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Finite Element Simulation of Particulate Contamination in EUV reticle masks during exposure chucking
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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
EUVL Symposium 2009 Slide 2
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
EUVL Symposium 2009 Slide 3
• 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
EUVL Symposium 2009 Slide 4
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.
EUVL Symposium 2009 Slide 5
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.
EUVL Symposium 2009 Slide 6
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.
EUVL Symposium 2009 Slide 7
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
EUVL Symposium 2009 Slide 8
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
EUVL Symposium 2009 Slide 9
Elastic Response Elastic Plastic Response
Chuck / Particle Properties E = 100 GPa Y = 12 GPa
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
EUVL Symposium 2009 Slide 10
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
EUVL Symposium 2009 Slide 11
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
EUVL Symposium 2009 Slide 12
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 ----
EUVL Symposium 2009 Slide 13
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
EUVL Symposium 2009 Slide 14
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
EUVL Symposium 2009 Slide 15
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
EUVL Symposium 2009 Slide 16
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
EUVL Symposium 2009 Slide 17
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
EUVL Symposium 2009 Slide 18
Elastic Response Elastic Plastic Response
Chuck / Particle Properties E = 100 GPa Y = 12 GPa
Chuck / Particle Properties E = 100 GPa Y = 12 GPa
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
EUVL Symposium 2009 Slide 19
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
EUVL Symposium 2009 Slide 20
0.0 0.2 0.4 0.6 0.80
1000
2000
3000
4000
5000 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 Results5.0 μm Cylindrical and Spherical Particles
EUVL Symposium 2009 Slide 21
0.0 0.5 1.0 1.5 2.0 2.5 3.00
2000
4000
6000
8000
10000 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 Results10.0 μm Cylindrical and Spherical Particles
EUVL Symposium 2009 Slide 22
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.
EUVL Symposium 2009 Slide 23
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)
EUVL Symposium 2009 Slide 24
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)
EUVL Symposium 2009 Slide 25
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.
EUVL Symposium 2009 Slide 26
Acknowledgments
• The authors wish to thank Nikon Corporation for supporting this research, and the following individuals:
– Thomas Novak– Hidemi Kawai– Tsuneyuki Hagiwara– Hajime Yamamoto
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