Optimization of Soft X-Ray Fresnel Zone Plate Fabrication Through Joint Electron Beam Lithography and Cryo-Etching Techniques

Abstract

The ability to manufacture complex 3D structures with nanometer-scale resolution, such as Fresnel Zone Plates (FZPs), is crucial to achieve state-of-the-art control in X-ray sources for use in a diverse range of cutting-edge applications. This study demonstrates a novel approach combining Electron Beam Lithography (EBL) and cryoetching to produce silicon-based FZP prototypes as a test bench to assess the strong points and limitations of this fabrication method. Through this method, we obtained FZPs with 100 zones, a diameter of 20 µm, and an outermost zone width of 50 nm, resulting in a high aspect ratio that is suitable for use across a range of photon energies. The process incorporates a chromium mask in the EBL stage, enhancing microstructure precision and mitigating pattern collapse challenges. This minimized issues of under- and over-etching, producing well-defined patterns with a nanometer-scale resolution and low roughness. The refined process thus holds promise for achieving improved optical resolution and efficiency in FZPs, making it viable for the fabrication of high-performance, nanometer-scale devices.

1. Introduction

In the rapidly evolving field of nanotechnology, the ability to fabricate structures at the nanometer scale is crucial for advancing a myriad of applications. Among the techniques that have emerged to meet this demand, lithography and cryoetching stand out for their precision and versatility [1]. Lithography, a process that uses electrons to transfer a pattern onto a substrate, and cryoetching, which involves etching at cryogenic temperatures to achieve smooth high-resolution patterns, together provide a powerful toolkit for nanofabrication. This combination is pivotal in the creation of intricate nanometric structures essential for the miniaturization and enhancement of various devices encompassing high-density memory elements, structural elements, and functional surfaces, such as cantilevers or lamellae, as well as the fabrication of arrays of Josephson junctions for quantum computing, to cite just a few examples. X-rays, widely used for their ability to penetrate matter and unveil intricate structural details at electronic, atomic, and molecular levels in space and time, with unprecedented resolution, serve as an indispensable tool across numerous scientific fields, such as materials science, medicine, chemistry, and physics [2,3,4,5,6]. The full exploitation of the latest generation of Free Electron Lasers and synchrotron light sources [7,8,9,10,11,12,13] requires the use of state of the art devices that are able to focus X-rays at their diffraction limit, at a resolution of at least tens of nanometers. In addition to the aforementioned established players in the field, laser-driven X-ray sources are emerging as a promising and rapidly evolving field [14,15,16], which require a set of new tools to take advantage of their capabilities.

A soft X-ray beam can be successfully monochromatized and focused at photon energies below 1400 eV with a high transmittance of up to 20% using reflection zone plates (RZPs), which are made of elliptical zones constructed as laminar grating structures on a mirror surface. Nevertheless, RZPs can only be built for a single photon energy and are extremely chromatic. A reflection zone–plate array (RZPA), which covers a wide bandwidth while maintaining pulse form and flux, is the new solution proposed by Maria B. et al. [17] to mitigate this issue. Unprecedented new methods for examining the electronic structure and dynamics of transition metal systems are made possible by X-ray free-electron lasers, or XFELs. One effective method for these kinds of investigations is L-edge absorption spectroscopy, which has been shown to be feasible at XFELs for both liquids and solids. However, further monochromatization is required, and the necessary X-ray bandwidth is an order of magnitude smaller than that of self-amplified spontaneous emission (SASE). A novel method based on the self-seeding of a linac coherent light source (LCLS) is compared with the L-edge X-ray absorption spectroscopy (XAS) of a prototypical transition metal system, based on monochromatizing the SASE radiation of the LCLS, by Thomas K. et al. [18].

In high-precision optical systems, scanning focused light with corrected aberrations is crucial. Nevertheless, traditional optical systems that depend on extra dynamical correctors to remove scanning aberrations invariably produce unwanted complexity and bulkiness. Xiaotong Li et al. [19] suggest that by rotating just two cascaded transmissive metasurfaces, adaptive aberration corrections can be achieved in tandem with focus scanning. They designed and built two all-silicon terahertz meta-devices that can scan the focal spot with adaptively corrected aberrations. Laser-induced breakdown spectroscopy (LIBS) has been utilized extensively in industrial measurement and monitoring as a vital detecting tool in the age of digital transformation. Combining LIBS technology with other technologies has become an unavoidable trend for present and future development, with the goal of diversifying detection functions. Minchao C et al. [20] thoroughly examine the state of LIBS in conjunction with laser-induced fluorescence spectroscopy, Raman, X-ray fluorescence, acoustic signals, photoacoustic spectroscopy, and hyperspectral imaging, among other methods, and differentiate the respective advantages of LIBS and these techniques.

Grazing incidence mirrors and Fresnel Zone Plates (FZPs) are currently the optical devices that are able to reach the highest imaging resolutions in the soft X-ray range [21,22,23], since FZPs offer an unrivaled performances in terms of compactness, as well as a superior stability with respect to environmental parameters. This ability to establish fine structural details in zone fabrication not only facilitates high-resolution focusing but also eliminates the need for complex multilayer reflective coatings or the stringent alignment requirements inherent to RZPAs. As a result, FZPs provide a more efficient and practical solution for the high-resolution demands of soft X-ray microscopy, achieving a greater imaging performance in this spectral range.

Various fabrication techniques have been employed by researchers to create Fresnel zone plates (FZPs) from a wide range of materials, with diverse dimensions. For example, Di Fabrizio et al. [24] fabricated a silicon nitride and nickel FZP with a diameter of 5000 µm and a thickness of 1.3 µm using electron-beam lithography. Rogers et al. [25] utilized ion-beam milling on aluminum to produce a significantly thinner FZP (0.1 µm) with a diameter of 40 µm. Kong et al. [26] employed photolithography to create an ultra-thin graphene FZP with a diameter of 100 µm and a thickness of less than 0.005 µm. Li et al. [27] achieved a 10 µm thick carbon nanotube-based FZP with a diameter of approximately 650 µm using lithography. Additionally, Zheng et al. [28] and Low et al. [29] employed femtosecond direct laser writing (FsDLW) on graphene oxide, utilizing adaptive optics and a 3D stage or Galvano scanner, to fabricate FZPs with thicknesses of 0.28 µm and 0.9 µm and diameters of approximately 8 µm and 656 µm, respectively.

The key factors and challenges in FZP manufacturing can be condensed during extreme control (i.e., required resolutions at the nm-scale) of the manufacturing process of a full 3D device over a range of tens of µm (i.e., the overall transverse size) and thicknesses at the µm scale. As a starting point in the design of the FZP, a mean photon energy $E_0$ and focal length will be defined [30,31,32]. The FZP topology used throughout this work is composed of concentric zones, alternatively illuminated by photons with a half wavelength of phase difference. The focusing effect is achieved by alternating zones absorbing and transmitting the incoming radiation. The absorbing zones will be characterized by a given material of a constant thickness devoted to attenuating radiation. Transmission zones would be made out of a material thin enough to minimize X-ray absorption. Once the material composition of the absorbing zones is chosen, the photon mean energy thickness t of the FZP is set. The radius of the concentric nth zone is given by the following expression:

$$r_n^2=n\lambda f+{\displaystyle \frac{n^2{\lambda }^2}{4}}$$

(1)

where (n) is the zone number, ($\lambda$) is the radiation wavelength, and (f) is the focal length. By increasing n, Equation (1) encompasses a constant area for each zone, while the spacing between adjacent zones $\Delta r_n=r_n-r_{n-1}$ would progressively shrink. Clearly, the technological limit of the fabrication process would determine the width of the outermost zone $\Delta r$, and hence, the diameter of the FZP, its numerical aperture (NA), and the imaging resolution. The $\Delta r$ limit would also set the aspect ratio of the FZP, $t/\Delta r$. This is an important figure of merit, as it summarizes the most challenging aspects of FZP fabrication, which make the outermost zones challenging to manufacture, and extremely fragile.

There have been various approaches to fabricating such FZPs, such as photolithography [33], focused ion beam milling [34,35], interference lithography [36], and electron beam lithography (EBL) [37]. Achieving the nanometer-scale resolution required for cutting-edge applications necessitates the development of diminutive lenses with sharp and smooth edges. To fabricate such high-precision FZPs, it is imperative to push the limits of electron beam lithography (EBL). EBL, known for its exceptional resolution, can define the intricate patterns required for FZPs. When combined with cryoetching, the production of FZPs with sharp and smooth edges would become significantly more feasible. However, achieving defined nano-metric patterns with EBL presents challenges. During exposure, the energy deposition distribution within the resist significantly influences the patterning performance of the masks produced. Incident electrons penetrate the resist and substrate, undergoing scattering and energy loss [38], which can hinder the technique’s applicability at the nanoscale. To mitigate these issues, the implementation of a capping layer is crucial. A capping layer helps minimize the backscattering effects, ensuring that electrons are effectively absorbed or scattered away from the underlying layers, thereby reducing the risk of unwanted exposure and pattern distortion [39,40]. Various materials, such as Al-Cu, Ti, TiN, and Cr, have been evaluated for this purpose, with Cr emerging as one of the most promising options [41,42].

In this study, we thoroughly report on the fabrication steps of a Si-based FZP structure, with 100 differentiated zones, a lens diameter of 20 µm, and an outermost zone width of 50 nm and thickness of 4.3 µm. Our goal is to investigate the limits of the combination of electron beam lithography (EBL) and cryoetching for the design of structures that might be used in prototypical FZPs when conveniently scaled, as the employed aspect ratio of 86 is quite challenging and poses severe issues in the manufacturing process as well as in the handling of the FZP. As an example, by using the scaling law given by Equation (1), we could use the structure synthesized directly as a Si-FZP for photons of 1.2 keV, for a focal length of 970.87 µm, and for 3 keV (with 2.5 times the initial focal length), or, conversely, as a masking pattern used to make the deposition of conventional absorbing materials (e.g., Ni, Au, Ta, W) suitable for harder X-rays (e.g., 9 keV). We developed a robust process utilizing EBL to ensure a fine definition of intricate micrometric structures is achieved. This method is combined with a chromium mask, which guarantees the successful fabrication of a vertical-step FZP comprising a large number of differentiated zones via cryoetching [1]. This approach aims to significantly improve the focusing performance of the FZP. Building on the results presented by K. Parfeniukas and J. Rahomäki [43], who demonstrated an improved method for the nanofabrication of high-aspect-ratio tungsten structures for high-efficiency hard X-ray nanofocusing zone plates, we addressed the issue of the efficiency loss towards the edge of the zone plate. This loss was partly attributed to flaws in the vertical zone profile. In our work, we demonstrate how the use of cryogenic etching for the FZP allows for the precise control of the side wall angle and the roughness at the edges [44], which are crucial for achieving a high lens efficiency

2. Fabrication and Discussion

2.1. PMMA Mask Preparation

Here, we report a process based on EBL, aiming for the sharp definition of micrometric structures to create an FZP suitable for a wavelength of 1.03 nm (1200 eV), which would allow for an optical resolution of 61 nm and could accordingly be scaled at higher photon energies, as previously stated. The rest of the parameters of the FZPs’ design are detailed in

Table A3. Fresnel zone plate parameters.

Parameter	Notation	Values
Radiation wavelength	$\lambda$	1.03 nm (1.2 keV)
Outer zone width	$\Delta r_n={\displaystyle \frac{\lambda f}{2r_n}}$	50 nm
Number of zones	N	100
Focal length	$f={\displaystyle \frac{r_n^2}{n\lambda }}$	970.87 µm
Diameter	$D=4N\Delta r$	20 µm
Numerical Aperture (1st order)	NA = ${\displaystyle \frac{\lambda }{2\Delta r}}$	0.0103
Spatial Resolution (1st order)	${\delta }_{\mathrm{res}}=1.22\Delta r$	61 nm

in the Appendix C. In order to define the microstructures, resist PMMA layers were deposited on freshly cleaned 550 µm thick silicon substrates, which served as the template for the design of the FZP. The standard cleaning process of the substrate was achieved through rinsing in acetone and isopropanol (IPA), followed by a plasma cleaning treatment for 5 min, utilizing a power of 29.6 W, and an oxygen flow rate of 30 mL/min, while maintaining a stable base chamber pressure of 1000 mTorr. The PMMA layers were spin-coated using a resist solution (2% PMMA in chlorobenzene), followed by a soft-bake at 160 °C for 10 min [1].

The design of the Fresnel zone plate pattern was constructed in the GDSII file format using the ELPHY PLUS software release 6 SP 6.0 (see Figure A1 in the Appendix A), and considering various parameters, since our goal is to design structures that could be of use in focusing X-rays. For the selection of substrate materials for the FZP with a high X-ray transmittance, low absorption, and an appropriate refractive index, commonly utilized options include diamond and silicon nitride [45,46]; the selection of these substrate materials is fundamental. Spatial resolution is determined by the width of individual zones using the expression $\delta r=\lambda /2\left(\mathrm{NA}\right)$, and strongly depends on the fabrication process and methods. The overall efficiency is dependent on parameters such as the number of zones, their thickness, and their accurate placement. A zone plate’s resolving power depends on the illumination conditions, i.e., the numerical aperture (NA) of the condenser system [47]. Specific zone plate parameters, including the number of zones (N), the zone diameter (D), the zone thickness (t), and the outermost zone width ($\Delta r$) require a delicate balance between spatial resolution and efficiency.

Once the design was complete, the subsequent electron beam lithography exposures were carried out with a scanning electron microscope (SEM) Sigma, manufactured by Zeiss (Jena, Germany). The EBL process was executed employing a 15 keV electron beam energy and a 7.5 µm column aperture, maintaining a typical beam current of 0.016114 nA. Specific details of the EBL settings are found in

Table 1. Exposure parameters for the e-beam lithography.

E-Beam Lithography Parameters
Substrate	Si chip 1 cm × 1 cm
Resist	PMMA 2%
Resist thickness	87 nm
Electron beam current	0.016114 nA
Electron beam energy	15 keV
Step size	2 nm
Dwelltime	0.000284 ms
Column aperture	7.5 µm
Z stage position	17 mm
Working distance	5 mm
Exposure field	100 µm × 100 µm
Magnification	1500

, ensuring consistency and reproducibility in the manufacturing process.

Following the EBL exposure, the sample underwent a sequence of post-processing steps. It commenced with a 45 s immersion in a 1:3 mixture of MIBK (4-Methyl-2-pentanone) and isopropyl alcohol (IPA), designed to develop the patterned resist. Afterwards, the sample was immersed in isopropyl alcohol (IPA) for an additional 45 s, ensuring the removal of any residual materials. The fabricated structures were thoroughly examined using Scanning Electron Microscope (SEM). A typical FZP structure produced by EBL is shown in Figure 1a, where an already developed PMMA mask is presented. The outermost zones’ decrease in width poses a challenge known as the collapse problem in micrometric-size structures due to their high aspect ratios. Figure 1a depicts a concentric FZP mask made of PMMA, showing a large portion of undesired, overexposed (and hence collapsed) areas at the outermost zones due to the undesired over/underexposure. The collapse problem is caused by the proximity effect [48,49,50]. This significantly affects each pattern and its neighbors and leads to pattern interference during exposure. When an electron beam and a substrate come into contact, this leads to the production of forward- (electrons are deflected at tiny angles as they enter the substrate and resist) and backscattering (electrons are usually deflected in a large angle) electrons, which can result in the resist material being exposed beyond the initial point of impact. To be more specific, during the EBL manufacturing process, the electron gun uses a series of lenses and apertures to directly imprint patterns on wafers. When a primary electron beam shoots from the electron cannon and hits the resist and substrate, the electrons may scatter, and the scattered electrons produce backscattered electrons. Rescattered electrons can be created when these backscattered electrons strike the objective lens’s bottom [51]. As a result, the resist is inaccurately exposed in areas that are close to those that the electron beam is targeting due to the electrons that are dispersed within the resist and from the substrate. This collapse of the PMMA structures after their development, as well as the lack of definition of the walls, led to an improvement in the optimization process of this work. The final procedure is sketched in Figure 1b.

To address these initial collapse problems more effectively, we combined two strategies. First, a thin chromium layer (typically of 7 nm) was deposited directly on top of the bare Si, which avoids the majority of undesired electron backscattering [52,53,54]. Directly using the PMMA layer as a mask, without an additional chromium layer for silicon etching, affects the resulting patterns and leads to roughness and undulation in the side walls (as shown in Figure A2 in the Appendix B). Secondly, novel structures containing element fragmentation and reinforcing structures were designed and implemented, alongside different doses for the lithography. These were applied to different regions of the pattern, allowing for better control and the optimization of scan directions [55]. Chromium is widely used as a hard mask material for plasma etching for a number of reasons; it is known for its ease of deposition through physical vapor deposition methods, the etching can easily be removed, and it has a low atomic mass, making it easier to image pre-patterned metal structures for alignment purposes. Moreover, it is also an effective hard masking material for dry etching, as it exhibits high sputter resistance and selectivity in fluorine and bromine chemistries [56,57]. These advantages allow for chromium to serve as an etching mask for various materials, including silicon, SiO₂, ZnO, Si₃N₄, TiO₂, MoSi, and GaAs [58].

The effect of the Cr layer is immediately observed. Figure 2a displays a concentric PMMA mask for the generation of FZP without the previously deposited Cr on top of the bare Si, showing a large portion of undesired, overexposed (and hence collapsed) areas throughout the whole structure where the pattern was harmed by the excessive clearance of PMMA. The observed overexposure is directly linked to the electron dose that is applied; in this case, a uniform dose of 100 $\mathsf{\mu }$C·cm⁻² was administered across the entire mask, from the center to the edges. As shown in the zoomed-in section of Figure 2a, the central region exhibits signs of overexposure. On the other hand, Figure 2b presents the final patterned resist mask using the same initial CAD design and the same dose of 100 $\mathsf{\mu }$C·cm⁻², with a previous Cr layer showcasing a much-improved final structure without any distinguishable damaged areas. The improvement was most evident in the zoomed-in area of Figure 2b, where collapse is absent and the overexposure has been eliminated. The metal coating serves two purposes, i.e., it eliminates the charge buildup that occurs during EBL and allows for a more precise beam-focusing without obstructing the patterning process and, secondly, it facilitates the better adherence of the PMMA [59,60].

The four different CAD geometries developed in this work are displayed in Figure 3a–d, with their already developed PMMA counterparts shown in panels Figure 3e–h, respectively. Firstly, from the common stem of the concentric-like shape, we added 72 radial lines with a spacing of five degrees, which helped to ease the majority of the overexposure at the outermost regions, as shown in Figure 3b. This was translated onto a final PMMA mask in Figure 3f. Figure 3c shows an evolution of the design shown in Figure 3c, where not all 72 lines start from the first radial structure but commence at different distances from the origin, alleviating the undesired overstructure that occurs close to the center. This design still provokes collapse and causes stress to the final PMMA mask next to the edges, as shown in Figure 3g. Finally, Figure 3d displays the final CAD design where the majority of the external concentric rings are interrupted in the vicinity of the radius. Different doses of electron beam exposure were applied to different parts of the pattern, allowing for better control and the optimization of scan directions [55]. Three different dosages were employed in the four CAD designs (Figure 3): 200 $\mathsf{\mu }$C·cm⁻², 170 $\mathsf{\mu }$C·cm⁻², and 185 $\mathsf{\mu }$C·cm⁻². These dosages were used for the middle six rings, the last three rings, and the rings between these groups, respectively. This technique helps mitigate the collapse problem by minimizing the interaction between neighboring patterns and reducing the overall stress on the resist material.

The final optimized PMMA mask for Cr/Si, presented in Figure 3h, shows an overall improvement oin the desired structure, with no traces of overexposure or collapse. These results demonstrate that the strategy of combining the metal coating and element fragmentation was successful in reducing backscattering during EBL exposure. This approach succeeds in minimizing the proximity effects and leads to an efficient optimization of the PMMA mask. A more detailed picture of the produced mask is shown in Figure 4. The optimized CAD design is shown in Figure 4a while an SEM image of the final mask is displayed in Figure 4b, from which a zoomed area, Figure 4c, displays intact and well-defined structures, where no over-etch effects are found.

A detailed examination using the SEM of the produced PMMA structures is fundamental to enhancing the outer zone patterns in order to identify significant pattern collapse, as was observed in the images shown in Figure 5a. This phenomenon was produced due to the presence of residual resist material during the development stage. The constraints imposed by the narrowest separation between patterns hindered the developer’s efficacy. To overcome this challenge and achieve optimization, we employed DESCUM etching techniques. This strategic approach not only facilitated the removal of the persistent resist material but also played a pivotal role in refining the overall pattern morphology.

The DESCUM process serves as a critical step in the integrated circuit manufacturing process, specifically designed to eliminate residual organic residues that persist after the photolithography stages. It consists of a low-temperature, oxygen-based plasma process operating at low power, and is specifically engineered to remove a few hundred targeted angstroms of resist material. This process guarantees a clean and uncontaminated surface, setting the stage for the subsequent critical process steps, including wet and dry etching. By effectively eradicating organic residues, DESCUM improves the overall quality of the structures [61].

The DESCUM process was carried out in the PlasmaPro 100 Estrelas system, (Oxford Instruments Plasma Technology, North End, Yatton, UK) where the specific etching parameters employed in this study included a pressure of 60 mTorr, an RF power of 50 W, O₂ flow set at 50 sccm, and a temperature maintained at 25 °C. The etching duration was optimized at 5 s. DESCUM using oxygen plasma produces radical oxygen species to chemically eliminate the silicon wafer’s resist layer, where oxygen molecules can be broken down by intense electrons in the plasma to produce reactive oxygen atoms; moreover, oxygen plasma ashing produces non-toxic byproducts. In comparison to the wet etching method, it is more ecologically friendly. The findings are displayed in Figure 5b, which displays the precisely defined and narrow patterns of the outermost zone, contrasted with the scenario in which DESSCUM was not used, indicating that the decision to use DESCUM was successful in eliminating the remaining resist, which was challenging to eliminate when using only development. This result shows that the PMMA 2% resist mask is effective and ready for the next step of chromium etching. The strong and controlled DESCUM process sets the stage for a smooth fabrication, guaranteeing the creation of high-quality, well-defined patterns.

2.2. Chromium Mask Fabrication

Once the PMMA mask has been produced, ensuring the high quality of the desired structures, the Cr layer is ready to be etched, and the pattern is ready to be transferred in order to create the final mask (as shown in the schematic in Figure 1b)

To transfer the patterned features of the thin PMMA layer to the underlying material with a Cr mask, we used the Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE) technique [62]. The first chromium etchings were developed at room temperature. To achieve optimal results, a specific gas flow rate comprising 14.7 sccm of Cl₂ and 2 sccm of O₂ was maintained within the chamber. Additionally, the chamber pressure was regulated at 12 mTorr, the ICP power set at 600 W, and the RF power at 8 W. (all other Cr etching recipes tested in this study are depicted in the Appendix B,

Table A1. Parameters for chromium dry etching recipes that were tested in this study.

Parameter	Recipe 1	Recipe 2	Recipe 3	Recipe 4
Pressure (mTorr)	5	100	12	6.5
Rf power (W)	30	50	10	8
ICP power (W)	500	0	1200	600
Cl2 flow (sccm)	20	17.2	45	44
O2 flow (sccm)	20	4	5	6
Temperature (°C)	10	19	50	15

). The duration of the processes varied between 30 and 55 s, ensuring the desired pattern was accurately transferred to the underlayer material. Following the completion of the chromium etching, a thorough cleansing was achieved, utilizing 100 sccm of Argon (Ar) for one minute. This step ensured the removal of any remaining trace materials, resulting in clean and overall well-defined patterns, as depicted in Figure 6, which clearly shows the process of successfully etching away the chromium layer. The zoomed area in (c) depicts some fine pattern details where the structures are well-defined and suited for their use as FZPs. By using the method presented above, the etching rate for chromium was 7.64 nm/min. We were able to completely etch the 7 nm chromium film after 55 s. Regarding the PMMA (with a thickness of 83 nm), the etching rate was 89 nm/min. This indicates that there was a very small amount of PMMA left (about 2 nm) after a 81 nm etch over 55 s, as seen in Figure 6c. An ultra-thin layer of PMMA (around 2 nm thick) remains on top of the Cr mask.

2.3. Silicon Cryogenic Etching

In order to overcome the faulty definition of the outermost zones of the FZP, where nm-size structures are required, we extensively made use of cryo-etching, allowing for the production of clean structures with highly controlled edge shaping. In silicon-based devices, this has been successfully implemented with defined low-roughness side walls [63], generating clean samples with a high aspect ratio [64] in nanometric structures [44].

The cryo-etching was performed using an Inductively Coupled Plasma (ICP) Reactive Ion Etching (RIE) system; specifically, the Oxford Instruments Plasma Pro 100 Cobra (Oxford Instruments Plasma Technology North End, Yatton, UK). This process involved the controlled introduction of sulfur hexafluoride (SF₆) and oxygen (O₂) gases and was executed at extremely low cryogenic temperatures, with the operational temperature maintained below −100 °C [65]. For a comprehensive overview of the typical operational conditions employed in our cryo-etching process, please refer to

Table 2. Typical control values for the silicon reactive ion etching, generating underetched profiles, as shown in Figure 7.

Silicon Reactive Ion Etching
Pressure	10 mTorr
Rf power	4 W
ICP power	1000 W
SF6 flow	60 sccm
O2 flow	8 sccm
Temperature	−110 °C
Time	15 s
etching rate	2.63 µm/nm

. All Si etching recipes tested in this study are shown in the Appendix B,

Table A2. Parameters for silicone cryogenic etching recipes tested in this study.

Parameter	Recipe 1	Recipe 2	Recipe 3
Pressure (mTorr)	10	10	10
Rf power (W)	4	4	4
ICP power (W)	1000	1000	1000
SF6 flow (sccm)	60	60	60
O2 flow (sccm)	10	12	18
Temperature (°C)	−110	−120	−120

Under-etching, the lateral erosion of material beneath a mask during etching, can occur in cryogenic silicon etching. This effect, resulting from lateral etching under the mask, leads to side wall tapering or undercut areas. During cryogenic reactive ion etching (RIE) at low temperatures, the isotropic etching process causes noticeable lateral and undercutting, especially in narrow designs like our lens, with an outer zone width of 50 nm. Strong under-etching can be seen in the structures depicted in Figure 7. This under-etching made the patterns thinner and brittle, which damaged the narrowest lines and led to the bending of the Cr mask. By adjusting the oxygen flow or temperature, we can manipulate the thickness and hardness of the passivation layer (SiO_xF_y). This, in turn, affects the resulting etch profiles and etch rate (see Figure A5 and Figure A6 in the Appendix B). Increasing the oxygen flow or reducing the temperature leads to thicker and harder passivation layers, resulting in positive etch profiles (as displayed in Figure A4 in the Appendix B). Conversely, reducing the oxygen flow or increasing the temperature results in thinner and softer passivation layers, leading to negative etch profiles [66] (again, refer to Appendix B, Figure A3). To this end, we performed a thorough study of the etching rates as a function of temperature and gas flow, as introduced in the Appendix B.

Lowering the wafer temperature to cryogenic levels reduces the volatility of the SF₄ reaction product and enhances the passivisation process [67]. Consequently, etching occurs only in the direction of ion bombardment, resulting in a higher level of anisotropy as the base sustains higher kinetic energy [68]. In this area, the passivation layer is removed, exposing the silicon, and etching proceeds accordingly. We determined that by reducing the etching cryo temperature to −120 °C and increasing the oxygen gas flow to 15 sccm, while maintaining the other parameters as previously specified (see

Table 3. Selected parameters for silicon reactive ion etching, resulting in vertically etched features and precisely defined patterns, as shown in Figure 8.

Silicon Reactive Ion Etching
Pressure	10 mTorr
Rf power	4 W
ICP power	1000 W
SF6 flow	60 sccm
O2 flow	15 sccm
Temperature	−120 °C
Time	2 mn
etching rate	2.25 µm/nm

), we can achieve deeper and steeper trenches, as required for the generation of FZPs.

The resulting vertically well-defined and intact structures are shown in Figure 8, which presents SEM images of the etching profile after a two-minute process, clearly illustrating the well-defined patterns. A standard cleaning process of rinsing in acetone and isopropanol would complete the process by removing the remaining PMMA layer. Keskinbora et al. reported the fabrication of FZPs suited for soft X-ray microscopy with a similar wavelength (1.2 keV), which were able to achieve a spatial resolution in the first order of 61 nm [69]. In those works, trapezoidal-like profiles were obtained via the etching process, which were detrimental for the fluence found in the first order due to the lower lens efficiency provoked by the nonvertical feature profiles and the roughness at the edges [23]. This reduction in the performance of the FZP provokes an increment in the measurement dwell time, which can be overcome using the sharper structures that we fabricated. Moreover, with the correct definition for the outermost vertically well-defined structures obtained via cryo-etching, we are able to increase the lens efficiency [23], overcoming other dry etching methods [70] where a thorough etching was not achieved for the comparable outermost zone widths, which is indispensable for the fabrication of an efficient FZP [71].

Finally, we describe the shadow mask evaporation process, an additional technique used in our study to enhance the etching results. Specifically, we applied the shadow mask method during Fresnel lens fabrication to increase pattern depth. After two minutes of silicon etching, we deposited a gold layer over the lens to protect the existing patterns, allowing for further etching to achieve a greater pattern depth. During the evaporation process, the sample was tilted approximately 30 degrees to target and coat the side walls that were not protected by the chromium mask, thereby enabling further silicon etching. In our e-beam evaporator, the base pressure of the main chamber is normally in the range of ${10}^{-10}$ mbar. The sample is loaded from the load chamber when the pressure reaches a value of ${10}^{-6}$ mbar. Using our Telemark e-beam gun, we applied an acceleration voltage of 8 keV to direct electrons onto the crucible. The gold, pre-melted for optimal evaporation, required a gradual increase in the emission current to prevent material spitting. In our setup, gold begins to evaporate at an emission current of 160–170 mA; however, reaching 220 mA is necessary to achieve a stable deposition rate of 0.1 nm/s. Upon completing the final deposition, we transferred the sample from the main chamber to the load lock and powered down the system. Applying a 20 nm thick gold layer to seal the etched silicon patterns resulted in a significant improvement in the etching process. This enhancement allowed us to create more complex and deeper patterns by extending the etching time beyond 3 min, completely preventing under-etching. As shown in Figure 9, the addition of the gold layer substantially improved the process by protecting the side walls from over-etching. This layer preserved the integrity and shape of the etched patterns, enabling a controlled and precise etching that produced patterns with greater a depth and definition.

3. Conclusions

Our research presents an advanced method for crafting nm-size Fresnel zone plates, combining a precise CAD design with etching at cryogenic temperatures, a technique that surpasses traditional etching methods in terms of the definition of the vertical edges of such structures. We demonstrate that this approach is ideal for producing complex structures with high accuracy. We successfully created a silicon FZP with 100 zones measuring 20 µm in diameter, with an outermost zone of just 50 nm wide and a very high aspect ratio, suitable for direct employment at lower photon energies, as well as a deposition mask for high-Z materials at higher photon energies. Our method combines Electron Beam Lithography for a precise microstructure definition with a chromium mask, ensuring flawless FZP fabrication via cryoetching. Through our refinement of the chromium mask and exploration of different designs, we successfully addressed the issue of pattern collapse. Despite the challenges presented by PMMA resist, we effectively utilized this as a mask for chromium layer etching. By employing cryogenic etching techniques and selecting an optimal processing method, we achieved a silicon etch depth of approximately 4.3 µm, along with well-defined vertical side walls. Additionally, the incorporation of a 20 nm thick gold layer, although complex and time-consuming, provided crucial protection to the outermost regions, enabling the production of high-quality patterns with high aspect ratios. This approach effectively prevents undesired under- or over-etching, making it well-suited for generating nm-scale patterns with low roughness profiles.