Poisson Effect‐Assisted Replication Lithography for Rapid Fabrication of Three‐Dimensional Microstructures

Demands for micro‐ and nano‐fabrication techniques have been increasing over recent decades due to their foundational importance in fields such as electronics, sensors, displays, biotechnologies, and energy technologies. Still, the rapid and efficient fabrication of complex 3D microstructures has long been a challenge due to the inherent limitations of conventional imprint lithography and the slow fabrication speed of maskless lithography systems using femtosecond lasers. This study introduces a novel lithographic replication method for the rapid replication of intricate 3D microstructures with closed‐loops by leveraging the Poisson effect‐driven lateral deformation of soft molds. Specifically, the suggested technique employs an elastomeric soft mold, engraved with negative cavity parts of the target structure separated by intentional gaps. Lateral deformation of the material allows the separated cavities to assemble for replication of target microstructure and defectless release from the soft mold. In addition to the experimental demonstrations of the proposed method using well‐known materials like polydimethysliloxane (PDMS) for the soft mold and UV‐curable polyurethane acrylate (PUA) for replication, essential considerations such as material selection and master mold design are discussed. The presented method not only broadens the capabilities of imprint lithographic techniques but also holds promise for the large scale, continuous fabrication of complex 3D microstructures.


Introduction
35][36][37][38] Imprint lithography is a particularly efficient method for fabricating micro-and nano-scale surfaces over large quantities and areas. [28,39]By replicating the negative geometry of a mold using polymers with high resolution, micro-and nano-scale surfaces can be fabricated at a relatively rapid pace. [23]Since the fabrication of negative replicas from the mold does not require expensive equipment once the mold has been prepared, the cost efficiency of imprint lithography is highly favorable. [40]When integrated with mass-production techniques such as step-and-flash for larger scale fabrication, and roll-to-roll for continuous fabrication, productivity can be further enhanced to meet industrial-level requirements. [41,42][48] Closed-loop microgeometries present a clear example of a simple structure that cannot be replicated by conventional imprint lithography without risking fractures in either the mold or the replica. [49]onversely, the 2PP-based direct laser writing technique offers a significant advantage in terms of versatility in fabrication geometries.Utilizing femtosecond laser-assisted local polymerization, it permits the fabrication of almost any microgeometry, encompassing even intricate 3D structures.However, there are inherent limitations associated with its operation principle.[52][53] Although the technique is widely employed by researchers given its capacity to fabricate diverse complex microstructures without extensive processes, its applications have largely been confined to laboratory-scale samples.
[56] While there are inherent constraints, replication of certain 3D microgeometries has been successful.These studies suggest the potential for rapid and straightforward replication of 3D microgeometries.Still, incorporating these techniques into general fabrication processes is challenging, primarily because their methods rely on the unpredictable, inconsistent behavior of elastomers such as cracks, membranes, and partially cured precursors.
[64][65] By harnessing the Poisson effect-driven lateral deformation inherent to elastomeric materials, soft molds can be designed to prepare cavities for replication of intricate microstructures without inevitable fractures-a capability that conventional imprint lithography cannot achieve. [66]n this work, we introduce a novel lithographic replication technique for fabrication of 3D microstructures.A fabrication strategy leveraging Poisson effect of elastomeric soft molds is proposed and experimentally investigated.Especially, the replication of microstructures with closed-loop geometries is demonstrated as basic examples using widely adopted materials for conventional soft lithography.The lateral deformation of soft mold induced by normal compressive strain was extensively utilized for preparation of the negative cavity of target structure and subsequently release of the polymerized structures from the mold without fractures.Additionally, theoretical considerations for successful replication and limitations of the proposed technique are discussed.

The Fabrication Strategy, Design Principle, and General Process
The fabrication strategy of the proposed technique in this work is utilizing lateral deformation of the soft mold, which is induced by the normal compressive strain of the elastomeric material.This approach facilitates the replication of complex 3D microgeometries which are challenging, if not impossible, to replicate by conventional imprint lithographic methods, as illustrated in Figure 1.When normal compressive strain is applied to the elastomeric soft mold containing vertical gaps at specific intervals, lateral expansive deformation of the material occurs, effectively closing the gap.With parts of the target structure's negative cavity engraved on each of the split walls, this gap closure allows separated cavity parts to assemble and form a whole cavity of the target structure.With resin for the replication applied on the soft mold, the interface between the bottom plane of the soft mold and the substrate is lubricated during the deformation by the residual resin.Through the lateral expansive deformation induced by normal compressive strain, the resin in between the facing split walls is squeezed out, ensuring only the negative cavity of the target structure remains filled with the resin.In this "closed" state, UV or heat can be applied to polymerize the resin.After the polymerization, removing the normal compression induces reopening of the gaps by restoring the soft mold material to its original position.The reopening of the gaps permits the polymerized microstructure to be released from the soft mold through the openings without fracture.For successful replication, the soft mold should be carefully designed and precisely fabricated so that the negative cavity of the target structure can be precisely prepared as a result of the Poisson effect-driven deformation.Such a soft mold can be fabricated by soft lithographic replication from the 2PP-printed master mold that has the negative geometry of the desired soft mold.
In the designing step of the master mold, various factors including the soft mold material's properties, aspect ratio of the deformable block, and pattern density (number of structures per area) should be thoroughly considered.These factors are integral for achieving the desired deformation of the soft mold and subsequently preparing the target structure's cavity.For instance, the gap distance should be at least wider than the width of the target structure to ensure defectless release from the soft mold.However, an excessive gap distance necessitates extra strain to the soft mold to achieve gap closure.The period of the gap should be sufficiently high to ensure structural stability of each deformable block, but excessive period would result in a lower pattern density.The height of the vertical gap should be high enough to induce the required lateral deformation, but excessive gap height might compromise the structural stability of the deformable block, potentially leading to disruption of the pattern arrangement.Additionally, excessive protrusions on the master mold can cause damage during the demolding of the soft mold.Therefore, the size and angle of the protrusions should be adjusted through stress analysis for the given target structure during the design phase to avoid damage to the soft mold.
Since the deformation of the soft mold for the gap closure requires relatively large strain, ideal candidates for the soft mold material would be hyperelastic materials with nonlinear elastic properties.Accordingly, nonlinear finite element method (FEM) analysis is useful to predict the deformation of the soft mold and design the geometry of the master mold (Figure S1, Supporting Information).The positional error of each boundary node of the soft mold after the deformation can be analytically calculated to adjust the initial node positions.By conducting an iterative compensation method, the specific geometry of the master mold can be analytically determined with a satisfactory level of error.
The designed master mold can be fabricated by using a 2PP 3D printing system.From the master mold, the soft mold can be replicated through conventional soft lithographic replication.After applying the resin for the replication on the soft mold, UV or heat can be applied to polymerize the resin in the assembled cavity while applying proper normal compression for the required stain.After the polymerization, the normal compression can be removed, and the soft mold can be demolded from the substrate to release the cured microstructures.
For the soft mold material, while the selection of specialized materials is not necessarily required since the Poisson effect is a general characteristic of common materials, it is advantageous to use materials with a high Poisson's ratio to maximize the benefit of the Poisson effect.In this regard, hyperelastic elastomers that can replicate submicron features are suitable.In this work, polydimethysliloxane (PDMS) was used as the demonstrative soft mold material for its well-established properties including high Poisson's ratio, wide range of applications, easy accessibility, transparency, and fine replication resolution.As a resin material for the 3D microstructure replication, UV-curable polyurethane acrylate (PUA) was used.

Experimental Demonstrations
For basic experimental demonstrations of the proposed method, the simplest 3D geometries with closed-loops, namely "bipod" and "tripod", were designed as shown in Figure 2a,b.For the defectless release of the bipod structure, the soft mold should facilitate two-way openings, and three-way openings for the tripod structure.To prepare such soft mold, master molds with linear wall structures and hexagonal wall structures were designed for replication of bipod and tripod, respectively.The diameter of both bipod and tripod structure was designed to be 10 μm, thus other parameters such as gap distance, pattern period, and block aspect ratio were designed accordingly to ensure successful replication.From the master mold, the soft mold was prepared by using PDMS and typical soft lithographic procedure.After applying the UV-curable PUA onto the as-prepared PDMS soft mold, UV was irradiated to polymerize the PUA resin within the assembled cavity while the soft mold was pressurized to the required normal strain to close the gap.After the polymerization, the pressure was removed, followed by manual demolding to release the replicated microstructures from the soft mold.
Microscopic and SEM images of the replicated bipod and tripod microstructures are shown in Figure 2c,d.As shown in Figure 3a,b, without the normal strain to the soft mold, residual walls replicated from the open gap remain on the resultant surface.With the normal strain required for the lateral deformation of the soft mold to close the gap, the 3D microstructures were replicated without residual walls.Notably, a seamline is visible on the replicated microstructures, hinting that the structures were replicated from the assembly of multiple cavities.A staircase-like geometry, which successively replicated from the 2PP-fabricated original master mold, is also noticeable.

Theoretical Considerations
To achieve successful replication, proper normal strain is required to induce the intended assembling of the split cavities as shown in Figure 4.That is, normal compressive strain ε ¼ ΔL=L where ΔL and L are change and initial height of a deformable block, respectively, should be large enough so that Poisson effect-induced lateral deformation Δd of a deformable block with initial width d cover the initial gap distance between deformable blocks g 0 .By regarding the soft mold material as incompressible and the shape of a deformable block as simple rectangular, gap distance g s can be described as below, and the target strain ε s at given g 0 and d can be calculated. [64] To more accurately account for the nonlinear elastic behavior of hyperelastic materials and the intricately curved geometry of soft mold, it is beneficial to conduct a nonlinear FEM analysis.As an example, gap distances g f and g s , results of the FEM analysis and the simplified incompressible assumption, respectively, of the soft mold for overlapped bipod pattern is shown in Figure 4b, and the replicated microstructures at various normal strain are shown in Figure 4c.In the case of insufficient normal strain, the resin remaining in between the unclosed gaps is replicated as unwanted residual walls.In the case of excessive normal strain, cavities for the target structures are also deformed, resulting in narrower structures, or even broken structures.For the best result, a normal strain slightly above the analytical target strain is recommended, since it helps squeezing the resin out of the  gaps and ensuring a tight closure while avoiding excessive deformation of the designated cavity.
To ensure the required deformation for assembling the negative cavities of the target structure, it's essential to maintain a uniform pattern arrangement in the soft mold.Thus, preserving the structural stability of the deformable blocks on the soft mold is important to prevent any disruptions to the arrangement.Among different types of structural collapses, lateral collapse or self-mating is the most probable type (Figure S2a, Supporting Information) especially since the deformable blocks should be closely packed with the minimal gap distances.For the sake of simplicity in calculations, if we consider deformable blocks for two-way openings as simple cuboid without curved surfaces, the critical condition to avoid the lateral collapse can be described as where E Ã is defined as Þ, E is the elastic modulus, ν is the Poisson's ratio, and γ is the surface energy of the material, respectively. [67,68]For openings with more than two-ways, regular hexagon, square, and equilateral triangle blocks can be considered since these are only three regular polygons that can tessellate a plane. [69]In cases of simple hexagon, square, triangle deformable blocks for three-way, four-way, six-way openings, respectively, the maximum height L M and the minimum side length d m for the lateral stability are where C is a constant defined from the moment of inertia =16 for triangle, square, hexagon, respectively. [67]The maximum pattern density ρ, that is, the maximum number of replicated structures per area, can be calculated as where N is the number of replicated structures per block, for triangle, square, and hexagon, respectively, A is the area per block, and D and k are geometrical constants as shown in Figure 5a, The ratio between the maximum pattern density of two different regular polygon block α, and β can be described as , which becomes ( 7) The maximum pattern density ratio lies within a range with upper and lower limits determined only by geometric constants.As shown in Figure 5b, the range of the ratio between square and triangle blocks ρ s =ρ t is 2.40 < ρ s =ρ t < 2.60, and 2.31 < ρ h =ρ s < 2.68 is the range for hexagon and square.Thus, at given material and target structure, hexagonal deformable block is better at achieving a denser pattern replication with higher lateral stability than square, and square is better than triangle.
During the deformation, while the bottom part of the deformable block moves parallel to the substrate plane, there is no lateral movement at the top apex of the gap.Since the gap distance should be larger than the diameter of the structure to be released, designing the cavity at a relatively higher part of the gap wall should be avoided, or the diameter of the cavity should be at least equal to the opening of the gap at the same relative height to prevent fractures.
The mechanical deformation of the elastomer, which is the most critical leverage of the proposed method, remains consistent across all dimensional scales.However, since the master mold that requires precise design and fabrication is prepared by using a 2PP 3D printing system, the minimum scale feasibility of the proposed method inevitably depends on the resolution of the 2PP 3D printing system, which is typically in the 100 %200 nm range. [51,70]Although once the master mold is fabricated soft molds and target structures can be easily replicated, inherent limitations of the 2PP 3D printing including slow speed and small fabrication areas remain on the master mold fabrication stage.
Since the elastomeric soft mold is subjected to relatively large strain, mechanical and chemical degradation can accumulate over iterative replications.Employing a two-step UV curing strategy and performing various surface modification methods, such as metal deposition and silanization to lower surface energy and improve durability, has been found beneficial for the reusability and lifespan of the soft mold.However, due to the accumulation of degradation, eventual deformation or damage is inevitable after extensive reuse. [41,71,72]In contrast, the master mold for the preparation of the soft mold can be fabricated using robust material, and repetitively used for soft mold replication with additional surface modification.Since the soft mold can be replicated from the master mold easily, it would be more practical to replace the soft mold after extended use, considering it as an expendable component in the process.
On its very first stage of development, the proposed replication technique may have many more theoretical considerations for successful processes, and limitations due to various aspects including materials properties, devices required for the process, and inevitable intrinsic limitations of the process itself.Still, the benefit of the proposed method features worth further research.For example, research on seamless stitching of micropatterns to prepare large area master mold can be investigated to apply the method to cover larger areas and higher productivity.Also, by investigating the causes of errors that can occur at each stage, including nonlinear deformation prediction through the hyperelastic model, the resolution of 2PP 3D printing, stitching errors, and polymer shrinkage during the replication process, it would be possible to compensate for and optimize these errors, thereby minimizing the occurrence of residues.Applying the method to photolithographically prepared wafer-scale pattern can also be investigated for replication of simple bridge geometries, overhangs, and mushroom-like structures.In addition, the characteristic of the polymerized microstructures being released from the soft mold in multiple directions can reduce the maximum stress applied to the replicated microstructures compared to conventional imprint lithography.Through the application of the same principle of the Poisson effect, replication of non-periodic 3D microstructures via a master mold designed for the specific target structures may also be possible.It can be advantageous for replicating microstructures with a high aspect ratio, which are vulnerable to fracture during the demolding process.

Demonstrative Applications
By extensively leveraging the proposed method considering aforementioned factors, microstructures with even more intricate geometries can be replicated.For example, by incorporating not only planar direction to the surface area of the substrate but also the normal direction, a denser 3D pattern per area can be achieved as shown in Figure 6a,c.Furthermore, interconnected closed-loops of microstructures, such as movable chains, can be replicated by engraving a part of a chain-shaped cavity on the split walls as shown in Figure 6b,d.Here, four-way split deformable blocks were employed to assemble multiple cavities to prepare a part of the target structure.The diameter of the target structure was set to 10 μm, and other parameters are designed accordingly.

Conclusion
In this work, we successfully demonstrated a novel lithographic replication method for rapid fabrication of 3D microstructures, leveraging the lateral deformation of elastomeric soft mold under normal compressive strain.This approach introduces a strategy that utilizes the lateral deformation of elastomeric soft mold under normal compressive strain for the replication of 3D microstructures.In addition to the general design guidelines for successful replication processes, basic and more complex microstructures with closed-loops were fabricated by using the proposed replication method for the demonstration of the feasibility.Also, theoretical and practical considerations and limitations for the successful replication process are further discussed.
Although there are still many limitations, the fabrication method proposed in this work opens the possibility of commercialization of numerous complex 3D microstructures, including microrobots, metamaterials, 3D scaffolds for cell culturing, etc. Applying normal deformation to the soft mold is relatively easy, simple, and does not require expensive additional equipment.0]

Experimental Section
Materials: IP-S photoresin (Nanoscribe GmbH, Germany) was used for the fabrication of the master mold.As soft mold material, polydimethylsiloxane (PDMS, Sylgard 184) was purchased from Dow Corning Co. (USA) and Ecoflex 00-30 was purchased from Smooth-On, Inc. (USA).As UV-curable resin for target microstructure replication, polyurethane acrylate (PUA, MINS-311RM) was provided from Minuta Technology Co., Ltd.(Republic of Korea).Urethane-coated polyethylen terephtalate (PET, I-One Film Co., Republic of Korea) was used as purchased, as a substrate.
Fabrication of the Master Mold: The master mold was fabricated by using 2PP 3D printing system (Photonic Professional GT, Nanoscribe GmbH, Germany).IP-S photoresin and ITO glass substrate were used for the process.After the printing, the master mold was cleaned by immersing it in isopropyl alcohol.The surfaces of the printed master mold went through a passivation process.
Preparation of the Soft Mold: The soft mold was replicated from the prepared master mold.PDMS-type soft mold was prepared by casting Sylgard 184 precursor on the master mold (10:1 base to curing agent mixing ratio), followed by 2 h of thermal curing in a 70 °C oven.For the Ecoflex-type soft mold, mixed precursor with 1:1 part A and B ratio was poured onto the master mold, followed by curing for 4 h at room temperature.Fully cured soft molds were manually demolded from the master mold.
Replication of the 3D Microstructures: Compressed air-driven actuator was prepared and used for the normal compression of the soft mold.A droplet of PUA resin was applied over the patterned surface of the soft mold using a pipette.After applying PUA resin between the soft mold and a PET substrate, the soft mold was pressurized using the actuator, followed by UV irradiation by using UV-LED.After the polymerization of the resin, the pressure was slowly removed, followed by manual demolding.

Figure 1 .
Figure 1.Conceptual schematics of each fabrication step of the Poisson effect-assisted replication lithography.a) Isometric schematic of the master mold and its cross section.b) Isometric schematic of the soft mold replicated from the master mold and its cross section.c) Isometric schematic of the target 3D microstructures with closed-loops and its cross section.d) Schematics depicting deformation of the soft mold and subsequent polymerization for the replication of the target 3D microstructures.

Figure 3 .
Figure 3. SEM images of the replicated microstructures with and without normal compressive strain to the soft mold.a) Bipod and tripod microstructures replicated from the soft mold without normal compressive strain, showing residual walls replicated from the unclosed gaps.b) Bipod and tripod microstructures replicated from the soft mold with the normal compressive strain required for the gap closure.

Figure 2 .
Figure 2. Schematics of each fabrication step of the basic experimental demonstrations and corresponding microscopic images.a,b) Schematics of the master mold, deformable blocks in the soft mold, and the target structures for the replication of the bipod pattern and the tripod pattern, respectively.c,d) SEM and optical microscopic images of the fabricated master mold, soft mold, and replicated 3D microstructures, respectively.

Figure 4 .
Figure 4.The gap distance according to the normal compressive deformation of the soft mold and replication results at various normal strains.a) Schematics of the soft mold before and after the normal compressive deformation required for the replication.b) The gap distance g according to the normal compressive strain ε, showing the simplified incompressible assumption g s and FEM analysis g f , and the corresponding target strain required for the gap closure ε s and ε f .c) Optical microscopic images of the replicated bipod overlap pattern at various normal strain.

Figure 5 .
Figure 5. Cross sections of simplified deformable blocks and the maximum density ratio between different regular polygon tessellations.a) Schematics of cross sections of deformable blocks, showing area per block A (gray-filled area), geometrical constants D and k for equilateral triangle, square, and regular hexagon.b) Maximum pattern density ratio between square and triangle tessellations (red), and hexagon and square (blue) as functions of ðg 5 0 =L 4 Þ 1=3 , showing range of the ratio with lower and upper limits determined only by geometrical constants.

Figure 6 .
Figure 6.Examples of 3D microstructure replication process using the Poisson effect-assisted replication lithography and its results.a,b) Schematics of each fabrication step for overlapped bipod pattern and microchain link, respectively.c,d) SEM and optical microscopic images of each fabrication step for the replication of overlapped bipod pattern and microchain link, respectively.