1. Spin Coating
Introduction to Spin Coating and
Derivation of a Simple Model
Presented By: Katie Weigandt

2. Agenda
 Introduction to spin coating
 Definition and brief history of spin coating
 Uses of spin coating technology
 Common spin coating defects
 Physics of spin coating
 Basic physics behind spin coating
 The Spinning Disk Problem
 Further work on spin coating in relation to my
honors college thesis

3. What is Spin Coating?
 A process in which solution is spread
evenly over a surface using centripetal
force.
 Spin coating will result in a relatively
uniform thin film of a specific thickness.
 Spin coating is an important way of
creating thin films in the microelectronics
industry.

4. Brief History of Spin Coating
 Spin coating was first used to apply coatings
of paint and pitch around seventy years ago.
 In 1958 Emslie et. al. developed the first spin
coating model.
 This model has been used as a basis for
future more specific or complicated models.
Lawrence and Zhou: “Spin Coating of Non-Newtonian Fluids”

5. Spin Coater Schematic
Lid
 Wafer is held to chuck
with vacuum pump.
 Lid is placed over
Wafer Basin spinning basin before
spin is initiated.
Vacuum
Chuck

6. Basic Physics of Spin Coating
• Centripetal force is responsible for the spread
of liquid across the wafer.
• At long times the fluid will flow only negligibly,
resulting in a lower limit of the final thickness.

7. Industrial Uses of Spin Coating
 Photoresist for patterning wafers in microcircuit
production.
 Insulating layers for microcircuit fabrication such as
polymers.
 Flat screen display coatings.
Antireflection coatings and
conductive oxide.
 DVD and CD ROM
 Television tube
antireflection coatings.

8. Common Spin Coating Defects
•Bubbles on the surface of the
coated wafer.
•This occursiswhen fluid is deposited
as the wafer spinning, and may be
caused by a faulty dispense tip.
•A swirling pattern may be
observed.
•Causes: deposited off center
•Fluid
•Acceleration shorthigh
too
•Spin timerate too high
to
•Exhaust http://www.cise.columbia.edu/clean/process/spintheory.pdf

9. Common Spin Coating Defects
•A mark or circle in the center of the
wafer could indicate a chuck mark.
•If a chuck markchanged. type of
chuck should be
occurs the
•Streaks can occurincluding: for a
number of reasons
on the wafer
•Acceleration toooff center
high
•Fluid deposited prior to spin
•Particles on surface
http://www.cise.columbia.edu/clean/process/spintheory.pdf

10. Common Spin Coating Defects
•Uncoated areas is deposited on the
when to little fluid
on wafer occur
wafer.
•Pinholebubbles can be caused by:
defects
•Air in fluid
•Particles on substrate.
•Particles
http://www.cise.columbia.edu/clean/process/spintheory.pdf

11. Agenda
 Introduction to spin coating
 Definition and brief history of spin coating
 Uses of spin coating technology
 Common spin coating defects
 Physics of spin coating
 Basic physics behind spin coating
 Derivations of common spin coating models
 Further work on spin coating in relation to my
honors college thesis

12. Spin Coating Process
 Four main processing steps:
 Step 1: Deposit fluid onto
substrate.
 Step 2: Accelerate wafer to
final radial velocity.
http://www.mse.arizona.edu/faculty/birnie/Coatings/

13. Spin Coating Process
 Four main processing steps:
 Step 3: The coating thins at a
rate that depends on the
velocity at which the wafer is
spinning and the viscosity of
the fluid.
 Step 4: Solvent is evaporated
from the film, resulting in
further thinning.
http://www.mse.arizona.edu/faculty/birnie/Coatings/

14. The Spinning Disk Problem
 Problem:
 Consider unsteady behavior of liquid film
thickness under centripetal force.
 Goal:
 Develop relationship between film thickness and
time.
Middleman, Introduction to Fluid Dynamics

15. The Spinning Disk Problem
 Assumptions
∂uθ
 Axisymmetric flow of fluid across the wafer =0
 Laminar flow of the thinning film
∂θ
 Film thickness decreases slowly with time
 Angular velocity of fluid is equivalent to the angular
velocity of the disk
 Film is thin and has uniform thickness over the wafer
 Newtonian and incompressible fluid
 Liquid is not volatile
Middleman, Introduction to Fluid Dynamics

16. The Spinning Disk Problem
Continuity Equation:
1 ∂ (ru r ) ∂u z 1 ∂ (ru r )
0= + ≈
r ∂r ∂z r ∂r
Momentum Equation:
∂ur uθ2 ∂p ∂ 2u r
ρu r −ρ =− +µ 2
∂r r ∂r ∂z
ρrω 2
∂ur ∂ 2u r
ρur − ρrω 2 = µ 2
∂r ∂z
Middleman, Introduction to Fluid Dynamics

17. The Spinning Disk Problem
By assuming the nonlinear term in the momentum
equation is small compared to other terms we are able
to solve the resulting equation:
∂ ur 2
− ρrω = µ 2
2
∂z
Boundary Conditions:
dur
= 0 at z = h(r )
dz
ur = 0 at z = 0
Middleman, Introduction to Fluid Dynamics

18. The Spinning Disk Problem
We can now say that the volumetric flow, Q, across the
edge of the spinning disk is equal to the rate change
of the solution volume on disk:
HR dH
Q = 2πr ∫ ur ( z , R )dz = −πR 2
0 dt
d H 2πρω 2 R 2 3
− πR 2 = H R ; Initial Condition H = H R = H 0
dt 3µ
dH 2πρω 2 R 2 3
− πR 2 = H
dt 3µ
Middleman, Introduction to Fluid Dynamics

19. The Spinning Disk Problem
Integrating the previous equation we obtain an expression for film
thickness, H, in terms of time, t :
1 1 4 ρω 2
− 2 = t
H2 H0 3µ
−1
H (t )  4 ρω H  2 2 2
∴ = 1 +
 t

0
H0  3µ 
Middleman, Introduction to Fluid Dynamics

20. Model Limitations
−1
 This model is limited by the
H (t )  4 ρω H  2 2 2
assumptions used to derive ∴ = 1 +
 t

0
equations so it only applies to: H0  3µ 
 Newtonian and non-volatile liquids
 Uniform substrates
 Development of more general models is significantly
more difficult
 When developing a model for non-Newtonian flow it must
be considered that the viscosity changes with shear
force.

21. Agenda
 Introduction to spin coating
 Definition and brief history of spin coating
 Uses of spin coating technology
 Common spin coating defects
 Physics of spin coating
 Basic physics behind spin coating
 Derivations of common spin coating models
 Further work on spin coating in relation to my
honors college thesis

22. Honors College Thesis Topic
 Model flow of spin coated Newtonian fluid using
FEMLab, a finite element modeling program.
 Extend the FEMLab model to flow of non-Newtonian
and viscoelastic fluids on spin coated wafer.
 Verify experimentally that the model is valid by spin
coating fluids with relevant properties on 6 in silicon
wafers and comparing the resultant film thickness
with the predicted film thickness.

23. References
Lawrence, C.J, Zhou, W. “Spin coating of non-Newtonian Fluids”.
Journal of Non-Newtonian Fluid Mechanics, 39 (1991) 137-187
Middleman, S. An Introduction To Fluid Dynamics. John Wiley and
Sons. New York. 1998
http://www.cise.columbia.edu/clean/process/spintheory.pdf
http://www.mse.arizona.edu/faculty/birnie/Coatings

24. Questions?