Towards sub-10 nm spatial resolution by tender X-ray ptychographic coherent diffraction imaging

Ptychographic coherent diffraction imaging (PCDI) is a lensless microscopy technique that surpasses the spatial resolution limitations of lens-based microscopy. ^1,2) This method involves scanning a coherent beam across a sample, measuring diffraction patterns at each scan point, and reconstructing the sample image through iterative phase retrieval calculations from the dataset. The spatial resolution of the image is determined by the maximum scattering angle of the diffraction pattern. X-ray PCDI, in particular, has advanced significantly at synchrotron radiation facilities in recent years. ³⁾ In transmission geometry, X-ray PCDI reconstructs both phase and amplitude images, which, respectively, reflect the projection of the electron density distribution of the sample and the X-ray absorption by the sample. Spatial resolutions better than 10 nm have been achieved in both the hard ⁴⁾ and soft X-ray regions. ⁵⁾ The high penetration power of hard X-rays has facilitated phase imaging of micrometer-order thick samples, such as semiconductor devices ⁶⁾ and alloy particles. ⁷⁾ In contrast, the soft X-ray region, suited primarily to thin samples less than 1 μm, is promising for imaging organic thin films ⁸⁾ and cells. ⁹⁾ From soft X-rays in the lower energy range to high-energy hard X-rays, absorption images with a high signal-to-noise (S/N) ratio have been obtained. The spatially resolved X-ray absorption fine structure can be derived from the energy-dependent absorption images at the absorption edge. This technique, known as spectroscopic PCDI, is utilized for chemical state imaging of various functional materials, such as catalyst, battery, and magnetic materials. However, both hard and soft X-ray PCDI pose challenges in observing thick light-element materials, such as rubbers and thick cells. In the hard X-ray region, the small scattering cross-section makes it difficult to measure high-angle diffraction patterns with a high S/N ratio, while in the soft X-ray region, limited penetration power restricts measurements to thin specimens in transmission geometry.

Tender X-rays with an energy range of approximately 2–5 keV lie between soft and hard X-rays and possess the scattering cross section and penetration power necessary to observe micrometer-thick light-element materials at a high spatial resolution. In addition, this energy range includes the K absorption edges of 3p elements, such as sulfur and phosphorus, and L edges of 4d metals, such as ruthenium, rhodium, and palladium, which are significant in polymer, battery, catalyst materials and biological science. Given the relatively large absorption cross section, applying high-resolution spectroscopic PCDI is facilitated. However, the availability of synchrotron radiation beamlines capable of delivering high-brilliance tender X-rays has been limited, with no reports of tender X-ray PCDI until 2021. In 2021, the first demonstration of tender X-ray PCDI was reported at BL27SU in SPring-8, achieving approximately 50 nm resolution on a 200 nm thick tantalum test chart. ¹⁰⁾ Subsequently, tender X-ray PCDI has been employed to analyze the microstructure and chemical state of sulfur in sulfurized polymer with a resolution of approximately 141 nm. ¹¹⁾ The current challenge lies in further improving spatial resolution, which requires an increase in the coherent flux of tender X-rays.

The 3 GeV high-brilliance synchrotron radiation facility NanoTerasu, ^12,13) which commenced operations in April 2024, provides higher brilliance synchrotron radiation than SPring-8 in both the soft X-ray and tender X-ray regions. BL10U, the X-ray coherent imaging beamline at NanoTerasu, offers several tens of times higher brightness for tender X-rays than BL27SU at SPring-8. In this study, we report the first experiments of tender X-ray PCDI conducted at BL10U and discuss strategies to achieve sub-10 nm resolution in the near future.

To assess the performance of tender X-ray PCDI at NanoTerasu BL10U, two types of samples were evaluated: a test pattern with known structures and an actual material. The test sample was a 200 nm thick Ta chart (XRESO-50, NTT Advanced Technology Corp.). As the actual material, particles of sulfurized poly (n-butyl methacrylate) (SPBMA), ¹¹⁾ developed as a cathode active material for lithium-sulfur batteries, were used. Figure 1 illustrates a schematic of the experimental setup. The experiment utilized X-rays monochromatized to 3.5 keV by higher harmonics rejection mirrors and a Si(111) double-crystal monochromator. The slit was installed immediately after the monochromator, which was located approximately 26 m downstream from the light source. Spatial coherence of the incident X-rays was ensured by setting the slit opening to 10 μm (H) × 100 μm (V). A Fresnel zone plate (FZP, NTT Advanced Technology Co.) was placed approximately 28 m downstream from the slit. The FZP featured a diameter of 106.7 μm, an outermost bandwidth of 412 nm, and at 3.5 keV, a focal length of approximately 124 mm and a diffraction efficiency of 16%. A pinhole with a center beam stop, featuring a 10 μm thick Ta beam stop (20 μm diameter) and 107 μm diameter aperture, was positioned immediately upstream of the FZP. The sample was illuminated by focused X-rays from the FZP. A 200 μm thick Si square aperture (20 × 20 μm²) was placed immediately upstream of the sample as the order-sorting aperture to block high-order diffraction from the FZP. Diffraction patterns from the samples were captured by an image detector EIGER 1M-RW (DECTRIS Ltd.) with a pixel size of 75 μm, positioned approximately 1.57 m downstream from the sample. The sample was positioned using a piezo stage (PI GmbH Co., P-621.ZLC, P-621.1CL) with a raster scan at 200 nm intervals. The number of scanning points for the Ta chart and the SPBMA particle was 21(H) × 21(V) and 32(H) × 31(V) points, respectively. The exposure time per scan point was 10 s. The X-ray intensities measured at the sample positions with a PIN diode (A) and EIGER 1M-RW, at a threshold setting of 2.7 keV, were 8.6 × 10⁷ photons s⁻¹ and 2.8 × 10⁷ photons s⁻¹, respectively. The estimated detection efficiency of EIGER 1M-RW for 3.5 keV X-rays was approximately 33%.

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The ptychographic diffraction pattern datasets were cropped to 924 × 924 and 744 × 744 pixels for the image reconstruction of the Ta chart and SPBMA particle, respectively. The pixel sizes of the reconstructed images under these conditions are approximately 8 nm and 10 nm, respectively. Phase retrieval calculations were performed using the extended ptychographical iterative engine (ePIE) algorithm ¹⁴⁾ in conjunction with a correction algorithm ¹⁵⁾ for probe positioning errors. The initial sample function was set to 1 for all pixel values, and the initial probe function was a wave field propagated 500 μm from a 400 nm diameter pinhole on the computer. The raw measurement dataset can be immediately transferred to a large-scale storage system of the Tohoku University Cyberscience Center on the same campus via a dedicated high-speed network. Then, the reconstruction calculations were performed either by GPU parallel computing with MATLAB programs from the laboratory, or by Python-based data processing on Supercomputer AOBA ¹⁶⁾ tightly connected to the storage system. The AOBA system is powered by the latest-generation vector processors. ¹⁷⁾ With fine-grained access control, the resultant data can securely be shared via the SINET6 network. ¹⁸⁾

Figure 2(a) displays the diffraction pattern obtained from the 200 nm thick Ta chart, revealing a clear pattern in the spatial frequency region higher than 50 μm⁻¹. This pattern indicates the high coherence of the X-rays supplied from the beamline. Figure 2(b) presents the intensity and phase distributions of the probe function reconstructed by the phase retrieval calculation. The horizontal and vertical full widths at half maximum of the intensity distribution were 367 nm and 394 nm, respectively. These dimensions are approximately equivalent to the outermost bandwidth of the FZP, suggesting that the X-rays illuminating the FZP were nearly plane waves. Figure 2(c) depicts the phase shift distribution (phase image) at the sample plane obtained from the reconstructed sample function, where structures as small as 50 nm are clearly visible.

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To quantitatively evaluate the spatial resolution of the reconstructed images, two approaches were employed. Initially, the full periodic spatial resolution was evaluated to be 19.8 nm by the phase retrieval transfer function (PRTF), ¹⁹⁾ calculated from the inverse of the spatial frequency below the 1/e threshold, as illustrated in Fig. 3(a). Subsequently, the spatial resolution was evaluated using line profiles of edge structures in the image. Three line profiles from the phase images are presented in Fig. 3(b). By fitting each profile with an error function and averaging the full width at half maximum as indicated by its derivative, the resolution was evaluated to be 17.9 nm.

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Figure 4(a) displays the scanning electron microscopy (SEM) image of the SPBMA particle, alongside the distribution of sulfur and carbon elements as analyzed by energy-dispersive X-ray spectroscopy (EDX). The distribution of sulfur elements in these particles varies with the sintering temperature of the powder mixture of sulfur and poly (n-butyl methacrylate) (PBMA) during the fabrication process. ¹¹⁾ In the EDX image, the sulfur signal is predominant; however, a carbon signal is observed in the lower region, indicating the detachment of the sulfur shell, exposing the carbon-rich bulk region.

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Figure 4(b) shows the reconstructed phase image of this particle, clearly mirroring the particle shape observed in the SEM image. The spatial resolution of this image was evaluated to be 49.3 nm using PRTF, as shown in Fig. 4(c). Previously, the most optimal spatial resolution achieved in our PCDI measurement of SPBMA particles at BL27SU of SPring-8 using 2.5 keV X-rays was 141 nm. ¹¹⁾ Therefore, the substantial enhancement in spatial resolution in tender X-ray PCDI for actual material observation is evident due to the improvement in effective coherent flux. Thanks to this enhancement, we were now able to observe new structures with sizes less than 100 nm in the bulk of sulfur-rich region of SMPBA particles, as in Fig. 4(d), which could not be found in the previous PCDI experiments. ¹¹⁾ Although detailed investigation is needed, these nanostructures may be the seeds of active (or interfering) species, potentially serving as optimization parameters crucial for enhancing the performance and durability of lithium-sulfur batteries.

In discussing the achievable resolution by tender X-ray PCDI at BL10U in NanoTerasu, we must first consider the coherent flux of incident X-rays. The flux of 3.5 keV monochromatic X-rays was approximately 1.6 × 10¹² photons s⁻¹, measured with the PIN diode (B) upstream of the beam stop when the X-ray beam passed completely without the slit. Given that the coherence ratio of the tender X-rays provided by the source is estimated at approximately 2.4%, ¹²⁾ the maximum coherent flux available under the same conditions is approximately 3.8 × 10¹⁰ photons s⁻¹. With the current ring current at 160 mA, the ring current is anticipated to increase to 400 mA in the near future. Assuming that the flux is proportional to the ring current, the maximum coherent flux of 3.5 keV X-rays at BL10U is estimated to be approximately 9.5 × 10¹⁰ photons s⁻¹.

Next, we address the optics used to efficiently utilize this coherent flux. The two primary factors contributing to flux loss in the current setup were the low focusing efficiency of the FZP and the low detection efficiency of the EIGER 1M-RW image detector. An effective approach to improving focusing efficiency is the use of high-precision total-reflection focusing mirrors. For example, the advanced Kirkpatrick–Baez (AKB) mirror ²⁰⁾ can create a focused beam with high focusing efficiency and excellent positional stability, and high-resolution X-ray ptychography using the AKB mirror with a focusing efficiency of over 66% has been reported. ²¹⁾ By employing the AKB mirror, BL10U could ideally illuminate samples with coherent X-rays of 6.3 × 10¹⁰ photons s⁻¹ at 3.5 keV. Another significant improvement would be the use of CITIUS, ²²⁾ the next-generation image detector. The sensor of the CITIUS detector has an entrance-window structure with a thin insensitive layer, which gives a nominal quantum efficiency better than 97% in the photon energy range of 1.5–5 keV. Furthermore, CITIUS facilitates a count rate beyond the photon counting limit. High-resolution and high-sensitivity X-ray ptychography in the hard X-ray region have been demonstrated using the CITIUS detector and total-reflection mirrors at BL29XU in SPring-8. ²³⁾ By integrating the AKB mirror and CITIUS detector, the coherent flux gain at BL10U can be estimated to be approximately 2.2 × 10³ (=0.97 × (6.3 × 10¹⁰)/(2.8 × 10⁷)). According to Porod's law, ²⁴⁾ the scattering intensity in the high spatial frequency region is proportional to the reciprocal of the spatial frequency raised to the fourth power (q⁻⁴). Since spatial resolution is expressed as the inverse of spatial frequency, the intensity gain raised to the power of −1/4 corresponds to the spatial resolution gain. With the current resolution from the measurements of the 200 nm thick Ta chart and SPBMA at 19.8 nm and 49.3 nm, respectively, the achievable resolutions with these improvements are estimated to be 2.9 nm and 7.2 nm, respectively.

In this study, tender X-ray PCDI was conducted as the first experiment at BL10U in NanoTerasu, utilizing tender X-rays with exceptional coherent flux. The experiment measured a 200 nm thick Ta test chart, achieving a spatial resolution of 19.8 nm. Additionally, the SPBMA particle, used as a cathode active material for lithium-sulfur batteries, was also examined. This analysis achieved a spatial resolution of 49.3 nm and revealed fine structural details within the particles. We further discussed resolution enhancements at BL10U, concluding that sub-10 nm spatial resolution in the observation of actual light element materials is attainable using the AKB mirror and the CITIUS detector.

Achieving sub-10 nm resolution in tender X-ray PCDI holds significant potential across various fields such as materials science and life sciences. For example, it could enable the microscopic visualization of chemical state distributions of sulfur and phosphorus within biological tissues, which are crucial to diverse biological functions. ^25,26) This capability could lead to deeper insights into intracellular functions and disease mechanisms. Moreover, in the realm of functional materials with nanoscale structures—such as battery materials for lithium-sulfur batteries and catalysts for exhaust gas purification using palladium and rhodium—it could provide valuable knowledge that aids in the optimized design of structures and chemical states, thereby enhancing performance. Therefore, the enhanced resolution of tender X-ray PCDI is expected to facilitate the generation of new knowledge across a wide range of fields.

Acknowledgments