EUVL Symposium 2009 - Poster

EUVL Symposium 2009 Slide 1

Elastic and Elastic-Plastic Simulation of Entrapped Particles

during Exposure Chucking

Preetish Sinha, Vasu Ramaswamy, Andrew R. Mikkelson and Roxann L. Engelstad

Computational Mechanics Center (UW-CMC)University of Wisconsin, Madison, WI

Michael R. Sogard

Nikon Research Corporation of America Belmont, CA


Introduction and Problem Description

• Imaging of circuit patterns with critical dimensions less than 32 nm in extreme ultraviolet lithography (EUVL) requires stringent control of all sources of image placement errors.

• Characterizing the sources of these errors is an important step in achieving successful pattern transfer.

• The flatness of the EUVL mask during exposure chucking is a key issue to minimize image placement (IP) errors due to nontelecentric illumination.

152 mm152 mm

Front and Backside Flatness:~ 30 - 100 nm p-v flatness

Low Order Thickness Variation (LOTV):~ 30 - 100 nm p-v flatness

Freestanding Substrate Requirements (within Quality Area)

Quality Area: 142 mm x 142 mm


• Two sources of IP error (during exposure chucking) are out-of-plane

distortions (OPD) and in-plane distortions (IPD) of the patterned reticle.

• Among the causes of OPD and IPD is particle entrapment, where small pieces of debris become lodged between the reticle and chuck.

Motivation for Research

• Experimental assessment of the effects of particle-induced reticle distortion is extremely difficult, thus computational studies using finite element (FE) models are required.

Micron-sized entrapped particle

OPD and IPD of patterned surface Clamping pressure

Millimeter-sized void


Predicting the Effects of Particle Entrapment

Effective Particle Height

• The effects of entrapped particles are difficult to assess because the size, shape, number, and material properties of these contaminants are not well defined.

• It is also difficult to develop a model of a domain that is hundreds of millimeters in size, but contains sub-micron details.

• The problem needs to be studied under two regimes, the micro-scale response and the macro-scale response.


Particle Entrapment

Macro-Scale Response

- develop global models- use macro properties- consider “effective particle height” - predict OPD and IPD of reticle- identify IP errors (wafer level)

Micro-Scale Response

- develop local models- use nanoscale properties- simulate crushing or embedding - assess particle crushing force- identify “effective particle height”

• In this study, we look at the micro-scale response of the entrapped particulates under different chucking pressures / forces.

• Spherical and cylindrical shaped particle responses were analyzed by running finite element simulations, and particle response as a function of the crush force has been presented.

• For the micro-scale response, particle deformation depends only on the local applied chucking force. How the force is created (e.g., by a vacuum chuck or electrostatic chuck) is not relevant.


Spherical Particle - Description

• Spherical particles with an initial diameter of 1.0 µm, 5.0 µm and 10.0 µm were considered.

• Two FE models were created:

(a) an FE model with purely elastic properties, and

(b) an FE model with elastic-plastic properties.

• Particle crushing force was increased linearly, and the effective particle height was determined.

• For the same crushing force, a comparative analysis of the effective particle heights between the purely elastic and the elastic-plastic FE models was completed, and the results are discussed.


Spherical Particle – Details of the Model

Component MaterialElastic Modulus

(GPa)Yield Strength

(GPa)

Substrate ULE® * 66.3 8.5

Backside Layer chrome* 250 9.0

Particle 100 12.0

Chuck 100 12.0

* Measured via nanoindentation testing

Component Parameter Range

Particle Diameter, dp 1.0 µm to 10.0 µm

Axisymmetric FE Model

Substrate

Chuck

Particle

ChromeBackside

Layer

dp

Axis of symmetry

F

Model Parameters


Particle:E = 100 GPaY = 12 GPa

Substrate:E = 66.3 GPaY = 8.5 GPa

Spherical Particle - Meshing the FE Model

Chrome Layer:E = 250 GPaY = 9 GPa

Chuck:E = 100 GPaY = 12 GPa


Elastic Response Elastic Plastic Response

Chuck / Particle Properties E = 100 GPa Y = 12 GPa


ULE®

E = 66.3 GPaY = 8.5 GPa

ChromeE = 250 GPaY = 9.0 GPa

Spherical Particle - ResponseEffect of Nonlinear Behavior – 1.0 μm Spherical Particle

ULE®

E = 66.3 GPa Y = 8.5 GPa

ULE®

E = 66.3 GPaY = 8.5 GPa


0.000 0.005 0.010 0.015 0.020 0.0250

200

400

600

800

1000

Elastic FE Elastic Plastic FE

Effe

ctiv

e P

artic

le H

eigh

t (nm

)

Crush Force (N)

Spherical Particle – FE Simulation Results1.0 μm Spherical Particle


Analytical and Numerical Analyses

Substrate

Chuck

Particle

MetalBackside

Layer

H

Axis of symmetry

• The local model includes a cylindrical particle with an original height of H and radius R.

• It is necessary to determine the “effective particle height” (h) after the particle is deformed and embedded into the reticle substrate and the chuck.

• The FE simulations facilitate determining the “elastic” and “elastic-plastic” response.

• The particle responses are characterized and subsequently compared.

R

Local Axisymmetric Model

Cylindrical Particle – Details of the Models


Cylindrical Particle - Analytical Model

The total amount a particle is deformed and embedded (wtotal) into the reticle and chuck is given by:

wtotal = wc + ws + wp

Since H was the original height of the particle, the effective height of the particle (h) is then given by: h = H – (wc + ws + wp)

wc = max embedded into the chuck

ws = max embedded into the reticle substrate

wp = max deformation of the

particle

Substrate

Chuck

h

wc , ws and wp are calculated in the following slides ----


Cylindrical Particle - Analytical ModelEmbedding into the Chuck

c

cc RE

Fw

2

)1( 2

Particle is assumed to be rigid when analyzing just the chuck deformation

Embedding in chuck:

Ec = elastic modulus of chuck

c = Poisson’s ratio of chuck

where,

F = applied force

R H

Axis of symmetry

Axisymmetric Model

Chuck


fsfsss

III

R

Fw

00

1

)1()(1

4

22

2

0 1

1ln)21(

)1(2

1arctan

2)(

s

s

I

2

2

1

1lnarctan

2)(

I

R

t

R H t

)1(2 s

ss

E

)1(2 f

ff

E

Axis of symmetry

Particle is again considered rigid

* H. Xu and G. M. Pharr, Scripta Materialia, Vol. 55, 2006, pp. 315-318

Embedding in substrate:

where,Axisymmetric Model

*

F = applied force

Es = elastic modulus of reticle

s = Poisson’s ratio of reticle

Ef = elastic modulus of backside layer

f = Poisson’s ratio of backside layer

Substrate with Metal Backside Layer

Cylindrical Particle - Analytical ModelEmbedding into the Substrate


RH

pp ER

HFw

2

Deformation of particle:

Particle is considered to be elastic.

F = applied force

Ep = elastic modulus of particle

where,

Axis of symmetry

Cylindrical Particle - Analytical ModelParticle Deformation


R H

362.5 μm

36

2.5

μ

m362.5 μm

36

2.5

μ

m

Axis of symmetry

Substrate

Chuck

• The analytical models were verified numerically by employing FE methods.

• For the FE models, the effective height is evaluated as the total deformation and embedding of the particle measured along the axis of symmetry.

• Reticle substrate: ULE®

• Metal Backside Layer: 60 nm of Chrome

• Chuck and Particle of Same Material Ec = Ep = 100 GPa cp = 0.3

• H was varied 1.0 μm, 5.0 μm, 10.0 μm • ( H / R ) was fixed at 2.0 to compare response

of cylindrical particles to equivalent spherical shaped particles.

Cylindrical Particle – Details of FE Model


Particle:E = 100 GPaY = 12 GPa

Substrate:E = 66.3 GPaY = 8.5 GPa

Chrome Layer:E = 250 GPaY = 9 GPa

Chuck:E = 100 GPaY = 12 GPa

Cylindrical Particle - Meshing the FE Model


Elastic Response Elastic Plastic Response



chromeE = 250 GPaY = 9.0 GPa

ULE®

E = 66.3 GPaY = 8.5 GPa

ULE®

E = 66.3 GPa Y = 8.5 GPa

Cylindrical Particle - ResponseEffect of Nonlinear Behavior – 1.0 μm Cylindrical Particle


0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.0350

200

400

600

800

1000 Spherical Elastic FE Spherical Elastic Plastic FE Cylindrical Elastic Analytical Cylindrical Elastic FE Cylindrical Elastic Plastic FE

Effe

ctiv

e P

art

icle

He

igh

t (n

m)

Crush Force (N)

Comparison of FE Simulation Results1.0 μm Cylindrical and Spherical Particles


0.0 0.2 0.4 0.6 0.80

1000

2000

3000

4000


Effe

ctiv

e P

art

icle

He

igh

t (n

m)

Crush Force (N)



0.0 0.5 1.0 1.5 2.0 2.5 3.00

2000

4000

6000

8000


Effe

ctiv

e P

art

icle

He

igh

t (n

m)

Crush Force (N)



Cylindrical to Spherical Particles

• It is difficult to accurately predict the shape of the particles generated during chucking. In general, particles are cylindrical or spherical. However, particles having a geometry between that of a perfect cylinder and a perfect sphere cannot be discounted.

• This study also investigates how the force required to completely crush or embed a particle varies as a function of the geometry of the particle.

• Cylindrical particles of initial height 5.0 µm and 10.0 µm (H / R = 2) were considered, and their corners were subsequently rounded in increments of 0.2 µm and 0.4 µm respectively to represent intermediate geometries between a perfect cylinder and a perfect sphere.

• Previous elastic FE models were used to predict the necessary crush force required to completely embed/deform the particle, as the geometry was varied from a perfect cylinder to a perfect sphere.


FE Results for 5.0 μm Particle

Sphere

Cylinder

r

2.5 m

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60.50

0.55

0.60

0.65

0.70

0.75 5 um particle

Cru

sh F

orce

(N

)

Corner Radius, r (um)


FE Results for 10.0 μm Particle

Sphere

Cylinder

r

5.0 m

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

2.2

2.4

2.6

2.8

3.0 10 um particle

Cru

sh F

orc

e (

N)

Corner Radius, r (um)


Summary and Conclusions

• 2-D FE models describing the relationship between the crush force and the effective particle height for a 1.0 µm, 5.0 µm and 10.0 µm initial diameter spherical particle and a comparable cylindrical particle of the same initial height have been developed. Both elastic as well as the elastic-plastic cases have been considered.

• All the FE results have been plotted to represent the effective particle height as a function of crushing force, for both spherical and cylindrical particles.

• The FE results show that it is easier to crush a spherical particle as compared to a cylindrical particle, for both elastic as well as elastic-plastic cases.

• Also, the elastic FE and analytical solutions for the cylindrical particle are in good agreement, and are most accurate for small displacements.

• However, the FE analysis which includes nonlinear effects is a more accurate representation of the particle crushing / embedding.


Acknowledgments

• The authors wish to thank Nikon Corporation for supporting this research, and the following individuals:

– Thomas Novak– Hidemi Kawai– Tsuneyuki Hagiwara– Hajime Yamamoto

Documents

EUVL Symposium 2009 - Poster