Transcript FIDAP Numerical Modeling

FIDAP Numerical Modeling
Scott Taylor
List of Topics
1.
2.
3.
4.
Fixed Gap – Rigid Pad
Fixed Gap – Deformable Pad
Modified Step
Free Surface Integration
1. Fixed Gap – Rigid Pad
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Model Length = 10 mm
Rigid Pad
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Step dimensions
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no deformation
10 μm high
1 mm long
Gap thickness = 20 μm
Boundary Conditions
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Velocity (x,y)
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Pad = (0.278, 0) m/s or --- 70 RPM
Wafer = (0) m/s
Inlet/Outlet = (--, 0) m/s
Slurry Properties
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Density = 1164 kg/m^3
Viscosity = 2 cp
Wafer
Pad
Fixed Gap Width: 10 μm step
Results
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Results for streamline, UX, UY are as
expected.
A change in magnitude of velocity only
results in magnitude change of solution.
Pressure contours need to be
investigated.
Pressure Contour
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Large pressure variation at step face
High (Low) pressure ‘pocket’ offset from
corner
Couette flow (no step) run as validation.
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No abnormal results
Step sensitivity study
Step Sensitivity
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Step
height
increased
to 30 μm.
All other
conditions
the same
Step Sensitivity
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Step
height
decreased
to 3 μm.
All other
conditions
the same
Step Sensitivity
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Unexpected pressure contour most
likely the result of sharp geometric
discontinuity and not a genuine
solution.
Possible way to reduce is to introduce
sloping sides, rather than sharp corner.
2. Fixed Gap – Deformable Pad
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Pad now modeled as a continuum
instead of a line boundary.
Pad Properties – Homogeneous &
Isotropic
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Density = 630 kg/m^3
Young’s Modulus = 20 - 40E6 Mpa
Poisson’s ratio = 0.3
Model
WAFER
SLURRY
INLET
OUTLET
PAD
• Model is NOT to scale
Boundary Conditions
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Old method – Minimal BC
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UX wafer = 0.84 m/s
UY inlet/outlet = 0 m/s
DX/DY bottom of pad = 0 m
Lack of BC’s allow FIDAP to get
smoother results.
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Create ‘edge effects’ that are undesirable.
Boundary Conditions – New Method
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Pad given velocity
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Model ‘attachment’ of pad boundary to
continuum help attain convergence.
BC additions:
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UX pad = 0.278 m/s
DY/DX pad bottom = 0 m:
DY pad sides (left & right) = 0 m
UX/UY wafer = 0 m
• Discontinuity
more apparent,
but edge effects
are eliminated,
which will help
with free surface
integration.
General Results
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Deformation in X, Y directions small
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Order of nanometers
Depends on E, υ, velocity
Pressure Contours similar to rigid pad
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Deflections don’t appear to affect pressure
distribution
3. Modified Step
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Slope given to step to reduce any errors due
to discontinuity.
Old
New
• Angle reduced to 45 degrees from 90.
• NOTE: Currently, any model with the modified
step has more nodes than the older model, but
resolution near the step is decreased.
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Pressure contour now located around step.
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Deflection in
Ydirection is
very similar to
90 deg. step.
Other results
are as
expected.
4. Free Surface
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FIDAP capable of coupling pad
deformation with a movable wafer
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Force balance
Moment balance
Attempts to use ‘standard’ free surface
rigid body motion unsuccessful.
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Solution diverges
Model database related
Free Surface - Subroutine
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Using USRBCN user subroutine, surface
position can be modified explicitly.
Subroutine currently being written to
work with wafer ‘step’.
Subroutine successful for a flat wafer.
USRBCN Problems
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Not robust
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Model locked
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Nodes
Geometry
Parameter changes difficult
Substantial computational time
Error prone
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Potential to inadvertently modify solution arrays
To Do
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Finish writing subroutine for models.
Determine grid dependence.
Gather results for variety of conditions.
Complete thesis/manual
Backup Slides