 lines/mm grating. High harmonics were suppressed by a 0.5 µm Al filter and a 3-mirror low pass filter using the Si-coated strips. The low pass filter’s input and output mirrors are set at an angle of incidence of 3.5°. We used an Al-coated Si photodiode as the detector. The calibration in the energy of the monochromator was confirmed by measuring the position of the Al L_2,3 absorption edge. The theoretical polarization of the beam was estimated to be higher than 90% s-polarization. To measure the diffraction efficiencies, we rotate the detector with a fixed incidence angle and wavelength in order to scan the order of diffraction of interest and we repeat these detector scans for each wavelength in the range of interest.

3. Al/Mo/SiC design for multilayer grating

3.1 Multilayer design optimization

In previous literature [32], multilayers composed of Al and SiC materials show interesting results in EUV applications in the range of 17-35 nm. On one hand, it has been observed that no interdiffusion appears between the two materials by x-ray emission spectroscopy [33]. On the other hand, large interfacial roughness is formed and negatively affects the reflectance. Because of this issue, a Mo thin layer is recommended to be added to decrease the roughness and enhance the optical performance [32].

Periodic and aperiodic designs of Al/Mo/SiC multilayer have been optimized by IMD to reach the maximum possible reflectance in the wavelength range of 25-29 nm. The optimal thicknesses for periodic coating with 6 periods are 8 nm for Al, 2.68 nm for Mo, and 3.69 nm for SiC. As we found that the dependence of optimal thicknesses with N is small, we chose the same layer thicknesses for the other values of N. The thicknesses of the 12 layers in the aperiodic coating design range between 3 and 11 nm. The detail of the aperiodic structure is given in the appendix section (Table 4 and Table 5). Figure 3(a) shows the simulated reflectance spectra at 5° incidence for the periodic multilayer as a function of wavelength and number of periods. As the number of periods increases from 2 to 16 the peak FWHM is reduced, and the peak reflectance is enhanced. With 14 periods or more, the reflectance spectra almost remain constant. Figure 3(b) shows the reflectance spectra at 5° incidence of the periodic multilayers that we chose for deposition on the gratings (N = 2,4,6,8, and 16). It shows that one can select the optimal number of periods depending on the spectral bandwidth required for the targeted application. In the case of broadband applications, this will however result in a significant reduction of the peak reflectance. We also plotted in Fig. 3(b) the simulated reflectance of the aperiodic multilayer for comparison. Even though the optimization wavelength band was limited to 25-29 nm, the aperiodic multilayer design provides high efficiency from 22 nm to 32 nm. It clearly shows that the use of an aperiodic coating allows the achieve higher reflectance on a broad spectral range as compared to the periodic coating (N = 4).

 

Fig. 3. (a) Simulated reflectance of the optimized periodic Al/Mo/SiC multilayer as a function of wavelength and number of periods (N) at θ= 5°, (b) Simulated reflectance of optimized periodic Al/Mo/SiC multilayer with different numbers of periods and aperiodic Al/Mo/SiC multilayer as a function of wavelength at θ= 5°.

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3.2 Multilayer grating simulation

We present in Fig. 4 and Fig. 5 RCWA simulations of a grating coated with a periodic Al/Mo/SiC multilayer (N = 6) and of a grating coated with the aperiodic Al/Mo/SiC multilayer. Figure 4(a) and 4(b) shows the fill factor-dependent transverse electric (TE) efficiency at different grating depths for 0 and +1 diffraction orders, respectively. The other simulation parameters are kept constant: θ= 5°, N = 6, α= 90° (lamellar configuration), λ= 27 nm, and P= 277.78 nm. It may be seen in Figs. 4(a) and 4(b) that 0-order and +1-order exhibit opposite behavior when the depth varies: a maximum in 1^st order corresponds to a minimum in 0-order. As expected from theory, the 1^st order efficiency is optimal when the depth equals 1/2 (or 3/2) of the period of the multilayer and the profile is symmetric (ff = 0.5). These correspond to the phase and amplitude conditions to null the 0-order. Figure 4(b) also shows that the tolerance on the ff parameter is quite large: for ff in the range 0.45 to 0.55, the grating 1^st order efficiency is reduced by less than 0.4% relative to ff equal to 0.5. The simulations of 0-order and +1-order efficiencies for the aperiodic multilayer grating are plotted in Figs. 4(c) and 4(d), respectively. These calculations show features similar to the case of periodic multilayer (Figs. 4(a) and 4(b)) with lower efficiency. Moreover, Figs. 4(b) and 4(d) confirm that the designs of the periodic and aperiodic multilayers are optimal for a depth in the range of 20 to 21 nm which matches the depth measured on our grating samples.

 

Fig. 4. Calculated 0-order (a) and +1-order (b) grating efficiency in transverse electric mode at λ=27 nm as a function of fill factor and grating depth. The parameters for the simulation are θ=5°, N = 6, α=90° (lamellar), and P = 277.8 nm. The grating efficiency for the aperiodic multilayer with the same grating parameters are plotted in (c) 0-order and (d) +1-order.

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Fig. 5. Calculated 0-order (a) and +1-order (b) grating efficiency in transverse electric mode at λ=27 nm as a function of α and grating depth. The parameters for the simulation are θ=5°, N = 6, ff = 0.5, and P = 277.8 nm. The grating efficiency for the aperiodic multilayer with the same grating parameters are plotted in (c) 0-order and (d) +1-order.

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Figures 5(a) and 5(b) show respectively the 0-order +1-order transverse electric (TE) efficiency calculated as a function of α and grating depth (d). The other simulation parameters are kept constant: θ= 5°, N = 6, ff= 0.5, λ= 27 nm, and P= 277.78 nm. These simulations clearly show that the 0-order and +1-order efficiencies are maximum when α=90° (lamellar shape) and decrease when α decreases (trapezoidal shape). This indicates that, when operating in near-normal incidence, the slope of the trapeze profile can be considered as a fabrication imperfection that affects the efficiency of the grating. However, this dependence on α is no longer true when the grating operates far from normal incidence. In particular, Liu et al. simulated EUV gratings in the case of grazing incidence (gold-coated grating working under total reflection) and reported that the effect of α on the efficiency is not significant for α in the range 35-90° [24]. In the case of our multilayer grating at 45° incidence (θ= 45°) for λ=18 nm, simulations show that the +1-order efficiency reaches a maximum of 24.49% for α=70° and decreases slightly for higher α values, down to 24.37% at α=90° (lamellar shape). This effect can be explained by the shadowing effect that modifies the amplitude condition required to null the 0-order. The 0-order and +1-order grating efficiencies in the case of the aperiodic multilayer are plotted in Figs. 5(c) and 5(d), respectively. The general behavior remains the same as in the previous case (periodic multilayer), with lower peak efficiencies. It is interesting to notice that the effect of α on the +1-order efficiency is similar in the case of periodic and aperiodic multilayers. For example, the change of α from 90° to 45° induces a relative decrease of the +1-order efficiency at d = 20.5 nm of ∼5% for both periodic (N = 6), and aperiodic cases.

4. Multilayer coating characterization and modeling

Two Al/Mo/SiC multilayers have been deposited on flat Si substrates to determine the layer thicknesses and the eventual interfacial defects (interdiffusion and/or roughness): sample MP20065 corresponds to the periodic Al/Mo/SiC design with 10 periods (N = 10) and sample MP20070 corresponds to the aperiodic design (12-layers). It is expected that the top surface of SiC oxidized after deposition when the sample is exposed to air. In previous work, x-ray photoelectron spectroscopy was used to analyze Al/Mo/SiC multilayers, and about 1.6 nm of SiO_x was detected at the top surface of the SiC layer [32].

Figure 6(a) shows a high angle annular dark-field (HAADF) STEM image of the sample MP20065, where the bright lines represent the high-density Mo layers. Alternatively, the dark lines represent the low-density Al and SiC layers. It is difficult to distinguish between Al and SiC layers from Fig. 6(a) due to the similar densities of Al and SiC. Figure 6(b) presents the EDX-STEM analysis of Fig. 6(a). EDX allows us to identify specific atom locations and we plotted in Fig. 6(b) the images corresponding to aluminum (green), molybdenum (blue), silicon (red), carbon (cyan), oxygen (purple), and platinum (yellow) atoms. The image on top of Fig. 6(b) is the addition of the images corresponding to Al, Mo, Si, and Pt. We can clearly distinguish three different layers in each of the 10 periods of the coating. We have also plotted in Fig. 6(b) vertical lines that correspond to the position of the interfaces between Al, Mo, and SiC layers used in our x-ray and EUV models (see Fig. 7 and Table 1). The thicknesses of these layers are 7.72 nm, 2.74 nm, and 3.91 nm for Al, Mo, and SiC respectively. We did not include the images corresponding to C and O atoms in the top image because of the significant background due to cross-section sample contamination. Nevertheless, it could be seen from these images that the C atoms appear at the same positions as the Si atoms, and the O atoms are mainly found at the surface of the Si substrate (Si substrates were not deoxidized before deposition) and at the surface of the top SiC layer (which corresponds to the top SiO_x layer mentioned previously). Finally, we plotted in Fig. 6(c) the atomic profiles for Al, Mo, and Si atoms. By measuring the slope of the different atomic profiles at each interface, we can obtain a qualitative comparison of the width of interfaces due to roughness and/or interdiffusion. This analysis reveals that the Mo-on-Al and Al-on-SiC interfaces are more diffuse/rough than the SiC-on-Mo ones.

 

Fig. 6. TEM analyses of sample MP20065: (a) HAADF (b) EDX images and (c) profile of the atom concentration, in arbitrary units (a.u.), as a function of the position.

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Fig. 7. GIXR measured and fitted curves at λ=0.154 nm for the 10-periods Al/Mo/SiC multilayer (sample MP20065) and the 12-layers aperiodic Al/Mo/SiC multilayer (sample MP20070).

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Table 1. Layer thickness and interfacial roughness used to model the periodic Al/Mo/SiC coating (sample MP20065) on Si substrate

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We used the fact that the Mo-on-Al and Al-on-SiC interfaces look more diffuse than the SiC-on-Mo ones to propose a model which fits the experimental GIXR and SXR data for both samples (MP20065 and MP20070). The model parameters are given in Table 1 for sample MP20065 and in the appendix (Table 5) for sample MP20070.

Figure 7 shows the GIXR analysis for samples MP20065 and MP20070. This type of measurement is particularly useful to extract the structural parameters of the coating as the period thickness and the interfacial roughness. We also plot in Fig. 7 the models that we have optimized in order to fit the GIXR and SXR experimental data. The details of the periodic and aperiodic models are given in Table 1 and the appendix (Table 4 and Table 5), respectively. The total thickness of the periodic and aperiodic models, without considering the oxidation layers, is equal to the targeted ones (143.7 nm and 64.77 nm, respectively). Figure 7 shows a good agreement between the measured data and the model for the periodic multilayer (sample MP20065). The Bragg peaks are well defined up to the 8^th order, which demonstrates the good periodicity of the structure and the quality of the interfaces. The periodic multilayer model includes interfacial roughness values in the range of 0.3 nm to 0.7 nm at the different interfaces (see Table 1). These roughness values are consistent with Fig. 6(c). On the other hand, it is more difficult to extract accurate thicknesses from the fitting of twelve layers aperiodic because of the absence of well-defined interference peaks and the large number of parameters. However, by combining GIXR and SXR data, we were able to propose a model that fits well the GIXR data for grazing angles up to 5°. Notice that the individual layer thicknesses were kept equal to the initial values (IMD optimized model) and that the interfacial roughness values are in the same range as for the periodic model.

Samples MP20065 and MP20070 have also been characterized at the Metrology beamline, SOLEIL synchrotron, to measure their reflectance with EUV wavelengths from 17 nm to 32 nm. Figure 8 shows the measured data and the model at θ=5°. The polarization factor is fixed to 0.96 for the simulation (i.e. 96% s polarized light), although its effect on the reflectance is negligible in near-normal incidence. A top oxide layer needs to be introduced in the model to fit the SXR data. The presence of an oxide layer on the top SiC layer has been confirmed by the TEM analyses (see Fig. 6(b)). Following previous work, we used SiO₂ (density 2.2 g/cm³) to simulate the top oxide layer [5,10]. The best-fitting results were obtained with a top oxide layer thickness of 1.4 nm for MP20065 and 1.1 nm for MP20070.

 

Fig. 8. SXR measured and fitted spectra at θ=5° for the 10-periods Al/Mo/SiC multilayer (sample MP20065) and the 12-layers aperiodic Al/Mo/SiC multilayer (sample MP20070).

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We obtained an excellent agreement between fit and measured data for the aperiodic multilayer (MP20070). However, a difference exists between measured and fitted peak reflectance for the periodic sample (MP20065). This is probably due to the inaccuracy of the Mo optical constants in this region (λ>24 nm) [34].

Finally, the samples MP20065 and MP20070 have been measured at θ=45° on the Metrology beamline, SOLEIL synchrotron, to refine the two models. At θ=45°, the influence of the polarization factor on the peak reflectance is maximized because the angle is close to the Brewster angle. The best-fitting results were obtained with a polarization factor of 0.96 (i.e., 96% s polarized light). We obtained a very good agreement between the fitting and measured data for the two samples as shown in Fig. 9. The accuracy on the polarization factor was estimated to be ±0.02.

 

Fig. 9. SXR measured and fitted spectra at θ = 45° for the 10-periods Al/Mo/SiC multilayer (sample MP20065) and the 12-layers aperiodic Al/Mo/SiC multilayer (sample MP20070).

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We also plotted in Figs. 8 and 9 the simulated spectra using the models with no interfacial roughness. All simulation parameters are identical to the previous models for periodic and aperiodic except for the interfacial roughness values that are set to 0 nm. As expected, the influence of the roughness is higher in near-normal incidence (θ=5°) than at 45°. One can see also in Fig. 8 that the peak reflectance of the periodic model is slightly more affected by roughness than the reflectance of the aperiodic model. In details, the peak reflectance for the periodic (respectively aperiodic) multilayer is reduced by a factor of 0.94 (respectively 0.96) because of interfacial roughness.

In conclusion, the periodic and aperiodic multilayer models with a top oxide layer and interfacial roughnesses in the range of 0.3-0.7 nm are satisfactory. They allow to obtain accurate fits of GIXR data (see Fig. 7), and of SXR data at 2 different incidence angles (see Figs. 8 and 9).

5. Multilayer grating characterization and modeling

5.1 Surface profile evolution

The grating samples have been characterized by AFM before and after the multilayer deposition, to analyze the evolution of the surface profile with the number of deposited periods. Figure 10(a) shows an example of grating surface morphology before deposition. The average grating parameters before deposition were computed from profiles measured on all samples. The average values of h, ff (FWHM), and α are 22 nm, 0.51, and 48.9°, respectively. This is consistent with the values reported by Zeiss. Figure 10(b-d) shows the grating surface morphology after deposition for 6, 8, and 16 multilayer periods, respectively. Figure 10(e) shows the average surface profile evolution with the number of periods. Each profile is computed by averaging the entire image along the direction of the groove. Every profile is shifted by 30 nm in Z-Scale from the previous one. It is interesting to notice that the surface shape remains trapezoidal up to N = 6. The top parts of the trapeze start to the curve at N = 8 and then tend to a sinusoidal shape as N increases. AFM analyses also show that the depth after multilayer deposition remains almost equal to the initial depth of the grating when N increases up to sixteen. This means that the deposition rate on the bottom and top parts of the trapeze are identical.

 

Fig. 10. The 2 µm x 2 µm AFM surface morphology of trapezoidal grating substrate before deposition (a), and after deposition of Al/Mo/SiC multilayer with (b) N = 6, (c) N = 8, (d) N = 16. (e) Average groove profiles as a function of the number of periods; every profile is shifted by 30 nm in Z-Scale. N = 0 corresponds to the measurement N = 6 before deposition.

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Table 2 reports the grating surface roughness values before and after deposition. The average RMS roughness before the deposition is 0.23 nm on the top parts and 0.32 nm on the bottom parts. This slight difference may be attributed to the groove etching process. After deposition, the average RMS roughness becomes 0.42 nm and 0.47 nm for the top and bottom parts respectively. These results indicate that the roughness at the top and bottom parts of the grating slightly increases after the deposition and that these values are independent of the number of periods.

Table 2. RMS roughness of the surface before and after deposition measured by AFM

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Note that the AFM roughness values after deposition are similar to the average interfacial roughness used in the modeling of the Al/Mo/SiC multilayer (see Tables 1 and 5).

The values of average α calculated from the AFM profiles (Fig. 10(e)) are plotted in Fig. 11 as a function of the number of multilayer periods (N). The error bar represents the standard deviation of computed α. The value before deposition for trapezoidal grating (∼ 48.9°) was averaged on all grating substrates and is displayed at N = 0. Figure 10(a) shows that α diminishes almost linearly as N increases. A similar evolution of the angle a has been reported previously in the case of a trapezoidal grating coated with Mo/Si and analyzed by TEM [35]. In this paper, Feng et al. report that the grating shape remains trapezoidal after the deposition of 20 Mo/Si periods and that a is slightly reduced. In their study, however, the initial grating depth (d∼ 6 nm) and density (1800 l/mm) were much smaller than in our case. Alternatively, in the case of very high groove density (10.000 l/mm), Voronov et al. reported a significant smoothening of the grating profile after deposition of 20 Al/Zr periods on a blazed grating (d∼ 10 nm) [16]. In this paper, Voronov et al. establish that materials of the multilayer were redistributed on the surface of blazed grating: they observed by TEM that the thickness of deposited materials was less for convex areas and more for concave areas [16]. This phenomenon can explain qualitatively the evolution of a that we present in Fig. 11. More studies would be needed however to determine more precisely the influence of the initial grating parameters, and the multilayer material combination, on the grating profile evolution.

 

Fig. 11. variation of the trapeze angle α with the number of periods deposited on the grating.

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Concerning the grating with an aperiodic multilayer design, we found a trapezoidal surface profile after deposition with an average α value of 28.70° with a standard deviation of 1.53°. This value could be compared with the periodic design at N = 4, which contains the same number of layers and a similar total thickness: 57.5 nm compared to 64.8 nm for aperiodic (without considering the surface oxide layer). This difference in profile shape between periodic and aperiodic design might be due to the difference in individual material thicknesses. Further research will be needed to fully understand this phenomenon. Indeed, the average α value for the aperiodic multilayer grating is similar to the α value obtained for a periodic multilayer with twice the number of layers (N = 8).

5.2 Multilayer grating diffraction efficiencies

The +1-order diffraction efficiencies of the 6 different multilayer grating samples were measured as a function of wavelength at Soleil synchrotron and are plotted in Figs. 12 and 13, for an incidence angle θ of 5° and 45° respectively. Figures 12(a-c) and Figs. 13 13(a-c) show that the experimental diffraction peak efficiency increases and the peak narrows when the number of periods increases from 2 to 6. This is in good agreement with the evolution of the multilayer reflectance spectra as a function of the number of periods (see Fig. 3). However, for a higher number of periods (N = 8 and 16) the experimental peak efficiency starts to decrease (Figs. 12(d,e) and 13(d,e)). This behavior is not expected from the multilayer response (Fig. 3) and may be attributed to the evolution of the grating profile with the deposition. Indeed, AFM measurements show that the surface profile remains trapezoidal up to N = 6 and starts to degrade for 8 periods and more.

 

Fig. 12. Measured and modeled +1 order diffraction efficiency of the multilayer gratings at θ=5°: (a) N = 2, (b) N = 4, (c) N = 6, (d) N = 8, (e) N = 16, and (f) aperiodic.

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Fig. 13. Measured and modeled +1 order diffraction efficiency of the multilayer gratings at θ=45°: (a) N = 2, (b) N = 4, (c) N = 6, (d) N = 8, (e) N = 16, and (f) aperiodic.

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Each sample has been modeled by RCWA simulation using the same multilayer grating model for both incidence angles (θ=5° and 45°). The simulation results are also plotted in Figs. 12 and 13. Table 3 shows the grating parameters used for fitting the +1 order measurements. We used the layer thicknesses determined previously for the periodic and aperiodic multilayer (see Tables 1 and 5) and a 1.7 nm SiO₂ layer as the top oxide layer for all the grating models. The interfacial roughnesses were not included in the RCWA simulations. We used the polarization factor that we have determined from multilayer sample measurements (96% s polarization, see section 4). It should be noted that the effective ff reported in Table 3 was determined from the AFM measurements and that the fitted α values are approximately equal to the α values measured by AFM before deposition. This indicates that the grating diffraction efficiencies are influenced by the profile of the grating before deposition.

Table 3. Grating parameters used to simulate +1 order efficiencies in Figs. 12 and 13

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The fits in Figs. 12 and 13 are in good agreement with the measured data for all samples except N = 16. It is interesting to note that, whereas the profile of the grating evolves at each period (see Fig. 10), the model with a constant average profile that we use is sufficient to simulate with good accuracy the diffraction efficiency, as long as the profile remains trapezoidal. The large discrepancies between model and experimental data for N = 16 (see Figs. 12(e) and 13(e)) reveal that this simple model is no longer valid when the grating profile changes to sinusoidal patterns.

As shown in Figs. 12 and 13, SXR measurements extend from the Al L_2,3 absorption edge (∼17.2 nm) to 31 nm. For longer wavelength (λ>31 nm) the photon flux delivered by the beamline was too low to obtain reliable measurements. This wavelength range was sufficient to measure the peak efficiency for all samples, but the peak width was out of reach for some samples. Therefore, we used the simulation models shown in Fig. 12 and 13 to estimate the peak bandwidth. Figure 14 shows the evolution of the experimental peak efficiency and the bandwidth computed from the model as a function of the number of periods. The bandwidth is defined as λ_a-λ_b, where λ_a and λ_b correspond to (peak efficiency/2^½). It may be seen in Fig. 14(a) and Fig. 14(b) that the peak efficiency linearly increases up to N = 6 and then start decreasing, while the bandwidth reduces as the number of periods raises. These results clearly show that there exist an optimum number of periods (N = 6 in this case) after which the efficiency does not improve anymore and the bandwidth continues to diminish. It also confirms experimentally that one can tune the number of periods in order to adjust the peak bandwidth to the desired value. Increasing the bandwidth (by reducing the number of periods) leads however to a lower peak efficiency (see Fig. 14). The SXR measurements shown in Figs. 12(f) and 13(f) demonstrate however that it is possible to overcome this limitation by using an aperiodic multilayer design. We obtained a bandwidth of 5.1 nm with the aperiodic multilayer grating in near-normal incidence (Fig. 12(f)) with a peak efficiency higher than 6%. As shown in Fig. 14, this value of bandwidth is not attainable with a periodic design. It is worth noting that, despite the complexity of the multilayer design, the simulation models in the case of the aperiodic multilayer agree very well with the experimental data at 5° and 45° (see Figs. 12(f) and 13(f)). Compared to previous literature [13], [36], this aperiodic multilayer grating provides a unique combination of peak efficiency and bandwidth.

 

Fig. 14. order maximum efficiency and bandwidth for SXR at (a) θ=5° and (a) θ=45°.

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The influences of d, α, and ff on the diffraction efficiency have been examined for N = 6 at λ=27.24 nm for θ=5°, while the other parameters are kept constant (see Table 3). We found that the +1-order diffraction efficiency is maximized when d= 20.5 nm, α= 90°, and ff = 0.5. The peak efficiency reaches 9.27%, while the simulation model in Fig. 12(c) achieves 9.98%. In detail, we determine that the main increase in efficiency is caused by the change in d and α. ff has almost no effect on the efficiency because the initial model value was very close to the optimal value. In addition, we compared the bandwidths of the multilayer gratings with the bandwidths of the corresponding multilayers (using simulated reflectance spectra at 5°). In the case of periodic multilayers with 4 periods or more, the grating bandwidth is about 80% of the multilayer bandwidth. It is interesting to note however that, for broader multilayer design (N = 2 and aperiodic) this ratio decreases: the grating bandwidth is about 60% of the multilayer bandwidth for N = 2 and 40% for the aperiodic multilayer. This can be explained by the fact that for wavelengths too far from 27 nm (= peak central wavelength), the groove depth is no more optimal, and the grating efficiency starts to decrease.

Finally, we compare in Fig. 15 the measured grating efficiency in near-normal incidence for N = 4, N = 6, and aperiodic coatings. We have also added for comparison previous experimental data from Seely et al. [13] that corresponds to a 20 periods Mo/Si multilayer grating. They obtained a peak efficiency of 7.88% at 27 nm and a bandwidth of 2.64 nm. Note that the 6 periods of Al/Mo/SiC grating provide a higher efficiency from 25.5 to 29 nm, with a peak of 9.27%. It is also interesting to compare the measured data of the 12-layers aperiodic with the periodic N = 4 coating which contains the same number of layers. Both gratings reach similar peak efficiency, but the aperiodic coating provides a significant increase in the bandwidth: 5.1 nm for aperiodic as compared to 3.3 nm for periodic N = 4. Indeed, the bandwidth obtained with this aperiodic multilayer grating is almost double compared to previous results from Seely et al. Our results confirm that aperiodic multilayer gratings are promising components for high-resolution EUV spectroscopy applications on a wide wavelength range.

 

Fig. 15. order efficiency measurement at θ=5° for the gratings for N = 4, N = 6, and aperiodic coatings. Experimental data from Seely et al. [13] are also plotted for comparison.

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6. Conclusion

Periodic and aperiodic Al/Mo/a-SiC multilayer designs were optimized with the aim of broadband efficiency centered at 27 nm wavelength. Five periodic multilayers with a varying number of periods (from N = 2 to N = 16), as well as an aperiodic multilayer, were deposited on high-density trapezoidal grating substrates. The optimized designs target to balance between higher efficiency and broader bandwidth for solar EUV spectro-imaging applications in the 22-32 nm wavelength range. First, periodic and aperiodic Al/Mo/SiC multilayers were deposited on Si samples by magnetron sputtering and characterized by TEM, GIXR, and SXR. This combination of techniques allows us to propose realistic models for the periodic and aperiodic coatings. Then the grating substrates were characterized by AFM before and after the multilayer deposition in order to determine the evolution of the initial profile with multilayer deposition. The results reveal that the slope of the trapeze decreases almost linearly when the number of periods increases and that, after a certain number of periods, the top profile starts to change from a trapeze to sinusoidal patterns.

Furthermore, we proposed a model of the multilayer grating that we implement to perform RCWA simulations. Simulations confirm that the increase of the trapeze slope negatively affects the diffraction efficiency in the case of near-normal incidence. However, in the case of oblique incidence (45°), the influence of the slope on the efficiency is much lower.

Finally, the +1-order diffraction efficiency of periodic and aperiodic multilayer gratings was measured in the EUV range at two different incidence angles (5° and 45°). A good agreement was achieved between measured data and simulated diffraction efficiencies based on trapezoidal profile models. Experimental results show that the peak efficiency increases to reach a maximum at N = 6 and then starts to decrease. This can be explained by the evolution of the surface profile, determined by AFM, which starts to depart from the trapeze shape when N > 6. Compared to previous work, the 6-period Al/Mo/SiC multilayer grating provides higher efficiencies on a broader bandwidth. In addition, an unprecedented broad bandwidth was achieved with the aperiodic multilayer grating while maintaining a reasonable efficiency. These results open the way to the design of instruments with extended performance for EUV high-resolution spectrometry or spectro-imaging applications.

Appendix

It is worth noting that the substrate material used for ‘IMD Design’, and ‘Grating Model’ was SiO₂, while the substrate material was Si for ‘Si Sample Model’

Table 4. the model design thickness for aperiodic design

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Table 5. the model design roughness for aperiodic design

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Funding

Centre National d’Etudes Spatiales (210134).

Acknowledgments

This work was performed under the auspices of the Institut d’Optique Graduate School, Université Paris-Saclay. The authors are thankful to Pascal Mercere (SOLEIL Synchrotron) for technical assistance and advice during synchrotron measurements.

Disclosures

The authors declare no conflicts of interest.

Data availability

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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