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Fast simulation of pattern dependencies in thermal nanoimprint lithography13 November 2009Hayden Taylor and Duane Boningy y gMassachusetts Institute of Technology
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Nanoimprint modeling needs
• Cell-level• Hundreds of featuresHundreds of features• Guide iterative layout design • Desktop processing in minutes
• Chip-level• Many millions of featuresy• Pre-fabrication check: overnight?• Guide process selection
• Need for flexibility• Rapid innovation in resist and
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stamp materials• Richness of geometries
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We need a unified simulation approach for micro- and nano-embossing/imprinting
stamp
w10 mm
Initial polymer thickness, r0
polymerpolymersubstrate
r010 mm
1 mmBiological micro-/nano-devices
100 µm
10 µm
Tissue engineeringDiffractive optics
µ
1 µmFlat-panel displays
PlanarizationPhotovoltaics100 nm
Cavity
PlanarizationPhotovoltaics
MetamaterialsPhotonicsSemiconductorsHard-disk drives
3
ywidth, w1 nm 10 nm 100 nm 1 µm 10 µm 100 µm
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We need a unified simulation approach for micro- and nano-embossing/imprinting
Initial polymer thickness, r0
10 mm
Biological micro-/nano-devices
10 mm
1 mm
Tissue engineeringDiffractive optics
100 µm
10 µm
Flat-panel displays
PlanarizationPhotovoltaics
µ
1 µm
Cavity
PlanarizationPhotovoltaics
MetamaterialsPhotonics100 nm
SemiconductorsHard-disk drives
4
1 nmy
width, w1 nm 10 nm 100 nm 1 µm 10 µm 100 µm
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Key: model impulse response g(x,y,t) of resist layer
Model in time:Model in space:x
Newtonian: impulse response
t t i
g Mechanical impulse applied Resist constant in
time for t > 0uniformly over small region at time t = 0
Resist
Viscoelastic: impulse response is
Resist
response is function of time.
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ResistSubstrate
After Nogi et al., Trans ASME: J Tribology, 119 493-500 (1997)
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Change in topography is given by convolution of impulse response with pressure distribution
Stampp(x,y,t) ?Small, unit
ResistSubstrate
,disp.
Time increment
1 ttyxgtyxp ),,(),,(
Pressure Impulse Unit displacement
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Pressure Impulse response
Unit displacement in contact region?
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Contact pressure distributions can be found for arbitrary stamp geometries
2.3 µm-thick polysulfone film embossed at 205 °C under 30 MPa for 2 mins
Stamp design Simulated pressure Optical micrograph
160 MPa0Cavity 200 µm
Taylor et al., SPIE 7269 (2009).
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Successful modeling of polysulfone imprint2.3 µm-thick polysulfone film embossed at 205 °C under 30 MPa for 2 mins
8Taylor et al., SPIE 7269 (2009).
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Representing layer-thickness reductions
pg defined in terms of:
t ttJd
g
• True pressure p(x, y, t)• Material compliance J(t)
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ht
hg ttttJtyxptyxp
0
2 dd
d,,)1(,,
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Modeling stamp and substrate deflectionsIndentation Indentation and bending
λ λ
tstamp
Elastic point-load responsesIndentation Bending
Elastic point load responses
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Modeling stamp and substrate deflectionsIndentation Indentation and bending
λ λ
tstamp
log(magnitude ( gof stamp deflection)
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log(λ/tstamp)~4
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Simulation method: step-up resist compliancePMMA 495K, c. 165 °C, 40 MPa, 1 min
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Abstracting a complex pattern
Local relationships between pressure-compliance and RLT:
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Simulation results: abstracted pattern
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Simulation time
Simulation time (s) N
E t d
104Expected:
time ~ O(N2logN)
100
1000Stamp 1Feature-scale
10
100
10 100 1000 104
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10 100 1000 10 Stamp 2AbstractedSimulation size, N
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Strengths of the simulation method
• A unified simulation approachC ith l thi k• Can cope with any layer thickness
• Can integrate feature sizes ranging over many orders of magnitude
• Can model any linear viscoelastic material• Speed
• At least 1000 times faster than feature-level FEM
Implicit periodic bo ndar conditions are sef l• Implicit periodic boundary conditions are useful• Realistic representation of whole-wafer imprint of many chips• Can use edge-padding for non-periodic modeling
• Suited to quick adaptation for new NIL configurations• Use to explore the use of flexible stamps and substrates• Explore the imprinting of non-flat substrates
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g• Micro-contact printing; roll-to-roll
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Varying stamp’s bending stiffness: simulations
Stamppthicknesses:
5 mm5 mm
0 5 mm
Features
0.5 mm0.12 mm
Features
200 nm Residual layer
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4 mm
layerthickness
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Summary: fast nanoimprint modeling
• Contributions• Flexible modeling approach• Pattern abstraction optional• Suited to cell and chip scalesSuited to cell and chip scales• 1000+ times faster than FEM
O tl k• Outlook• We will need NIL-aware design
checking• Can use as an engine for
“Mechanical Proximity Correction”
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Acknowledgements
• Funding• The Singapore-MIT Alliance
• Colleagues• Colleagues• Matt Dirckx, Eehern Wong, Melinda Hale, Aaron Mazzeo,
Shawn Chester, Ciprian Iliescu, Bangtao Chen, Ming Ni, and James Freedman of the MIT Technology Licensing OfficeJames Freedman of the MIT Technology Licensing Office
• Helpful discussions• Derek Bassett, Roger Bonnecaze, Siddharth Chauhan, Grant
Willson, Yoshihiko Hirai, Wei Wu, Roger Walton, and John Mutkoski
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