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13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100...

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Fast simulation of pattern dependencies in thermal nanoimprint lithography 13 November 2009 Hayden Taylor and Duane Boning Massachusetts Institute of Technology
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Page 1: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Fast simulation of pattern dependencies in thermal nanoimprint lithography13 November 2009Hayden Taylor and Duane Boningy y gMassachusetts Institute of Technology

Page 2: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

2

stamp materials• Richness of geometries

Page 3: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

Page 4: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

Page 5: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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.

5

ResistSubstrate

After Nogi et al., Trans ASME: J Tribology, 119 493-500 (1997)

Page 6: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

6

Pressure Impulse response

Unit displacement in contact region?

Page 7: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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).

Page 8: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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).

Page 9: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Representing layer-thickness reductions

pg defined in terms of:

t ttJd

g

• True pressure p(x, y, t)• Material compliance J(t)

9

ht

hg ttttJtyxptyxp

0

2 dd

d,,)1(,,

Page 10: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Modeling stamp and substrate deflectionsIndentation Indentation and bending

λ λ

tstamp

Elastic point-load responsesIndentation Bending

Elastic point load responses

10

Page 11: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Modeling stamp and substrate deflectionsIndentation Indentation and bending

λ λ

tstamp

log(magnitude ( gof stamp deflection)

11

log(λ/tstamp)~4

Page 12: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Simulation method: step-up resist compliancePMMA 495K, c. 165 °C, 40 MPa, 1 min

12

Page 13: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Abstracting a complex pattern

Local relationships between pressure-compliance and RLT:

13

Page 14: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Simulation results: abstracted pattern

14

Page 15: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Simulation time

Simulation time (s) N

E t d

104Expected:

time ~ O(N2logN)

100

1000Stamp 1Feature-scale

10

100

10 100 1000 104

15

10 100 1000 10 Stamp 2AbstractedSimulation size, N

Page 16: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

16

g• Micro-contact printing; roll-to-roll

Page 17: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

Varying stamp’s bending stiffness: simulations

Stamppthicknesses:

5 mm5 mm

0 5 mm

Features

0.5 mm0.12 mm

Features

200 nm Residual layer

17

4 mm

layerthickness

Page 18: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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”

18

Page 19: 13 November 2009 Hayyy gden Taylor and Duane Boning ... · 1 nm1 nm 10 nm 100 nm 1 µm 10 µm 100 µm width, w. Key: model impulse response g(x,y,t) of resist layer Model in space:

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

19


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