FIDAP Numerical Modeling

Scott Taylor

List of Topics

1. Fixed Gap – Rigid Pad2. Fixed Gap – Deformable Pad3. Modified Step4. Free Surface Integration

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

Boundary Conditions

Velocity (x,y) Pad = (0.278, 0) m/s or --- 70 RPM Wafer = (0) m/s Inlet/Outlet = (--, 0) m/s

Slurry Properties Density = 1164 kg/m^3 Viscosity = 2 cp

Fixed Gap Width: 10 μm step

Pad

Wafer

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.

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

Step Sensitivity

Step height increased to 30 μm.

All other conditions the same

Step Sensitivity

Step height decreased to 3 μm.

All other conditions the same

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.

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 = 20 - 40E6 Mpa Poisson’s ratio = 0.3

Model

SLURRY

WAFER

INLET OUTLET

PAD

• Model is NOT to scale

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.

Boundary Conditions – New Method

Pad given velocity Model ‘attachment’ of pad boundary

to continuum help attain convergence.

BC additions: 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

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

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.

Pressure contour now located around step.

Deflection in Ydirection is very similar to 90 deg. step.

Other results are as expected.

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

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.

USRBCN Problems Not robust

Model locked Nodes Geometry

Parameter changes difficult Substantial computational time Error prone

Potential to inadvertently modify solution arrays

To Do

Finish writing subroutine for models.

Determine grid dependence. Gather results for variety of

conditions. Complete thesis/manual

Backup Slides