Numerical analysis of effects of mold features and contact

J. Microlith., Microfab., Microsyst. 5�1�, 011004 �Jan–Mar 2006�

Numerical analysis of effects of mold featuresand contact friction on cavity filling in thenanoimprinting process

H. HochengC. C. NienNational Tsing Hua UniversityDepartment of Power Mechanical EngineeringHsinchu, TaiwanE-mail: [email protected]

Abstract. Nanoimprinting has been recognized as a highly potentialmethod of volume production for nanoscale devices. In the nanoimprint-ing process, the filling process of the mold cavity plays a key role indetermining the productivity of the nanoimprinting process and the qual-ity of the final imprint product. A defective filling of the mold affects theuniformity, precision, and throughput of the imprint. The mold filling issubjected to the applied imprinting pressure and temperature, repetitivemold use, mold sticking, or factors regarding mold features. It involvesphysical contact between the mold and the polymer layer on the sub-strate surface; thus, how the polymer fills up the cavity is of major inter-est and is vital in pattern transfer. The proposed study employs a finiteelement model for the single mold cavity to simulate the nanoimprintprocess. The mold is assumed to be a linear elastic body and the poly-mer preheated above its glass transition temperature is considered to benonlinear elastic, described by the Mooney-Rivlin model. The numericalmodel is able to predict the mold filling at any nanoimprint stage and themold cavity with various aspect ratios. To study the effects of patterndensity and contact friction existing between the mold and polymer dur-ing the mold filling of the nanoimprinting process, an imprint mold withmixed pattern density is simulated and a sensitivity analysis of a contactfriction coefficient on the mold filling is performed. Both the cavity featureand pattern density have significant effects on mold filling of the nanoim-printing process, while the contact friction coefficient has a mild effect.The obtained results support the development of a process recipe andautomatic large-scale industrial production for nanoimprinting. © 2006 So-ciety of Photo-Optical Instrumentation Engineers. �DOI: 10.1117/1.2177286�

Subject terms: nanoimprint lithography; Mooney-Rivlin model; mold filling; finiteelement method; contact friction; aspect ratio.

Paper NP-04 received Jan. 1, 2005; revised manuscript received Mar. 1, 2005;accepted for publication Jul. 1, 2005; published online Mar. 10, 2006.

1 Introduction

As the semiconductor industry continues the trend of min-iaturization leading to nanoelectronics, the demand for sub-100-nm feature size in lithography becomes indispensable.This critical need has made photolithography face seriousobstacles due to the limitation of wavelength. The alterna-tive nonphotolithographic techniques not limited by the ef-fects of wave diffraction, scattering, and interference in aresist, and backscattering from a substrate have becomemore prominent in the semiconductor industry. During thepast several years, some major efforts have been directedtoward developing nonphotolithographic techniques forfabricating nanoscale patterns. Imprint-based alternative li-thography techniques have been demonstrated on a labora-tory scale, namely nanoimprint lithography, mold-assistedlithography, and microcontact printing.1 Among them,nanoimprint lithography has received the highest attentionand has been recognized as one of the most promising non-

1537-1646/2006/$22.00 © 2006 SPIE

J. Microlith., Microfab., Microsyst. 011004-

photolithographic methods for nanoscale device manufac-turing since it was presented by Chou, Krauss, andRenstrom.2–5

Basically, nanoimprint lithography �NIL�, also known ashot embossing lithography �HEL�, involves an imprint stepwith physical deformation of a thin film of a thermoplasticpolymer cast on a substrate by using a rigid stamp under

Fig. 1 Schematic diagram of the nanoimprint lithography process.

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Hocheng and Nien: Numerical analysis of effects of mold feature¼

pressure and elevated temperature, followed by a patterntransfer step involving the complete removal of the residualresist layer in the compressed areas by using an anisotropicetching process, such as reactive ion etching �RIE�, to openthe windows to the substrate. A typical NIL process is il-lustrated in Fig. 1.

Nanoimprint lithography has the potential to play a veryimportant role for nanoscale pattern generation, because ofits attractive characteristics such as flexibility, low cost, andhigh resolution. In addition, nanoimprint lithography couldalso be an alternative to conventional lithography for beingable to define patterns down to sub-10 nm and can providea wide range of interesting potential applications as well asnew opportunities for micro- and nanofabrication.6,7 Whilenanoimprint lithography has been studied and investigatedin great detail by several research groups worldwide, andsome significant achievements of the extensibility and ap-plication capabilities have been demonstrated in recentyears,8,9 nanoimprint lithography has been capable of pat-terning only fairly small samples, which severely limits theindustrial applications of the technique. As a consequence,how to improve throughput to meet the requirements forlarge-scale industrial use is the most challenging issue forthe research community of nanoimprint techniques at thepresent time.

For the nanoimprinting process, since it involves physi-cal contact between the mold and the polymer layer on thesubstrate surface under applied pressure and temperature,the process of polymer filling of the cavities is a very im-portant step in the patterns transfer for nanoimprinting. In

Fig. 2 Structure and cross section of imprint mold-PMMA polymer.

Fig. 3 Boundary conditions, dimensions, and geometry of imprintmold-polymer system with single mold cavity �axis symmetrical; unit:
nanometers�.

practice, this mold filling process governs the quality of thefinal imprint product and plays a key role in determiningthe productivity of the nanoimprinting process. Incompletemold filling has a detrimental effect on the final imprintedpattern dimensions. Once incomplete mold filling exceedsan acceptable level, it can result in the final transferredpattern dimension going out of specifications and losingfidelity as well as uniformity, leading to poor quality of thefinal imprinted products. Hence, the reduction of variationsin mold filling is required. Mold filling must be of particu-lar concern as the dimensional requirements of the finalimprinted product become more stringent and efforts are

Fig. 4 Finite element model of imprint mold-PMMA polymer withsingle mold cavity �axis symmetrical�.

Fig. 5 Boundary conditions, dimensions, and geometry of imprint
mold-polymer system with multiple mold cavities �unit: nanometers�.
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directed to improve the nanoimprint technique as a reliableand high-throughout process for large-scale industrial use.

As a result of the concern of mold filling during thenanoimprinting process, various qualitative investigationshave reported models and explorations on the behavior ofpolymers and mold filling mechanisms. For instance,Scheer and Schulz10 indicated that two major problems thatarise with respect to the pattern transfer are the problems ofsticking, and mass transport and viscous flow. Heydermanet al.11 reported that imprinting conditions �time, tempera-ture, and pressure� required for replication at microscalealso result in good replication at nanoscale. The key factorfor a good and fast molding process is the viscosity of thematerial, which is largely dependent on the imprinting tem-perature. The investigation conducted by Scheer andSchulz12 proved that the flow behavior of the polymer is thelimiting factor in the replication of micrometer-sized fea-tures, but does not adversely affect nanometer structuring.Schift et al.13 explored the principle of pattern formationduring the imprint of a thin molten polymer film and indi-

Fig. 6 Finite element model of imprint mold-PMMA polymer withmultiple mold cavities.

Fig. 7 Mold filling stages corresponding to differe


cated there are two different types of filling mechanisms:simple flow of polymers from the borders and formation ofpolymer mounds.

In contrast to the qualitative investigations on patternformation of the nanoimprinting process, little work can befound in the quantitative characterization of mold fillingduring the nanoimprinting process. The present work, con-tinuing on a recent study,14 takes a further step toward un-derstanding pattern formation and exploring the quantita-tive information on mold filling variations during thenanoimprinting process. To this end, and to understand themechanical behavior of the contact process between thesilicon imprint mold and the thin film of polymethyl meth-acrylate �PMMA� spin-coated on silicon substrate, a finiteelement model for the single mold cavity has been con-structed. The commercial finite element code ANSYS �AN-SYS Inc., Canonsburg, PA� was used to simulate the im-print process. The material behavior of the mold is assumedto be linear elastic, and the polymer preheated above itsglass transition temperature is considered to behave as anonlinear elastic body described by the Mooney-Rivlinmodel. Using the developed numerical model, the mold fill-ing variations can be determined at any nanoimprint stageand for a mold cavity with a variety of aspect ratios. More-over, to investigate the effects of pattern density and con-tact friction existing between the mold and polymer onmold filling of the nanoimprinting process, the model for animprint mold with mixed patterns in an active area has beenconstructed and used to explore mold filling in the nanoim-

nt load steps for the 100-nm cavity depth.

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printing process. A sensitivity analysis is finally performedto investigate the influence of contact friction on mold fill-ing.

The subsequent sections of this work present the detailsof this study and are organized as follows. Section 2 de-scribes the simulation model used here. Section 3 gives thesimulation results and illustrates the contact friction sensi-tivity analysis. Finally, Sec. 4 provides the conclusion.

2 Modeling and Simulation of the NanoimprintProcess

2.1 Finite Element Modeling

In this section, the finite element model is developed todetermine the filling process of a mold cavity for a typicalisothermal nanoimprint process. While modeling, we as-sume that the imprint mold satisfies the plane strain condi-tions, and since the imprint mold and polymer geometry,and also the loading conditions, are close to the axiallysymmetrical ones, the model for the nanoimprint processcan therefore be simplified to be a 2-D and axis-symmetrical finite element model. Also, the material behav-ior of the imprint mold is assumed to be linear elastic, andthe polymer preheated above its glass transition tempera-ture is considered to behave as a nonlinear rubber-elasticbody, described by the Mooney-Rivlin model. Furthermore,the nanoimprint process is inherently one involving largedeformations, particularly under the elevated mold areaswhere polymer materials of PMMA may be displaced somedistance. Thus, the polymer material, geometry, and contactnonlinearity need to be considered in the finite elementmodel.

The 2-D model was entirely generated using ANSYS®8.0. The imprint mold was meshed using four-noded ele-ments PLANE42, 2-D plane elements with two degrees offreedom at each node. The element selected to model thepolymer behavior was the hyper-elastic HYPER56 axis-symmetrical element. It should be noted that due to the thinnature of the polymer film, an extremely fine mesh wasrequired to produce adequate element aspect ratios. Thecontact was defined in the mold-polymer system using 2-Dline-to-line contact elements. The finely meshed cavity sec-tion of the imprint mold was chosen as contact nodes, whilethe polymer was selected as the target surface. Meanwhile,the contact interaction between imprint mold and thin filmof PMMA was simulated with the use of the elementsTARGE169 and CONTA171. Figure 2 shows the imprintmold and PMMA polymer system.

The required boundary conditions, dimensions, and ge-ometry of the axis-symmetrical imprint mold and PMMApolymer model are depicted in Fig. 3. As shown, the con-straints were applied to the bottom, right-hand side, andsymmetrical line of the model. Along the right-hand sideand the symmetrical line, the degree of freedom in the xdirection was fixed. Hence, there is no displacement in thex direction. By constraining the nodes along the bottomsurface of the polymer from displacement in the x and ydirections, the boundary conditions on the finite elementmodel were complete. Figure 4 shows the meshed finite
element model.

2.2 Numerical CalculationsTo investigate the effects of cavity aspect ratio and patterndensity on the mold filling of the nanoimprinting process,two representative cases were simulated by the numericalmodel outlined in the previous section, namely, the singlemold cavity with various aspect ratios, shown in Figs. 3 and4, as well as the imprint mold with aperiodic cavities. Thecases studied here consist of an isothermal imprinting op-eration of a 300-nm-thick PMMA polymer, and the widthsfor all mold cavities are also 300 nm. As in the case of asingle mold cavity, the required boundary conditions, geo-metrical data, and meshed finite element model for the im-print mold with various pattern densities are shown in Figs.5 and 6, respectively.

As previously mentioned, during the imprinting process,the PMMA polymer preheated above its glass transitiontemperature is considered to behave as a nonlinear rubber-elastic material and its mechanical properties can be char-acterized by means of the Mooney-Rivlin strain energyfunction.15,16 The Mooney-Rivlin strain energy function foran incompressible isotropic elastic material is expressed as

W = C10�I1 − 3� + C01�I2 − 3� , �1�

where C10 and C01 are physical constants characterizing thematerial, and I1 and I2 are strain invariants. The two invari-

Fig. 8 Mold filling stages corresponding to different load steps forthe 200-nm cavity depth.

ants I1 and I2 are defined by

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I1 = �12 + �2

2 + �32, �2�

I2 = �12�2

2 + �22�3

2 + �32�1

2, �3�

where �1, �2, and �3 are the three principal extension ratiosfor the deformation.

According to the literature,17,18 the values of C10 and C01can be derived from the following equations,

C01 = 0.25C10, �4�

6�C10 + C01� � E , �5�

where E is the Young’s modulus of the polymer.In all of these finite element method �FEM� simulations,

the material properties adopted for the polymer as well asthe silicon imprint mold are as follows. First, above thepolymer glass transition temperature, the Young’s modulusE of the polymer PMMA was assumed to be 10 MPa19 andPoisson’s ratio was chosen v=0.49967. Second, using Eqs.�4� and �5� and taking 10 MPa for Young’s modulus E ofthe polymer, one obtains the values of C10 and C01, used inall simulation cases, as 1.3 and 0.3 MPa, respectively.Third, during the isothermal imprinting process, the siliconimprint mold was assumed to be linear elastic, and itsYoung’s modulus and Poisson’s ratio are 165 GPa and 0.3,respectively. Moreover, all cases studied here are based onthe assumption that the coefficient of the contact frictionbetween the polymer and imprint mold is 0.0 due to theimprint mold surface always being coated by an antistick-ing layer in practical imprinting operations.

Once the material properties and boundary conditionswere specified as described earlier, numerical simulationscan be performed by applying a vertical load on the uppersurface of the imprint mold.

3 Results and Discussion

3.1 Single Mold Cavity with Various Aspect RatiosTwo different mold cavity depths have been adopted in our

Fig. 9 PMMA displacement against applied pressure.

simulations for the category of a single mold cavity. One is


100 nm and the other is 200 nm. The mold filling stages,represented by the maximum displacement of PMMA un-der the mold cavity and named PMMA displacement in thefollowing for convenience, corresponding to different loadsteps for cavity depths of 100 and 200 nm are presented inFigs. 7 and 8, respectively. A typical PMMA displacementversus the applied pressure for the imprint mold-PMMApolymer system is shown in Fig. 9. Figures 7 and 9 showthat the final applied pressure required to fully fill the moldcavity is up to 6 MPa, and the total PMMA displacement is75.1 nm for the 100-nm cavity depth. For the 200-nm cav-ity depth, Figs. 8 and 9 show that the final applied pressurerequired to fully fill the mold cavity reaches 13.5 MPa, andthe total PMMA displacement is 150.3 nm.

One can see that the applied pressure required to fullyfill the mold cavity with 200-nm cavity depth is about twotimes that of the mold cavity with 100-nm cavity depth.This is expected, because once the imprint mold withdeeper mold cavity is pressed into the PMMA polymer, thevolume of the displaced polymer required to fill up themold cavity increases substantially. Since the volume of thedisplaced polymer becomes larger, larger force is required

Fig. 10 Mold filling stages corresponding to different load steps forthe imprint mold with various pattern densities.

for the imprint mold to further compress the polymer.

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3.2 Imprint Mold with Aperiodic CavitiesThe status of mold filling for the imprint molds with vari-ous pattern densities in a patterned field in the sequentialstages of the imprinting process is shown in Fig. 10. Obvi-ously, under the applied 5.2-MPa load on the imprint mold,cavity 3 has been fully filled, while cavities 1 and 2 havenot yet been filled completely. The nonuniform mold fillingcan be explained by the existence of different moving dis-tances of polymer and uneven forces required to move thepolymer in a patterned field with various pattern densitiesduring the imprinting process. The existence of differentmoving distances of polymer is caused by the fact that thepolymer filling cavities 1 and 2 needs to be supplementedby the polymer around cavity 3. This need naturally resultsin the polymer traveling the longest distance to fill cavity 1,and the traveling distance for the polymer to fill cavity 2ranks second. On the other hand, the uneven forces are theresult of the higher force being required to move the largervolume of polymer in the dense feature region to fill upmultiple cavities at the same time. Due to the larger forcesfor moving polymer in the region of cavities 1 and 2, aslower movement of imprint mold in the region of cavities1 and 2 than in the region of cavity 3 happens and results inunequal mold filling among mold cavities.

Figure 11 presents the quantitative variations of thePMMA displacement among the cavities. From the datashown on the curves in Fig. 11, we found that the differ-ence of PMMA displacement between cavities 1 and 3 mayreach 21 nm at the stage of cavity 3 being filled completely.This phenomenon will cause nonuniformly imprinted pat-terns.

3.3 Sensitivity Analysis of the Effect of the ContactFriction Coefficient

In the previous simulated cases, to simplify the problem,the contact friction coefficient is assumed to be zero at theinterface of the imprint mold and polymer. However, inpractical nanoimprinting operations, the contact friction co-efficient should not be zero and the introduction of frictionmay be critical. Due to these considerations, a sensitivitystudy of the effect of the contact friction coefficient wasconducted to understand its effect on mold filling and the

Fig. 11 PMMA displacement of various cavities against appliedpressure.

applied pressure during the nanoimprinting process. In the


sensitivity analysis, in regard to the similarity of the simu-lation process, we took a case where the depth of the im-print mold cavity is 100 nm as a representative example.Meanwhile, the considered nanoimprint process was simu-lated with a series of contact friction coefficients of 0, 0.01,0.02, 0.04, 0.06, 0.08, and 0.10.

The results of the sensitivity analysis are illustrated inFig. 12. The increment of the contact friction coefficientfrom 0 to 0.1 does not influence the applied pressure levelrequired to fully fill up the mold cavity, and the correspond-ing variation in PMMA displacement is less than 1 nm. Theanalyses show that a small variation of the value of thePMMA displacement has been observed at the given varia-tion of the assumed value of the contact friction coefficient.Thus, it is reasonable to draw the preliminary conclusionthat the contact friction coefficient has mild effect on moldfilling.

4 ConclusionsThe isothermal stage of the imprinting process is investi-gated above the transition temperature of the PMMA poly-mer in this work. The effects of cavity aspect ratio, patterndensity, and contact friction existing between the mold andpolymer on the applied pressure and mold filling with dif-ferent cavity aspect ratios and mixed pattern density aresimulated, and a sensitivity analysis of the effect of contactfriction coefficient is also performed. The simulation resultsshow that both the cavity feature and pattern density havesignificant effects on mold filling of the nanoimprintingprocess, while the contact friction coefficient has mild ef-fect.

The imprinting process for PMMA polymer can be mod-eled effectively using the Mooney-Rivlin model and finiteelement discretization. The numerical simulations can pro-vide not only information on the initial and final states ofthe process, but also on the intermediate state of mold fill-ing. The results arising from the model indicate that theimprint mold with varied pattern density has nonuniformdisplacement during the imprinting process, which causespoor uniformity of the imprinted patterns. The obtained re-sults can support the development of the process recipe andautomatic large-scale industrial production for nanoim-printing.

During the numerical simulation of imprinting pro-cesses, special attention is paid to the adopted simplifica-tions. These simplifications include the assumed material

Fig. 12 Sensitivities of PMMA displacement and applied pressurewith respect to the contact friction coefficient.

model, choice of finite element, and the boundary condi-

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tions. A proper estimation of the condition on the contactbetween the imprint mold and the PMMA polymer is alsovery essential. This work concentrates on the isothermalstage of the complete imprinting process, under the as-sumption that the friction coefficient between the PMMApolymer and imprint mold is zero as a trial run. To build anaccurate model of imprinting processes for performing op-timum mold design and simulation, the cooling anddemolding stages of the imprinting process need to be ana-lyzed, and the temperature effects should be included in themodel to obtain an effective simulation of the completeimprinting process.

AcknowledgmentThe authors would like to thank the Ministry of EconomicAffairs of Taiwan for grant 94-EC-17-A-99-R1-0337, underwhich the investigation was possible.

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H. Hocheng obtained his BSc from NationalTaiwan University, Taiwan, in 1980, andlater his Diplom-Ingenieur from TechnischeHochschule Aachen, Germany. He receivedhis PhD from the University of California,Berkeley, in 1988. Presently Dr. Hocheng isa professor at National Tsing Hua Univer-sity. His fields of interest are innovativemanufacturing processes.

C. C. Nien obtained his BSc from NationalTaiwan University, Taiwan, in 1982, and hisMSc from Asian Institute of Technology,Thailand, in 1991. Presently he is a re-search engineer at Industrial TechnologyResearch Institute and also pursuing hisPhD at national Tsing Hua University. Hismajor research areas are mechanical sys-tems design and advanced manufacturingtechnologies.

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Numerical analysis of effects of mold features and contact