1. Introduction

X-ray microscopy is an invaluable and powerful characterization tool applied in many scientific fields, such as materials science, biology, environmental science, and energy research [1–4]. In recent years it has been driven by rapid developments of novel technologies and systems, and resulted in imaging experiments elucidating structural inhomogeneities and chemical reactions at the nanometer-scale [5–10]. Fresnel zone plates, Kitkpatrick-Baez (KB) mirrors, and multilayer Laue lenses (MLLs) are the optics mostly used for x-ray nanofocusing [11–13]. Among others, MLLs have been proposed and used for high-efficiency nanofocusing in the hard x-ray regime [14–16]. MLLs are the diffractive optics comprised of layers of alternating materials with different refractive indices, such as WSi₂/Si, W/SiC, WC/SiC, MoSi₂/Si, Mo/C/Si/C, and Ti/ZrO₂, and they are fabricated via various methods including magnetron sputtering deposition and pulsed laser deposition [16–19]. Since MLLs are one-dimensional focusing elements, point focusing requires a pair of MLLs being aligned orthogonally with respect to each other [20]. In total, eight degrees of rotational and translational motions are required to perform full alignment of two linear MLLs. Moreover, when nm-scale spatial resolution imaging is considered, the stability of the MLLs and their respective alignment needs to be controlled on the nm-scale. In practice, this poses significant technical challenges on a microscopy system itself, and requires an extremely complex and stable instrument. A number of sophisticated MLL-based instruments have been designed, constructed and commissioned in the recent years [21–25]. For example, a high-resolution scanning hard x-ray microscope has been developed at the Hard X-ray Nanoprobe (HXN) beamline of the National Synchrotron Light Source II (NSLS-II). It provides ∼10 nm spatial resolution imaging when using MLL optics [11,25]. Alignment procedure of two individual MLLs is rather complex, and involves satisfaction of Bragg conditions for both multilayers along with overlapping of their focal planes to avoid astigmatism. Development of a monolithic 2D MLL nanofocusing optics could greatly reduce the complexity of an instrument and minimize degrees of a nano-scale motion needed for MLL alignment. There has been an increasing number of efforts in the past few years targeting development of monolithic 2D MLL optics [26–29]. S. Niese and A. Kubec et al. have bonded two identical MLL structures together and demonstrated sub-100 nm resolution during full-field imaging and ∼43 nm 2D focusing during ptychography experiments [26,29]. UV-adhesive assisted direct bonding has also been explored and yielded 12 × 24 nm² point focus [28]. However, uncontrollable stress and potential contamination of the MLL optics due to UV adhesives make direct bonding approach extremely challenging. It is especially true in the case of wedged MLLs, when parameters of the lenses are tailored to a specific photon energy and astigmatism could not be compensated by varying x-ray energy without compromising efficiency.

When two MLLs are perfectly aligned, the optical path function is zero at their common focal plane. This results in a wavefield being expressed as a Fourier transform of the pupil function. When deviation from the perfect alignment is present (γ – deviation from orthogonality and focal distances f₁ ≠ f₂), the point focus becomes distorted. It has been shown that tolerance for the angular alignment γ can be expressed as γ < C_γ S/A, where C_γ is a constant defined by the criterion used (either 0.5 based on a maximum phase change argument or 0.9 based on a Strehl ratio of 0.8), S = 0.5λ/NA, λ is the wavelength, A is the lens aperture, and NA is the numeric aperture [30]. For example, for a 10 nm diffraction limited resolution lens, which is 40 µm thick (40 µm is a thickness of the multilayer structure), has a focal length f of 4000 µm and the photon energy equals 12 keV, γ should not exceed 0.01° in order to preserve diffraction limited point focus. The separation between two focal planes f₁ and f₂ should be within the depth of focus, which is ∼2 µm for this particular example. This defines bonding requirements in terms of angular and lateral positions of two lenses with respect to each other.

In present work, we report on the novel approach to fabrication of monolithic 2D MLL optics utilizing MEMS-based technology. We have developed a dedicated Si template that accommodates two linear MLLs in pre-aligned configuration and defines their azimuthal and lateral positions with respect to each other. We have verified validity of the developed bonding method and demonstrated astigmatism-free point focusing of ∼14 nm and ∼13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy. Developed approach significantly simplifies alignment procedure of the MLL optics (and a result reduces complexity of the required x-ray microscope) and makes 2D MLL optics more accessible to the x-ray microscopy community. The newly developed 2D MEMS-based structure allows straightforward integration of MLLs into conventional zone plate x-ray microscopes, contributing to wider application of MLLs for the x-ray microscopy community.

2. Results

2.1 Design of integrated MEMS-based templates for two linear MLL optics

The key idea for integrated 2D MLLs nanofocusing optics is based on utilization of monolithic microalignment pillars (referred to as ‘teeth’) together with a set of soft springs that force-align MLL optics against these pillars. Microfabricated within double-sided MEMS-based template these features provide accurate alignment of two individual MLLs in a simple, precise and controllable way. Figure 1(a) is a schematic representation of a MEMS-based template which accommodates two linear optics. Due to the small form factor of the template (10 mm × 10 mm × 0.5 mm in size and ∼0.2 g in weight), the resonance frequency of the springs is calculated to be greater than 500 Hz. When compared to conventional manipulation systems used in the MLL microscopes (typical weight is hundreds of grams and resonance frequencies are on the order of ∼150 Hz), our MEMS template provides a much more robust and stable platform for the MLL alignment and focusing.

 

Fig. 1. Monolithic MEMS-based 2D MLLs nanofocusing optics. a High-level view of an MLL template, showing key features. b a top view of the 2D monolithic MLL. c Magnified view of the active part of the MLLs showing x-ray beam through the aperture and two overlapping MLLs.

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The template contains two holding slots, one on each side, aligned orthogonally with respect to each other. Each holding slot includes four alignment ‘teeth’ as well as two cantilever-type silicon springs. At the center of a template, where two holding slots cross, there is an etch-through aperture, which allows the x-rays to go through and illuminate both lenses. To mount two MLLs on a template, each MLL is placed into a holding slot on each side and is secured with respect to the alignment ‘teeth’ (Fig. 1(b)). Since the ‘teeth’ of the holding slots fabricated on both sides of a template are rigidly positioned and aligned orthogonally, the MLLs packed inside the slots are also aligned accordingly. In case an MLL does not fit into the holding slot and could not be directly mounted, a universal adapter (a silicon piece with well-defined dimensions) can be used. In this case, an MLL is first attached to an adapter, and then the combined MLL/adapter assembly is mounted onto a template. Due to the presence of an adapter, small angular misalignment between two MLLs could be introduced. To ensure perfect orthogonality between two lenses (even when an adapter is present) we have designed a series of batch fabricated templates where the angle between two slots ranges between 89.7° and 90.3°. This is achieved by changing the length of adjacent alignment ‘teeth’. By choosing a template with the most appropriate misalignment angle we always offset small angular deviations from 90° introduced by the presence of an adapter, MLL surface roughness and other factors. The template is fabricated through multiple steps of photolithography and dry etching, and cumulative fabrication tolerances define the accuracy of the final MLL alignment. For our prototypes angular error can be controlled to a level of few millidegrees (e.g., using SUSS MicroTec MA6 mask aligner). Both lenses overlap at the aperture location for x-ray focusing (Fig. 1(c)). The separation between two MLLs along the beam direction is controlled through a depth of Si etching and the thickness of used adapters.

2.2 Fabrication of MEMS-based templates and MLL optics

The MEMS-based templates were fabricated from silicon wafers (∼510 µm thick) through a developed microfabrication process, which includes multiple steps of photolithography and deep reactive-ion etching (DRIE). The entire fabrication process is depicted in Fig. 2(a). In particular, a 4-inch silicon wafer with 3 µm thick oxide layer (Fig. 2(a)-1) was first spin-coated with photoresist (AZ4620, MicroChemicals, Germany) at 4000 rpm for 40 seconds. It was then exposed using a mask aligner (MA-6, SUSS MicroTec, Garching, Germany) in soft-contact mode after baking at 110 °C for 90 seconds. In the following, the exposed wafer was developed in developer solution (AZ400K, 1:3, MicroChemicals, Germany) and baked at 110 °C for 90 seconds (Fig. 2(a)-2). After the photoresist AZ4620 was patterned on the substrate, the SiO₂ layer was etched away through a dry etching process (Oxford PlasmaLab 100, Oxford Plasma Technology Inc.) (Fig. 2(a)-3). The substrate was then spin-coated with AZ4620 again using the second photomask, followed by the exposure and development (Fig. 2(a)-4). The patterned photoresist and SiO₂ served as etching masks to etch the silicon substrate through two steps of the Bosch etching process (Oxford PlasmaPro System 100 Cobra, Oxford Plasma Technology Inc.) (Fig. 2(a)-5, 2(a)-6). The same photolithography and etching process then proceeded on the backside of the silicon substrate to have the holding slots etched on each side, and meanwhile to release the silicon springs and etch through the aperture on the template (Fig. 2(a)-7–2(a)-9).

 

Fig. 2. MEMS template for the package and alignment of MLLs. a Fabrication process of the MEMS template (a simplified schematic is used to show the key features). Adapters are used for the assembly of MLLs when it is necessary. b The optical image of a microfabricated MEMS template. c The SEM image showing the details of the holding slot, aperture, alignment ‘teeth’, and springs of the template.

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Figure 2(b) shows an example of the microfabricated MEMS template. The overall lateral dimensions of the template are ∼10 mm × 10 mm. The etched-through aperture located near the center of the template is 500 µm × 500 µm. Near the aperture, two holding slots are etched, one on each side of the template. The width of the slots is 1.6 mm (from the alignment ‘teeth’ to the edge on the spring side), and it could accommodate MLLs with a height between 1.4 mm to 1.6 mm. When the height of MLLs is out of this region, an adapter could be used for mounting of MLLs. The depth of the etched holding slots and the thickness of adapters (if used) is calculated based on the focal length difference between two packed MLLs, so that their focal points overlap after lenses are placed into the slots. In this work, the depth of slots is between 180 and 240 µm. The roughness of etched area (S_a) is ∼0.14 µm (Profilm3D, Filmetrics, San Diego, CA, USA). Four alignment ‘teeth’ are located on the top of the holding slots. In a series of batch fabricated templates, the length of adjacent alignment ‘teeth’ is gradually changing, allowing for the angle between two slots precisely changed from 89.7° to 90.3°. The angular increment was set to 50 millidegrees from one template to another. It should be noted that the range and increment of the angle can be re-designed based on the requirements of particular applications. Two silicon springs are at the bottom of each holding slot and secure MLLs in place. Each spring is 2850 µm long and 20-40 µm wide. The maximum 1^st principal calculated stress applied on silicon springs has a linear relationship with the displacement of springs, which increases to ∼923 MPa when the displacement increases to 200 µm (for 40 µm wide and 200 µm thick springs, see Appendix A). The stress is substantially lower than the yield strength of silicon (i.e., 7 GPa), which ensures mechanical robustness of the springs enabling safe loading MLLs. Figure 2(c) shows the details of the holding slot, aperture, alignment ‘teeth’, and the springs.

The MLL optics were fabricated via magnetron sputtering deposition on a silicon substrate and further sectioned by reactive ion etching followed by the focused ion beam (FIB) milling. The pair of MLLs used in this work have aperture sizes (thickness of multilayer structure) of 53 µm (MLL-53) and 43 µm (MLL-43), respectively. They are comprised of alternating flat layers of Si and WSi₂. The total number of layers equals 8016 and 6510 for MLL-53 and MLL-43 respectively with the thinnest zone being 4 nm for both lenses. The nominal focal length equals 5200 µm for the upstream (MLL-53) and 4200 µm for the downstream (MLL-43) lenses calculated for 12 keV photon energy. Figure 3(a) shows the schematic of an MLL lens. The overall dimensions of MLL-43, including the silicon substrate, are ∼2.7 × 1.5 × 0.7 mm³. The MLL structure itself of the MLL-43, is 150 µm long, 43 µm high, and 4.0 µm thick (Fig. 3(b) and 3(c)). The MLL-53 is larger than MLL-43 with a dimension of ∼3.4 × 2.0 × 0.4 mm³. The MLL part of MLL-53 is 130 µm long, 53 µm high, and 4.8 µm thick. The focal length difference between two MLLs was estimated to be ∼1000 µm at 12 keV photon energy according to the zone placements inferred from the SEM images and our previous work [28]. Therefore, when fabricating Si template, a gap of 1000 µm between two MLLs is required to achieve astigmatism-free point focus at 12 keV photon energy. It should be noted that focal length estimates obtained from SEM images could have an error of a few percent and therefore may need to be corrected through an adjustment of the photon energy. Precise knowledge of the focal length becomes especially important when wedged MLLs are considered. For wedged MLLs the actual focal length needs to be determined first, and then a MEMS template has to be adjusted to fully benefit from high efficiency of a wedged multilayer structure.

 

Fig. 3. MLL optics. a Schematic of an MLL optics, including MLL structure, Si/WSi₂ multilayers, and silicon substrate. b and c SEM images (b: tilted view, c: top view) of the focused-ion-beam (FIB)-etched MLL structure of the MLL-43.

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2.3 Assembly of MLLs on a template

After initial characterization (see Appendix A) fabricated MLLs were mounted on a MEMS-based template. As shown in Fig. 4(a), MLL-53 was mounted on the upstream side of a template. Since its height (2.0 mm) is greater than the width of a holding slot (1.6 mm), MLL-53 was attached to an intermediate silicon piece (an adapter) with a height of 1.5 mm for fit into the template, as illustrated in Fig. 4(b). The dimensions of MLL-43 fit the holding slot, and the lens was directly mounted on the downstream side of a template. The small angular misalignment between adapter and MLL-53 has been compensated by choosing a template with a precisely pre-fabricated adjustment angle. The position of two MLLs was adjusted under an optical microscope to have their active areas overlap through a template aperture, as shown in the inset of Fig. 4(a). The orthogonality of the assembled 2D MLL has been characterized using a reference prism (the method is described in Appendix A). Figure 4(c) shows the surface profiles of individual MLLs with respect to the sides of a reference prism, and measurements have been carried out using Zygo profilometer (Zygo NewView 6300, Zygo, CT, USA). According to the measurements, the angular misalignment between two MLLs was determined to be ∼6 millidegrees (below 10 millidegrees required for a 10 nm point-focus). It should be noted that linear fitting to the MLLs surface profiles has been used to calculate orthogonality between two individual lenses. Surface roughness of MLLs induced by the deposition stresses appeared to be uniform along the lens length; however if extreme cases on the MLLs surface are considered, orthogonality uncertainty may approach ∼ 3 millidegrees. The separation distance between two MLLs has also been measured using Zygo profilometer, and yielded the value of 1050 µm, see Fig. 4(d).

 

Fig. 4. MLLs mounted on a MEMS template. a Both MLLs mounted on a MEMS template, red dashed lines in the image on the right indicate the overlapping lens area. b Mounting configuration of MLLs on a template using intermediate adapter. c The surface profiles of MLLs and the reference prism measured using Zygo profilometer. Left: MLL-53. Right: MLL-43. d Measurement of separation between two MLLs.

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2.4 X-ray evaluation of focusing performance

The focusing performance of the developed monolithic MLL optics has been evaluated at the Hard X-ray Nanoprobe (HXN) Beamline at 3-ID of the National Synchrotron Light Source II (NSLS-II) [25]. The monolithic structure has been mounted in a dedicated apparatus used for optics characterization [23]. Ptychography has been used for point-focus evaluation; 1µm thick gold Siemens star test pattern with smallest features of 20 nm has been placed 24 µm downstream from the focal plane and laterally scanned across the focused x-ray beam. The scan trajectory followed a Fermat spiral pattern [31] with an incremental step size of 20 nm and covered the 1.2 µm × 1.2 µm region with 1145 points. The far-field diffraction patterns have been recorded using Merlin pixel-area detector placed 0.533 m downstream from the sample. Data sets were reconstructed through 100 iterations of a maximum-likelihood based algorithm [32] to give the complex-valued transmission function of the object and the wavefront of the probe with 5 nm pixel resolution. The reconstructed line-focusing profiles for horizontal and vertical directions yielded the full width half maximum values of ∼14 nm and ∼13 nm, respectively, see Fig. 5(a). The inset in Fig. 5(a) represents the reconstructed x-ray wavefront at its focal plane with the amplitude being displayed with brightness and the phase with color. It is important to note that most intensity is confined within the central peak with only minor side-lobes, making the optics suitable for direct (transmission or fluorescence) high-resolution imaging. The side-lobes are mainly due to imperfections of the deposition process (zone placement error) and do not exceed fraction of a wavelength for both lenses. Design parameters for both lenses used in this work have a diffraction-limited focus of 10 nm (Rayleigh criterion) if no phase aberrations are present. The slightly larger size of the point focus may be attributed to two reasons, first, zone placement error introduced during the deposition process and second, possible slight orthogonality error not captured by our measurement technique. We further verified deviation from a diffraction-limited point focus by propagating the wavefield back into the pupil plane. The phase error could not be completely removed by adding a cross term due to non-orthogonality, which suggests there are contributions from other types of errors, and non-orthogonality may not be the main reason for worse-than-designed focusing performance. In Fig. 5(b) and 5(c) the reconstructed wavefront has been propagated from −70 µm to +30 µm for both vertical and horizontal directions with 500 nm step. The focal plane is located 24 µm upstream from the measurement plane, but it has been offset to the center in panels b) and c) of Fig. 5 for clarity.

 

Fig. 5. X-ray focusing performance of monolithic MEMS-based MLL optics. a Results of ptychography measurements. A point focus of ∼14 nm and ∼13 nm in horizontal and vertical directions has been reconstructed. The inset shows the shape of a probe with the amplitude being displayed with brightness and the phase with color. b and c Starting from the measurement plane, the reconstructed wavefront (b: horizontal plane, c: vertical plane) has been propagated from −70 µm to 30 µm in 500 nm steps. The focal plane is located 24 µm upstream from the measurement plane (it is offset to the center of images for clarity). d,e,f were acquired during the fly-scan measurements with the test pattern being in the focal plane. For details see text. d Scanning Transmission x-ray d Scanning Transmission x-ray Microscopy (STXM) image formed by plotting the total transmission as a function of sample position. e and f ptychography images for the STXM measurement (e: amplitude, f: phase). Smallest features of 20 nm (gaps between inner and outer spokes) can be resolved.

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To confirm focusing performance, the second x-ray measurement has been performed. The Siemens star has been placed in the focal plane and raster scanned across the focused beam. The scan covered the area of 2 µm × 2 µm with a step size of 10 nm and the dwell time of 0.1s per point. Figure 5(d) demonstrates the STXM image formed by plotting the total transmission as a function of sample position. For comparison, Figs. 5(e) and 5(f) illustrate amplitude and phase of the ptychography image acquired at the same time. The smallest features of 20 nm (gaps between inner and outer spokes) can be resolved.

3. Conclusions

In summary, we have developed a monolithic MEMS-based 2D multilayer Laue lens nanofocusing optics for high-resolution hard x-ray microscopy. By utilizing microfabrication technologies, we have manufactured MEMS-based templates which significantly simplify MLLs alignment process. Assembled 2D optics exhibited orthogonality between two individual lenses to be better than 6 millidegrees, suitable for 10 nm focusing experiments. The x-ray ptychography measurements yielded astigmatism-free point focusing of ∼14 nm and ∼13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy. The developed 2D optic significantly reduces complexity of scanning microscopy instrumentation, and makes 2D MLLs, combined with tip-tilt positioning systems for Bragg angle alignment [33], compatible with more conventional, zone plate-based scanning x-ray microscopes. An adoption of MEMS-based 2D MLLs allows a large number of x-ray microscopy beamlines to implement high-resolution MLLs with minimal effort dedicated to retrofitting of the existing x-ray microscopes. The present work marks an important step forward in making MLL optics more accessible to the hard x-ray microscopy community.

Appendix A: Characterization of MEMS templates

Prior to assembly, microfabricated MEMS templates were characterized in terms of MLL loading/unloading process, orthogonality, and separation along the beam direction. Two dummy MLL samples, which have similar dimensions with the actual MLLs, were used for characterization. As shown in Fig. 6(a), a dummy MLL was placed into the right corner of the holding slot, and then slowly pushed into a designed position. (Figure 6(a)-(i)). With the movement of the lens, the silicon springs gradually bent securing the lens (Fig. 6(a)-ii) with the active area of the MLL being at the aperture position (Fig. 6(a)-iii). The three alignment ‘teeth’ were in contact with the top surface of the MLL sample defining its angular position. To remove the MLL, it has been pushed from the left to right, relaxing the spring and restoring them in the original position (Fig. 6(a)-iv to Fig. 6(a)-vi). During a consecutive loading/unloading process, the springs remained unaffected. Figure 6(b) is the FEA analysis illustrating the stress being applied to the silicon springs when an MLL is loaded. The maximum 1^st principal stress applied on the silicon springs increases to ∼923 MPa when the displacement of springs increases to 200 µm (Fig. 6(c)), which is much lower than the yield strength of silicon (i.e., 7 GPa).

 

Fig. 6. The load of MLL on the MEMS template. a The loading/unloading process of a dummy MLL sample on the MEMS template. b The deformation and stress applied to the template with the load of MLLs. c The change of maximum 1^st principal stress applied on the silicon springs with the deformation of springs.

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We further studied orthogonality and separation of the MLLs packed on a template. To measure the orthogonality of two MLLs, we placed a right-angle prism near MLLs as a reference, and measured the angle between each surface of the prism and a respective MLL. The orthogonality error of a right-angle prism used for characterization is about four millidegrees (N-BK7 high tolerance right-angle prism, Edmund Optics, NJ, USA) and defines the accuracy limit for orthogonality measurements. The measurements yielded the average error between designed and actual angles around 5.7 millidegrees (see Fig. 7(c)), which determines the limitations of the microfabrication process (including the measurement error). The separation distance between two MLLs is defined as a sum of the gap between two holding slots, an offset of the active part of MLL with respect to the surface of MLL substrate, and the thickness of adapters (if used). In this work, we have used 510 µm thick silicon wafers for fabrication of templates. The holding slots were etched to a depth between 180 and 240 µm. Figure 7(d) shows the cross-section of a holding slot. Bosch process has been used to etch the Si wafer with ∼ 0.7 µm increments per etching cycle, as shown in Fig. 7(e). By adjusting the number of etching cycles the depth of the holding slots can be precisely controlled.

 

Fig. 7. Characterization of MEMS templates. a The MEMS template with alignment ‘teeth’. b The angle between two holding slots ranges between 89.7° and 90.3°. c The designed and measured angle offset between two slots on different templates. d The cross-section of the etched holding slot. e Details of the sidewall of the holding slot demonstrating ∼ 0.7 µm increments per etching cycle.

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Funding

Brookhaven National Laboratory (LDRD 17-017); Office of Science (DE-SC0012704).

Acknowledgments

This work was partially carried out at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704 and used resources of the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704. This work was also performed in part at the Advanced Science Research Center NanoFabrication Facility of the Graduate Center at the City University of New York.

Disclosures

The authors declare no conflicts of interest.

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