Outermost Zone Width Research Articles

Numerical analysis of X-ray multilayer Fresnel zone plates with high aspect ratios

Abstract A partition calculation method (PCM) for calculating the diffraction efficiency of multilayer Fresnel zone plate with high aspect ratio is proposed. In contrast to the traditional theory, PCM designs and evaluates Fresnel zone plate (FZP) considering material pairs, all zone widths, thicknesses and X-ray energy more completely. The results obtained through PCM are validated by comparing them with the complex amplitude superposition theory and coupled wave theory numerical results. The PCM satisfies the requirements of the theoretical investigation of FZP with small outermost zone width (drN) and large thickness (t). Combining proper numerical analysis with the experimental conditions will present a great potential to break through the imaging performance of X-ray microscopy.

Fabrication of multilayer Fresnel zone plate for hard X-ray microscopy by atomic layer deposition and focused ion beam milling

Fresnel zone plate (FZP) is a widely used optics in X-ray microscopy. In contrast to soft X-ray, high aspect ratio is essential for FZP to focus hard X-ray efficiently. Multilayer FZP (ML-FZP) is a promising solution to fabricate high-aspect-ratio FZP due to the unique sputter-sliced technique. In this work, atomic layer deposition (ALD) and focused ion beam (FIB) milling were utilized to prepare ML-FZP for hard X-ray microscopy. Al2O3/HfO2 ML-FZP with total zone thickness 10 μm was successfully obtained. The zone thickness is much greater than the reported ML-FZPs fabricated by the same method and of great significance to the increase of FZP active region. The ML-FZP with outermost zone width 40 nm and aspect ratio 157 was also tested in transmission X-ray microscopy (TXM) at 9 keV and achieved a 29 nm half-pitch cut-off resolution.

Implementation of a Large-Area Diffractive Lens Using Multiple Sub-Aperture Diffractive Lenses and Computational Reconstruction

Direct imaging systems that create an image of an object directly on the sensor in a single step are prone to many constraints, as a perfect image is required to be recorded within this step. In designing high resolution direct imaging systems with a diffractive lens, the outermost zone width either reaches the lithography limit or the diffraction limit itself, imposing challenges in fabrication. However, if the imaging mode is switched to an indirect one consisting of multiple steps to complete imaging, then different possibilities open. One such method is the widely used indirect imaging method with Golay configuration telescopes. In this study, a Golay-like configuration has been adapted to realize a large-area diffractive lens with three sub-aperture diffractive lenses. The sub-aperture diffractive lenses are not required to collect light and focus them to a single point as in a direct imaging system, but to focus independently on different points within the sensor area. This approach of a Large-Area Diffractive lens with Integrated Sub-Apertures (LADISA) relaxes the fabrication constraints and allows the sub-aperture diffractive elements to have a larger outermost zone width and a smaller area. The diffractive sub-apertures were manufactured using photolithography. The fabricated diffractive element was implemented in indirect imaging mode using non-linear reconstruction and the Lucy–Richardson–Rosen algorithm with synthesized point spread functions. The computational optical experiments revealed improved optical and computational imaging resolutions compared to previous studies.

Single-focus phase singularity generated by spiral zone plate with quasi-random distributed quantum dots

We report on a new vortex lens for producing a single-focus phase singularity which is termed as a quasi-random-dot-array binary spiral zone plates (QBSZPs). Differing from the abrupt transitions of the conventional spiral zone plates (SZPs), the key idea of the QBSZPs is to realize a sinusoidal transmittance by properly arranging lots of quantum dot arrays which take on the values of 0 and 1 in two dimensions. In this typical design, the number density of the selected primitives obey sinusoidal distribution along the radial direction and quasi-random in the azimuthal direction. Theoretical analysis indicates that the higher-order foci which inevitably exist in the SZPs have been indeed effectively suppressed with the QBSZPs. Moreover, the focusing performance of the QBSZPs is influenced by the ratio of circumcircle diameter of the primitives to the outermost zone width. These findings, which have been demonstrated by the performed experiment, may offer a new direction towards improving the performance of biomedical imaging, quantum computation and optical manipulation.

Tunable hard x-ray nanofocusing with Fresnel zone plates fabricated using deep etching.

Fresnel zone plates are widely used for x-ray nanofocusing, due to their ease of alignment and energy tunability. Their spatial resolution is limited in part by their outermost zone width dr N , while their efficiency is limited in part by their thickness t zp. We demonstrate the use of Fresnel zone plate optics for x-ray nanofocusing with dr N = 16 nm outermost zone width and a thickness of about t zp = 1.8 μm (or an aspect ratio of 110) with an absolute focusing efficiency of 4.7% at 12 keV, and 6.2% at 10 keV. Using partially coherent illumination at 12 keV, the zone plate delivered a FWHM focus of 46 × 60 nm at 12 keV, with the first order coherent mode in a ptychographic reconstruction showing a probe size of 16 nm FWHM. These optics were fabricated using a combination of metal assisted chemical etching and atomic layer deposition for the diffracting structures, and silicon wafer back-thinning to produce optics useful for real applications. This approach should enable new higher resolution views of thick materials, especially when energy tunability is required.

Metal-Assisted Chemical Etching and Electroless Deposition for Fabrication of Hard X-ray Pd/Si Zone Plates.

Zone plates are diffractive optics commonly used in X-ray microscopes. Here, we present a wet-chemical approach for fabricating high aspect ratio Pd/Si zone plate optics aimed at the hard X-ray regime. A Si zone plate mold is fabricated via metal-assisted chemical etching (MACE) and further metalized with Pd via electroless deposition (ELD). MACE results in vertical Si zones with high aspect ratios. The observed MACE rate with our zone plate design is 700 nm/min. The ELD metallization yields a Pd density of 10.7 g/cm, a value slightly lower than the theoretical density of 12 g/cm. Fabricated zone plates have a grid design, 1:1 line-to-space-ratio, 30 nm outermost zone width, and an aspect ratio of 30:1. At 9 keV X-ray energy, the zone plate device shows a first order diffraction efficiency of 1.9%, measured at the MAX IV NanoMAX beamline. With this work, the possibility is opened to fabricate X-ray zone plates with low-cost etching and metallization methods.

High-intensity x-ray microbeam for macromolecular crystallography using silicon kinoform diffractive lenses.

Macromolecular crystallography often requires focused high-intensity x-ray beams for solving challenging protein structures from micrometer-sized crystals using current synchrotron radiation sources. The design of optical focusing schemes for hard x-rays showing high efficiency and flexibility in beam size is therefore continuously pursued. Here, we present an innovative solution based on a two-stage demagnification of the undulator source for photon energies from 6keV to 19keV, commissioned at the X10SA beamline of the Swiss Light Source, where a secondary source is imaged by two crossed silicon kinoform x-ray diffractive lenses with 75nm outermost zone width. A source-size limited spot with a size of 4.8 μm×1.7 μm(h×v,FWHM) and flux of 7.5×1010 photons/s at 12.4keV is demonstrated at the sample position.

High-throughput synthesis of modified Fresnel zone plate arrays via ion beam lithography

Fresnel zone plates (FZP) are diffractive photonic devices used for high-resolution imaging and lithography at short wavelengths. Their fabrication requires nano-machining capabilities with exceptional precision and strict tolerances such as those enabled by modern lithography methods. In particular, ion beam lithography (IBL) is a noteworthy method thanks to its robust direct writing/milling capability. IBL allows for rapid prototyping of high-resolution FZPs that can be used for high-resolution imaging at soft X-ray energies. Here, we discuss improvements in the process enabling us to write zones down to 15 nm in width, achieving an effective outermost zone width of 30 nm. With a 35% reduction in process time and an increase in resolution by 26% compared to our previous results, we were able to resolve 21 nm features of a test sample using the FZP. The new process conditions are then applied for fabrication of large arrays of high-resolution zone plates. Results show that relatively large areas can be decorated with nanostructured devices via IBL by using multipurpose SEM/FIB instruments with potential applications in FEL focusing, extreme UV and soft X-ray lithography and as wavefront sensing devices for beam diagnostics.

A scanning transmission X-ray microscope at the Pohang Light Source.

A scanning transmission X-ray microscope is operational at the 10A beamline at the Pohang Light Source. The 10A beamline provides soft X-rays in the photon energy range 100-2000 eV using an elliptically polarized undulator. The practically usable photon energy range of the scanning transmission X-ray microscopy (STXM) setup is from ∼150 to ∼1600 eV. With a zone plate of 25 nm outermost zone width, the diffraction-limited space resolution, ∼30 nm, is achieved in the photon energy range up to ∼850 eV. In transmission mode for thin samples, STXM provides the element, chemical state and magnetic moment specific distributions, based on absorption spectroscopy. A soft X-ray fluorescence measurement setup has been implemented in order to provide the elemental distribution of thicker samples as well as chemical state information with a space resolution of ∼50 nm. A ptychography setup has been implemented in order to improve the space resolution down to 10 nm. Hardware setups and application activities of the STXM are presented.

An amplitude and phase hybrid modulation Fresnel diffractive optical element

An Amplitude and Phase Hybrid Modulation Fresnel Diffractive Optical Element (APHMFDOE) is proposed here. We have studied the theory of APHMFDOE and simulated the focusing properties of it along the optical axis, which show that the focus can be blazed to other positions with changing the quadratic phase factor. Moreover, we design a Composite Fresnel Diffraction Optical Element (CFDOE) based on the characteristics of APHMFDOE. It greatly increases the outermost zone width without changing the F-number, which brings a lot of benefits to the design and processing of diffraction device. More importantly, the diffraction efficiency of the CFDOE is almost unchanged compared with AFZP at the same focus.

Fabrication of tungsten Fresnel zone plates for hard x-rays using wet etching

A novel and scalable method to fabricate tungsten Fresnel zone plate (FZP) structures with a high aspect ratio using the wet etching method is presented. FZPs with an outermost zone width of 370 nm and a height of 1.1 μm were fabricated in tungsten on a 35 μm polyimide film. They were designed for a focal length of 50 cm at 8 keV such that the radius is 100 μm for 142 zones, with an opaque center zone. The fabrication method presented is a simple single step resist process. The testing of FZP was carried out at the Indus-2 synchrotron source, where focusing was observed as per design parameters. The transmission characteristics of polyimide coupled with the phase shifting properties of tungsten make the FZP useful also at lower energies. An improvement in the zone plate structural parameters and hence its performance has also been discussed.

Tight focusing of laser light using a chromium Fresnel zone plate.

Using near-field scanning microscopy, we demonstrate that a 15-µm zone plate fabricated in a 70-nm chromium film sputtered on a glass substrate and having a focal length and outermost zone's width equal to the incident wavelength λ = 532 nm, focuses a circularly polarized Gaussian beam into a circular subwavelength focal spot whose diameter at the full-width of half-maximum intensity is FWHM = 0.47λ. This value is in near-accurate agreement with the FDTD-aided numerical estimate of FWHM = 0.46λ. When focusing a Gaussian beam linearly polarized along the y-axis, an elliptic subwavelength focal spot is experimentally found to measure FWHMx = 0.42λ (estimated value FWHMx = 0.40λ) and FWHMy = 0.64λ. The subwavelength focal spots presented here are the tightest among all attained so far for homogeneously polarized beams by use of non-immersion amplitude zone plates.

Hard X-ray multilayer zone plate with 25-nm outermost zone width

We have improved the performance of a previously reported multilayer zone plate by reducing its outermost zone width, using the same multilayer materials (MoSi2 and Si) and fabrication technique. The focusing performance was evaluated at the BL24XU of SPring-8 using 20-keV X-rays. The line spread function (LSF) in the focal plane was measured using a dark-field knife-edge scan method, and the point spread function was obtained from the LSF through a tomographic reconstruction principle. The spatial resolution was estimated to be 30 nm, which is in relatively good agreement with the calculated diffraction-limited value of 25 nm, while the measured diffraction efficiency of the +1st order was 24%.

Differential-phase-contrast knife-edge scan method for precise evaluation of X-ray nanobeam

A differential-phase-contrast knife-edge scan method is proposed to precisely evaluate X-ray nanofocusing beam profiles. A thin phase object can be used as a knife edge in this method, whereas the conventional absorption knife-edge scan method requires a thick opaque edge. The precision of the focal beam profile measurement was confirmed by numerical calculation. The performance test was carried out at the undulator beamline 20XU of SPring-8, by evaluating the focal spot profile of a tantalum Fresnel zone plate with an outermost zone width of 25 nm. The edge pattern of a tantalum test chart with a thickness of 500 nm was used as the knife edge. The measured beam profile with a size of 25 nm ± 1 full-width at half-maximum was carefully compared with the theoretical values and found to be in good agreement.

Focused Ion Beam Micromachining Enables Novel Optics for X-ray Microscopy

X-ray microscopy is a strong analytical tool with a plethora of applications in physics, materials science and life sciences [1]. In many high resolution X-ray microscopes, a focusing optic such as a Fresnel zone plate (FZP) is utilized as a lens to form an image. The FZP is a diffractive optic composed of a series of concentric rings (zones) of radially varying grating period, where the width, Δr, of the outermost zone determines the resolution. Synchrotron radiation facilities are required as bright and coherent X-ray sources as the FZPs are usually quite limited in diffraction efficiency. The diffraction efficiency depends on FZP properties such as geometry, material, structure thickness and on the outermost zone width for small Δr. Conventional FZP profiles are binary and can have up to 10-40 % diffraction efficiency for ideal absorption and phase reversal zone plates, respectively. In practice the efficiencies are lower due to fabrication difficulties and errors. Electron beam lithography (EBL), the usual fabrication method, allows fabrication of binary FZPs with ultra-high resolution via processes of ever increasing complexity. However, due to the scattering of electrons within the resist, it is very difficult to fabricate ultra-high resolution FZPs with high structural thicknesses to achieve high aspect ratios. This, so called, proximity effect limits the aspect ratio, restricting the utilization of high resolution FZPs to softer X-ray energies. One special type of refractive/diffractive X-ray optic is the kinoform lens, with a continuous 3D surface profile. Ideally, it has a theoretical diffraction efficiency of 100 %. While in a real lens absorption would hinder 100 % efficiency, diffraction efficiencies well above 40 % are already demonstrated [2] using these lenses. Nevertheless, in order to fabricate these kinoforms, researchers resorted to step approximations using several consecutive overlay EBL steps, which is complicated and lead to much lower efficiencies than theoretically expected due to the vulnerability of the optics to fabrication errors amplified by error accumulations. To solve the issues that are intrinsic limitations of the EBL-FZPs we introduced novel, precise and mostly direct methods relying on the FIBs. The powerful method potentially allows for higher resolutions than EBL [3] and precise 3D sculpting capability enables the realization of highly efficient X-ray optics with high fidelity [4]. We have used a standard multi-purpose FIB instrument (Nova 600 NanoLab, DualBeam, FEI) to fabricate binary FZPs, kinoform lenses and multilayer FZPs (Figure 1).

Near field stacking of zone plates for reduction of their effective zone period

Here we analyze the potential of a new fabrication method for high resolution zone plates with high aspect ratios based on near field stacking of frequency doubled atomic layer deposited (ALD) zone plates. The proposed method enables reduction of the effective zone period by a factor of four with two zone plate layers compared to the initial e-beam lithography exposed outermost zone period. It also overcomes the problem that very small zone widths with high aspect ratios have to be fabricated for high-resolution hard X-ray microscopy. Using rigorous coupled wave theory, we have analyzed the diffraction behavior of these near field stacked zone plates and investigated strategies to optimize fabrication parameters to compensate for separation of stacked zone plates. The calculations performed for 8 keV photon energy and effective outermost zone widths of 28 nm and 15 nm predict diffraction efficiencies ≥ 20% suggesting that such optics could find widespread practical applications.

Direct-write X-ray lithography using a hard X-ray Fresnel zone plate.

Results are reported of direct-write X-ray lithography using a hard X-ray beam focused by a Fresnel zone plate with an outermost zone width of 40 nm. An X-ray beam at 7.5 keV focused to a nano-spot was employed to write arbitrary patterns on a photoresist thin film with a resolution better than 25 nm. The resulting pattern dimension depended significantly on the kind of underlying substrate, which was attributed to the lateral spread of electrons generated during X-ray irradiation. The proximity effect originated from the diffuse scattering near the focus and electron blur was also observed, which led to an increase in pattern dimension. Since focusing hard X-rays to below a 10 nm spot is currently available, the direct-write hard X-ray lithography developed in this work has the potential to be a promising future lithographic method.

Towards multi-order hard X-ray imaging with multilayer zone plates.

This article describes holographic imaging experiments using a hard X-ray multilayer zone plate (MZP) with an outermost zone width of 10 nm at a photon energy of 18 keV. An order-sorting aperture (OSA) is omitted and emulated during data analysis by a 'software OSA'. Scanning transmission X-ray microscopy usually carried out in the focal plane is generalized to the holographic regime. The MZP focus is characterized by a three-plane phase-retrieval algorithm to an FWHM of 10 nm.

Use of combined zone plates as imaging optics for hard x-rays

We have carried out modeling of an image formation in hard x-ray coherent radiation using a Rayleigh-Sommerfeld integral. Combined zone plates have been used to form the image. The resolution of the combined zone plate was numerically shown to increase up to 10 times (equaling 20 nm) when compared with a traditional Fresnel zone plate without any changes of the outermost zone width (205 nm). The zone plate consisted of 6 areas operating in 1, 3, 5, 7, 9 and 11 diffraction orders. An efficiency improvement of 42% has been numerically achieved in contrast to a traditional Fresnel zone plate used in the third diffraction order. For the combined zone plate, the efficiency of 3.7 % has been achieved.

Characterization of x-ray phase vortices by ptychographic coherent diffractive imaging

We have characterized the x-ray phase vortices generated at the focal spot of various spiral Fresnel zone plates with an outermost zone width of Δr=50 nm. The complex-valued wavefields of phase vortices as small as 50 nm in size (FWHM) and several topological charges were reconstructed using ptychographic coherent diffractive imaging. The reconstructed focal spots demonstrate good agreement with the theoretically expected wavefields and diffraction-limited focusing.