Fast simulation of nanoimprint lithography: modelling capillary pressures during resist deformation

20 October 2011

Hayden Taylor and Eehern WongSimprint Nanotechnologies LtdBristol, United Kingdom

Namil Koo, Jung Wuk Kim and Christian Moormann AMICA, AMO GmbH Aachen, Germany

hkt@simprintnanotech.com+44 117 2302566

Simulation can help select process parameters and refine designs in NIL

1 Taylor NNT 2009; 2 Taylor SPIE 7641 2010; 3 Boning et al. NNT 2010

0

0.5

1Pattern abstraction

Den

sity

Resist surface’s impulse response

Resist Substrate

Stamp’s load response (bending, indentation)

Resist

Stamp

Example questions:

Does changing stamp material affect

residual layer uniformity? 1,2

Can ‘dummy fill’ accelerate stamp cavity filling? 3

Simulations need to be highly scalable

At least 103 times faster than FEM

Can trade off spatial resolution and speed

92

99

10

165

Elastomer Silicon

(nm)

Tim

e (s

)

101 102 103 104

102

103

104

Simulation size, N

~O(N2logN)

101

N

Chip-scale imprint simulation has until now addressed only thermal NIL

10-2 1 102 104 106 Pa.s

Resist viscosity during imprinting

Externally applied pressure

Capillary pressures

10 103 105 107 109 Pa

Thermal 4UV 5

ThermalUV

4 e.g. Garcia-Romero, NNT 2008; 5 e.g. Auner, Organic Electronics 10 p.1466 2009

Externally applied

pressure

Stamp

Substrate

Resist

Pressure

Low High

Capillary forces

η

Hydrophobic

We incorporate capillary pressures into our fast NIL simulation algorithm

Need to know: Resist viscosity, η Stamp-resist contact angle, θ Resist’s surface tension, γ

Externally applied

pressure

Pressure

Low High

Stamp

Substrate

Resist

Capillary forces

θ

γ

η

Stamp

Hydrophilic

η

θ = 90°

A simple modification to the simulation algorithm captures capillary effects

r

pg

r

pg

r

pg

No significant reduction in solution speed compared to thermal NIL simulation

Consider pressures acting on stamp in quasi-equilibrium:

pcapillary(x,y) is pattern-dependent. Examples:

pcapillary(x,y) falls to zero where cavities are filled

s

cos2

cos1

2

s

w

s

2

cos4

s

w

θ

γ

γ resist surface tensionθ resist-stamp contact angles feature pitch w cavity width

w s

Contribution of capillary pressures diminishes with increasing feature size

w

The new model has been tested experimentally

50 μm 100 μm

PDMS stampE = 1.5 MPa;Thickness >> 150 μm

Spun-on UVNIL resistInitial thickness: 85–165 nm; Viscosity: 30 mPa.s

Silicon substrate

Stamp much wider than pattern

Parallel lines:Protrusion width 85 nmOut-of-page length ~ 2 mmProtrusion height nom. 85 nm

Parallel lines:Protrusion width 185 nmOut-of-page length ~ 2 mmProtrusion height nom. 85 nm

A B C D E

A B D

Simulation captures experimentally observed RLT variations

StampViscosity: 30 mPa.s

Fast capillary-driven filling is followed by residual layer homogenisation

Boning, Taylor et al. NNT 2010

For droplet-based resist dispensing, a different approach is needed

1 pL dropletDiameter > 10 μm

1. Reddy et al., Phys Fluids 17 122104 (2005)2. Reddy and Bonnecaze, Microel. Eng. 82 60 (2005)3. Morihara et al., Proc NNT 20084. Liang et al., Nanotechnology 18 025303 (2007)

Phenomena of interest: Speed of resist spreading 1

Likelihood of gas bubble entrapment 1-4

Gas elimination after entrapment 4

Pressure distributions can be found for multiple droplets simultaneously

Resist viscosity 50 mPaSurface tension 28 mN/mContact angle 30° Resist thickness 200 nm

With zero external pressure:Stamp velocity = 56 nm/ms

Summary and outlook

Capillary pressures are added into our spin-on resist simulation algorithm

Minimal increase in computation time

RLT homogenisation time is crucial for spun-on UVNIL processes

A pressure algorithm is proposed for droplet-dispensed NIL

Simulation Engine

Physical prediction

Resist model

Chip design

Process

Acknowledgements

Matthew Dirckx Theodor Nielsen, Brian Bilenberg and Kristian

Smistrup at NIL Technology Duane Boning, MIT James Freedman, MIT Technology Licensing Office Mark Breeze

Index

Simulation uses Viscosity/pressures Model capillary pressures Integrate with model Dependence on feature size Experimental Model vs expt RLT homogenisation Droplet demo