Introduction

Biological three dimensional (3D) hierarchical structures from the compound moth eye (Figure 1A) serve as a multifunctional optical meta-surface (MOMS) that not only performs focusing and broadband, omnidirectional anti-reflection (AR) [1] but also deliver anti-fouling behavior similar to that observed in shark skin (Figure 1B). [2] To reproduce them into synthetic, inorganic devices, many researchers have utilized modern DOI: 10.1002/adma.202504983 nanomanufacturing tools, both nanoscale additive [3][4][5] and forming methods [6,7] with ample success in polymer-based lenses containing MOMS. [8][9][10] While MOMS have been successfully translated into planar inorganic semiconductor wafers (e.g., Si, Ge), which are key IR transparent materials, their integration onto 3D curvilinear substrates such as lenses is severely limited due to the lack of compatible, parallel, and scalable techniques to fabricate them. [11] If possible, MOMS monolithically integrated onto IR lenses (Figure 1C) could solve several issues associated with commercial AR coatings for harsh environments (e.g., space exploration), such as thermal degradation and image distortion due to coefficient of thermal expansion mismatch in ceramic coatings [12,13] meanwhile providing desired functions such as regolith dust anti-fouling on the Moon or Mars [14][15][16][17] for its long-term exploration and human inhabitation, or self-cleaning functionality in night vision military goggles.

3D parallel lithographical methods for polymeric resins and micromachining processes can be combined to etch 3D microscale geometries into planar inorganic wafers. [18] Due to the incompatibility of planar masks used in lithography to non-planar substrates, conformal lithography approaches were invented to pattern onto curvilinear surfaces (e.g., lenses) such as microcontact printing, [19,20] detachment lithography, [21] or nanoimprint lithography. [22,23] Although these processes have worked well with formable materials such as plastics, glasses, and ceramic particles, [23] they remain incompatible with inorganic crystalline semiconductors that are brittle and not formable. However, when nanoimprint is combined with micromachining processes such as deep-reactive ion etching, not only it is plagued by its traditional limitations such as (i) limited control of the etch selectivity of the mask and (ii) the aspect ratio-dependent etch rate, both of which result in-depth spatial inaccuracies and limit the 3D shape patternability, [24,25] but also by (iii) pattern distortions associated with the misorientation of the incident directional ion flux relative to the normal vector of the surface of curvilinear substrates resulting in spatially varying etch rates and depths. [11,26] Metal-assisted electrochemical nanoimprinting (Mac-Imprint) is an established contact-based catalytic wet etching method [27][28][29][30] capable of micromachining 3D hierarchical patterns (i.e., 10 nm -100 μm) in pre-patterned silicon wafers with sub-10 nm roughness. It works by catalyzing the selective dissolution of silicon at the contact points between itself and catalyst-coated rigid stamps in the presence of an etching solution. [31] In this work, a new generation of conductive, stretchable, and chemically stable composite stamps based on gold-coated porous polyvinylidene fluoride (PVDF) is introduced to enable a conformal format of Mac-Imprint for non-planar substrates (Figure 1D). This is achieved by synthesizing patterned nanoporous PVDF via lithographically templated thermally induced phase separation (lt-TIPS) (Figure S2, Supporting Information), which serves as electrolyte storage, patterned media, and flexible stamp. Next, patterned PVDF membranes are coated in gold and laminated with a solid polyimide film for integration with pneumatic actuation during Mac-imprint for patterning both flat and curved silicon substrates (Figure S1, Supporting Information). The next paragraphs present an evolution of rational materials selection for Mac-Imprint stamps contextualized to prior work that culminates with the demonstration of patterning of hierarchical microscale sharklet patterns onto a silicon lens (Figure 1E,F).

Results And Discussion

Proof of Concept. Plate-to-Plate Mac-Imprint

In the "first generation" of stamps developed for Mac-Imprint of silicon, the enabling mechanism is the diffusion path created through a network of nanopores embedded in the thinfilm catalyst [29,32] that allowed for uniform patterning of 3D microscale features with high-fidelity (i.e., sub-22 nm shape deviations) over features as wide as tens of microns while imprinting the catalyst's pore morphology into the substrate. This demonstration highlighted Mac-Imprint's ability to, in a single step, deterministically pattern hierarchical structures whose width spans ≈3 orders of magnitude. Suppression of the catalyst's pore size via dealloying in far-from-equilibrium conditions to within an order of magnitude of the Debye Length (i.e., 0.9 nm) yielded roughness reduction down to sub-10 nm, comparable to that generated by deep-reactive ion etching and fine periodic structures as small as 220 nm, opening up applications for designer rib waveguides. [33] However, the first generation required embedded gaps in substrates or stamps in the order of 100′s of micrometers to store solution (e.g., pre-etched pillars) since neither the substrate nor the stamp was porous and could offer ample solution storage, which limited etching depths to sub-1 μm. [32,33] To overcome this limitation, this work draws inspiration from literature in water filtration, [34] and proposes to use goldcoated porous PVDF commercial membranes as a new class (i.e., 2 nd generation) of HF-resistant stamps for Mac-Imprint, which not only provides diffusional pathways but also stores reactants within its millimeter-scale thickness at the vicinity of the metal-silicon interface (Figure 2A), expanding Mac-Imprint to chip-and, potentially, wafer-scales (Figure 2B; Figure S3, Supporting Information). This approach possesses two key challenges. First, its patterning capabilities are restricted to randomly textured Si surfaces (Figure 2C) that represent the inverse morphology of the membrane's pores (Figure 2D). Through engineering the membrane's pore morphology during its synthesis via phase inversion, [34] it can be tailored to design monolithically integrated surfaces with hydrophobicity (Figure 2F) for selfcleaning and anti-fouling applications [35,36] and broadband omnidirectional anti-reflection (Figure 2G) for infrared optics. [1,37] The results in Figure 2G represent an improvement in reflection of ≈50% in the visible range compared to a bare polished wafer, but fall short of the performance of leading nanoengineered surfaces [38] due to its unoptimized geometry of the imprinted structures. Second, most of these membranes are made from high-throughput roll-to-roll processes and possess macroscopic imperfections such as scratch marks, spatial variations of the pore sizes and limited flatness (Figure S4, Supporting Information) that are deterministically transferred onto Si (e.g., dark marks on Figure 2B).

To overcome these limitations, lithography-grade patternable porous membranes are synthesized by the lithographically templated thermally induced phase separation (lt-TIPS) as a 3 rd generation of Mac-Imprint stamps (Figure 2H). Among a short list of processes for patterning nanoporous polymers [39] including phase inversion micro-molding (PSμM) and nanoimprinting lithography (NIL), the lt-TIPS was selected due to its unique capability of minimizing defect formation resulting from the spatial confinement during phase separation and maintaining a uniform and narrow pore size distribution. More importantly, lt-TIPS has been experimentally demonstrated to be compatible with micromolding, allowing for high-fidelity shaping of mesoscale geometries (i.e., sharklet pattern) in porous polymers (Figure 2K) from a lithography-grade micromachined hard master mold. [40] Its hierarchical feature sizes -i.e., approximately 30 μm, 4 μm, 1.5 μm and 200 nm corresponding to the sharklet pattern period, its grating period, spacing and pore morphology, respectively -were successfully Mac-Imprinted deterministically over the entire contact area (Figure 2I) with no observable loss of nanometric detail (Figure 2J) owning to the short Debye length of the electrolyte. [33] Similar to prior work in Mac-Imprint with nanoporous gold catalysts, [29,32,33] the stamp's pore size limits the smallest lateral feature size that can be imprinted as well as its line-edge roughness (Figure 2J).

Albeit not optimized, the imprinted hierarchical sharklet pattern possesses broadband anti-reflection in the mid-IR range (Figure 2N) owing to the sub-and near-wavelength geometries reducing backward light scattering. [1] The monolithic nature of Mac-Imprinted AR surfaces makes it a great candidate for enhancing thermal imaging in extreme environments, particularly in space exploration, since it overcomes (i) the environmental and thermal degradation associated with ceramic-based coatings [13] and (ii) the thermal-induced stress and distortions associated with ceramic-based coatings owing to their mismatch in the coefficient of thermal expansion. [12] In fact, if higher aspect ratio surfaces could be Mac-Imprinted in the future, it is possible its performance in terms of broadband and omnidirectional antireflectivity would be comparable to or better than traditional interferometric coatings as was demonstrated in prior literature on silicon nanowires and nanocones. [38,41] Note that the aspect ra-tio in Mac-Imprint, as well as in other nanoimprint technologies, is limited by the large contact surface area and adhesion between stamp and substrate, which results in demolding issues (e.g., delamination and degradation of the catalyst). [42] In the future, advancements in patterning technologies for nanoporous polymers with reduced pore size and feature dimensions could expand the application of the 3 rd generation of Mac-Imprint stamps to more complex geometries and toward shorter operating wavelengths [15] in the visible [43] and X-ray [44] spectrum. It should be noted that the relatively high total hemispherical reflectance of Si textured with random tips and sharklet pattern (i.e., 35% and 27% in the near IR range, respectively) is partially attributed to the IR light reflected from the un-patterned back side of Si chip. This observation suggests that for efficient reflection suppression, both the front and back sides of the Si have to be patterned. A similar concept has been demonstrated on polymer AR coatings by Raut et al. [45]

Conformal Electrochemical Nanoimprinting

The elastic properties of thin, porous membranes, such as low Young's modulus (330 MPa) and their extended elastic limit, allow them to achieve mechanical flexibility, and limited stretchability (up to 2% strain). When coated with a conformal gold catalyst thin-film layer with sub-80 nm thickness, the membrane remains flexible and stretchable because the gold coating is so thin that its 3D morphology is allowed to flex, mimicking materials used in stretchable electronics. [46] In Mac-Imprint, these mechanical characteristics are now exploited to create stamps that can conform to both flat and curvilinear silicon substrates, which is a new capability for Mac-Imprint. This is achieved by laminating them with a solid polyimide (PI) film and applying hydrostatic pressure on its back to inflate the laminate composite against the curvilinear surface of a silicon substrate (Figure S7, Supporting Information), which mimics the stamp's actuation strategy of modern NIL equipment. [47,48] When immersed in the electrolyte, the gold-coated membrane micromachines the silicon surface while in a bi-axial state of stress (Figure 3D). This configuration overcomes key limitations of plate-to-plate Mac-Imprint [49] such as (i) the tip-and-tilt misalignment which leads to uneven etching and (ii) pressure non-uniformity which leads to stress concentrations and catalyst delamination (Figure S8, Supporting Information). To test the stretchability limit of the laminate composite in a bi-axial state of stress (Figure 3B), the catalysts with different thicknesses (i.e., 20, 80, 320, and 3000 nm) were deposited through a 3 mm wide shadow mask to form a line through the center of the membrane (Figure 3A). The electrical conductance across it was measured as a function of catalyst layer thickness and applied hydrostatic pressure (Figure 3C). All gold-coated laminated stamp composites withstand up to 20 psi of back pressure without the break of electrical contact, except for the sample with the catalyst thickness of 20 nm, which failed at 17 psi (Figure 3C, black dots). In all Mac-Imprint experiments performed in this study, pressures of less than 2 psi were applied to guarantee that the stamp did not yield or fracture.

The longevity and robustness of Mac-Imprint's pattern transfer quality and uniformity depend on the mechanical durability of composite stamps, which can be achieved through operating within their elastic limits. A mechanical finite-element model (FEA) was developed to analyze the elastic deformation of the stamp (Figure 3H) and its clamping unit (i.e., polytetrafluoroethylene top, o-ring, silicon substrate, and metal base, Figure S12, Supporting Information). The FEA model incorporated nonlinear elastic constants (Neo-Hookean model) for the rubber oring, its compression level during assembly, Young's modulus, and Poisson's ratio extracted from uniaxial tensile testing (Figure S14, Supporting Information), and the stamp's initial strain induced during its attachment to the imprinting set-up. The model was experimentally validated by measuring as a function of applied pressure (i) the membrane's free maximum vertical center deflection as a function of pressure (Figure S13, Supporting Information and related discussion) and (ii) the induced bi-axial strain distribution in the stamp as it makes contact with the substrate (Figure 3J) via digital image correlation (DIC) (Figure 3I). The FEA model predicted the deformations of these two experiments without a single fitting parameter (Figure S15, Supporting Information) and found the existence of stress concentrations in the top surface of the stamp near its contact area with the o-ring (Figure 3L). At applied pressures of 0.4-1.6 psi, the strain levels experienced by the porous PVDF stamp are below 0.2%, which translates to minimal distortion of its pitch (see pitch distortion analysis in Figure S5, Supporting Information) and reduction of damages to the stamp during an imprint operation. Note that the stiffness change to the stamp due to the deposition of the thin catalyst is neglected. The stamp, composed of a ≈50 μm thick PI and a ≈100 μm thick PVDF layer exhibits plastic deformation at the stress concentration areas (Figure 3L) when subjected to hydrostatic pressures exceeding 2 psi. All experiments were conducted within the operational limits predicted by the computational model to prevent plastic deformation. The plano-convex Si lens with a 36.4 mm radius of curvature was numerically modeled and simulated (Figure 3M). The simulation predicts a contact area covering ≈40% of the lens surface (Figure 3K), which aligns closely with experimental results (Figure 1E). Lastly, this validated model can in the future be used for inverse design of stamps (Figure 3L) and, thus, account for deformations inherent to Mac-Imprint.

Unlike previous plate-to-plate Mac-Imprint systems that use rigid and stiff materials, [32,49] the membrane-to-plate system uses flexible and softer stamp materials, which eliminate regions of stress concentrations between the stamp and substrate known to plastically deform and damage the catalyst layer and stamp. At low strain and pressure levels (i.e., <0.2% and <1.6 psi, respectively), no damage is observed in the stamp or catalyst after an imprint operation (Figure S9A-C, Supporting Information). On the silicon substrate, there is no evidence of catalyst detachment of any kind. That being said, the low applied strain during imprinting does not solve damages to the stamp associated with its retraction and demolding after the imprinting operation is completed and, in instances when the stamp is retracted quickly from the mac-imprinted substrate or pressures in excess of 10 psi are applied, the stamp can be permanently damaged and fractured due to its high-surface area contact and strong adhesion with the substrate (Figure S9D-F, Supporting Information). It is worth noting that demolding issues are not new in nanoimprinting literature, and that, in the Mac-Imprint case, it is likely exacerbated for highaspect ratio features, which would scale up the contact surface area and adhesion. After prolonged exposure to concentrated hydrofluoric acid, it is expected that the porous PVDF would eventually deteriorate, although its associated timescale is unknown.

While thicker catalysts can withstand higher operational pressures during Mac-Imprint, their thickness cannot exceed half the pore size of the membrane, as it will clog them and no longer be able to support solution diffusion. Thus, to evaluate its mass transport, a two-electrode electrochemical set-up for anodizing a silicon wafer was created, and the gold-coated membrane was placed as a "separator" between the counter electrode (i.e., Pt coil) and the working electrode (i.e., Silicon wafer), creating a top and bottom reservoir as illustrated on Figure 3E. At first, a baseline current density with a fully blocking separator (i.e., a copper foil) was measured at a fixed voltage applied between counter and working electrodes (Figure 3G, green). The observed non-zero current density is explained by the Cu foil acting as a bipolar electrode, which can support redox reactions in its extremities [50] and thus allow for the charge transfer between the top and bottom reservoirs of the cell without actual mass transport through it. At the same applied voltage, the current density for the membrane with the highest catalyst thickness of 3000 nm was approximately equal to that of the baseline (Figure 3G, blue) suggesting a lack of mass-transport through the membrane (Figure 3F), which is in agreement with completely clogged pores confirmed by SEM (Figure S16, Supporting Information). With the decrease of the catalyst thickness, the pores are no longer clogged (Figure S16, Supporting Information), which allows for the ionic mass-transport between the top and bottom reservoirs of the cell and leads to an increase in the amplitude of the current density (Figure 3G, red and black).

Similarly to the classical nanoimprint lithography with flexible stamps, conformal Mac-Imprint can be applied to non-planar surfaces (Figure 1D), which was exploited for the first time to micromachine a sharklet pattern onto the surface of a planoconvex Si lens (Figure 1E) with the radius of curvature of 36.4 mm (Figure 1E -inset). The photograph of the lens demonstrates uni-form patterning of its central portion with an area coverage of 40% and strong light diffraction (i.e., rainbow coloration along the reflected light beams) (Figure S17, Supporting Information).

Conclusion

Electrochemical nanoimprinting of silicon lenses is achieved via engineered composite stamps made of gold-coated stretchable porous PVDF polymers that can be inflated and conformed to a curved surface while supporting ionic storage and transport for large-area patterning. As a demonstration, the surfaces of planoconvex Si lenses were directly micromachining with 3D corrugated sharklet pattern with feature sizes spanning more than two orders of magnitude and individual details as small as sub-20 nm, yielding multi-functional optical components with demonstrated anti-reflectivity and hydrophobicity, thus paving the way toward advanced infrared optics and its applications in harsh environments.

Experimental Section

Substrate Preparation: Mac-Imprint of plane substrates was performed onto boron-doped Si wafers with 1-10 Ω•cm resistivity and (100) crystal orientation. Si wafers were prime grade and purchased from Uni-versityWafer. Mac-Imprint of curvilinear substrate was performed on an undoped plano-convex Si lens with a radius of curvature of 36.4 mm. Uncoated Si lenses were purchased from ThorLabs. Prior to Mac-Imprint, substrates were thoroughly rinsed with acetone, isopropyl alcohol, and deionized (DI) water, followed by RCA-1 cleaning and another DI water rinsing before Mac-Imprint.

Stamp Preparation: Mac-Imprint stamps were fabricated out of porous PVDF membranes (both commercial flat and TIPS patterned) with an average pore size of 1 μm. The details of the TIPS patterning protocol were described elsewhere. [40] At the start of the TIPS membrane fabrication process, a mold made of polyethylene terephthalate (PET) with the sharklet-patterned template was acquired commercially from sharklet Technologies Inc. (product name: "SharkShield"). To ensure identical pattern replication from the original PET template to the PVDF membrane, the negative sharklet patterns were first transferred onto a polydimethylsiloxane (PDMS) mold (positive sharklet) through a casting and molding process. PDMS was picked as the mold for patterning PVDF membranes because it tolerates the high temperature needed for the membrane fabrication. Subsequently, the high-temperature lt-TIPS was performed on the positive sharklet-patterned PDMS mold, which promoted the transfer of the sharklet patterns to the PVDF membrane (negative sharklet) through a soft lithography process. The entire patterning process was schematically illustrated in Figure S2, Supporting Information) to better depict the steps involved in the sharklet patterns transfer.

For the plate-to-plate Mac-Imprint PVDF membranes were first thoroughly rinsed with isopropyl alcohol and DI water, followed by drying with compressed clean dry air. After drying, membranes were placed inside the NSC-3000 magnetron sputter chamber at 20 cm distance from the Cr and Au targets and coated with 20 nm Cr adhesion and 80 nm Au catalytic layers. Then Au-coated PVDF membranes were cut into square pieces and attached to the equally sized Si chips using double-sided Kapton tape. The photographs of the stamps were demonstrated on the insets of Figure 2B-I.

For the conformal Mac-Imprint, the membrane cleaning and drying were the same. After drying, membranes were placed inside the NSC-3000 magnetron sputter chamber at 20 cm distance from the Cr and Au targets and subsequently coated with 20 nm Cr adhesion and 80 nm Au catalytic layers through the circular shadow mask with 15 mm diameter opening. This step was done in order to minimize the catalyst surface area and prevent substrate porosification. [32] Then Au-coated PVDF membranes were cut into circular pieces and laminated onto polyimide (PI) film to fit into the Mac-Imprint Teflon cell. The photograph of the PVDF membrane with shadow-sputtered central area was presented in Figure 3D.

Mac-Imprint Setup and Conditions: The plate-to-plate Mac-Imprint setup was composed of an electrochemical cell holding Si substrate and etching solution, a PTFE rod holding Mac-Imprint stamp, a motorized linear stage bringing the stamp in parallel contact with Si, and a load cell measuring the forces developed upon contact. The detailed description of the Mac-Imprint set-up, protocol, and critical steps (i.e., alignment between stamp and substrate) can be found elsewhere. [33,51] The conformal Mac-Imprint set-up was composed of an electrochemical cell holding flexible Mac-Imprint stamp and etching solution, a PTFE rod holding Si substrate, a motorized linear stage bringing Si substrate in close proximity with the stamp, an electronic pressure regulator applying air pressure to the back of the stamps to achieve conformal contact with Si substrate and a load cell measuring the forces developed upon contact (Figure S7, Supporting Information).

The schematics of electrochemical cell for conformal Mac-Imprint was presented on Figure S7A (Supporting Information). It consists of a stainless-steel base and PTFE top. Flexible Mac-Imprint stamp was clamped between the base and the upper part of the electrochemical cell using a stainless steel washer and bolts. The chemically stable Aflas o-ring was placed between the stamp and PTFE top to prevent etching solution leakage outside the cell. The PI film of the flexible stamp was used to prevent etching solution leakage through the porous PVDF into the base of the cell. The base has a chamber, connected to the electronic pressure regulator through a PVC hose.

The demonstration of conformal Mac-Imprint was presented on Figure S7B (Supporting Information). Here, Si substrate was connected to the PTFE rod, which was backed by a load cell and attached to a vertical stepper motor stage. The substrate was brought into to close proximity with the stamp (gap ≈ 200 μm) upon which the air pressure was applied immediately. At the end of the imprinting process, air pressure was reduced to 0 psi, and the substrate was brought away from the stamp. The contact forces were maintained below 1.5 lbf. The contact duration was varied from 5 to 30 min. Note that the electrochemical cell on Figure S7B (Supporting Information) was missing the PTFE top part, which was intentionally removed to capture the conformal contact between the flexible stamp and Si substrate upon Mac-Imprint in dry conditions.

The etching solution with 𝜌 equal to 95% is prepared by mixing HF (48% by vol.) and H 2 O 2 (30% by vol.) in a 6.5:1 ratio (HF: H 2 O 2 by vol.). Moreover, pure ethanol was added to the etching solution (11% of the etching solution volume) in order to improve the solution's wettability. A fresh etching solution was mixed prior to every Mac-Imprint operation. The etching solution was poured into the electrochemical cell to cover the porous PVDF stamps and let the latter absorb it for 2 min prior to Mac-Imprint. All chemicals were ACS grade, purchased from Sigma-Aldrich.

Numerical Modeling: The finite element method (FEM) was employed to model the mechanical behavior of the conformal Mac-Imprint setup using static structural in commercial ANSYS software. Due to it's axisymmetric nature, a half-symmetric 2D' geometry system was modelled, which consisted of a PTFE top part, rubber O-ring, two-layered composite stamp (PVDF and PI) and metal base. The final step of the simulation with compressed o-ring and inflated composite stamp was captured on Figure S12 (Supporting Information). The geometries of the system components were created using SolidWorks software, and subsequently imported as STP files into ANSYS design modeler (version 2021) for assembly and analysis. Frictional contact behavior (i.e., contact and target bodies can slide tangentially and separate perpendicularly to the contact interface) with a coefficient of 0.2 was assumed for O-ring -PTFE, O-ring -PVDF, and porous PVDF -polyimide surface-to-surface contact interface. Boundary conditions were sequentially applied to mimic the Mac-Imprint experimental test procedure, and pressure load was applied incrementally. The model underwent discretization, utilizing quadratic quadrilateral shape functions for each degree of freedom, and was solved employing the Newton-Raphson method. Discussion of the simulation results was provided in the Supplementary Text.

Extraction of Materials Constants:

The mechanical finite element model used several material constants such as Young's modulus (E), Poisson's ratio (μ) and yield strength (𝜎 y ), which were extracted via uniaxial tensile testing using ASTM D882 standard at the constant strain rate averaged over 5 measurements.

Membrane Permeability Test: The membrane permeability test was performed in a two-electrode electrochemical cell setup using potentiostatic mode. The platinum coil electrode (99.95% purity) was used as a cathode while a highly-doped Si wafer (n-type, (100), 0.0025-0.005 Ω•cm) was used as an anode. Constant voltage of 1 V was applied between them with respect to the open circuit potential, which within 10 min stabilized at -0.82 V. The voltage was controlled by a BioLogic SP-300 potentiostat.

Morphological, Structural, and Functional Characterization: Morphological properties of the Mac-Imprint stamps and imprinted Si surfaces were characterized by scanning electron microscopy (SEM) using Philips XL-30 FEG SEM and Zeiss Auriga FIB-SEM. Surface topology of Mac-Imprint stamps and imprinted Si surfaces was characterized by optical profilometry using the Witec Alpha 300 RA+ system. The total hemispherical reflectance of the samples was acquired using Perkin Lambda 950 spectrophotometer with a spectral resolution of 5 nm/pixel.