Pattern formation in thin polymeric films via electrohydrodynamic patterning

The free surface of a thin polymeric film is often unstable and deforms into various micro-/nano-patterns under an externally applied electric field. This paper reviews a recent patterning technique, electrohydrodynamic patterning (EHDP), a straightforward, cost-effective and contactless bottom-up method. The theoretical and numerical studies of EHDP are shown. How the characteristic wavelength and the characteristic time depend on both the external conditions (such as voltage, film thickness, template-substrate spacing) and the initial polymer properties (such as rheological property, electrical property and surface tension) is theoretically and experimentally discussed. Various possible strategies for fabricating high-aspect-ratio or hierarchical patterns are theoretically and experimentally reviewed. Aligning and ordering of the anisotropic polymers by EHDP is emphasized. A perspective, including novelty and limitations of the methods, particularly in comparison to some conventional patterning techniques, and a possible future direction of research, is presented.

Hongmiao Tian received his PhD degree in mechanical engineering from Xi'an Jiaotong University, Xi'an, China, in 2014. He is currently an Associate Professor with the State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University.
He has authored/ coauthored more than 70 research papers in international journal and conference proceedings and authorized 30 national invention patents. His research interests include bionic manufacturing and so actuators.
even though no long range order, is particularly attractive because the difficulty, time, and cost in designing and making pre-patterned templates limit the exibility and wide application of conventional lithography, especially when large numbers of different patterns are to be fabricated. 48 It is worth noting that a higher value of f (h/H, the ratio of the polymer lm thickness to the template-substrate spacing) leads to a denser packing of the polymer columns and to an enhanced electrostatic repulsion between the equally charged columns, resulting in columns with a perfect hexagonal symmetry and, however, an accelerating coarsening., 15 a lower value of f leads to the suppression of coarsening. 49,50 Hence, the highly ordered arrays of columns only can be obtained in a very narrow f range. 51 In addition, EHDP just need a minimized external force to maintain a proper air gap between the liquid polymer and the template, avoiding a poor geometrical integrity of the duplicated micro-/nano-structure or even to an irreversible damage of the substrate and the template. 52 The diagrammatic sketch of EHDP is shown in Fig. 1. 53 Firstly, a thin lm of the polymer is spin-coated on a conductive substrate (bottom electrode). Then a template (top electrode) is put on the top of the polymer lm, leaving an air gap. Secondly, the assembly is then thermally maintained above the glass transition temperature (T g ) of the polymer, and then an external voltage is applied between the bottom and top electrode. This applied voltage causes a destabilizing electrostatic force due to the mismatch of the dielectric constant or the electrical conductivity between polymer and air. Once the destabilizing electrostatic force overcomes the stabilizing surface tension and the viscous resistance, the at polymer surface will be  destabilized and forced to ow upward to the top electrode. The growth of peaks reduces the air gap between the polymer lm and the template, which strengthens the electrical eld and accelerates the evolution. As the peaks grow, the capillary pressure also increases. Therefore, the competition between destabilizing electrostatic pressure and the stabilizing capillary pressure selects a maximum characteristic wavelength l and a characteristic time s. 48 Finally, the micro-/nano-structure of the polymer will fully contact with the top electrode and then reach a steady state. Aer that, a slow cooling of the assembly to room temperature or UV light cures the micropillars array. In this process, the template can be either featureless (Fig. 1a), 15,17,27 generating an array of periodic pillars, or patterned (Fig. 1b), 15,37,39,41,46,[54][55][56][57][58][59][60][61][62][63][64][65] forming a positive replica of the template.

Theoretical and numerical studies
The overall pressure distribution at the viscous lm surface is where p 0 is the atmospheric pressure, p vdW (h) is the disjoining pressure (arising from dispersive van der Waals interactions), p g (h) is the Laplace pressure (stems from the surface tension g) and p e (h) is the electrostatic pressure. 16 For high enough values of electric eld intensity, only the Laplace and electrostatic terms need to be considered. In a stability analysis, a small sinusoidal perturbation of the interface with wave number q, growth rate u, and amplitude u is considered: h(x, t) ¼ h 0 + ue iqx+tu . The modulation of h gives rise to a lateral pressure gradient inside the lm, inducing a Poiseuille ow j where h is the viscosity of the liquid. A continuity equation enforces mass conservation of the incompressible liquid Eqn (1)-(3) establish a differential equation that describes the dynamic response of the interface to the perturbation. In a linear approximation, a dispersion relation is obtained As opposed to the inviscid, gravity-limited case (u f q), the viscous stresses lead to a q 2 -dependence of u in the longwavelength limit, typical for dissipative systems. Fluctuations are amplied if u > 0. With time, the fastest growing uctuation will eventually dominate When mobile free charge is absent (i.e. perfect dielectric), the characteristic wavelength l and the characteristic time s is and where 3 0 is the dielectric constant of free space, 3 p is the dielectric constant of the polymer lm, g is the surface tension of the polymer lm, U is the applied voltage, h is the thickness of the polymer lm, and H is the template-substrate spacing. When mobile free charge is present (i.e. leaky dielectric), the dielectric constant and a dimensionless conductivity parameter S jointly play roles. The latter represents a ratio of the process time scale to the time for charge conduction (3 g 3 0 /s) Especially, when S [ 1, the characteristic wavelength l and the characteristic time s is and where s is the electrical conductivity of the thin polymer lm. [67][68][69][70] 3 Effect of the external conditions on the pattern formation In continuing the steady development of integrated circuitrelated fabrication, the ability to rapidly pattern polymers into smaller feature size and/or higher aspect ratio in order to realize   wavelength l decreases with the increase in the applied voltage (below 10 V) at a given system, as shown in Fig. 2a. 71 However, the characteristic wavelength l no longer decreases or even increases with the increase in the applied voltage (above 10 V) due to the dielectric breakdown in at least one of the layers. If layers break down, submicrometer features are unlikely, as shown in Fig. 2b. Hence, though theory predicts that changing the external conditions will decrease the characteristic wavelength l to nanoscale level, the limit is set by the dielectric eld strength of the layers. In addition, increasing the pattern growth velocity not only shortens the patterning time but also exhibits enhanced scalability for replicating small and geometrically diverse features. 72 4 Effect of the polymer properties on the pattern formation In EHDP, polymer lm materials have played a critical role, since some limitations in accessing better-performance EHDP, such as higher efficiency, smaller feature size, and greater aspect ratio, are of material origin; moreover, the functionality of the generated EHD patterns is governed by EHD materials owing to the interesting properties these materials can offer.
Hence, the performance of EHDP depends on the comprehensive properties of the polymer lm to a certain extent.

Rheological property
The rheological property of the polymer noticeably governs the characteristic wavelength l and the characteristic time s of EHDP. [23][24][25][26][27][73][74][75] Sharma et al. has systematically studied the role of the viscoelastic property of the polymer lm in the pattern formation of EHDP. 24 The viscoelastic lms behaving like a liquid display long wavelengths governed by applied voltage (or electrostatic pressure) and surface tension, independent of its elastic storage and viscous loss moduli (Fig. 3a(i)); the viscoelastic lms behaving like a solid display wavelengths always scales as $4 Â lm thickness, independent of its surface tension, applied voltage, loss and storage moduli (Fig. 3a(ii)); and the viscoelastic lms behaving in a narrow transition zone between the liquidlike and the solidlike regimes display a wavelength governed by the storage modulus ( Fig. 3a(iii)). It is interesting to note that the viscosity of the polymer lm inuences the characteristic time s of EHDP. This offers an advantage in EHDP for decoupling time by varying the types or the molecular weight of polymers. For example, Dickey et al. showed that the photocurable systems (e.g. thiol vinyl ether,  19 It is worth noting that the rheology property of the polymer is closely related to its temperature. For instance, Cheng et al. showed a faster growth of the surface patterns of polystyrene lm at a higher temperature due to the lower viscosity. 20 However, the molding temperature cannot exceed the decomposition temperature of the polymer in the pattern formation process.

Surface/interface tension
The decrease of the surface/interface tension of the polymer lm is advantageous to fabricating the micro-/nanostructures with a smaller characteristic wavelength l and a shorter characteristic time s. 75,77,79-85 For example, a clear reduction in length scale (2 times) and time scale (50 times) of polyisoprene (PI) lm is observed by substituting the air gap with oligomeric dimethylsiloxane (ODMS) lm, as shown in Fig. 3b. However, there is a trade-off by replacing air with another uid because it may decrease the dielectric contrast difference of the system.     by loading nanoparticles is also limited as the excessive ller loading would result in the increase in the viscosity of the polymer and the undesirable nanoparticle agglomeration in the polymer lm.

Electrical conductivity.
Particularly interesting is the characteristic wavelength l and the characteristic time s that is predicted from leaky dielectric model is smaller than that from the perfect dielectric model. [87][88][89][90][91][92] Lv et al. demonstrated that a leaky dielectric could fulll high-performance EHDP with a featureless template. 32-34 A signicant reduction in the characteristic wavelength l (from 325.6 AE 14.7 mm to 154.5 AE 15.3 mm) and the patterning time (from 5 s to (1 s) are observed, as shown in Fig. 3d. Furthermore, according to the perfect and leaky dielectric model, the theoretical characteristic wavelength l is 368 mm (the perfect dielectric) and 150 mm (the leaky dielectric), respectively, hence, the experimental results herein demonstrate a convincing experimental distinction between the ''perfect'' and ''leaky'' dielectric models in spite of a slight mismatch between the theoretical and experimental values especially from the perfect dielectric model. Moreover, Tian et al. theoretically and experimentally demonstrated that a leaky dielectric could signicantly improve the aspect ratio of the micro-/nano-structures fabricated by EHDP with a structured template compared to a perfect dielectric, as shown in Fig. 3e.
Especially, the conducting polymer (CP), as a leaky dielectric, is a promising material for high-performance EHDP in order to realize devices with enhanced performance or even wholly new properties and then take a more prominent role in their advanced applications such as organic electronic devices, chemical sensors, eld-effect transistors, superhydrophilic/ superhydrophobic surfaces, micro-/nanouidic systems and micro-/nanoelectromechanical systems (MEMS/NEMS). [93][94][95][96][97][98][99] For instance, Rickard et al. fabricated well-dened conductive micro-/nano-structures using the thin conducting polymer (e.g. polypyrrole, poly(3-hexylthiophene), and so on) lms via EHDP, as shown in Fig. 4a-f. [100][101][102] Moreover, they showed the feasibility of the polypyrrole-based structures with a gate length of 700 nm and a pitch of 500 nm for the electrolyte-gated vertical eld-effect transistor (FET) devices, as shown in Fig. 4g-h.

Fabrication of hierarchical structures
To date, several techniques structure a single layer of the polymer. For many applications, however, it is desirable to control the spatial arrangement of more than one component. Morariu et al. describes a replication process where multiple materials with an air gap between the lm and the contactor are processed simultaneously, as shown in Fig. 5a. 103-112 Using a bilayer or trilayer formed by two or three different polymers, EHDP at both polymer surfaces produce a hierarchic lateral structure that exhibits two or three independent characteristic dimensions, as shown in Fig. 5b-e. [103][104][105][106][107][108][109][110][111][112] This approach might provide a simple strategy for large-area, sub-100 nanometre lithography.
EHDP with a featureless template shows the capability to fast and economically create large-scale three-dimensional microscale structures on various kinds of materials. However, conventional EHDP with a featureless template can only fabricate a low-aspect-ratio micro-/nanostructures. Therefore, much research have been devoted to increase the aspect ratio of the micro-/nanostructures. 113,114 For instance, Tian et al. developed a novel EHDP technique, EHDP-prepatterned polymer (PPP), to fabricate a hierarchical micro-/nanostructure with a high aspect ratio, as shown in Fig. 6a. 114 The simulation and experiment showed that EHDP-PPP approach can provide a stronger electric modulation at the same experimental settings, obtaining a hierarchical micro-/nanostructure with a higher aspect ratio compared to EHDP-prepatterned template (PPT), as shown in Fig. 6b. This method can deform various polymers to a mushroom-shaped micropillars with a well-controlled aspect ratio and tip diameter for dry adhesion, nanogenerator, superhydrophilic/superhydrophobic surfaces, microlens arrays, and so on, as shown in Fig. 6c. [115][116][117][118][119][120][121][122][123] Furthermore, to fabricate a hierarchically ordered structure, Tian et al. improved above EHDP-PPP method by substituting the featureless template with a patterned template which feature size is far less than the characteristic wavelength l of the given system, as shown in Fig. 7a and b. The hierarchically ordered structures with primary and secondary patterns for mass-production, such as, micropillar/nanopillar structure, micrograting/micropillar structure, micropillar/micrograting structure, and micrograting/micrograting structure, were fabricated, as shown in Fig. 7c. 124,125 Russel et al. design and utilize the special template patterns to guide pillars into alignment over regions much greater in extent than their natural domain sizes to pattern thin polymer lms via EHDP, as shown in Fig. 8a-c. Regular rows of pillars form under ridges, and ordered triangular arrays are generated within each individual triangular domain bounded by the Fig. 11 CNT-EHDP replicated patterns. Atomic force microscopy height and three-dimensional images and the corresponding crosssections of (a) curly nano-hair (CNH) surfaces, (b) straight nano-hairs (SNH), (c) single-level spikes with rounded edges (S1L), (d) two-levelled spiky cones (S2L), (e) two-tiered heretical spiky cones (S2L2) and (f) hexagonal pillars (HP) replicated from the various imposed CNT-based electrodes. Reproduced with permission. 22 Copyright 2017, Royal Society of Chemistry. Fig. 12 (a) Low-and high-magnification SEM images of the EHDP micro-pillars that contain vertically aligned MWCNTs. (b) SEM images of the EHDP micro-pillars with partial removal of the PS matrix. (c) SEM top-view of the EHDP micro-pillars with partially exposed vertical MWNTs. Inset: SEM images of the EHDP micro-pillars using CNTs which are slightly longer than the pillar height. Reproduced with permission. 128 Copyright 2011, WILEY-VCH. ridges, as shown in Fig. 8d. Moreover, the ordered pattern spanned more than 100 periods (400-500 mm), which is the largest array of ordered pillars from EHDP available in the literature. The ordered pattern had two identied characteristic wavelength: one is the spacing between pillars under the ridges, l 1 ($2.7 mm), and the other is the spacing between pillars within each small triangular array, l 2 ($4.0 mm), as shown in Fig. 8e-h. Li et al. presented an economical method for fabricating a concave microlens arrays (MLAs) with a high quality and high density, as shown in Fig. 9a and b. 44 The curvature of the MLA can be well-controlled by changing the air gap between the template and polymer lm. The MLA has a ll factor calculated as high as up to 93%, as shown in Fig. 9c. Moreover, the MLA has excellent focusing and imaging performances, as shown in Fig. 9d.
Sharma et al. showed that the spatiotemporal modulation of the applied electric eld inuences the pattern morphology in incompletely cross-linked viscoelastic polydimethylsiloxane (PDMS) lms, due to the appearance of secondary and tertiary structures, resulting in hierarchical, multiscale patterns, which can be observed in Fig. 10. 26 Park et al. also investigated secondary electrohydrodynamic instability in polymer lms by controlling the timescale parameter to produce secondary nanosized patterns between the micrometer-sized grooves. 127 Goldberg-Oppenheimer et al. proposed a tunable carbon nanotubes-based electrohydrodynamic patterning (CNT-EHDP) to fabricate unique multiscale structured cones and nanohairlike architectures with various periodicities and dimensions, successfully enabling surface energy minimization, as shown in Fig. 11. 22 By controlling the hierarchy of micro-to nano cones and spikes, these morphologies provide a range of architectures with sufficient roughness for very low wettability, with the highest contact angle achieved of 173 and their properties can be easily switched between lotus-leaf to rose-petal behavior.

Aligning and ordering of the anisotropic polymers
In order to take full advantage of the synergistic functions in carbon nanocomposites and hybrids, control of the dispersion, orientation, and interfacial chemistry of carbon materials in the organic or inorganic matrix is required. Moreover, anisotropic composite structures with vertically aligned carbon materials are essential to realize the full potential of carbon materialsbased composites both for optimization of their mechanical properties and integration into devices. Goldberg-Oppenheimer et al. showed that the EHDP micro-patterns along with the alignment of carbon nanotubes (CNTs) within these patterns can be fabricated for carbon nanotube-polymer nanocomposite lms by EHDP with a featureless template, as shown in Fig. 12a and b. 128 The degree of the carbon nanotube alignment within these patterns can be tuned by adjusting the EHDP parameters. Furthermore, patterned surfaces decorated by CNT brushes can be obtained using either etching techniques or by embedding relatively long nanotubes, as shown in Fig. 12c.
EHDP enables the structure formation of organic crystalline materials on the micrometer length scale while at the same time exerting control over crystal orientation, as shown in Fig. 13. 129 Well-ordered structures with nearly vertical walls, comprising stacks of crystals were shown for both PCL (Fig. 13a and b) and PDHA ( Fig. 13e and f). A set of nested rings have formed in the diffraction plane for both replicated structures of PCL ( Fig. 13c and d) and PDHA ( Fig. 13g and h), indicating polycrystalline samples.
EHDP of a block-copolymer (BCP) lm also gives rise to hierarchical pattern formation with a micrometer-sized polymer pillars and a 10 nm-scaled microphase morphology in one single step, as shown in Fig. 14. [130][131][132] Schematic drawing of the experimental procedure was shown in Fig. 14a. The pattern formation on the micrometer scale of lms with two different molecular weights was shown in Fig. 14c-e. The three different in-plane assemblies schematically was shown in Fig. 14b: onion-type concentric alignment of lamellae (Fig. 14f, arrow), parallel sheets (book sheets) (Fig. 14g) and bent lamellae pointing towards the column mantle ( Fig. 14h and i). Furthermore, Goldberg-Oppenheimer et al. showed a functional block copolymer that contains perylene bismide (PBI) side chains which can crystallize via p-p stacking to form an electron conducting microphase is patterned via EHDP. The patterned lm shows a hierarchical structure with three distinct length scales: micrometer-sized polymer pillars, a 10 nm BCP microphase morphology that is aligned perpendicular to the substrate surface, and a molecular length scale (0.35-3 nm) PBI p-p-stacks traverse the EHDP-generated plugs in a continuous fashion. 133

Conclusions and perspective
The review provides an illustrative commentary about the progress and recent developments on EHDP. The key emphasis of the review has been to theoretically and experimentally discuss how the characteristic wavelength and the characteristic time depend on both the external conditions (such as the applied voltage, lm thickness, template-substrate spacing) and the initial polymer properties (such as rheological property, electrical property and surface tension). We have theoretically and experimentally discussed various possible strategies for fabricating hierarchical patterns by combining the essential concepts of bottom-up and top-down approaches. Furthermore, we have emphasized aligning and ordering of the anisotropic polymers by EHDP. Table 1 shows some conventional patterning methods and their characteristics of the resulting patterned surfaces  including the cause, the pattern, the size range, the novelty and the limitation. Among the conventional patterning methods, photolithography is a pattern-fabricating technique with high resolution and high throughput, but the photolithography tools are rather expensive and the feature size is limited by optical diffraction limit; nanoimprint is a pattern-transferring technique with low cost, high throughput and high resolution, however, nanoimprint typically require a comparatively large external force to press a patterned template mechanically against the substrate, possibly leading to poor geometrical integrity in the duplicated structure or even to irreversible damage of the template and substrate, making multilayer overlay alignment difficult. EHDP also is a pattern-transferring technique with low cost, high throughput and high resolution. Moreover, the most major advantage of EHDP is the capability to fast and economically create large-scale three-dimensional micro-scale structures on various kinds of materials with featureless templates, even though no long range order and no nano-scale features due to the dielectric breakdown. 71 In addition, EHDP just need a minimized external force to maintain a proper air gap between the liquid polymer and the template, avoiding the shortcoming of nanoimprint.
A promising direction of EHDP is the conjugation with other patterning techniques (such as dewetting, nanoimprint, and hot embossing) to fabricate extremely high-aspect-ratio or hierarchical patterns such as, cages, microlens arrays, highaspect-ratio micropillars, mushroom-shaped micropillars with a well-controlled aspect ratio and tip diameter. [134][135][136][137] In addition, an attractive issue in EHDP is to extend its applicability to a larger class of materials. The benet of exploiting new kinds of EHD materials lies in that it provides the possibility to not only improve the performance of EHDP, but also integrate functionality into nal microstructures because of the interesting physical properties these materials can offer. So a promising direction in EHDP will include the structure formation in functional polymers and their various potential applications.

Conflicts of interest
The authors declare no competing nancial interest.