Elastohydrodynamics of roll-to-roll UV-cure imprint lithography

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Elastohydrodynamics of roll-to-roll UV-cure imprint lithography Andrew Cochrane, Kristianto Tjiptowidjojo, Roger T. Bonnecaze, and Peter Randall Schunk Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b03160 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 20, 2019

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Industrial & Engineering Chemistry Research

Elastohydrodynamics of roll-to-roll UV-cure imprint lithography Andrew Cochrane,∗,† Kristianto Tjiptowidjojo,‡ Roger T. Bonnecaze,¶ and P. Randall Schunk§ †University of New Mexico, Nanoscience and Microsystems Engineering Program, MSC01 1141, 1 University of New Mexico, Albuquerque, NM 87131, United States ‡University of New Mexico, Department of Chemical & Biological Engineering, MSC01 1120, 1 University of New Mexico, Albuquerque, NM 87131, United States ¶University of Texas at Austin, McKetta Department of Chemical Engineering, 200 E Dean Keaton St. Stop C0400, Austin, TX 78712-15989 §Sandia National Laboratoriesab, Advanced Materials Laboratory, 1001 University Blvd SE, Albuquerque, NM 87106 E-mail: [email protected] a

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. b This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Abstract Inextensible cylindrical shell theory and lubrication theory combine into a model for the elastohydrodynamics of a rolling-imprint modality of nanoimprint lithography (NIL). Foil-bearing theory describes the formation of the lubrication gap due to relative motion between a tensioned substrate and a rigid, cylindrical surface. Reproduction of

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the results of foil-bearing theory for both stiff and perfectly-flexible substrates validates this coupled model and reveals a highly predictable region of uniformity that provides low shear stress conditions ideal for UV-cure. These results show theoretical limitations that are used to construct an operating window for predicting rolling-mode NIL process feasibility.

Introduction In nanoimprint lithography (NIL) a template is pressed into a liquid to produce a nanopatterned substrate ready for subsequent processing steps 1 . 2 The patterning step is essential to unlock the benefits of nano-scale phenomena that enhance performance of devices like solar panels, 3 batteries, 4 optical films 5 and certainly many others. Augmenting roll-toroll (R2R) lines with nano-patterning, as in Figure 1a, will enable high-volume production of the nano-enabled materials used in next generation devices. This route to patterning relies on the interaction of hydrodynamic forces exerted by the liquid and the elastic forces exerted by the deformable substrate, an elastohydrodynamic interaction. UV-cure NIL uses photo-active monomers in solution that can quickly fill the nanofeatures in the template during the imprint step. Once the liquid assumes the shape of the template, an ultraviolet light is used to cure the photoresist, changing its phase from liquid to solid. The template is then separated from the solid photoresist resulting in the transfer of the pattern to its negative on the substrate. A residual layer forms between the pattern and the substrate, shown in Figure 1b. If the residual layer thickness (RLT) is thin enough, the pattern can be used as an etch mask for transferring the pattern into the substrate. 6 If a thin layer of active material had been placed on the substrate before patterning, the result would be a patterned layer of that material. 7 In other cases the pattern structure is used as a scaffold in the device, 5 as with the wire-grid polarizer. Using the pattern as a mask for etching or selective surface treatment requires a break-through process to eliminate the residual layer. For processes 2


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(a) Roll-to-roll imprint lithography

(b) Residual layer in imprint lithography

Figure 1: UV-Cure Imprint lithography and the residual layer that use the pattern as an etch mask, the residual layer may be thin enough for breakthrough by the substrate etch, but RLT non-uniformity will result in magnified variation in the substrate etch depth. For processes that use the pattern as a surface treatment mask, an isotropic breakthrough etch may degrade the pattern anywhere the RLT is on the order of the feature size. Non-uniform RLT degrades the yield of a process, in the case of the wire-grid polarizer, RLT non-uniformity could result in undesirable interference structures, affecting the performance of the product. In any case, the manufacturing-scale process designer needs insight into RLT non-uniformity. A mathematical model of the feature-fill regime can help one to understand the role of two-phase fluid mechanics and structural deformation that precede the UV-cure. R2R nanopatterning process refinement will enable economic high-volume manufacture of nanofeatured materials that can be used to accelerate consumer access to nanotechnology 8 . 9 Although the process has been demonstrated to achieve features as small as 4 nm, 10 low yield associated with RLT non-uniformity is a formidable barrier to its implementation. For the consumer electronics market, high-volume manufacturing processes must reliably produce materials with very high uniformity to keep costs down and remain profitable. 11 The challenge of depositing the liquid photoresist at uniform thickness below 100 nm rules out traditional liquid coating techniques like slot-die, gravure and kiss coating that bottom 3



out around 1 micron coat thicknesses. 12 One approach to overcoming this barrier is to use inkjet deposition to gain more fine control of liquid volume, thus creating the process depicted in Figure 2 (differentiated from Figure 1a by the inkjet head), a R2R modality of an NIL method called jet-and-flash imprint lithography (J-FIL) 10 . 13

Figure 2: Roll-to-roll jet-and-flash imprint lithography Due to the high degree of precision necessary to obtain high NIL process yield, models are constructed to predict process outcomes and reduce uncertainty. The fine control of fluid volume in J-FIL comes with the benefit being able to vary the amount of liquid dispensed based on the volume of the features to be filled. Smaller drops enable faster drop merger 14 and since inkjet heads can dispense drops as small as 1 pL, 15 average material thicknesses of 100 nm can be achieved with optimal densities of 10,000 drops per one cm2 . Although inkjet printing provides greater control of fluid placement, the drops are of finite volume and they trap pockets of gas as they merge in the closing gap. For merger of 10,000 drops per square centimeter, the size of the gas pockets is on the order of 100 μm. Reddy 14 and Chauhan 16 used a model to show that smaller inkjet drops are better because large viscous forces in the thin gaps act over the shorter distances between the drops. Figure 2 shows that in the R2R modality of J-FIL, pattern filling and UV-curing will occur as the substrate travels around the rotating imprint roller. In this configuration, the substrate is also a tensioned web. This work focuses on modeling a lubricated segment of

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substrate in order to predict the thickness of a solidified layer of photoresist after it has been cured in the gap between the substrate and the roll. The extent of the roll surface over which the gap is uniform determines the operating window available for photo-cure under minimal shear forces. The magnetic tape reader is analogous to the roller-wrapped-substrate system studied in this work. Tape reader systems consist of stationary read heads with precisely formed depressions that control gap thickness as the tensioned web (tape) is translated past it. 17 The study of these systems began with analysis of what are called prefectly flexible foil bearings in which the bearing material would offer no structural resistance to axial deformation. Blok and vanRossum 18 observed that pressure and thickness of the fluid gap are constant through the length of the bearing, except for the leading and trailing regions. They also derived a scaling law relating the nominal gap thickness, h∗ , to the journal radius, r, fluid viscosity, µ, foil tension per unit width, T , and rotation rate. The scaling prediction was refined by Eshel et al. 19 and experimentally validated by Ma 20 and later by Licht 21 to be ( ∗

h = Kr

6µU T

) 23 (1)

where U is the speed of the foil moving past the stationary journal and K is generally accepted to be 0.643 for perfectly flexible materials. Gross 22 codified much of the work done to understand effects of wrap angle, bending stiffness, inertia and foil width. The work of the magnetic tape reader community emphasizes the dimensionless foil-bearing number, ϵ = 6µU /T , which measures the ratio of viscous forces to tension forces. The study of tape reader systems were focused on cases in which either the read head or the web are stationary with respect to the motion of the other. Subsequent studies of web handling 23 24 have validated the similarity of using the average of roller surface velocity (ua ) and web velocity (ub ) in the foil-bearing number, ϵ = 12µ(ua + ub )/2/T . These expressions are

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equivalent because, U , the speed of one surface moving passed the opposite, stationary surface is double the average velocity, that is 12U /2 = 6U . Studies of the elastohydrodynamics of this nature were also conducted by the coating and conversion community. For kiss coating, film thickness is strongly influenced by conditions at the nip outflow because of the film split in the exit region 25 . 26 Transient substrate roll coating processes are constrained by whatever measures are necessary to avoid instabilities in film formation. 27 In slot-die coating of flexible substrates, 28 film thickness is set by flow rate and substrate speed. However the minimum film thickness achievable is dictated by flow and wetting instabilities. 29 The body of literature regarding coating processes is primarily concerned with the fluid film formation at the coater exit region. Only recently has the idea of attaining thinner films by curing merged drops between substrate and superstrate been investigated and designated Jet and Coat of Thin-films (JCT) by Singhal et al. 30 This idea was explored in the context of coating wafers in a step and repeat mode, but did not address the R2R processes directly. Jain et al. 31 studied the process modality that transfers patterns from a roller template onto a flat, rigid substrate. Their analytical work finds an expression for the time available for UV-cure after transfer, given the drops merge completely during the approach of the rigid template to rigid substrate. Computational solutions to the equations of flow and thin structures provide a basis for design rules concerning forces on a rigid substrate and gap thickness due to merger of drops during imprint. The model developed in this work is used to explore the sensitivity of the gap thickness to various controllable process parameters. Unique contributions of this work include computational determination of effects of bending stiffness, application of foil-bearing theory to R2R NIL processes and a two-phase lubrication model for fluid mechanics in such elastohydrodynamic systems. Predictions of the gap thickness where the photoresist is cured enable inference of the RLT. The model is constructed to assess the gap thickness as a function of processing speed, wrap angle and substrate tension. The model can also be

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adjusted to account for material properties of viscosity and substrate bending stiffness in addition to machine parameters of roller radius and idler position.

Model Development To study the gap thickness in the R2R imprint problem, the equations of flow and structure are solved for the case of a lubrication gap between a tensioned substrate translating synchronously with a rotating roller. The simulation domain shown in Figure 3 consists of three segments, two of which require only the substrate-structure equations, while fluid and structure equations are solved where a lubricated gap exists between the roller and the substrate. The boundary conditions follow from the problem description. The idlers are treated as fixed points. The lubricated segment is bounded at the inflow and outflow by the condition of atmospheric pressure. The top and bottom tangential boundary velocities of the lubricated region are set to be equal.

Figure 3: Problem description diagram For a flexible substrate wrapped around the the NIL pattern roller, gap thickness is governed by the interaction between viscous forces in the fluid and the elastic forces acting through the tensioned substrate. The mechanics of the fluid and solid are modeled by a coupled set of equations that captures the elastohydrodynamics of the system. Since the gap is thin, Reynolds’ lubrication approximation is invoked to reduce the model order 7



for the fluid mechanics. The deformation of the substrate is modeled with of inextensible cylindrical shell theory 32 . 27 The equations are solved using the Galerkin finite-element method with Goma, 33 an open-source, multi-physics software for solving differential equations using finite-element method. The numerical implementation of the model enables computer-based study of gap thickness in rolling imprint modalities. The search for similar results revealed an unexpected link between this work and foil-bearing literature. In the past, the study of foil-bearing theory provided better understanding of systems like magnetic tape readers and high-speed thrust bearings. This paper demonstrates how rolling imprint, UV-cure processes can benefit from the uniform region predicted by foilbearing theory. The region of uniformity is ideal for UV-cure because the fluid is under no/negligible shear stress and, moreover, a uniformly thick gap allows for longer residence time while curing. The model development in this section ties two-phase fluid mechanics to thin-shell structural mechanics, resulting in a coupled, reduced-order model that predicts regions of uniformity comparable to those of foil-bearing theory. The lubrication equations are reformulated with respect to a curvilinear coordinate, s, shown in Figure 4. In NIL flow systems, the gap thickness is much less than the flow

Figure 4: Lubrication domain with the moving mesh representing the reference plane length, h

Elastohydrodynamics of roll-to-roll UV-cure imprint lithography

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