Control of Morphologies and Length Scales in Intensified Dewettingof Electron Beam Modified Polymer Thin Films under a LiquidSolvent MixtureAnkur Verma, Satya Sekhar, Priyanka Sachan, P. Dinesh Sankar Reddy, and Ashutosh Sharma*

Department of Chemical Engineering and DST Unit on Nanosciences, Indian Institute of Technology Kanpur, Kanpur (UP), 208016India

ABSTRACT: We report fabrication of ordered polymericnanodomains and control of their morphology and size by self-organized intensified dewetting of ultrathin polymer filmswhich are selectively exposed to small doses of electron beam(e-beam). Both positive and negative e-beam tone polymersare used to produce variety of highly regular patterns overlarge area (∼mm2) in significantly lesser time as compared toe-beam lithography. Dewetting of selectively exposed thinfilms under a mixture of water and organic solvents enables theinstability to grow much faster and in very confined domains.Patterns ranging from straight and cross channels, array of circular and square holes, aligned nanowires and square grid to thearray of spherical droplets can be fabricated by selection of e-beam exposure patterns and the dewetting conditions. Fabricationof structures with sharp corners and edges becomes possible because of ultralow interfacial tension of polymer in the liquidmixture. Further, the length scale of pattern can be tuned over a wide range which in some case extends from about tenth of thenatural wavelength of instability in dewetting (λm) to 2λm. This is a significant improvement over the dewetting on physico-chemically patterned substrate where alignment of polymer structures is lost when substrate patterns are smaller than half of λm.The dewetting mechanism of e-beam exposed films is proposed as the change in the effective viscosity of e-beam exposed regionthat leads to the faster growth of instabilities in the low viscous regions and results in the formation of regularly alignedstructures. Nonlinear simulations are carried out which show very good agreement with the experimentally obtained patterns.

■ INTRODUCTION

Polymer patterning is a rapidly developing area because of itswidespread technological applications in micro- and optoelec-tronics, optical and protective coatings, adhesives, super-hydrophobic and other engineered surfaces, microfluidics, andmicroreactors.1−8 Traditional methods of polymer patterningare mainly based on top-down approaches such as photo-lithography and imprint lithography. One of the promisingalternatives to these methods is a bottom-up approach of self-organized dewetting. Self-organized microstructures originatingfrom the dewetting of ultrathin films (<100 nm) have beenextensively studied both theoretically and experimentally.Stability, mechanisms, and pathways of dewetting of liquidand polymeric films9−22 above the glass transition temperaturehave been extensively studied. Furthermore, the effect ofvarious destabilizing forces, substrate morphology, andbounding media have also been reported.22−32 Many of thesetheoretical studies have given clues to the experimental studiesand fabrication of various dewetted patterns and nanostruc-tures.33−46 Incorporation of periodic heterogeneities of thesubstrate has been shown to produce aligned dewettingpatterns.47−57 However, there are several major challenges:(1) limitations on the pattern length scale as well as the featuresize; (2) low aspect ratio because of the droplet contact angle inair is too small, and (3) pattern alignment as well as the

fabrication of densely packed structures. Recent developmentsin the self-organized dewetting under a solvent/nonsolventliquid mixture have overcome the first two challenges to a greatextent and pushed down the size limit in the sub-100 nmregime by overcoming the surface tension limitation.58,59 Forthe pattern alignment, reported literature mainly rely on thedirected dewetting with the introduction of physicochemicalheterogeneity on the substrate.33−43 This results in greaterprocess complexity, multi step fabrication protocols and pre/post processing of the substrate. Furthermore, the length scalesof patterns still remain close to the spinodal wavelength andmuch denser patterns cannot be fabricated. We report here amethod which takes advantage of high sensitivity of polymersto electron beam (e-beam) that alters its local viscosity bothways depending upon the polymer’s e-beam tone. Selectiveexposure of e-beam in extremely confined domains andsubsequent dewetting facilitates the formation of severalinteresting and useful morphologies on the course of dewettingand allows the template free fabrication of denser patterns.Nonlinear simulations are presented which incorporate thespatial variation of viscosity to elucidate the mechanisms of

Received: January 6, 2015Revised: March 29, 2015Published: May 7, 2015

Article

pubs.acs.org/Macromolecules

© 2015 American Chemical Society 3318 DOI: 10.1021/acs.macromol.5b00029Macromolecules 2015, 48, 3318−3326

ordered dewetting and pattern formation in the e-beam treatedthin films.Earlier, theoretical works on dewetting9−17 showed that the

dewetting on a homogeneous substrate initiates with theformation of randomly placed holes separated by a meandistance related to the spinodal length scale. The holes growand coalesce to eventually form droplets on the substrate. It isalso known that the mean distance between the holes dependson the initial film thickness (h), interfacial tension between thefilm and bounding medium (γ21) and the destabilizing potential(ϕ):18,19

λ π γ φ= − ∂ ∂h8 /( / )m2 2

21 (1)

Therefore, to reduce λm either γ21 has to be reducedsignificantly or the destabilizing potential has to be intensified.In the recent reports,58,59 both of these have been achieved bycarrying out dewetting under a mixture of water and organicsolvents which reduces the interfacial tension by ∼50 times andswitches the destabilizing field from the weak van der Waalsforce to stronger electrostatic interaction. It results in theminiaturization of dewetting length scale by more than 1 orderof magnitude and significant increase in the equilibrium contactangle of dewetted droplets and thus facilitates the fabrication ofsub-100 nm high aspect ratio dewetted structures.58,59

However, the dewetting on a flat homogeneous surfaceproduces randomly placed droplets, and this limits itsfunctionality in a number of applications.In contrast to the dewetting on a homogeneous substrate

which leads to random microstructures without any long-rangeorder, a number of recent experimental31−44 and theoreti-cal45−55 studies showed that dewetting on chemically andphysically heterogeneous substrates can lead to perfect orderingof microstructures when the periodicity of the substrate patternis nearly equal to the spinodal length scale. For example, thealignment of dewetted structures has been demonstrated by thedirectional rubbing of the film,34 dewetting on a topographicallypatterned substrates,44,59 and dewetting on chemicallypatterned substrates.42 Although these methods describe thefabrication of aligned droplets as a proof of concept but thecomplexity related to the prepatterning of the substrate as wellas the post processing for the selective removal of pre patternlimits the applicability of these methods in many applications. Anumber of detailed reviews on the dewetting of ultrathin filmsexist in the literature.11,19,20,55,56,60

In a recent report, we have proposed a method of direct andtemplate free fabrication of aligned droplets harnessing the highsensitivity of polymers to the extremely low doses of e-beam.61,62 The method is based on the creation of smalldomains of increased viscosity in polystyrene (negative tone)film with the application of selective exposure to e-beam. Thesubsequent dewetting of modified polymer thin film leads tothe formation of regularly spaced droplets by the sequentialdewetting of increasingly viscous domains.61 In present studywe consider both positive and negative tone polymers that haveopposite response to the e-beam exposure in terms of viscositychange and consider a variety of 1-D and 2-D e-beamprepatterns. We explore here the following: (1) the mechanismand the pathways of dewetting for complex e-beam patternswith the help of nonlinear simulations; (2) formation of variousinteresting and useful patterns during the spatiotemporalevolution of dewetting which can be made permanent at anystage; (3) generation of structures with sharp corners and edges

which become possible owing to ultralow interfacial tension ofpolymer in dewetting liquid, and (4) control over theperiodicity of dewetted structures by changing the pitch of e-beam pattern away from the spinodal wavelength.

■ MATERIALS AND METHODSMaterials. Poly(methyl methacrylate) (PMMA) of average

molecular weight (Mw) 996 kg mol−1 (polydispersity Mw/Mn =2.94) and polystyrene (PS) of average molecular weight (Mw) 280 kgmol−1, supplied by Sigma-Aldrich, were used in the experiments. The(100) type silicon wafers (Wafer world) with native oxide layer of <2nm were used as substrates and cleaned by RCA-1 cleaning protocol.63

Thin films were coated on thoroughly cleaned silicon wafers by using0.2−0.6 w/v % polymer solutions in toluene (HPLC grade, MerckChemicals) and spinning at 3000 rpm for 1 min. Thin films wereannealed for 1 h at room temperature and for 6 h at 65 °C with mildvacuum. Film thickness was measured using nulling ellipsometer(Nanofilm EP3). All the materials processing was carried out in class1000 clean room.

E-Beam Exposure. Annealed films were exposed to extremely lowdoses of e-beam using a field emission scanning electron microscope(FESEM, Zeiss Supra 40 VP) and pattern generator (XENOS XeDraw2). Single pixel parallel lines, square array of dots and square gridpatterns are drawn using 10 kV electron beam (beam current ∼250pA). Dwell time is varied from 500 to 5000 ns and the area of exposurewas 800 × 800 μm2. Applied e-beam dose (Q) can be calculated bymultiplying beam current (I ∼ 250 pA) and the corresponding dwelltime (t).

Dewetting. Intensified dewetting of selectively e-beam exposedfilms was done by immersing them in a mixture of water, methyl ethylketone (MEK) and acetone. The solvent molecules diffuse into thepolymer and render the film to a liquid state where the dewetting canhappen, while the water being majority phase inhibits the polymer todissolve into the solution. To capture the intermediate stages ofdewetting, the kinetics was slowed down by increasing the watercomposition in the dewetting mixture. MEK and acetone in a ratio of7:3 constitute the organic solvent in the dewetting mixture. Thisorganic solvent mixture was added in water in the proportions rangingfrom 1 part organic solution in 4 parts of water (for slow dewetting inthe initial stage) to 2 parts organic solvent in 3 parts water (for fastdewetting at the later stage). Time required for complete dewettingwas about 2 h for 17 nm and 5 h for 27 nm PMMA films. For solventvapor induced dewetting, thin films were exposed to a saturatedsolvent vapor of MEK or toluene in a sealed glass desiccator at roomtemperature (23 °C).

Imaging and Analysis. Imaging of patterned thin films was doneusing optical microscope, FESEM and atomic force microscope(AFM) depending on the feature size and the details to be captured.Pattern dimensions and profiles were measured using ImageJ65 or theproprietary software provided by the instrument manufacturer.Calculation of dewetting length scale was done by measuring theaverage area occupied by a droplet (reciprocal of number of dropletsper unit area) and then by taking the square root to obtain averageseparation between drops.

Nonlinear Simulations: Hydrodynamic Model.We consider anultrathin (<50 nm), isothermal, incompressible, Newtonian andperfectly dielectric fluid film on a conducting substrate (x−y plane)and bounded by a conducting water-solvent mixture of much largerthickness. The notations x and y denote the coordinates parallel to thesubstrate, z denotes the coordinate perpendicular to the substrate andu, v, w represent the corresponding velocities in these directions,respectively. The material properties of the films such as dielectricconstant (ε) and surface tension (γ) are assumed to be constant. Anelectrostatic potential difference (ψ) acts between the conductingsubstrate and the bounding conducting media57 to induce an electricfield across the film.

A. Evolution Equation. The basic formulation of the polymer film isfirst defined by creating significant spatial viscosity differentials in thefilm i.e. μ = f(x,y) where f(x,y) is a periodic function with wavelength

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λp, the e-beam pattern periodicity. The nonlinear evolution equationfor the polymer/water-solvent mixture interface is derived under thefollowing assumptions: (i) the inertial terms are neglected owing tothe fact that the films are thin and (ii) the long-wave approximation isvalid because all interfacial deformations have small slopes. In the longwave limit, by applying lubrication approximation10,18,21 the governingequations and boundary conditions are reduced to the followingforms: x-, y-, and z- momentum equations, Px = μuzz, Py = μvzz, and Pz= 0, the continuity equation, ux + vy + wz = 0, the kinematic boundarycondition, ht + uhx + vhy = w, no-slip and impermeability boundaryconditions at the solid−liquid interface (z = 0), u = v = w = 0 and theshear and normal stress balance at the interface (z = h), μuz= 0, μvz= 0,and p = −γ21(hxx + hyy). Details of the derivation of the 3-D case aregiven elsewhere.23 The resulting evolution equation is as follows:

μ∂ ∂ − ∇ ∇ =h t h P/ (1/3) [( / ) ] 03 (2)

eq 2 describes the stability and spatiotemporal evolution of thepolymer-liquid interface h(x,y,t). The total pressure P at the polymer-liquid interface can be written as57,59

εε ψ γ= − + +P h h h B h( /2 ) ( ) ( / )xx yy02 2

217

(3)

Linear stability analysis of eq 2 gives spinodal wavelength ofinstability (λm) as eq 1.Recently it is reported that the destabilizing force field gets

intensified for dewetting of a polymer film under water-solvent mixtureand alters the initial wavelength of instability and its dependence onthe film thickness with an exponent of 1.5 (λm ∼ h1.5).59 Thisintensification is attributed to the presence of electrostatic attraction59

for which the use of the potential ϕ = (εε0ψ2/2h2), in eq 2 is

consistent with this scaling. The excess pressure generated because ofthe electrostatic attraction overcomes the stabilizing Laplace pressurebecause of curvature (second term in eq 3) and induces instability atthe interface. Here ψ, ε0, ε, and γ21 represent the electrostatic potentialdifference, permittivity of free space, dielectric constant of the polymerand interfacial tension between the film and the bounding liquid,respectively. In the last term of eq 3, B denotes the coefficient of thevery short-range repulsive potential required to remove the non-physical singularities at solid contact (h = 0) and to ensurenonpenetration of the liquid at the solid substrate by maintaining anultrathin cutoff precursor thickness.18,23

The evolution equation is then nondimensionalized for a compactrepresentation of numerical results by introducing the followingnondimesional variables:{X,Y} = K1/2{x,y}/h0; T = (γ21K

2/3 μ0h0); H= h/h0; μr = μe/μ0; P = Ph0/Kγ21; and K = (εε0ψ

2/2γ21h0), which leadseq 2 to

μ∂ ∂ − ∇ ∇ =H T H P( / ) [( / ) ] 0r3

(4)

2D and 3D forms of eq 4 are numerically solved using a centraldifference scheme with half node interpolation. The resulting stiffODE in time is solved using Gear’s algorithm with a volume preservinginitial perturbation and periodic boundary conditions in space. Thegrid independence of the solutions is ensured by varying the numberof grid points. The computational domain is chosen to be sufficientlylarger than the nondimensional dominant wavelength, Λ, which isevaluated from the dimensional dominant wavelength λm obtainedfrom the linear stability analysis in eq 1.18,19 For simulations, themagnitude of potential ψ is taken as 36 mV from the earlier publishedresults59 where it was calculated by fitting the experimental data of thedewetting wavelength versus film thickness for PS thin films.59 Thevalues of ε and γ21 for PS are taken as 2.6 and 0.55 mN m−1

respectively.59 For PMMA, the potential is assumed to be similar toPS, owing to their similar electric and dielectric properties. Theinterfacial tension, γ21 for PMMA, is taken as 1.14 mN m−1 insimulations, which is calculated from the experimentally observeddewetting wavelength.

■ RESULTS AND DISCUSSIONExposure to low doses of e-beam creates viscosity contrast inthe polymer by changing effective molecular weight of thepolymer by chain-fission (positive e-beam tone resist, PMMA)or by cross-linking and increased entanglement (negative e-beam tone resist, PS). The change in the viscosity, thus leads tothe change in the dewetting dynamics where instabilities growfaster in the low viscous regions.60,61 Here we investigate: (1)how change in viscosity leads to the ordering of structures withthe help of nonlinear simulations and compare these resultswith the experiments; (2) how to control the length scale aswell as morphology of dewetted structures to produce usefuland densely packed structures.Figure 1(I) shows the schematic diagram of one type of e-

beam exposure and subsequent spatiotemporal evolution of

dewetting in thin polymer film. Figure 1(II) shows schematicdiagram of a thin polymer film with different viscosity domainson a conducting substrate bounded by a conducting liquidmedium. The viscosity contrast or the viscosity ratio (μr), i.e.,the ratio of viscosity of exposed region to the unexposed regionis estimated by the dewetting time scales in experiments. Incase of PMMA the dewetting time is at least 2 orders ofmagnitude less in the exposed part and hence μr is taken as 0.01while for PS it is about 1 order of magnitude higher andtherefore μr is taken as 10. One can thus also estimate thechange in molecular weight of the e-beam exposed regions. ForPMMA the viscosity decreases by nearly 100 times which gives

Figure 1. (I) Schematic diagram of one type of e-beam exposurepattern and the resultant dewetting of a positive e-beam tone resist(PMMA) thin film. (a) Polymer film is exposed to e-beam in a squarearray of dots pattern. (b) Dewetting starts with the formation of holesin the exposed area. (c) Holes grow in size and allow polymer to getaccumulated along the high viscosity (unexposed) regions. (d) Thesquare grid of polymer eventually breaks up to form droplets at theintersection points. (II) Schematic diagram of a thin polymer film on aconducting substrate bounded by a conducting liquid medium. Thelocal and varying film thicknesses are denoted by h0 and h(x,y,t),respectively. The gray patches in the film indicate the lower viscosity(μe) regions after the film is exposed to the e-beam.

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the change in molecular weight to about one-fourth of theoriginal value (considering μ ∼ Mw

3.4).64 Similarly in case of PS,viscosity increases by approximately 10 times which gives anestimated rise in effective molecular weight of about twice.Unless otherwise stated, the polymer film thickness is taken as17 nm (PMMA) and 15 nm (PS), which is relatively thick toallow slower kinetics so as to capture intermediate stages ofdewetting. E-beam exposed polymer thin films were put in themixture of water and organic solvents (dewetting solution) andexamined at regular intervals to track the spatiotemporalevolution of dewetting structures. Organic solvent selectivelydiffuses into the polymer film bringing it to the liquid state,while the majority phase being water inhibits the dissolution ofpolymer in to the dewetting solution. Kinetics of dewetting canbe further controlled by the amount of water in the dewettingsolution; higher the amount of water, slower is the kinetics. Wehave used water and organic solvents in a ratio 4:1 for slowerdewetting during initial phase of dewetting and 3:2 for fasterdewetting afterward. However, there were no distinguishablechanges in the dewetting wavelength or the droplet size in thesetwo dewetting solutions. The dewetting can be stopped at anyintermediate stage by simply removing the film from dewettingsolution and subsequent drying in a stream of hot air makes thestructure permanent. Drying process is fairly quick and takestypically 1−2 s. For the 17 nm PMMA films the spinodalwavelength (λm) is found as 3.9 ± 0.9 μm with equilibriumdroplet size of 1.44 ± 0.3 μm.On the basis of the evolution equation (eq 4), 2-D and 3-D

nonlinear simulations are performed to explore the dewettingpathways and the resulting morphologies of the thin polymerfilm confined between the conducting substrate and boundingmedia. In simulation results, the dimensionless viscosity ratioμr(X,Y) = μe/μ0 is the parameter that reflects the influence ofthe e-beam exposure on the polymeric film. Here, μr > 1, μr < 1,and μr = 1 represent the negative e-beam tone, positive e-beamtone, and unexposed regions, respectively. Through thesenonlinear simulations, many of the key features of theexperimental results could be qualitatively reproduced asshown below.The effect of local thinning or thickening of the polymeric

film through e-beam exposure can be clearly distinguishedthrough the early stages of morphological evolution obtainedthrough the 2-D nonlinear simulations. Plots a−c in Figure 2summarize the long time evolution of a 17 nm thick, spinodallyunstable uniform viscosity and nonuniform viscosity films overa flat substrate. In Figures 2a−2c, the gray lines (curve 1) depictthe interface of the polymeric film before the initiation of theinstability. With a uniform viscosity film (μr = 1), the dewettingtakes place through formation of an undulating structure with acharacteristic spinodal length scale, ∼λm (Figure 2a) and theevolution process is uniform over the substrate as shown inmany of the previous studies.10,16

However, in case of a nonuniform viscosity film (μr <1 or μr>1), where the periodicity of the viscosity variation isconsidered to be equal to the spinodal length scale, a rapiddeformation of the film surface occurs in the low viscousregions, resulting in the formation of a localized hole at theinitial stages. Local thinning (reduced viscosity) of the film incase of PMMA reduces the nondimensional time of rupture (T= 1.4) nearly by 4.5 times compared to the rupture time of auniform viscosity film (T = 6.3), while the local thickening(enhanced viscosity) of the film in case of PS nearly doublesthe rupture time (T = 12.7). The important observations made

in the morphological evolution of these nonuniform viscosityfilms are as follows: (i) All the low viscous regions are dewettedcompletely without any liquid remnants of the film exactlyabove (in between) the patches for a PMMA (PS) film,represented by curves 1 and 2 in Figure 2b(c), (ii) the liquiddisplaced from the low viscous regions gets accumulated asperfectly aligned liquid droplets of constant cross sectionalcurvature over the high viscous regions (curves 4 in Figure 2,parts b and c), and (iii) these ordered liquid droplets formedover the high viscous regions remain stable or quasi-stable for along period of time.Next, we show the experimental results obtained by writing

lines, dots and square-grid patterns of e-beam followed bydewetting under water-solvent mixture and compare them with3-D equilibrium morphologies obtained from nonlinearsimulations by varying μr at a periodicity of Λ in the samepattern. The pitch of e-beam pattern employed in theexperiments (λP) is 4 μm, i.e. very close to the spinodalwavelength λm (∼3.9 μm) of the 17 nm thick PMMA film. Theodd rows of images in Figure 3 show experimentally obtainedpatterns, labeled as 3a-l and the even rows show simulationresults of respective pattern, labeled as 3a′ - l′. Parts a and a′ ofFigure 3 are the schematic of the e-beam line pattern written onthe PMMA film, and in Figure 3a′, bright regions have lowerviscosity as a result of e-beam exposure. The dewetting startswith the formation of holes in the e-beam exposed regions

Figure 2. 2-D spatiotemporal evolution of a 17 nm thick polymer filmof uniform viscosity (plot a) and periodically nonuniform viscosity(plots b and c) in a 4Λ domain. Curves 1−4 show the profiles at thefollowing nondimensional times: in plot a, T = 0, 6.28, 6.43, and 6.62,in plot b, T = 0, 1.4, 1.48, and 1.56, and in plot c, T = 0, 12.67, 13.65,and 14.85.

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(Figure 3, parts b and b′). At a later stage, all the polymerdisplaced from low viscosity regions gets accumulated along thehigher viscous parts forming parallel threads of polymer (Figure3, parts c and c′). Finally, these threads start breaking into thesmaller droplets that are aligned only in y- direction (Figure 3,parts d and d′). The average droplet size (1.54 ± 0.19 μm)remains nearly the same as in the case of the homogeneousfilms (1.44 ± 0.29 μm) with slightly improved monodispersity,while the periodicity along the lines (3.34 ± 0.26 μm) is similarto the spinodal wavelength (λm ∼ 3.9 μm). Both experimentsand theory show good agreement for the initiation andevolution of instability. However, in the nonlinear simulations,breakage of polymers threads is only beginning to appear in theinvestigated time (Figure 3d′). The control over the dewettingdynamics can thus allow the fabrication of some usefulstructures ranging from micro/nanochannels to nanowires toan array of nanodroplets.

While e-beam line pattern brings one directional ordering inthe dewetted droplets, lack of strict order in the other directionlimits its applicability. To introduce 2-d ordering, e-beamexposure is done in the form of a square array of dots onpolymer film with the periodicity of 4 μm, matching closelywith spinodal wavelength (Figure 3, parts e and e′). As shownin parts f and f′ of Figure 3, the dewetting starts with thenucleation of holes at each low viscosity domain correspondingto the e-beam exposed region. As instability evolves further,holes grow in size and coalesce to form a square grid likenetwork of polymer (Figure 3, parts g and g′). This networkfinally breaks up into droplets precisely positioned at the nodesof squares (Figure 3, parts h and h′). It can also be noticed thatthere are few tiny droplets present in between the primarydroplets in experiments (Figure 3h) whereas simulation showsone tiny droplet between two primary droplets almosteverywhere (Figure 3h′). This leads to some imperfection inthe pattern. The average droplet size (1.49 ± 0.17 μm) here isalso close to the droplet size on homogeneous film with slightlyimproved monodispersity (neglecting tiny droplets). There isan excellent match between experiments and theory. Bycurtailing the dewetting process by quick removal of solvent,one can obtain a variety of patterns all starting from an array ofuniform size holes, where the hole diameter can be controlledby varying the dewetting time.Further, an alternate pattern of a square-grid of lines is also

applied for the 2-D ordering of droplets (Figure 3, parts i andi′). The periodicity of lines is kept 4 μm, which is close to thespinodal wavelength. In this case the dewetting starts in lowviscous regions, forming isolated square patches of polymerwhich gradually shrink into droplets (Figure 3j−l). Thesimulation results follow a similar path (Figure 3j′−l′). Thegrowth of this instability eventually leads to the formation ofaligned dewetted structures. Formation of thicker ridges at thecorners of receding square patch is observed both inexperiment and simulation (Figure 3j, 3j′). Experimentally,the alignment as well as the uniformity of droplets is found tobe the best in this case. The average droplet size here ismeasured at 1.57 ± 0.04 μm with significantly improvedmonodispersity. In this case as well, the intermediate structuresform some interesting patterns including cross channels andsquare patches of controllable dimension. Total time elapsedfrom the initiation of dewetting is mentioned on the bottomright corner of experimental images in Figure 3. In case of 17nm PMMA film dewetting completes in about 2 h.While shrinking, the square patches of polymer retain their

square shape because of the pinning of receding contact line(Figure 3, parts j and k). This phenomenon is even moreprominent in the thicker films where the contact line pinningleads to the formation of 4 point stars before it transforms intodroplet. Figure 4 shows the evolution of instability on a 27 nmthick PMMA film which is exposed to the square grid linepattern using e-beam. The initiation of instability is very muchsimilar to the previous case of thinner film. But as the instabilityevolves further, the edges of square recede relatively faster thanthe corners (Figure 4b). This may be because of theaccumulation of extra polymer mass at the corners of squarepatch during the initial stage of dewetting when the polymerfrom low viscosity (e-beam exposed) regions dewets quicklyand the displaced mass gets accumulated along the squarepatch. Meanwhile, it results in the formation of some veryunique sharp structures like the stars and crosses (Figure 4,

Figure 3. Time evolution of dewetting of 17 nm PMMA film exposedwith e-beam different pattern: Fabrication of various geometries ofaligned nanostructures. Images a, e, and i are schematic diagram of e-beam exposure routine; lines, dots, and cross-grid respectively; imagesa′, e′, and i′ are viscosity distribution scheme on a flat film after e-beamexposure; darker regions have higher viscosity. Images b−d, f−h, andj−l are experimentally fabricated patterns and images b′−d′, f′−h′, andj′−l′ are the corresponding nonlinear simulation results showing 3-Dspatiotemporal evolution of instability of the free interface when theviscosity (μr =0.01) is altered in the domains with a periodicity of Λ.Aligned patterns ranging from nanochannels (b), nanowires (c), holearray (f), cross grid (g), cross channels (j), square islands (k) tocircular drop array (d, h, l) can be fabricated. Total time elapsed fromthe initiation of dewetting is mentioned on the bottom right corner onimages b−d, f−h, and j−l. Scale bar: 4 μm.

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parts b and c) before eventually forming spherical droplets(Figure 4d).To capture the surface morphology of the very early stage of

dewetting, we have taken a slightly thicker (29 nm) film whichslows down the dewetting kinetics. A square grid e-beampattern is written on it and then the film is exposed todewetting mixture for the shortest duration that is exper-imentally feasible (<1 s). The film was then quickly dried tostop the dewetting process. Figure 5a shows AFM scans of this

film where series of holes have formed in the low viscousregions obtained by e-beam exposure. Figure 5b is the depthprofile which reveals that these holes are almost all the waythrough the thickness of the film. Figure 5c shows higherresolution scan where instability is visible all across the film inform of small depressions. However, the instability in theexposed area grows much faster and thus dominates themorphology of subsequent dewetting structures. The accumu-lation of the polymer from the dewetted region can be seen in

form of ridges around the holes (Figure 5, parts b and c). Theonly difference we observed between dewetting in e-beamexposed and unexposed region is the time scale of dewetting.Since the exposed region of the film is extremely small, wecould not verify the mass conservation experimentally on thinfilm. However, we checked the solubility of PS and PMMA(pellet) in water dewetting mixture which was below thedetection limit. Hence the dissolution of e-beam exposedPMMA in dewetting mixture during the time window ofdewetting can be ruled out.Next, we explore the alignment of dewetted droplets when

the periodicity of e-beam pattern (λP) significantly differs fromthe spinodal wavelength λm. Figure 6 shows the collection ofthe experimentally obtained aligned structures in three types ofe-beam patterns, namely, parallel lines (Figure 6a−c), squarearray of dots (Figure 6d−f) and square grid of lines (Figure6g−i). In case of parallel lines, the 1-D ordering remains intactwhen the pattern periodicity is varied from 800 nm (Figure 6a)to 10 μm (Figure 6c). In terms of the spinodal wavelength forhomogeneous film (3.86 μm), it is an unprecedented range of0.21−2.6 λm. In contrast to the average droplet size forhomogeneous film (1.44 ± 0.29 μm), droplet size varies herefrom 0.24 ± 0.02 μm (Figure 6a) to 2.17 ± 0.27 μm (Figure6c). For square array of dots, the alignment was found forperiodicity ranging from 500 nm (Figure 6d) to 8 μm (Figure6f). In terms of λm, this range is 0.13−2.1 λm, which is againsignificantly wide. The average droplet size in this case variesfrom 0.23 ± 0.04 μm (Figure 6d) to 1.78 ± 0.42 μm (Figure6f).For small λP (as small as one-eighth of λm), this is a good way

to fabricate densely packed array of droplets (Figure 6d).However, for larger λP, there are additional tiny dropletspresent in between the primary droplets, which bringimperfections in the pattern and increased polydispersity ofdroplets (Figure 6f). In the third case, i.e. patterns obtained bye-beam pattern of square grid of lines, near perfect ordering canbe seen throughout the remarkably wide range of periodicityfrom 900 nm (Figure 6g) to 10 μm (Figure 6i) (0.23−2.6 λm).Here the average droplet size varies from 0.235 ± 0.009 μm(Figure 6a) to 2.27 ± 0.10 μm (Figure 6i), which againreinforces the better quality of these pattern in terms ofmonodispersity. This is again to point out that not only thedroplets as shown in Figure 6, but also the intermediatestructures described in Figures 3 can be fabricated at differentlength scales by varying λP and the dewetting time.Figure 7 depicts the effect of change of periodicity of the

viscosity variation ΛP, on the self-organization of the PMMAfilm by nonlinear simulations. Image sets 1 and 2 in Figure 7correspond to a periodicity of 0.5Λ and 2Λ, respectively. Inboth the cases, the evolution starts with localized holes on thelow viscosity regions which further widen up and the displacedliquid accumulates as isolated droplets on the more viscousregions. The final morphologies in image sets 1 and 2 show thatthe length scales of the patterns can be fine-tuned while partlyretaining the order. Moreover, there are some signature featuresin these image sets that can also be seen in experimental results.For instance, clubbing of 4 nearby droplets in to one giantdroplet at the center in Figure 7(1d) is qualitatively similar to afew clumped structures seen in experiments (Figure 6d). Theseresults are in qualitative agreement to the experimentallyobtained ordered droplet arrays (Figure 6), where the patternswith even wider range of length scale are presented.

Figure 4. Time evolution of dewetting patterns on 27 nm PMMA filmexposed with e-beam cross grid pattern. The contact line pinning ismuch prominent here which leads to the formation of 4 point star likestructures. Total time elapsed (t) from the initiation of dewetting ismentioned on the bottom left corner on each image. Scale bar: 20 μm(5 μm inset).

Figure 5. 3-d topography in the AFM image showing early stage ofdewetting where series of holes have formed in the e-beam exposedregion. (a) 30 × 30 μm area scan of early stage of dewetting, (b) depthprofile of the line marked as 1 in image a, and (c) enlarged view of thearea marked in image a.

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Similarly, we have carried out nonlinear simulations fornegative e-beam tone polymer PS and the final morphology ofdewetted structure is in close agreement with the previouslyreported experimental results.60 In Figure 8a the dark spotsshow the regions of increased viscosity on a PS film which iscreated by short e-beam exposure. The intermediate stagesshow that the instability starts in the unexposed (lowerviscosity) regions (Figure 8b,c). This leads to the formation ofaligned droplets which coincide on the e-beam exposed regions(Figure 8d).Intensified dewetting under water-solvent mixture is critical

to the fabrication of highly confined domains whereas

dewetting in air (thermal or solvent vapor induced) cannotproduce patterns on same length scale.26,43,59 PMMA filmsused here are stable for thermal and solvent vapor annealingand do not dewet even in 48 h of annealing. Therefore,intensification of dewetting is essential to start the dewettingprocess in case of PMMA thin films. However, PS films areunstable and dewet when exposed to solvent vapor.26,43

Previously, it was shown that intensified dewetting was ableto produce ordered droplet array on highly confined patternedsubstrates where the dewetting in air was not able to proceed.59

Here, we have done similar comparison for e-beam exposedfilms. In Figure 9, we compare the dewetting of 15 nm PS filmsunder water-solvent mixture and solvent vapor. Top row inFigure 9 shows images of completely dewetted structures whendewetting is carried out under liquid while the bottom rowshows corresponding cases of dewetting with the exposure ofsolvent vapor. Spinodal wavelengths for the dewetting of 15 nmPS film in liquid and in air are 2.9 μm (Figure 9a) and 8.4 μm

Figure 6. Controlling the length scale of dewetting by changing the pitch of e-beam exposure pattern (λP): Experimental results. Images a−c show 1-D array of droplets obtained by drawing e-beam line pattern, where λP is varied from 0.21 to 2.6 λm. Images d−f show 2-D array of droplets obtainedby drawing e-beam dot pattern, where λP is varied from 0.13 to 2.1 λm. Images g−i show 2-D array of droplets obtained by drawing e-beam squaregrid pattern, where λP is varied from 0.23 to 2.6 λm. Scale bar: 20 μm (white); 1 μm (black).

Figure 7. Controlling the length scale of dewetting: Simulation results.The image set 1 (first row) shows the 3-D spatiotemporal evolution ofinstability of PMMA film when the altered viscosity domains areseparated with 0.5 Λ while in the image set 2 (second row) they areseparated by 2 Λ. The domain sizes are 3Λ × 3Λ and 6Λ × 6Λrespectively. Darker regions in the image are polymer.

Figure 8. Evolution of instability in a 15 nm PS film exposed to asquare array of e-beam dots. Image a shows the viscosity variation inthe e-beam exposed film where dark regions have higher viscosity.Images b−d show 3-D spatiotemporal evolution of instability of thefree interface in a 3Λ × 3Λ domain.

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(Figure 9d) respectively. We have exposed PS films with e-beam dot pattern with periodicity 2 and 5 μm and then carriedout dewetting under liquid and in air. Dewetting in liquid hasresulted in the aligned array of droplets in both the cases(Figure 9, parts b and c). While dewetting in air was able toproduce aligned droplet array in case of 5 μm pattern (Figure9f) but not in case of 2 μm pattern (Figure 9e). In Figure 9ethe e-beam exposed area is above the dotted line, and while thedewetting is complete in that region, there is no distinctalignment of droplets. Therefore, it is clear that dewetting inliquid allows the fabrication in much smaller domains byreducing interfacial tension and intensifying dewetting kineticsand thus providing a greater control over the length-scale of thefabricated patterns by e-beam exposure.As shown, the thin films of both positive and negative tone e-

beam resists can be effectively used to obtain highly orderedself-organized patterns by modifying the effective viscosity andcontrolling the periodicity of differential viscosity domains.Same e-beam pattern can be used to generate range of differentpatterns by controlling the extent of dewetting (Figure 3). Alsosimilar structures can be made by different e-beam patterns onPMMA and PS (Figures 3g and 8b). Since the effect of the e-beam exposure is different on PMMA and PS, the same e-beampattern leads to the initiation of dewetting in opposite regions.In PMMA, dewetting starts from the exposed regions which canbe efficiently controlled by e-beam writing and that makes it abetter candidate to fabricate structures where intended patternforms at the initial stage of dewetting, whereas in PS, dewettingstarts in the area that is not exposed which makes the initialstage of dewetting relatively less ordered and it performs bestwhere target pattern is at the later stage of dewetting process. Interms of time required for e-beam exposure and dewetting,PMMA performs better than PS since PMMA is significantlymore sensitive to e-beam exposure (requires less e-beam dose)and e-beam accelerates the dewetting kinetics in PMMA whilemaking it harder for PS to dewet.

■ CONCLUSIONSIn this work, we have shown both experimentally andtheoretically that the spatially ordered viscosity variation in athin polymer film leads to the formation of ordered self-organized structures by deweting under a solvent/nonsolventliquid mixture. The viscosity variation in a thin film isintroduced by a short exposure to e-beam and both positiveand negative tone polymers produce ordered patterns. Theintensified dewetting under a mixture of water and organicsolvents allow the instability to initiate and grow in veryconfined domains and at much faster rate. Nonlinearsimulations are also performed using a mathematical modelbased on long wave approximation to support the experimentalresults. Simulation results match reasonably well with theexperimentally obtained patterns in most of the cases. Both thepattern morphology and the length scale can be varied over awide range by controlling the dewetting time and periodicity ofe-beam pattern. Dewetting length scales (wavelength anddroplet diameter) can be tuned over a wide range as high as 1order of magnitude (from <0.2λm to >2λm) which is asignificant improvement over the patterns produced byphysicochemical patterning of substrates where typicallyalignment is compromised in case of patterns less than 0.5λm.This leads to the fabrication of significantly dense packeddroplet arrays which may be crucial in some applications suchas nanolens arrays. Freezing the dewetting at intermediatestages by removing solvent can produce a variety of complexstructures such as parallel and cross channels, array of circularand square holes, thin wires, 4 point stars and dots. Fabricationof structures with sharp corners and edges becomes possiblebecause ultralow interfacial tension allows these structures toretain their shape for a longer duration. Since the complexity ofe-beam patterns can be further increased, this method providessingle step solution to fabricate much more complex patterns.These structures have potential applications in microfluidics,micro-optics, and templated synthesis of nanostructures and inthe periodic distribution of catalyst nanoparticles.

■ AUTHOR INFORMATIONCorresponding Author*(A.S.) Telephone +91−512−259 7026. Fax +91−512−2590104. E-mail ashutos@iitk.ac.in.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is supported by Department of Science andTechnology, Government of India by its Unit on SoftNanotechnology at IIT Kanpur.

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