2007 EUVL Symposium
Comparison of Coulombic and
Johnsen-Rahbek Electrostatic
Chucking for EUV Lithography
M. R. Sogard
Nikon Research Corporation of America, Belmont, CA
A.R. Mikkelson, V. Ramaswamy, M. Nataraju,
K.T. Turner and R.L. Engelstad
University of Wisconsin, Madison, WI
Acknowledgments
Research funded by Nikon, SEMATECH, Intel, and SRC.
Computer support provided by Intel and Microsoft.
UW - Madison
Computational Mechanics Center
Slide 1
2007 EUVL Symposium
Presentation Outline
• Motivation and objectives
• Characteristics of electrostatic chucking
• Finite element (FE) model description and
simulation results
• Chuck comparisons and conclusions
• Clamping performance
• Effects of reticle non-flatness
• Effects of particle entrapment
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Computational Mechanics Center
Slide 2
EUVL Flatness Requirements
2007 EUVL Symposium
SEMI Standard P37 and P40
• The flatness of the EUVL mask is a key issue to minimize
image placement errors due to non-telecentric illumination.
• Achieving this level of flatness requires the use of an
electrostatic chuck to hold the reticle.
Specifications in the EUVL Mask Standard (SEMI P37):
15 2
mm
Frontside and Backside
in Quality Area (QA):
~ 30 - 100 nm p-v flatness
Low Order Thickness
Variation (LOTV) in QA:
Quality Area = 142 mm × 142 mm
~ 30 - 100 nm p-v flatness
Specifications in the EUVL Mask Chucking Standard (SEMI P40):
-- stiffness ≥ 30 kN-m
-- flatness ≈ 50 nm (p-v)
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Computational Mechanics Center
Slide 3
2007 EUVL Symposium
Electrostatic Chucking
Types of Chucks
Coulomb
Johnsen-Rahbek
Chuck
Body
tD
+ + + + + + + +
Electrode
Insulator
Dielectric
- - - - - - - -
Reticle
+ + + + + + + +
Finite Resistance
+ + + + + + + + +
- - - - - - - -
tCL
• Type of chuck is characterized by the dielectric material and the
resulting mechanism of force generation.
• Chucks can be either monopolar or bipolar.
• Slab-type or pin-type based on the surface characteristics. A
pin-type chuck is proposed to minimize the effects of particles.
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Computational Mechanics Center
Slide 4
2007 EUVL Symposium
Coulomb Chuck
Schematic and Working Principle
Chuck body
Monopolar Chuck
εV K
F
= o o
A 2( t D + Kδ ) 2
2
P=
2
+
Vo
Electrode
Dielectric layer
tD
Mask
P = electrostatic pressure
Bipolar Chuck
F = electrostatic force
2
A = area of the electrode
ε oVo K 2
F
P= =
Vo = applied voltage
A 8( t D + Kδ ) 2
εo = permittivity of free space (or air gap)
K = relative permittivity of the dielectric material
tD = the dielectric film thickness
δ = total gap between the backside of the mask and the dielectric surface
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Computational Mechanics Center
Slide 5
2007 EUVL Symposium
Johnsen-Rahbek (J-R) Chuck
Schematic and Working Principle
RV
+
Vo
Chuck
-
Reticle
RCL
++
++
-- -
+
-
+
++
+
-- - -
++ - - +
+- - - -
tCL
charge accumulation
• The dielectric has a finite resistance.
• Current
flowing
through
the
dielectric and the substrate creates a
charge layer at the dielectricsubstrate interface (contact layer
thickness tCL), yielding a strong
attractive force.
tCL = contact layer thickness
(mean charge separation distance)
RV = volume resistance of the dielectric
RCL = effective resistance of contact
layer
tCL is related to surface roughness
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Computational Mechanics Center
Slide 6
2007 EUVL Symposium
Johnsen-Rahbek Chuck
Phenomenological Model
Coulomb term
P=
ε0 V
2
2
0
⎡⎛
K
⎢⎜
⎢ ⎜⎝ t D + K ( δ + t CL
⎣
J-R term
⎛
⎞
( R CL R V )
⎟ +α ⎜
⎜ t {1 + ( R
) ⎟⎠
RV
CL
⎝ CL
2
⎞
⎟
) } ⎟⎠
2
⎤
⎥
⎥
⎦
εo :
Vo : applied voltage
permittivity of free space
tD: dielectric layer thickness
K:
relative dielectric constant
tCL : contact layer thickness
RCL: resistance of the contact layer
RV : volume resistance of the dielectric material
δ : physical gap between reticle and dielectric
α : empirical factor of the nonuniform charge distribution on the interface
In practice, RCL and RV can be measured; tCL is then obtained from a
measurement of pressure at a given voltage.
Often the Coulomb term is negligible, because tD >> tCL in many cases.
UW - Madison
Computational Mechanics Center
Slide 7
2007 EUVL Symposium
Contrasting Chuck Properties
Coulomb Characteristics
J-R Characteristics
•
Clamping
pressure
exists
everywhere between reticle and
chuck.
•
J-R force depends on contact
between
substrate
and
dielectric.
•
Effects of nonflat substrates or
particles don’t affect the clamping
force very much (for small gaps).
•
How effectively will it deal
with non-flat substrates or the
presence of particles?
entrapped particle
No J-R force here because
no physical contact
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Computational Mechanics Center
Slide 8
2007 EUVL Symposium
Nonuniform Distribution of Charge
• The empirical factor α represents the effect of the nonuniform
distribution of charge on the interface surfaces.
• A relationship for α as a function of gap has been assumed for
modeling purposes and was initially introduced to help with FE
model convergence.
3.0
• However, short range forces
exist over a comparable
distance:
2.5
2.0
1.5
– Casimir (∝ 1 / gap4)
1.0
α
– van der Waals (∝ 1 / gap3)
• So this gap dependence is
physically reasonable.
αmax = 2.5
Gapα=0 = 30 nm
0.5
0.0
0
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Computational Mechanics Center
10
20
30
40
50
Gap (nm)
Slide 9
2007 EUVL Symposium
FE Simulation of Electrostatic Chucking
• Full 3-D FE models developed for both Coulomb and J-R chucks.
• Nonflatness measurements of the frontside and backside
surfaces of the reticle, as well as the top surface of the chuck, are
used as input.
• The non-flatness values are consistent with SEMI P37, P40
• Models include:
-- gap-dependent pressures
-- contact friction (µ = 0.2)
-- stiffness of the chuck
• FE simulations predict:
-- final flatness of reticle patterned surface
-- final flatness of reticle backside surface
-- final bow of the chuck
-- final gap between the reticle and chuck
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Chuck
Gravity neglected.
Chuck
Slide 10
2007 EUVL Symposium
FE Electrostatic Chucking Models
Chuck and Reticle
Chuck
Y
X
Z
Reticle
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Computational Mechanics Center
Chuck with Pin Array
(with no reticle)
Slide 11
2007 EUVL Symposium
Chuck Geometry and Stiffness
Dielectric Layer
Pin Layout
152 mm
Coulomb Chuck
142 mm
150 µm
J-R Chuck
Y
Z
X
2.0 mm
Chuck Body (Bulk Layer)
Effective stiffness = 380 kN-m
Elastic modulus = 380 GPa
Poisson’s ratio = 0.24
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Computational Mechanics Center
Pin coverage area: 142 mm × 142 mm
Pin size: 2.5 mm × 2.5 mm × 10 µm
Pin pitch: 12.67 mm
Pin coverage: 4%
Slide 12
2007 EUVL Symposium
Nonflatness of Electrostatic Chuck
• Nonflatness
of
interferometrically.
a
Coulomb
chuck
was
measured
• Measured chuck data scaled to meet the flatness specified in the
EUVL chucking standard.
Interferometric Measurement
Coulomb Pin Chuck
Mathematical Fit
of Chuck Surface
p-v = 45.3 nm
nm
Interferometric measurement of the chuck surface is represented by
Legendre polynomials and used as input into the FE models.
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Computational Mechanics Center
Slide 13
2007 EUVL Symposium
Polished Nonflatness of Reticle
Example Case
Frontside (FS)
Backside (BS)
Thickness Variation
Max = 100 nm
p-v = 50 nm
p-v = 50 nm
• Thickness variation was
calculated by subtracting
the backside flatness
data from the frontside
flatness data.
Interferometric measurements represented by Legendre
polynomials are used as input into the FE models.
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Computational Mechanics Center
Slide 14
Simulating Reticle Multi-layer
2007 EUVL Symposium
Thin Film Deposition
• After generating the FE model of the EUV substrate with the FS and BS
nonflatness, the deposition of the ideal (uniform stress and thickness)
layers is simulated.
• For the Example Case, the out-of-plane distortion (OPD) of the FS is
1000 nm p-v. The shape is convex due to the net compressive stress.
FE Model illustrating OPD contours.
OPD Frontside (p-v = 1000 nm)
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Computational Mechanics Center
Slide 15
2007 EUVL Symposium
Pressure as a Function of Gap
Ave. Pressure of 3 kPa
1000
Coulomb Chuck Parameters
(insulating dielectric)
J-R Chuck Parameters
(finite resistance dielectric)
tD = 2 mm
tCL = 1 µm
Pin height = 10 µm
Vo = 492 V
K = 10
RCL / RV = 0.2
100
Pressure (kPa)
tD =150 µm
Vo = 633 V
tCL = 1 µm
K =10
Pin height = 10 µm
J-R at pins
Coulomb at pins
Coulomb between pins
J-R between pins
10
1
0.1
0.01
0.001
0.01
0.1
1
10
Gap
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Computational Mechanics Center
Slide 16
2007 EUVL Symposium
Final Resulting Gap
After Chucking with P = 3 kPa
Coulomb
Vo = 633 V
Y
Z
X
Max gap = 6.8 nm
Johnsen-Rahbek
Vo = 492 V
6.8
6.0
5.3
4.5
3.8
3.0
2.2
1.5
0.8
nm 0
Gap Before Chucking
Max: 1 µm
Y
Z
X
Max gap = 6.3 nm
Note: Size of pin areas exaggerated for display purposes.
UW - Madison
Computational Mechanics Center
Slide 17
2007 EUVL Symposium
Finite Element Reticle Pattern Surface
Nonflatness after Chucking with P = 3 kPa
Coulomb
Johnsen-Rahbek
Vo = 633 V
Vo = 492 V
Y
Z
X
88
78
68
59
49
39
29
19
10
nm 0
Y
Z
X
p-v = 86.7 nm
QA p-v: 74.8 nm
p-v = 87.8 nm
QA p-v = 75.2 nm
Before Chucking
p-v = 1.0 µm
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Computational Mechanics Center
Slide 18
2007 EUVL Symposium
Finite Element Reticle Chucking Surface
Nonflatness after Chucking with P = 3 kPa
Coulomb
Johnsen-Rahbek
Vo = 633 V
Vo = 492 V
Y
X
Z
88
79
69
59
49
39
29
20
10
nm 0
p-v = 88.3 nm
QA p-v: 47.8 nm
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Computational Mechanics Center
Y
X
Z
p-v: 85.5 nm
QA p-v: 47.2 nm
Before Chucking
p-v = 1.0 µm
Slide 19
Reticle Pattern Surface
From Analytical Prediction
Thickness Variation
Chuck Nonflatness
+
Complete Chucking Final Flatness
(from interferometer measurements only)
2007 EUVL Symposium
Reticle Flatness Prediction
=
J-R Chuck Final Flatness
(from FE model)
Y
Z
p-v = 94.9 nm
UW - Madison
Computational Mechanics Center
X
88
78
68
59
49
39
29
19
10
nm 0
p-v = 86.7 nm
Slide 20
2007 EUVL Symposium
Summary of Simulation Results
Remaining Gap (nm)
24
20
Coulomb
16
Johnsen-Rahbek
12
8
4
0
0
1
2
3
4
5
Average Pressure (kPa)
6
Conclude there is little difference in basic clamping
properties between Coulomb and Johnsen-Rahbek chucks
•
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Computational Mechanics Center
Slide 21
2007 EUVL Symposium
Reticle Nonflatness Results
•
The effects of reticle blank non-flatness (before application of the multilayers) were also studied.
•
Non-flat blanks were simulated using 2D Legendre polynomials. Below
is Legendre mode (5,5).
Legendre Mode (5,5)
p-v
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Computational Mechanics Center
Slide 22
Legendre Mode (5,5); p-v: 100 nm
2007 EUVL Symposium
JR Chuck Model
Final Chuck Shape
-.053209
-.047287
-.041366
-.035445
-.029524
-.023603
-.017681
-.01176
-.005839
.822E-04
Y
X
Z
Final Reticle Pattern Surface
Residual Gap
Y
Z
X
-.01199
-.010658
-.009326
-.007993
-.006661
-.005329
-.003997
-.002664
-.001332
0
Max gap: 12.0 nm
p-v: 53.3 nm
Coulomb Chuck Model
Y
Z
X
p-v: 54.0 nm
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-.053928
-.04793
-.041931
-.035932
-.029934
-.023935
-.017936
-.011938
-.005939
.597E-04
Y
Z
X
Max gap: 12.1 nm
-.012103
-.010759
-.009414
-.008069
-.006724
-.005379
-.004034
-.00269
-.001345
0
Y
Z
X
-.123832
-.110066
-.0963
-.082534
-.068769
-.055003
-.041237
-.027471
-.013706
.602E-04
p-v: 123.9 nm
qa p-v: 51.9 nm
Y
Z
X
-.126023
-.111996
-.097969
-.083942
-.069915
-.055888
-.041861
-.027834
-.013807
.220E-03
p-v: 126.2 nm
qa p-v: 52.9 nm
Slide 23
2007 EUVL Symposium
Effects of Particle Entrapment: Coulomb
vs. Johnsen-Rahbek Electrostatic Chucks
Coulomb Chuck
J-R Chuck
entrapped particle
Force generated everywhere
No J-R force here because
no physical contact
• Do entrapped particles have similar effects on
both types of chuck?
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Computational Mechanics Center
Slide 24
2007 EUVL Symposium
Particle Macro-Scale Model Details
Cutaway view of reticle
clamped to a rigid chuck
P
Reticle
Chuck
r
Effective particle height, h
Original particle size
Gap radius
• Reticle is assumed to be of ULE® material and initially bowl shaped
• Chuck is perfectly flat and rigid
• Effective particle height (h) is the residual height of the deformed
particle (neglecting local deformation of the chuck and reticle
surfaces). Pressure loading (P) is gap dependent with a maximum
pressure of 15 kPa occurring at zero gap. Note: in this model the
effective particle height says nothing about the original particle size.
• r is the radial coordinate from the location of the particle
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Computational Mechanics Center
Slide 25
2007 EUVL Symposium
Effective Particle Height: 30 nm
Initial Reticle Profile: Bowl
40
Initial reticle shape
Johnsen-Rahbek
Coulomb
30
Johnsen-Rahbek
Coulomb
6
IPD (nm)
OPD (nm)
4
20
10
2
0
0
-10
0
10
20
30
40
50
60
70
80
-2
-10
0
10
20
30
40
50
60
70
80
r (mm)
r (mm)
Half Symmetry Model
Plane of
symmetry
z
y
x
Reticle
Particle
location
Chuck
Results reported are for nodes along 0 ≤ x ≤ 76 mm
on the top surface of the reticle
UW - Madison
Computational Mechanics Center
Slide 26
2007 EUVL Symposium
Effective Particle Height: 60 nm
Initial Reticle Profile: Bowl
70
60
50
8
40
6
30
20
4
2
0
10
-2
0
-10
-10
Johnsen-Rahbek
Coulomb
10
IPD (nm)
OPD (nm)
12
Initial reticle shape
Johnsen-Rahbek
Coulomb
-4
0
10
20
30
40
r (mm)
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50
60
70
80
-10
0
10
20
30
40
50
60
70
80
r (mm)
Slide 27
2007 EUVL Symposium
Effective Particle Height: 100 nm
Initial Reticle Profile: Bowl
20
120
Initial reticle shape
Johnsen-Rahbek
Coulomb
100
15
80
10
IPD (nm)
OPD (nm)
Johnsen-Rahbek
Coulomb
60
40
5
0
20
-5
0
-10
0
10
20
30
40
r (mm)
UW - Madison
Computational Mechanics Center
50
60
70
80
-10
0
10
20
30
40
50
60
70
80
r (mm)
Slide 28
2007 EUVL Symposium
Effective Particle Height: 500 nm
Initial Reticle Profile: Bowl
600
60
Initial reticle shape
Johnsen-Rahbek
Coulomb
500
50
30
IPD (nm)
OPD (nm)
Smaller IPD
40
400
300
Larger
separation gap
200
100
20
10
0
-10
-20
0
-10
Johnsen-Rahbek
Coulomb
0
10
20
30
40
r (mm)
50
60
70
80
-30
-10
0
10
20
30
40
50
60
70
80
r (mm)
• The larger separation gap means the J-R chuck doesn’t clamp as
strongly.
•But the IPD is significantly smaller than for the Coulomb chuck.
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Computational Mechanics Center
Slide 29
2007 EUVL Symposium
Conclusions
• The J-R chuck is not as effective in “flattening” trapped
particles as the Coulomb chuck for large effective heights,
but the associated IPD is smaller.
• However for effective particle heights comparable to the
SEMI non-flatness specs (< 100 nm), there is little
difference between the two types of chuck.
• Effective particle height can be significantly less than real
particle size.
• The quantitative effects of particle and chuck/substrate
deformation are being investigated.
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Computational Mechanics Center
Slide 30
2007 EUVL Symposium
Chuck Comparison
Coulomb
Advantages
Lithography
industry experience
Disadvantages
Johnsen-Rahbek
Advantages
considerable
Disadvantages
limited
limited clamping
force - requires
high voltage
higher force
per volt in
contact areas
Force
force
insensitive to
gap, spatially
uniform
some distortion of
reticle between
pins
no distortion of
reticle between
pins
force highly
dependent on gap,
not spatially
uniform
Tolerance to
particles
force not
dependent on
particle
presence
needs tall pins to
tolerate particles –
this reduces force
pin height is
irrelevant –
more particle
tolerant
less able to handle
particles on pins
Applied voltage
Heat
generation
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some ohmic
heating due to
leakage current;
not serious
problem
Slide 31
2007 EUVL Symposium
Summary and Conclusions
•
The successful implementation of EUV lithography requires the use
of an electrostatic chuck to support and flatten the mask during
scanning exposure.
•
A phenomenological model describing the force-gap relationship for
a J-R chuck is presented and compared to the Coulomb response.
•
Full 3-D FE structural models have been developed to compare the
clamping performance of the two types of chucks. The relative
advantages and disadvantages of both have been identified.
•
The effects of entrapped particles on the clamping performance of
the two kinds of chuck have been examined in a global model.
•
FE simulation results are currently being used to establish
specifications for chuck geometry and to identify the range of
flatness variations that can be accommodated with electrostatic
chucking.
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Computational Mechanics Center
Slide 32