Process Simulation for Contact Print Microlithography

A. A. Darhuber*, S. M. Miller*, S. M. Troian*, and S. Wagner**

* Interfacial Science Laboratory, Dept. of Chemical Engineering

Princeton University, darhuber@princeton.edu

** Department of Electrical Engineering, Princeton University

Princeton, New Jersey 08544, USA

ABSTRACT

Using a combination of experiment and simulations,we have studied the conformation of liquid microstruc-tures on both at and corrugated, chemically heteroge-neous substrates. The arti�cial surface patterns, whichde�ne regions of di�erent surface energy, induce defor-mations of the liquid-solid contact line, which can eitherpromote or impede capillary break-up and the formationof bulges. We study numerically the in uence of the ad-hesion energies on the hydrophilic and hydrophobic sur-face areas, the pattern geometry and the deposited uidvolume on the liquid surface pro�les. Moreover, we in-vestigate the transfer of these microscopic ink patternsfrom the stamp surface to the target substrate duringthe printing process.

Keywords: Microlithography, O�set Printing, Intaglio,

Liquid Microstructures, Surface Pattern

1 INTRODUCTION

In the last ten years several attempts have been madeto �nd alternatives [1{3] to conventional photolithogra-phy for the fast, parallel and low-cost fabrication of pat-terns in the micrometer size range. For example, Mikamiet al. [3] have developed a gravure-o�set printing tech-nique to fabricate fully functional electronic devices.

Optimization of the stamp pattern design and the inktransfer process for the fabrication of electronic struc-tures requires knowledge of the liquid's equilibrium con-formation on a patterned surface. For liquid elementsin the micron range, the surface to volume ratio is verylarge. Thus, the energetics associated with the bound-ary surfaces completely determine the overall shape andstability of liquid microstructures. By understandingto which extent the various parameters a�ect the �nalshape, the edge resolution and pattern �delity can beimproved.

2 EXPERIMENTS

The samples were cut from standard silicon wafersand coated with a self-assembled monolayer of octade-cyltrichlorosilane (OTS), which serves as the hydropho-bic layer. The contact angle of water on OTS is about

112�. Subsequently, the OTS layer was removed locallyby exposure of the samples to deep-UV radiation froman ArF excimer laser through a chromiummask. The re-gions where the OTS was removed by photocleavage [4]are rendered hydrophilic, since the SiO2 underneath theOTS is now exposed. The experiments have mainly beenperformed with glycerol, because of its low volatility.Additional details of the experimental procedures canbe found in Ref. [5].

3 NUMERICAL SIMULATIONS

The numerical calculations presented in this articlewere performed with the Surface Evolver [6] software tak-ing into account the liquid's surface tension lv and theliquid-solid contact energy. Due to the small scale ofthe investigated structures, the Bond number de�nedas Bo = �gR2= lv is much smaller than one and hencethe in uence of gravity can be neglected. � is the inkdensity, g the gravitational acceleration and R the rele-vant length scale.

The surface of the ink droplets is discretized by meansof a triangular mesh and the total energy of the sys-tem is expressed as a function of the node coordinates.The numerical methods of steepest descent and conju-gate gradients are implemented for the minimization ofthe total energy. Constraints can be applied to vertices,edges, facets and volumes and boundary condition pa-rameters can be included in the optimization process.

4 INK ON FLAT SURFACES

An ink droplet on a homogeneous surface assumesthe shape of a spherical cap, which exhibits a constantcontact angle with the solid surface all around its perime-ter. If the surface is hydrophilic, the contact angle � isbelow 90�, if the surface is hydrophobic, � exceeds 90�.In the latter case, the droplet tries to minimize the solid-liquid contact area, whereas in the �rst case it has anincentive to maximize it, in each case to the maximumextent compatible with the magnitude of the liquid'ssurface tension lv.

If the surface is heterogeneous with both hydrophilicand hydrophobic patches, the contact angle is no longera constant, but is position dependent. The ink will try toreside only on the hydrophilic parts of the surface and to

recede from the hydrophobic areas. In this way, liquidcan be con�ned to certain imaging areas by chemicalsurface modi�cations, which is the basis of the classicalo�set printing technique. [8]

(a)

(b)

(c)

8 µm

Figure 1: In uence of an insoluble surfactant. The sideviews correspond to an ink droplet with a contact angleof 60� (a), to the same droplet with a surfactant whichreduces the surface tension by 20% (b) and by 50% (c).

One of the most elementary geometries comprises ahydrophilic rectangular patch on a hydrophobic plane.If a very small quantity of ink is deposited on the hy-drophilic channel, the droplet will assume a sphericalcap shape, if its contact angle is above 0�. If the volumeof the droplet is increased, the base radius of the spher-ical cap increases until it senses the channel boundaries.If the volume is increased further, the previous sphericalcap shape will deform and extend itself along the chan-nel. The side view of an ink droplet on a 1 �m � 8 �mchannel with a contact angle of � = 60� is presented inFig. 1(a). As can be seen, the liquid does not spreadalong the entire channel, but concentrates in a bulge.This behavior is undesirable for printing, since insteadof the designed 1 �m � 8 �m line only a much shorterpattern would be transferred.

There are two ways to overcome this problem. One isto increase the surface energy of the hydrophilic channelsuch that the contact angle of the ink is reduced. A valueof 30� is low enough to provide for complete wetting ofthe entire channel. In principle the SiO2 regions providea su�ciently high surface energy to bring the contactangle for water or glycerol close to zero. Unfortunately ahigh energy surface also attracts organic contamination,which can increase the contact angle signi�cantly.

A second possibility is the addition of surfactantswhich reduce the surface tension of the ink. If the sur-factant is insoluble, it will not a�ect the liquid-solidcontact energy and hence e�ectively reduces the ink'scontact angle, leading to complete wetting of the chan-nel. In Fig. 1(a), the droplet shape corresponding to acertain value of the surface tension lv and a contactangle of � = 60� is compared with the cases when thesurface tension is reduced by 20% [Fig. 1(b)] and 50%[Fig. 1(c)]. In the latter case, the channel is completelywetted.

If the surroundings of the channel are only weakly

Figure 2: Top views of an experimental and calculateddroplet shape of glycerol on a hydrophilic channel. Theliquid forms a bulge which leaks into the hydrophobicsurroundings.

hydrophobic, the droplet may not be con�ned to thechannel, but leak out of it in order to minimize theliquid-vapor interface area. This situation is depicted inFig. 2, where an optical micrograph of a droplet of glyc-erol on a 14 �m wide hydrophilic channel on a weaklyhydrophobic surface is compared with a simulation.

In microelectronic devices, large and small patternsare frequently connected. An example are bonding padsand the current leads running to and from them. Sincesmaller length scales are inherently equivalent to a highersurface-to-volume ratio, the liquid will try to avoid thenarrow parts and concentrate on the broader hydrophilicregions. As an example we present an ink droplet on ahydrophilic region which consists of a narrow rectangleof dimensions 1 �m � 4 �m, which is connected to abroader rectangle of size 6 �m � 3 �m in Fig. 3.

(b)

(c)

6 µm

1 µm

(a)

Figure 3: E�ect of disparate length scales of the hy-drophilic pattern (a) on the distribution of ink with con-tact angles of (b) 30� and (c) 10�.

In Fig. 3(a), the contact angle of the ink was as-sumed to be 30� whereas it was 10� in Fig. 3(b). In the�rst case, the liquid wets only a small fraction of thenarrower channel. In the latter case it wets the entirenarrow line, however, the height pro�les of the liquidare very uneven. Upon printing only the broad rectan-gle would be transferred. For a more detailed discussionincluding the in uence of topological and chemical de-fects the reader is referred to Ref. [5].

5 INK ON INTAGLIO SURFACES

The second main technique besides o�set printing isgravure or intaglio printing, where the ink �lls trenchesand grooves in the stamp surface. In this case the sur-face morphology helps to con�ne the ink. The groovesprovide a signi�cant local increase of surface area, whichmakes spreading energetically more favorable than theformation of bulges - even for comparatively large con-tact angles. In Fig. 4 we present a direct comparison ofthe ink conformations on an o�set [Fig. 4(a,b)] and anintaglio plate [Fig. 4(c,d)], where the hydrophilic regionhas a rectangular shape and dimensions 1 �m � 4 �m.The depth of the groove is 1 �m.

θ = 60º

8 µm

Intaglio

Offset

1 µm

(a)

(b)

(c)

(d)

Figure 4: Comparison of ink droplets on an o�set andan intaglio printing plate for a contact angle of 60�. (a)and (c) are side views, (b) and (d) are top views. Thevolume of the droplet on the o�set plate and the excessink volume on the intaglio plate are equal.

Whereas the ink droplet concentrates in a bulge inthe center of the hydrophilic patch on the o�set plate,the liquid spreads along the entire trench in the case ofan intaglio geometry. The contact angle was assumed as� = 60�. Thus the introduction of grooves and trencheshas a similar e�ect as the usage of surfactants. However,in the case of loops and corners, intaglio does not providean advantage over o�set printing.

6 INK TRANSFER

Figure 5(a) shows the equilibrium shapes of the inkmeniscus between stamp and target surfaces for increas-ing plate separations d = 0.5, 1, 1.5 and 2, stated inunits of 3

pV , where V is the ink volume. The contact

angle on the stamp surface is assumed to be � = 60�,whereas it is � = 45� on the target surface. In this caseno lateral con�nement of the contact lines due to chem-ical heterogeneities is taken into account. As the plateseparation increases, the neck-radius of the ink meniscusbecomes smaller and smaller and at some critical value,the meniscus breaks into two separated droplets on the

two plates.Fig. 5(b) shows the volume fraction of ink transferred

from the stamp to the target surface as a function of thecontact angle on the target substrate for two values ofthe contact angle � on the stamp surface, 30� and 60�.When the contact angles on both surfaces are equal, thetransfer ratio is 50% as dictated by symmetry. Whenthe two contact angles are disparate, the transfer ratiochanges rather rapidly either towards almost completetransfer or towards almost no transfer of ink to the tar-get substrate. As is clearly visible, the surface with thesmaller contact angle retains the bulk of the ink volume.

(a)

stamp

target

0 10 20 30 40 50 60 70 800.0

0.2

0.4

0.6

0.8

1.0

Contact angleon stamp

(b)

θ = 30°

θ = 60°

Tra

nsfe

r R

atio

Contact angle on substrate (deg.)

Figure 5: (a) Meniscus shape of a �xed volume of inkbetween parallel plates of di�erent composition. Thecorresponding plate separations are 0.5, 1, 1.5 and 2 inunits of 3

pV , where V is the ink volume. The contact

angles on the stamp and target surface are � = 45� and� = 60�, respectively. (b) Transfer ratio of the liquid inkfrom the stamp to the target surface for contact anglesof � = 30� and � = 60� on the stamp. The solid linesare guides to the eye.

The presented results were obtained under the as-sumptions of quasistatic printing, unconstrained contactline motion and perfectly at and parallel surfaces. Thusthey represent only the in uence of the surface chem-istry on the transfer process, regardless of the dynamic

properties of the liquid. Chadov [9] and Yakhnin [10]have shown that for a speed of the plate separation fastas compared to the intrinsic velocities (resonance fre-quencies) of the liquid meniscus, the transfer ratio isalways 50%, irrespective of the chemical composition ofthe plates. As the separation speed is reduced the trans-ferred fraction gradually converges to the quasistaticvalue which is determined by the chemistry alone.

Figure 6(a) shows an ink meniscus between the stampand the target substrate for equal contact angles of � =30� when a small tilt of 2� is present. This situationmight arise when the parallelity of the plates is notstrictly enforced by mechanical provisions during theirseparation. The ink on the stamp surface is con�ned to arectangular hydrophilic pad of dimensions 1 �m � 4 �m,whereas there is no con�nement on the target surface.Since a smaller separation corresponds to a smaller av-erage curvature of the liquid's surface, which is ener-getically favorable, the ink meniscus is attracted to theregion of minimum plate separation by capillary action.

InkTarget substrate

Printing plate(a)

4 mm

(b)

Figure 6: (a) Tilted o�set printing plates. As the plateseparation increases, the ink meniscus is attracted to theregion of minimum plate separation. (b) Tilted intaglioprinting plates. The liquid's contact line is pinned at thesidewall of the groove in the stamp, but free to move onthe target surface. The contact angles on both plateswere assumed to be (a) 30� and (b) 60�.

The analogous situation for intaglio printing is pre-sented in Fig. 6(b). Equal contact angles on both stampand target of � = 60� were assumed. The groove hasrectangular shape with dimensions 1 �m � 4 �m and a

depth of 1 �m. The same tilt angle of 2� as in Fig. 6(a)is assumed with the tilt axis parallel to the shorter edgeof the rectangle. Upon separation of the plates, the liq-uid's contact line is pinned to the sidewall of the groove,but it is free to move on the target surface. Thus again,the ink meniscus moves towards the zone of smaller plateseparation.

This would induce a loss of pattern �delity, which il-lustrates the necessity to provide for a mechanism to im-pede contact line motion on the target substrate. Sucha pinning of the contact line could be achieved by sur-face initiated polymerization of an ink which containsmonomers or oligomers, or by increasing the ink viscos-ity by means of a temperature induced phase transition(e.g. freezing) or chemical reaction with a thin layerof suitable material uniformly deposited on the targetsurface.

ACKNOWLEDGMENTS

This project is funded by the MLP program of theDARPA, the Austrian FWF via a postdoctoral fellow-ship (AAD) and the Eastman Kodak Corporation viaa graduate fellowship (SMM). Surface Evolver was de-veloped by Kenneth Brakke of Susquehanna University,Selinsgrove, PA.

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