modeling pattern dependencies in the micron-scale embossing of polymeric layers

8/4/2019 Modeling Pattern Dependencies in the Micron-scale Embossing of Polymeric Layers

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Modeling pattern dependencies in the micron-scale

embossing of polymeric layers

Hayden Taylor1,a

, Ciprian Iliescub

, Ming Nib

, Chen Xingc,d

,Yee Cheong Lam

c, and Duane Boning

a

aMassachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA. USA

bInstitute of Bioengineering and Nanotechnology,

31 Biopolis Way, The Nanos #04-01, Singapore 138669c

School of Mechanical and Aerospace Engineering,

Nanyang Technological University, Singapore 639798d

Singapore-MIT Alliance, N2-B2C-15, 50 Nanyang Avenue, Singapore 639798

ABSTRACT

We describe a highly computationally efficient method for calculating the topography of a thermoplastic

polymeric layer embossed with an arbitrarily patterned stamp. The approach represents the layer at the time ofembossing as a linear-elastic material, an approximation that is argued to be acceptable for the embossing ofthermoplastics in their rubbery regime. We extend the modeling approach to represent the embossing of

layers with thicknesses comparable to the characteristic dimensions of the pattern on the stamp. We present preliminary experimental data for the embossing of such layers, and show promising agreement betweensimulated and measured topographies. Where the thickness of the embossed layer is larger than thecharacteristic dimensions of the pattern being embossed, the stamplayer contact pressure exhibits peaks atthe edges of regions of contact, and material fills stamp cavities with a single central peak. In contrast, when

the layer thickness is smaller than the characteristic dimensions of the features being embossed, contactpressures are minimal at the edges of contact regions, and material penetrates cavities with separate peaks attheir edges. These two apparently distinct modes of behavior, and mixtures of them, are well described by thesimple and general model presented here.

Keywords: hot embossing, micro-embossing, polymethylmethacrylate, polysulfone, thermoplastic polymers, simulation

1. INTRODUCTION1.1 Hot thermoplastic embossingBeing transparent, inexpensive and mechanically tough in comparison with silicon or glass, thermoplastics are well

suited to the volume-manufacture of microfluidic devices. The hot embossing of thermoplastic polymers is a promising

means of forming the microstructures required in such devices: it offers processing cycle times on the order of a minute,

and can be deployed with substrates ranging from the size of an individual chip to continuous reels of material. A typical

embossing process for device- or wafer-sized polymeric layers is illustrated in Fig 1. Customarily, the material is heatedabove its glass-transition temperature and the embossing load is then applied in order to transfer a microstructure from a

hard stamp to the softened polymer. The polymer is then usually cooled to below its glass-transition temperature, and the

load is then removed and the part separated from the stamp.

[email protected]; telephone +1 617 2530075

Invited Paper

Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IVedited by Jung-Chih Chiao, Alex J. Hariz, David V. Thiel, Changyi Yang, Proc. of SPIE

Vol. 7269, 726909 2008 SPIE CCC code: 0277-786X/08/$18 doi: 10.1117/12.810732

Proc. of SPIE Vol. 7269 726909-1


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When hot embossing is used for the fabrication of microelectromechanical systems (MEMS) or microfluidics, it is

usually performed on homogeneous polymeric sheets that are much thicker than the characteristic feature sizes of the

patterns being embossed. These embossed layers then constitute the body of the device being manufactured. We have

previously put forward a highly computationally efficient simulation approach that can provide an approximation to the

topography of a thick polymeric layer after embossing with an arbitrarily micro-patterned stamp 1.

polymeric layerstampheated platen attachedto load frame

applied load

rigid backing plateelastomeric gasketheated platen

substrateapplied load

temperature

time

loading duration

Tg

(a) (b)

Fig. 1. Illustration of the hot embossing process. (a) The polymeric layer to be embossed is placed in contact with a micro-patterned stamp and both are inserted between two flat, heated platens. The polymeric layer may be self-contained or

alternatively may have been deposited or bonded on to a substrate such as a silicon wafer. (b) The temperature of thepolymer/stamp stack is increased above the glass-transition temperature of the polymer, and a load is subsequentlyapplied and held for some time, usually ~1 minute. The materials are then typically cooled to below the glass transitiontemperature of the polymer, before the load is removed.

There is, however, growing interest in micro-patterning polymeric layers whose thickness is comparable to the feature

dimensions being embossed. Embossed thermoplastic films with thicknesses in the approximate range 10100 m couldbe used to construct multi-layer disposable microfluidic devices especially if the layers could be pierced with inter-

layer fluidic conduits or vias. Such devices could perhaps be made flexible and could adopt a smart-card format.

Polymeric films with thicknesses in this range are already being industrially embossed with micron-scale patterns 2, 3

often having optical applications although there is not yet, to our knowledge, a computationally affordable way of

simulating the hot embossing of arbitrary, complex patterns in finite-thickness layers. Such a capability would provide

device designers with an estimate of the stamp-average pressure that would need to be applied at a certain temperature to

fill the cavities of a specific stamp with the polymeric material. Equipped with this capability, device designers would beable rapidly to refine new designs, making them more easily manufacturable. In this work we propose an approximate

way of modeling the embossing of finite-thickness thermoplastic layers in a rubbery regime. We show preliminary

experimental results, against which the modeling approach is evaluated.

2. THEORY AND SIMULATION APPROACH2.1 Material modelThe thermoplastic polymeric materials used in microfabrication are usually of a sufficiently large average molecular

weight and processed sufficiently far below their melting temperature that their behavior when embossed can adequately

be described as rubbery. This means that when compressed with a patterned stamp, the layer rapidly approaches a

limiting topography governed by the elastic component of the materials behavior. Such temperature-and time-dependentbehavior has been studied in detail for polymethylmethacrylate (PMMA), for example4.

For the purposes of our approximate simulation method, we capture this rubbery behavior with a linear Kelvin-Voigt

model of the material, illustrated in Fig 2. Both the elasticity, E, and the strength of intermolecular resistance to flow

signified by a viscosity, are assumed to be decreasing functions of temperature, T, exhibiting reductions of perhapsseveral orders of magnitude as the temperature increases through the glass-transition temperature, Tg. In a range of

temperatures from slightly above the glass-transition to several tens of degrees above it, we regard the intermolecular

resistance to flow as being small in relation to the elasticity. As a result, the time taken for the embossed material to



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approach its limiting topography is reduced to perhaps only a few tens of seconds, which is a substantially shorter time

than typical loading durations for hot embossing.

For embossing processes performed in this rubbery temperature range and with loading durations more than a few times

the materials time constant, it follows that an approximation to the embossed topography can be obtained by modeling

the material as a purely elastic layer whose elasticity isE(T). The topography is assumed to be frozen in place when it

is subsequently cooled under load and the intermolecular resistance to flow increases.

Embossing cases in which the materials flow time constant is comparable with the loading duration can be modeled

moderately well by a simple scaling of the effective elastic modulus of the material. In our previous work1 we showed

how this might be done for embossing temperatures only slightly above Tg, and a more comprehensive approach is laidout in work to be published separately.

(a) (b)

E T( ) ( )T

temperature, TTg

rubberybehavior

melt

storagemodulus

lossmodulus

log |modulus|applied load

Fig. 2. Material model assumed for approximate simulations of the embossing of thermoplastic polymeric layers. A Kelvin-

Voigt material model (a) is assumed, with temperature-sensitive elasticityEand intermolecular resistance, or viscosity,. We confine our attention to simulating embossing in the rubbery regime of the materials behavior (b), in which,when embossed, the layer quickly approaches a limiting topography governed by the elastic component of the

materials behavior. When cooled, the viscosity increases substantially, and is assumed to freeze this topography inplace.

The use of a linear model ignores the non-linear stressstrain relationship typical of true rubbers; this simplification is asacrifice that is made to enhance computational speed and it requires that strains in a sufficiently large proportion of the

volume of the embossed layer are sufficiently small that a linear stressstrain relationship remains an acceptable

approximation.

2.2 Simulation basisIn previous work we used a linear-elastic approximation to the behavior of a heated thermoplastic layer to develop a

simulation approach for the embossing of thick layers1. Assuming small deflections, and no friction between the stamp

and polymer, the out-of-plane surface displacement w(x,y) of an elastic half-space whose surface is exposed to a normal

contact pressure distributionp(x,y) is given by:

( )( ) ( )

ydxdyyxx

yxpE

yxw +

= 222

,1),( (1)

where v is Poissons ratio and Eis Youngs modulus5. To build a simulation, the elastic layer is discretized on a square

grid composed ofN N regions each having diameter d. We index these regions using m and n, where x = mdand

y = nd. The response, c[m, n], of the layers surface deformation to unit pressure applied across a d dregion centered at(m = 0, n = 0) is, via evaluation of (1):



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( ) ( ) ( ) ( )[ ]111221222

,,,,1

],[ yxfyxfyxfyxfE

nmc +

=

(2)

where

( ) ) )2222 lnln, yxyxyxxyyxf +++++= . (3)

and x1 = mdd/2; x2 = md+ d/2; y1 = ndd/2; y2 = nd+ d/2. (4)

We discretize our representation of the stamps topography on a grid of the same dimensions: each region of the grid is

assigned one topographical height representing the design of the stamp.

We then iteratively find the distribution of stamppolymer contact pressures that is consistent with the stamp remaining

rigid while the polymer deforms. The solution is further constrained by the requirement that the spatial average of

contact pressures must equal the specified average pressure applied to the stamp by the embossing apparatus. At each

step of the iterative process, the forward computation of the polymers topography is performed by convolving the

response of the elastic surface to unit pressure in one grid cell (Equation 2) with the candidate pressure distribution

p[m, n]. This convolution is implemented using fast Fourier transforms, and since the problem is solved discretely there

is an implicit assumption that the pressure distribution and hence the surface deformation of the elastic layer is

periodic in space, with periodNdin bothx andy directions. Since we anticipate our approach being used to simulate the

embossing of large arrays of identical microfluidic devices on a single polymeric layer, for example, we see this

assumption of periodicity as being an advantage.

The iterative solution process must also establish which regions of the stamp are in contact with the polymer when the

given embossing load is applied i.e. which cavities are filled with material. Therefore when a solution for the pressure

distribution is found, the corresponding polymer topography is computed and any parts of the simulation region in which

the polymer would intersect with the stamp are added to the set of cells assumed to be in contact. Any parts of the

contact set in which the computed pressure is tensile are removed from the contact set: the stamp is assumed to be unable

to stick to the polymer. This iterative process is repeated until either the contact set is unchanged with a new iteration, or

a specified maximum number of iterations have been completed. The solutions for contact pressure distribution and

polymer topography that exist at the end of this process are returned as the result of the simulation.

(a) (b)

polymer: ,E1 1n

substrate: E2 2, n

point load

polymer: ,E1 1n

h

Fig. 3. Comparison of the point-load responses of thick and thin polymeric layers. When the layer is much thicker than thecharacteristic lateral dimensions of the structure being imprinted (a), the layer can be well approximated as an elastichalf-space. When the layer thickness is comparable with the dimensions of the pattern being imprinted (b), a different

function, dependent on h, is required.Eiare the layers Youngs moduli; v

iare their Poissons ratios.

2.3 Extension to finite-thickness substratesThe procedure described in 2.2 was derived for infinitely thick substrates. For micro-embossed polymeric layers on the

order of 1 mm in thickness, such a model has been seen to represent experimental results well. For thinner layers,

however, a more general approach is needed (Fig 3). We begin by confining ourselves to cases in which, although the

layer may be thin in comparison with the diameters of the largest features on the stamp, the average thickness of the



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layer is reduced, during embossing, by only a small proportion of its original thickness. Such an assumption would

presumably be valid when modeling a process in which a stamp with a patterned relief of, say, 10 m was embossed into

a layer of thickness 100 m.

All that needs to change in our simulation approach is our description of how the materials surface deforms when

exposed to unit pressure across one element of the discretized polymer surface. We use an approach described by

OSullivan and King 6, and later employed by Peng and Bhusan7 and by Nogi and Kato8, in which an analytical solution

is found for the Papkovich-Neuber potentials in the upper layer, 1. The stresses and displacements in the layer are thenfound for the application of unit pressure to a central d dregion of the surface. The solution is performed in the spatial

frequency domain and the inverse Fourier transform is subsequently computed numerically to give a spatial

representation of the kernel function. The Fourier transform of the surface deflection of layer 1 is given by:

( ) ( ) ( )[ ] RhhhC

4exp2exp41

1,

1

1 +

= (5)

where and are spatial frequencies and

( )( )( ) ( )121

21

221

122

43

1;

431

141;

+

=+

=+= fk

( ) ( ) ( )[ ] 2122 4exp2exp41 +++= hhhR .

(6)

The thickness of layer 1 (as defined in Fig 3) is denoted as h and layer 2 is assumed infinite in thickness; i are the

layers shear moduli, equal to Ei/[2(1+i)]. The factor kf is introduced here as a way of tuning the model toexperimental results. It has no physical basis at present but has been found to be needed to model some of the results that

will be presented in Section 4. In the absence of tuning, kfis set to 1.

In this implementation, C[m,n] are computed over a range of 2Nform and n, where m = mkf/Ndand n= nkf/Nd. The

value of C[0, 0] is undefined according to (5); however, since most thermoplastics above their glass transition

temperature are almost incompressible, we set C[0, 0] to zero, with the result that the average value of the function in the

spatial domain will be zero consistent with conservation of the layers volume. After inverse Fourier transformation

ofC[m,n] and scaling up by the empirical factor kf, the central N N region of the resulting matrix is taken as the

kernel function, c[m, n], for use in simulation (Fig 4). This approach to constructing the kernel function has been found

necessary in order to give accurate simulations of long-range pattern interactions. (In the subsequent simulation, c[m, n]is again Fourier-transformed as part of the forward convolution with trial pressure distributions.)

inverseFourier

transform

kf

k Ndf /

h

x2N

d

y

xN

simulation

(a) frequency domain (b) spatial domain

domain

Fig. 4. Illustration of the relationship between frequency and spatial domains in the construction of the point-load responsekernel function. Coefficients in the frequency domain are calculated across a matrix with four times as many elementsas are in the spatial representation of the region to be simulated. The additional empirical factor kf is introduced to

allow the characteristic length of the kernel function to be tuned to experimental results if necessary. After inverseFourier transformation and scaling by kf, the central N Nelements of the resulting matrix are used as the kernelfunction. After Nogi and Kato8.



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The substrate would usually be expected to be much harder than the polymeric layer, although its stiffness and Poissons

ratio can be appropriately specified. The substrate is also assumed in this formulation to be bonded to the polymeric

layer. If the substrate is genuinely attached to the layer as it would be if the polymer had been spun on to a silicon

wafer prior to embossing we would almost certainly be comfortable with this assumption. If, however, the polymer

layer is self-contained (e.g. an extruded film), the assumption may be less valid. It would be possible to derive kernel

functions for various polymersubstrate coefficients of friction.

The kernel function was evaluated and is plotted in Fig 5 for three values ofh. In the functions plotted here, the layer isassumed to have a Youngs modulus of 2 MPa and a Poissons ratio of 0.5, and each function is discretized at a 1 m

pitch and evaluated over a 512 m 512 m region. Forh = 1 mm, the function produced by evaluating and inverseFourier-transforming (5) is almost indistinguishable from the analytical function of (2) for an elastic half-space. For

h = 75 m, the diameter of the kernel function has tightened somewhat but retains largely the same shape. For h = 2.2

m, however, the function has changed radically to a two-peak form in which material is displaced upwards around the

region of application of pressure.

radial position (m)radial position (m)

surfacedisplacement(

m)

h = 75 m

h = 1 mm

Elastichalf-plane

h = 2.2 m

h = 2.2 m

h = 75 mh = 1 mmand elastichalf-plane

Fig. 5. Comparison of kernel functions generated for three different layer thicknesses. The functions are discretized with

pitch d = 1 m and describe the displacement of an elastic materials surface in response to unit pressure applieddownwards across a region of size d d, centered at (0, 0). The layer, of thickness h, is assumed to have a Youngsmodulus of 2 MPa and a Poissons ratio of 0.5. The three function instances for which h is defined were generatedfollowing the method described by Nogi and Kato8. For h = 1 mm, the finite layer-thickness function is virtually

indistinguishable from the analytical function for the surface displacement of an elastic half-space5. Forh = 75 m, theshape is appreciably changed, and for h = 2.2 m, the function has morphed into one with two peaks, indicatingupwards displacement of material around the point of loading.

While the method for computing the kernel function for a finite-thickness layer produces a smooth result when h >> d,

the kernel function is noticeably rough when d~ h. Although, as will be seen in Section 4, the rough function is still ableto provide smooth and realistic simulated topographies, it may prove desirable to smooth the kernel function, perhaps by

evaluating C[m,n] over a larger range of frequencies and downsampling the inverse-transformed function.



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3. EXPERIMENTAL METHOD3.1 Test-pattern designThe test-pattern illustrated in Fig 6 was used to conduct embossing experiments against which to compare simulation

results. The pattern comprises a 30 mm square array of identical cells, with each cell having diameter 0.85 mm. The cell

design, when transferred to an embossing stamp, incorporates square holes and trenches with diameters and separations

ranging from 10 to 100 m. The design of the pattern is deliberately periodic, to allow for convenient simulation usingthe method described above.

0.85 mm

A

polymer sample silicon stamp

stamp cavity

stamp surface

B

A

B

Fig. 6. Test-pattern for embossing polymeric layers. The design of one unit of the pattern contains square holes, trenches and

ridges ranging from 10 to 100 m in diameter. The relief of the pattern on the test stamp is ~ 30 m. The stamp ispatterned with a square, homogeneous array of these units at a pitch of 850 m. The array of patterns extends beyondthe edges of the polymeric sample. Two sections through the pattern are defined for the analysis of results: AA,which is through embossed ridges/trenches, and BB, which is through square posts on the embossed part.

3.2 Test stamp fabricationThe test-pattern illustrated was etched into a silicon wafer using deep reactive ion etching to a depth of approximately

30 m. The etch mask was a 10 m-thick layer of AZ4620 photoresist and after etching this was removed from the wafer by a 30-minute oxygen plasma exposure followed by a 15-minute immersion in a hydrogen peroxide/sulfuric acid

pirahna mixture.

3.3 Embossing of 75 m-thick PMMA filmSheets of 75 m-thick Rohaglas 99845 PMMA were obtained as a gift from Degussa HPP Technical Films (Madison,

WI). Two preliminary 15 mm square samples were cut from the film and embossed with the silicon test stamp under the

following conditions: (i) 75 C, with a sample-average pressure ofc. 4 MPa; (ii) 80 C, with a sample-average pressure

of 13 MPa. In both cases the load was held for 2 minutes before cooling to 40 C and unloading. The embossing

apparatus used was a Carver (Wabash, IN) 4386 manual hydraulic press equipped with electrically heated platens and

water-assisted cooling.

A 1.5 mm-thick polycarbonate plate served as the rigid backing plate of Fig 1a: since the embossing temperature was

well below polycarbonates glass-transition temperature of ~137 C, it was assumed that the Youngs modulus of the

backing plate was 3 GPa and with a Poissons ratio of 0.3.

3.4 Embossing of spun-on 2.2 m-thick polysulfone filmPolysulfone (BASF, Florham Park, NJ) was dissolved at a concentration of 15 wt% in N-Methylpyrrolidone, and was

spun at 1000 r.p.m. on to silicon wafers on to which had first been deposited a silicon nitride layer using the process

detailed by Iliescu et al.9: it was found that the nitride layer promoted the adhesion of the polysulfone to the wafers

surface. After spinning, the wafers were baked on a hotplate at 110 C for 1 minute. A wafer coated in this way was



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diced into pieces c. 15 mm square. As a preliminary test, one of these pieces was embossed at 205 C with a sample-

average pressure of 30 MPa that was held for 2 minutes before cooling. The embossing temperature was 20 C above the

published value of polysulfones glass-transition temperature. Because of the high temperature of embossing, it would

not have been safe to use the water-cooling capability of the press, and the platens were instead allowed to cool, via

radiation and the convection of air, at a much slower rate, taking ~20 minutes to reach the unloading temperature of

~130 C.

3.5 MeasurementThe pre-embossing thickness of the spun-on polysulfone film was measured by scratching the film from part of a

fragment of a film-coated wafer, sputtering the fragment with ~50 nm gold, and profiling the surface with a Zygo

(Middlefield, CT) NewView scanning white-light interferometer. The PMMA films thickness, meanwhile, was

measured with a micrometer screw gauge.

The polysulfone sample, post-embossing, was scratched in a small region to reveal the underlying substrate. These

samples, and the embossed PMMA films, were sputtered with ~50 nm gold and their surfaces were profiled with the

white-light interferometer. Using this interferometer, the area of a single cell could be scanned at a lateral resolution of

~0.5 m in ~2 minutes. Measurement is quick enough that several measurements can efficiently be made at various

positions on a sample, giving an impression of the spatial uniformity of the embossed pattern or of the frequency of

defect occurrence. The topography of the etched silicon stamp was also measured by white-light interferometry.

4. RESULTS AND DISCUSSION4.1 75 m-thick PMMA layerWe consider first the results of embossing the 75 m-thick PMMA film. Cross-sections through the measured

topographies are plotted in Fig 7. For the sample processed at 75 C with a sample-average pressure of 4 MPa (Fig 7a

and 7b), penetration of the stamp cavities was everywhere less than 2 m. A finite-thickness linear-elastic model of the

embossed layer was fit to these experimental results, and the red solid lines in Fig 7a and 7b correspond to an effective

elastic modulus of 163 MPa. The effective modulus was the only fitting parameter; the factor kf was kept equal to 1. The

shape and magnitude of the simulated topographies match the measurements closely. We also plot, as a dashed green

line, the topography predicted by an infinite-thickness layer model having an effective Youngs modulus of 163 MPa.

Interestingly, the infinite-thickness model under-predicts by as much as 30% the degree of penetration of the narrower

cavities, but substantially overestimates the degree of penetration of the 100 m-wide cavity. In other words, for a givenapplied embossing pressure, cavities narrower than the layer thickness are penetrated further than they would be if the

layer were infinitely thick, while cavities wider than the layer thickness are penetrated less far than they would be for a

thicker layer. This result is worth noting, because it suggests that for a given stamp pattern there may be a finite

polymeric layer thickness that is optimal for embossing in the sense that it requires a minimal pressure to fill all its

cavities.

For the sample embossed at 80 C with a sample-average pressure of 13 MPa, the finite-thickness substrate model tracks

well the peak cavity penetration depths when an effective layer modulus of 10.7 MPa is chosen (Fig 8b). That this

modulus is more than a decade smaller than the modulus fit for the sample embossed at 75 C indicates that these

samples were processed in the glass-transition region of the polymer, in which the viscoelastic parameters vary rapidly

with temperature. Extensive further investigation would be needed to place fully in context these point-estimates of

effective modulus. Yet the point that can be taken from this experiment is that a linear-elastic material representation,

using an appropriately scaled modulus, can provide a good prediction of embossed topography.

Although the peak depth of cavity penetration is well captured by the model, theshape of the material penetrating each

cavity is not very closely represented: the simulation implies that material penetrating the narrow cavities adopts a

parabolic shape, while a scanning electron micrograph of the embossed part (Fig 8c) indicates a more rectangular shape

for the plug of material penetrating each cavity. A modified kernel function shape might better capture the embossed

topography, although the ability of this simulation technique to establish the necessary embossing pressure for near-

complete stamp filling may well prove to be adequate as it stands.



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topograp

hy

(m

)

75 C

4 MPa

(a) Section AA

(b) Section BB

(c) Section AA

(d) Section BB

simulation: finite-thickness model

experiment

measured tops of Si stamp cavities

lateral position (m)

topograp

hy

(m

)

80 C13 MPa

simulation: infinite-thickness model

Fig. 7. Results of embossing two samples of Rohrglas 99845 PMMA. One was embossed at 75 C and a sample-averagepressure ofc. 4 MPa, and the other at 80 C and c. 13 MPa. The loading duration was 2 minutes in each case. Measuredtopographies through sections AA (ridges) and BB (posts), as defined in Fig. 6, are shown for each sample (blackcircles), along with the equivalent simulated topographies (red solid lines) and the measured locations of the tops of thestamp cavities (blue dashed lines). In (a) and (b), green dashed lines also show the prediction of an infinite-thickness

model of the polymeric layer.



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( a ) s i m u l a t e d c o n t a c t p r e s s u r e ( M P a ) ( b ) s i m u l a t e d t o p o g r a p h y ( p m ) 3 51 5 0 : i i f f l I

0 0 I - - A U J L L . . J - . . . ' H J L L L . J -2 01 l z _ _ _ _ _ - , - J - -, f t 1 1 1 1 . 1 5 O / f J I i 4 i i I i i i 1 I , j: U U _ ! ! . . L _( c ) 5 0 0 p m

Fig. 8. Simulation vs. experiment for the embossing of Rohrglas 99845 PMMA at 80 C and a sample-average pressure ofc.

13 MPa for 2 minutes. The simulated contact pressure distribution (a) indicates that the contact pressure peaks at theedges of the stampsubstrate contact regions. A 3-D plot of the simulated topography (b) shows that wider featureshave been penetrated more deeply by polymer. A scanning electron micrograph of a region of the sample (c)demonstrates the reasonable fidelity of the simulation.

4.2 2.2 m-thick polysulfone layerWe now consider the embossing of the polysulfone film. Fig 9 shows topographies measured at two separate sites on thesame sample, which was embossed at 205 C for 2 min under 30 MPa. Whereas, with the 75 m-thick film, the wider

cavities on the stamp filled more readily, in the case of this thinner film the depth of cavity penetration is larger for the

smallercavities, and especially for those cavities surrounded by large regions of the stamp without cavities (Fig 10a).

Moreover, the topography of material penetrating each cavity wider than 10 m now exhibits separate peaks at the cavity

edges, in place of the single central peak seen with layers that are thicker than the cavity widths. This dual-peak filling

mode is similar to that observed at the considerably smaller scales of thermal nanoimprint lithography 1012.

The finite-thickness kernel function generated for the measured film thickness of 2.2 m yielded a simulated topography

with peaks that were rather too sharp and too close to the edges of the cavities. By tuning the scaling factorkf to 2.5, the

characteristic diameter of the kernel function is increased by that factor and the shapes of most peaks are now well

represented. The only exception is the very tall peak at the right hand side of the traces in Fig 9, which the scanning

electron micrograph of Fig 10c indicates has in reality curled over towards the substrate, reducing its height.

A corresponding effective elastic modulus of 4 MPa was fit for the layer.

Proc. of SPIE Vol. 7269 726909-10


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topograp

hy

(m

)

topograp

hy

(m

)

measuremen

ts

ite

1

measuremen

ts

ite

2

(a) Section AA

(b) Section BB

(c) Section AA

(d) Section BB

simulation experiment measured tops of Si stamp cavities

lateral position (m)

posts broken

Fig. 9. Comparison of experimental results and simulation for the embossing of a 2.2 m-thick spun-on film of polysulfone.

The sample was embossed at 205 C with a sample-average pressure of 30 MPa held for approximately 2 minutesbefore cooling to ~130 C over ~10 minutes and unloading. Measurements from two separate locations on the sample

are shown. Measured topographies through sections AA (ridges) and BB (posts), as defined in Fig. 6, are shown foreach location (black circles), along with the equivalent simulated topographies (red solid lines) and the measuredlocations of the tops of the stamp cavities (blue dashed lines).

Proc. of SPIE Vol. 7269 726909-11


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2 0 02 0 0 1 0 0

5 0 0 0 23 0 0

o 02 0 0

9 0 0- - 1 20 o

0 5

- - 3 2

h f r - f lL L n f l ; r T n _H

. 1

0

5

10

15

20

25

30surfaceposition (m)

20 m

200 m

(a)

20 m

(b)

(c)

Fig. 10. Simulation vs. experiment for the embossing of a 2.2 m-thick spun-on film of polysulfone. A 3-D plot of thesimulated topography (b) indicates that the narrower cavities, and especially those surrounded by few other cavities,have filled the most deeply. Scanning electron micrographs of the sample (a, c) verify this behavior.

As the thickness of the polymeric layer reduces, the nature of the simulated pressure distribution also changes

substantially. With the 75 m-thick layer, contact pressure exhibits peaks at the boundaries of cavities (Fig 8a), while for

the 2.2 m-thick layer, contact pressure is minimal at cavity edges and increases with distance from a cavity (Fig 11a).

The location of the peak of the simulated pressure distribution for the 2.2 m-thick layer corresponds to some interesting

artifacts in a portion of the sample (Fig 11b). Profiling of one of these artifacts showed that the layer thickness had

apparently sprung back to its original value at the center of the artifact. Further investigation of the causes of these

defects is needed.

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( b ) 5 0 0 p m

T I ! U U U b I i l l I : 9 [ jU : : : . . . J : : : : g , :U ! i I L u U U ! u U !i : u : . a c i : : : : . . 0I I D E - _ _ _ _ _ . 1 I l L E I . _ _ _ _ _ _ I I I L L I _ _ _ _ . . . . p I 1 c I c

r 2 1:

s )

.a

mt

s

i g F.

C (

' c t , - o 000

0 0 . 2 0 . 4 0 . 6 0 . 8L a t e r a l p o s i t i o n ( m m )

I i4 U - . IU a

Y ' i p( a ) - 2 0 p m ( b ) 2 0 0 p m ( c ) 2 0 p m

Fig. 11. (a) Simulation of stamppolymer contact pressure distribution in the embossing of a 2.2 m-thick spun-on film of polysulfone. The simulated pressure increases with distance from the edges of the contact region. An opticalmicrograph of several copies of the test pattern in part of the embossed sample (b) indicates defects in the compressed

region of the polysulfone film, corresponding in shape to that of the simulated pressure distribution. Profilometry ofone of these defects (c, d) indicates that the compressed layer has sprung back to approximately its original thicknessin the center of the defect region.

Fig. 12. Scanning electron micrographs of the embossed polysulfone sample. (a) Close-up of 10, 20 and 30 m-diameterposts and ridges, showing the edge-peaks in the topographies of incompletely filled features and the places where 10

m-diameter posts had been torn from the film during separation of the stamp from the layer. (b) Oblique view of threecopies of the test pattern, showing the topography of the embossed layer. (c) Close-up of the ends of two embossedridges, in a region where part of the film has been scratched away, revealing the SiN substrate and showing the

thickness of the compressed layer of polysulfone.

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Our current modeling approach is based on the assumption that, while the layer may be thin, it is compressed by only a

small proportion of its thickness. In fact, the minimum post-embossing layer thickness of polysulfone was measured as

1.6 m, which is around 70% of the starting layer thickness. This is a substantial reduction, and to be modeled properly

we might need to consider finding the true final pressure distribution as the superposition of a series of pressure

distributions associated with progressively thinner layers. We do not, however, anticipate that such a refinement would

deal with the modeling problem that the scaling factor kf is designed to overcome: thinner layers are associated with

narrower load-response kernel functions, while in contrast we found that we needed a broaderkernel function than was

directly predicted by the 2.2 m initial thickness.

4.3 Simulation speedThe test pattern was discretized for simulation on a 1m-pitch grid of 850 850 elements. In cases where the initial

guess for the contact set was accurate, the simulation, which was implemented in MatLab (The Mathworks, Natick,

MA), completed in between 30 and 90 s using a desktop computer equipped with two 3.2 GHz Intel Pentium 4

processors and 2 GB of RAM. In the case where material had touched the tops of some of the cavities (PMMA embossed

at 80 C), additional iterations to find the contact set extended the simulation time to up to ten minutes. In comparison

with full three-dimensional finite-element modeling of such a structure, we anticipate that our simulation approach will

be shown to be approximately two orders of magnitude faster.

5. CONCLUSIONWe have outlined a computationally inexpensive way of simulating the hot-embossing of thermoplastic layers of finite

thickness. A simulation in which the embossed layer is discretized on a grid of size 850 850 takes between one and ten

minutes to run. The results of such simulations have been shown to capture the key topographical features of real

embossed thermoplastic layers having two markedly different layer thicknesses. The thickness of one of these layers, 75

m, was larger than most of the feature dimensions of the embossed pattern, while the other, at 2.2 m, was substantially

thinner than all feature dimensions.

There remains much work to be done to establish the extent of validity of this modeling approach, but it appears to offer

a promising means by which to select appropriate processing parameters for the successful embossing of a given pattern.

The insights offered by this modeling approach could also be used to guide the design of embossed patterns for

example, by informing the introduction of dummy features on embossing stamps to relieve contact pressure

concentrations.

Ongoing work aims to refine the simulation method to deal with cases in which parts of a finite-thickness layer are

reduced, during embossing, to a small proportion of the initial layer thickness. When this refinement is accomplished, the

computationally efficient simulation of nanoimprint lithography will be an avenue along which this work can be

extended.

6. ACKNOWLEDGEMENTSWe thank N. Ames, L. Anand, B. Anthony, M. Dirckx, D. Hardt, and Y. Hirai for helpful discussions. We acknowledge

the support of the SingaporeMIT Alliance as well as the use of MITs Microsystems Technology Laboratories in the

course of this work.

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7. REFERENCES[1] Taylor, H., Boning, D., Iliescu, C. and Chen, B., Computationally efficient modelling of pattern dependencies

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modeling pattern dependencies in the micron-scale embossing of polymeric layers

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