1 challenge the future the lateral motion of wafer under the influence of thin-film flow leilei hu...

1Challenge the future

The Lateral Motion of Wafer under the Influence of

Thin-film Flow

Leilei Hu Solid and Fluid Mechanics

30-09-2013


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


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


Wafer in the chamber & problem definition

Wafer transporting in process chamber top view

side view

injecting direction


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.


Part I

Mathematical model

(Dynamic equation)


Mathematical model(1)

• Only lateral motion is considered• Length of wafer in y direction infinitely long

problem simplification

y

x

y-velocity


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


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


Part II

Numerical computation

(determination of "b")


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


Computation results

lateral forces----lateral displacements


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


Inlet boundary conditionnumerical implementation


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


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


Part III

Parameter study

(Modify the chamber based on the dynamic equation)


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


Parameter study -- supply pressureincrease the potential energy of the system


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


Parameter study -- height of chamber



Parameter study -- diameter of exhaust holes



Parameter study -- width of chamber



Analytical explanation of the resultsqualitative explanation of the flow model


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


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


Parameter study (2)configuration updated

initial configurations updated configurations

width of chamber (mm)

157 158

diameter of exhaust holes (mm)

0.9 1.5


Parameter study (2)configuration updated


Part IV

Experimental verification


Experimental verification (1)experimental frequency ≈ analytical frequency


Experimental verification (2)translational oscillation


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


Experimental verification (3)rotational oscillation


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


Experimental verification (4)

• In real system not all the flow contributes to the lateral stiffness of the wafer.

explanation of the difference


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.


Experimental verification (2)translational oscillation

1 challenge the future the lateral motion of wafer under the influence of thin-film flow leilei hu...

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