1. FIDAP Numerical Modeling
Scott Taylor

2. List of Topics Fixed Gap – Rigid Pad Fixed Gap – Deformable Pad
Modified Step
Free Surface Integration

3. 1. Fixed Gap – Rigid Pad Model Length = 10 mm Rigid Pad
no deformation
Step dimensions
10 μm high
1 mm long
Gap thickness = 20 μm

4. Boundary Conditions Velocity (x,y) Slurry Properties
Pad = (0.278, 0) m/s or RPM
Wafer = (0) m/s
Inlet/Outlet = (--, 0) m/s
Slurry Properties
Density = 1164 kg/m^3
Viscosity = 2 cp

5. Fixed Gap Width: 10 μm step
Wafer
Pad
Fixed Gap Width: 10 μm step

6. Results 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.

8. Pressure Contour Large pressure variation at step face
High (Low) pressure ‘pocket’ offset from corner
Couette flow (no step) run as validation.
No abnormal results
Step sensitivity study

9. Step Sensitivity Step height increased to 30 μm.
All other conditions the same

10. Step Sensitivity Step height decreased to 3 μm.
All other conditions the same

11. Step Sensitivity
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.

12. 2. Fixed Gap – Deformable Pad
Pad now modeled as a continuum instead of a line boundary.
Pad Properties – Homogeneous & Isotropic
Density = 630 kg/m^3
Young’s Modulus = E6 Mpa
Poisson’s ratio = 0.3

13. Model
WAFER
SLURRY
INLET
OUTLET
PAD
Model is NOT to scale

14. Boundary Conditions Old method – Minimal BC
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.
Create ‘edge effects’ that are undesirable.

16. Boundary Conditions – New Method
Pad given velocity
Model ‘attachment’ of pad boundary to continuum help attain convergence.
BC additions:
UX pad = m/s
DY/DX pad bottom = 0 m:
DY pad sides (left & right) = 0 m
UX/UY wafer = 0 m

17. Discontinuity more apparent, but edge effects are eliminated, which will help with free surface integration.

18. General Results Deformation in X, Y directions small
Order of nanometers
Depends on E, υ, velocity
Pressure Contours similar to rigid pad
Deflections don’t appear to affect pressure distribution

19. 3. Modified Step
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.

20. Pressure contour now located around step.

21. Deflection in Ydirection is very similar to 90 deg. step.
Other results are as expected.

22. 4. Free Surface
FIDAP capable of coupling pad deformation with a movable wafer
Force balance
Moment balance
Attempts to use ‘standard’ free surface rigid body motion unsuccessful.
Solution diverges
Model database related

23. Free Surface - Subroutine
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.

24. USRBCN Problems Not robust Substantial computational time Error prone
Model locked
Nodes
Geometry
Parameter changes difficult
Substantial computational time
Error prone
Potential to inadvertently modify solution arrays

25. To Do Finish writing subroutine for models. Determine grid dependence.
Gather results for variety of conditions.
Complete thesis/manual

26. Backup Slides