1. Finishing of Individual Sapphire Wafers
University of Florida
Center for Manufacturing Innovation
A.J Garcia
November 24, 2014

2. Sapphire (Al203) Background
• Hexagonal structure
• 9 mohs scale hardness
• Chemically and biologically
inert
• Non-thrombogenic
• 2040 °C melting point
• Low thermal expansion coeff.
• Wide transmission range
• 0.18 µm – 5.5 µm
• Stretches from IR to UV
• Birefringent
• Electrical insulator
• Anisotropic
2
(http://www.cyberphysics.co.uk/topics/light/emspec
t.htm)

3. Applications
• Electronics
• Epitaxial growth of semiconductors
• Gallium nitride LED manufacturing
• Silicon-on-sapphire integrated circuits
• Radiation hardened devices
• Scratch resistant screens
• Corrosion resistant components
• Nozzles, crucibles
• Optical windows and lenses in extreme
environments

4. Motivation
• Applications demand
precision surfaces
• Electrical industry
• Uniform semiconductor
growth
• Precision form
requirements
• Optical industry
• Image distortion
• Incomplete transmission

5. Effect of magnet arrangements
Guide magnet arrangement investigation
Workpiece
10 mm x 10 mm x 1 mm rectangular
sapphire
Slurry
50-70 µm diamond abrasive mixed with
lubricant
Abrasive surface P120 grit abrasive paper
Guide magnet arrangement 1, 2, 3
Set guide magnet rotation
speed
350 rpm
Finishing time 20 min
0.85 0.9
1.75
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 2 3
Ave.ThicknessReductionµm/min
Guide magnet arrangement
• Aim to improve tool motion
• Eliminating sticking
• Arrangement 3 enabled ideal motion
• Motion produced greater thickness reduction across
surface

6. Surface roughness
• 6 measurements along diagonal
• 2.02 mm spacing
• Abrasive: 0-0.5 µm diamond abrasive slurry
• Average initial roughness: 937 nm Sa
d
0
y
x
10 mm
10 mm
Measurement locations
(equally spaced)

7. WOT roughness reduction: Results
• Average roughness after finishing: 700 nm Sa
• Partial finishing of surface
• Smooth plateaus amid rough valleys
• 0-0.5 µm abrasive does not penetrate valleys
0
200
400
600
800
1000
1200
2.02 4.04 6.06 8.08 10.1 12.12
SurfaceRoughnessRa[nm]
Diagonal Distance From Corner [mm]
Before After

8. Results

9. Surface Roughness with Flooded
Basin
0
0.5
1
1.5
2
2.5
3
3.5
4
0 6.3 12.6 18.9 25.2 31.5
RoughnessSa[nm]
Radial distance from center [mm]
Before finishing
After finishing

10. Radial
Distance [mm] 0 6.3 12.6
Unpolished
surface
Polished
surface
Radial
Distance [mm] 18.9 25.2 31.5
Unpolished
surface
Polished
surface
Sa = 1.77 nm Sa = 3.24 nm Sa = 1.40 nm
Sa = 1.55 nm Sa = 1.68 nm Sa = 1.68 nm
Sa = 0.67 nm Sa = 0.77 nm Sa = 1.52 nm
Sa = 1.67 nm Sa = 1.35 nm Sa = 1.99 nm

11. Tool magnet sticking
• Evidence of excessive magnetic flux
• High magnetic force
• High normal reaction force
• High friction
• Exclusion of lubricant and diamond particles
N
S
N
S
Magnetic force
Guide
magnet
Tool magnet
Workpiece
Iron particle
Abrasive
particle
Normal
force
Jig

12. Magnetic field density
-10
10
30
50
70
90
110
130
0 5 10 15 20 25 30
Magneticfluxdensity[mT]
Radial distance from center, r [mm]
3mm
6mm
9mm
12mm
15mm
12.7 mm
r
Tool
magnet
Guide
magnet
• 3 mm jig height
• Steep drop in magnetic flux density
• Maximum of 121 mT
• 9 mm jig height
• 71 mT
• Consistent across tool magnet
Jig height
0
16 mm +
jig height

13. Surface roughness with 9 mm jig
height
• Average before: 6.0 nm Sa
• Average after: 0.9 nm Sa
0
1
2
3
4
5
6
7
8
9
10
0 6.3 12.6 18.9 25.2 31.5
SurfaceRoughnessSa[nm]
Radial Distance from Center of Polishing [mm]
Before Finishing
After finishing

14. Abrasive path simulation
• End goal:
• Develop method for predicting material removal
• Plan:
• Design mathematical model of ideal particle motion
• Observe correlation between surface changes and
number of particle passes
• Observe changes caused by parameter variation
• Introduce corrective terms

15. Simulation Plot
• Example parameters:
• R = 3, r = 1, h = 0.5, ω = 6.28, t = 1, res = 2
• xmin = -5, xmax = -4, ymin = -1, ymax = 1

16. Simulation inaccuracies
• Inaccuracies noticed when h = 0
𝑥 𝑡 = 𝑅 + 𝑟 cos(ω𝑡) − ℎ cos
𝑅 + 𝑟
𝑟
ω𝑡
𝑦 𝑡 = 𝑅 + 𝑟 sin(ω𝑡) − ℎ sin
𝑅 + 𝑟
𝑟
ω𝑡
𝑥 𝑡 = 𝑅 + 𝑟 cos(ω𝑡)
𝑦 𝑡 = 𝑅 + 𝑟 sin(ω𝑡)
• Becomes parametric
equations of a circle
• Simulation generates an
annulus

17. Simulation inaccuracies
• Generate circle using parametric circle equations
𝑥 𝑡 = 𝐴 cos(ω𝑡)
𝑦 𝑡 = 𝐴 sin(ω𝑡)
• A = 10, ω = 21 rad/s
• t = 0 s : 900 s
• Also generates an
annulus
• Thickness increases with
t
• res too low

18. High res circle
• Same parameters to generate circle
• res increased from 4 to 6
• Correctly represents a circle
• Lower res limit set to 6