The document discusses how heat dissipation during wafer exposure in a lithography process can cause deformations in the wafer and underlying table. A finite element model is developed to simulate the thermal expansion and resulting mechanical deformations, with the goal of understanding and reducing overlay errors between subsequent exposures on the wafer to within a tolerance of 1 nm. Simulation results show temperature distributions and deformations in the wafer, table, and chuck after exposing the first and last fields on the wafer.

1. Overlay als gevolg van ‘wafer heating’ in wafer steppers
March 2010
Willem Dijkstra

2. Company profile
MECAL BV
Location: Enschede, Veldhoven, Groningen
Consultancy & product development
# employees: 90
Customers: ASML, Zeiss, Océ, Philips, ICOS,
Nedinsco, BESI
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3. MECAL
Semiconductor industry
Simulation
Product development
Turn-key solutions
Optronics and Vision
(mainly Veldhoven)
Wind energy
Product development
Turn-key solutions
(mainly Enschede)
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4. Competencies semiconductor industry
• Statics ⇒ stress, stiffness, tolerances,
deformation, force path
• Dynamics ⇒ vibration, damping, mass, stick-slip,
mode shapes, eigen frequencies
• Kinematics ⇒ DOF, rigid body systems, acceleration,
inertia, set point, friction
• Thermal ⇒ conductivity, convection, radiation, thermo-mechanics
• Fluid dynamics ⇒ Air-bearing stiffness and loads, low vacuum,
contaminations, flow induced vibrations
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5. Analysis
At MECAL: FEM simulation is problem identification
a tool, not the goal
FEM simulation hand calculations
understanding the physics
= validation measurements
design optimization
output: performance
parameters
design improvement
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6. Lithographic process problem identification
Production of chips: lithographic process
For 175 wafers/hour: huge power required heat
Dissipated heat can lead to errors in chips:
Process chips: features of O(45 nm)
Total allowable error: O(15 nm)
Specific allowable error: O(1 nm)
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7. Exposure problem identification
reticle interfero-
meter
mirror
lens
interfero-
meter
wafer
table
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chuck
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8. Heat dissipation problem identification
first field Wafer is divided in fields
Fields are exposed one after another
Several exposures
95% of light is transformed to heat
and absorbed in wafer
Heat transfer to table
Chuck: very low conductivity
last field
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9. Deformations problem identification
Wafer + table deform due to thermal
expansion overlay
Wafer pressed onto chuck
Chuck deforms
Positioning is affected
Questions:
o Wafer deformations?
o Design improvements?
Keep in mind: mirrors, needed for
positioning, are also deformed
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10. Outline model problem identification
Input Power
Heat dissipation
Temperature profile
changing with time
Deformation chuck
Overlay at wafer Output
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Long path between input and output!
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11. Finite Element Model FEM simulation
Boundary conditions
Heat load at wafer surface in [mJ/cm2] air shower
Convection to environment [22 oC] (air shower at wafer)
Chuck statically fixed no reaction forces
Vacuum pressure to push wafer + table onto chuck
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12. Thermal results FEM simulation
Temperatures after exposure first field Wafer
0
0.098
0.196
Table
0 0.293
0.029 0.391
0.059 0.489
0.088 0.587
Chuck
0 0.118 0.685
0.002 0.147 0.782
0.004 0.176 0.880
0.006 0.206
0.008 0.235
0.010 0.265
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0.012
0.015
0.017
0.019
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13. Thermal results FEM simulation
Temperatures after exposure last field Wafer
0.017
0.126
0.236
Table 0.345
0.018 0.454
0.066 0.563
0.114 0.672
0.162 0.782
Chuck
0 0.210 0.891
0.012 0.258 1.000
0.025 0.306
0.037 0.354
0.049 0.402
0.062 0.450
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0.074
0.086
0.098
0.111
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14. Mechanical results FEM simulation
Deformations after exposure first field z-dir
-0.019
-0.008
0.003
y-dir 0.014
-0.047 0.025
z
y -0.031 0.036
-0.015 0.047
0.001 0.058
x-dir x
-0.049 0.017 0.069
-0.034 0.033 0.080
-0.019 0.049
-0.004 0.066
0.011 0.082
0.026 0.098
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0.041
0.056
0.071
0.086
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15. Mechanical results FEM simulation
Deformations after exposure last field z-dir
-0.306
-0.162
-0.017
y-dir 0.129
-0.285 0.275
z
y -0.236 0.419
-0.187 0.565
-0.139 0.709
x-dir x
-0.250 -0.090 0.853
-0.196 -0.042 1.000
-0.140 0.007
-0.084 0.055
-0.029 0.104
0.027 0.153
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0.082
0.137
0.193
0.248
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16. Output: performance parameters Performance parameters
100
Displacement plots
For each field, displacements are
50
plotted directly after exposure of die
0 Correction for chuck deformations
−50
−100
Overlay = O(1 nm)?
−150 −100 −50 0 50 100 150
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17. Validation Validation
model measurements
ux
Difference in
row number row number
amplitude:
model measurements ux: 32%
uy: 12%
uy
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row number row number
Row averaged displacements
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18. Validation Validation
model measurements
0
5
0
5
0
5
0
5
0
25 −20 −15 −10 −5 0 5 10 15 20 25
Exposure of one die in the center of the wafer
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Difference in style
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19. Materials Design improvement
Current materials:
- wafer: silicium: high conductivity, high CTE
- table: glass/ceramics: low conductivity, low CTE
Conductivity low / high ΔT high / low
Expansion = CTE * ΔT
ΔT CTE expansion
wafer high high high2
table high low low
Click + table high
wafer to edit Master title style
low FEM?
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20. Materials Design improvement
Other materials:
- wafer: silicium: high conductivity, high CTE
- table: material X : high conductivity, high CTE
- water cooling in table
best material:
machine dependent
ΔT CTE expansion
wafer low high moderate
table low high moderate
Click + table low
wafer to edit Master title style
high FEM?
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21. Conclusions
FEM model to predict overlay caused by wafer
heating
Good agreement with measurements
Model can be used for design improvements:
- add water cooling
- materials
- feed forward corrections
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