1 challenge the future the lateral motion of wafer under the influence of thin-film flow leilei hu...
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1Challenge the future
The Lateral Motion of Wafer under the Influence of
Thin-film Flow
Leilei Hu Solid and Fluid Mechanics
30-09-2013
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content of the presentation
Introduction to the problem
1. mathematical model (dynamic equation)
2. numertical computation (close the equation)
3. parameter study
4. experimental verification
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Introduction to the problem
• "Levitrack" is a solar-cell wafer processing device.
• The wafers are flying in the chamer in Levitrack where presursor gases are deposited onto the substrate of the wafers.
Wafer transporting in process chamber
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Wafer in the chamber & problem definition
Wafer transporting in process chamber top view
side view
injecting direction
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Targets
•Study and improve the dynamic behavior of the wafer in lateral directions.
•Modify the dimension of the chamber to reduce the possibility of the collision.
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Part I
Mathematical model
(Dynamic equation)
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Mathematical model(1)
• Only lateral motion is considered• Length of wafer in y direction infinitely long
problem simplification
y
x
y-velocity
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Mathematical background of the model(2)
dynamic equation----a result of force equilibrium
with
0...
kxxcxm
2
)(,
)( 21
21
21 yyw
yw LggbLbDk
gg
LLggc
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Mathematical background of the model(2)
• g1 ---- gap above the wafer
• g2 ---- gap below the wafer
• Lw ---- length of the wafer in lateral direction
• Ly ---- length of the wafer in transporting direction
• μ ---- viscosity coefficient
• m ---- mass of wafer
• Dw ---- thickness of wafer
• b ---- slope of the curve"average pressure difference----
lateral displacement" (to be determined)
dynamic equation
bxPP 21
x
ΔP
bo
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Part II
Numerical computation
(determination of "b")
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Determination of b
• compute pressure value for x=0, 0.1mm, 0.2mm, 0.3mm, 0.4mm, 0.48mm• stationary model
basic idea
x(lateral direction)
y
P1 P2
bxPP 21
x
ΔP
bo
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Computation results
lateral forces----lateral displacements
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physics coupling
• Avoid computation of full NS equations by dividing the flow into
laminar flow and thin-film flow.
numerical implementation
118.3157
5.0 3 eL
H less grids and less DoFs
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Inlet boundary conditionnumerical implementation
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Inlet boundary conditionnumerical implementation
2
4
..128
gdvL
pfPdQ ave
S
2
3
...128
)(
gL
pfPdv S
ave
Q ---- volume flowd ---- diameter of inlet holesη ---- dynamic viscosity of nitrogenPs ---- supplying pressurepf ---- pressure in the inter side of the inlet holesL ---- length of the inlet holesvave---- average velocity of flow
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Other numerical issues and solutions
• Mesh configuration generated according to the physics of the flow
• Mesh study performed to determine the size of the mesh
• Getting it converged step by step starting from lower Renolds number material
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Part III
Parameter study
(Modify the chamber based on the dynamic equation)
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Parameter study (1)
• supply pressure
• Height of chamber
• Diameter of exhausted holes
• Width of chamber
increase the potential energy of the system
2
)( 21 yyw
LggbLbDk
21
21 )(
gg
LLggc yw
initial velocity constant
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Parameter study -- supply pressureincrease the potential energy of the system
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supply pressure
supplying pressure (pa) stiffness coefficient (N/m)
Ratio of stiffness coefficients
500 -0.1437 1
1000 -0.2967 2.06
2000 -0.5987 4.16
3000 -0.8667 6.03
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Parameter study -- height of chamber
increase the potential energy of the system
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Parameter study -- diameter of exhaust holes
increase the potential energy of the system
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Parameter study -- width of chamber
increase the potential energy of the system
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Analytical explanation of the resultsqualitative explanation of the flow model
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Analytical explanation of the resultsqualitative explanation of the flow model
222
111
rR
PQ
rR
PQ
high
high
222
111
.
.
RQP
RQP
highPrR
R
rR
RPP )(
22
2
11
121
stiffness is proportional to supply pressure
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supply pressure
supplying pressure (pa) stiffness coefficient (N/m)
Ratio of stiffness coefficients
500 -0.1437 1
1000 -0.2967 2.06
2000 -0.5987 4.16
3000 -0.8667 6.03
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Parameter study (2)configuration updated
initial configurations updated configurations
width of chamber (mm)
157 158
diameter of exhaust holes (mm)
0.9 1.5
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Parameter study (2)configuration updated
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Part IV
Experimental verification
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Experimental verification (1)experimental frequency ≈ analytical frequency
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Experimental verification (2)translational oscillation
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Experimental verification (2)translational frequency
supplying pressure (pa)
analytical frequency (Hz)
experimental frequency (Hz)
ratio
500 3.00 2.17-2.46 1.22
1000 4.31 2.53-3.14 1.37
2000 6.12 1.94-4.14 1.48
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Experimental verification (3)rotational oscillation
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Experimental verification (3)rotational frequency
supplying pressure (pa)
analytical frequency (Hz)
experimental frequency (Hz)
ratio
500 1.69 0.75-1.48 1.14
1000 2.44 1.20-2.11 1.16
2000 3.46 1.49-2.68 1.29
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Experimental verification (4)
• In real system not all the flow contributes to the lateral stiffness of the wafer.
explanation of the difference
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Conclusions
• The dynamic equation and numerical computation are sufficient to show the oscillation behavior of the wafer.
• In reality,the leaking of the chamber is the dominant factor for the collision between the wafers and the walls, which causes much larger oscillation amplitude.
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Experimental verification (2)translational oscillation
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