The Lateral Motion of Wafer under the Influence

The Lateral Motion of Wafer under the Influence of Thin-film Flow Leilei Hu Solid and Fluid Mechanics 30 -09 -2013 Challenge the future 1

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 Challenge the future 2

Introduction to the problem Wafer transporting in process chamber • "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. Challenge the future 3

Wafer in the chamber & problem definition Wafer transporting in process chamber top view injecting direction side view Challenge the future 4

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. Challenge the future 5

Part I Mathematical model (Dynamic equation) Challenge the future 6

Mathematical model(1) problem simplification • Only lateral motion is considered • Length of wafer in y direction infinitely long x y-velocity y Challenge the future 7

Mathematical background of the model(2) dynamic equation----a result of force equilibrium with Challenge the future 8

Mathematical background of the model(2) dynamic equation • g 1 ---- gap above the wafer • g 2 ---- 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 o b x ---- slope of the curve"average pressure difference---lateral displacement" (to be determined) ΔP Challenge the future 9

Part II Numerical computation (determination of "b") Challenge the future 10

Determination of b o basic idea y • compute pressure value for x=0, 0. 1 mm, 0. 2 mm, 0. 3 mm, 0. 48 mm • stationary model P 1 b x ΔP P 2 x(lateral direction) Challenge the future 11

Computation results lateral forces----lateral displacements Challenge the future 12

physics coupling numerical implementation • Avoid computation of full NS equations by dividing the flow into laminar flow and thin-film flow. less grids and less Do. Fs Challenge the future 13

Inlet boundary condition numerical implementation Challenge the future 14

Inlet boundary condition numerical implementation Q d η Ps pf ---- volume flow ---- diameter of inlet holes ---- dynamic viscosity of nitrogen ---- supplying pressure ---- pressure in the inter side of the inlet holes L ---- length of the inlet holes vave---- average velocity of flow Challenge the future 15

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 Challenge the future 16

Part III Parameter study (Modify the chamber based on the dynamic equation) Challenge the future 17

Parameter study (1) increase the potential energy of the system • supply pressure • Height of chamber initial velocity constant • Diameter of exhausted holes • Width of chamber Challenge the future 18

Parameter study -- supply pressure increase the potential energy of the system Challenge the future 19

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 Challenge the future 20

Parameter study -- height of chamber increase the potential energy of the system Challenge the future 21

Parameter study -- diameter of exhaust holes increase the potential energy of the system Challenge the future 22

Parameter study -- width of chamber increase the potential energy of the system Challenge the future 23

Analytical explanation of the results qualitative explanation of the flow model Challenge the future 24

Analytical explanation of the results qualitative explanation of the flow model stiffness is proportional to supply pressure Challenge the future 25

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 Challenge the future 26

Parameter study (2) configuration updated initial configurations updated configurations width of chamber (mm) 157 158 diameter of exhaust holes (mm) 0. 9 1. 5 Challenge the future 27

Parameter study (2) configuration updated Challenge the future 28

Part IV Experimental verification Challenge the future 29

Experimental verification (1) experimental frequency ≈ analytical frequency Challenge the future 30

Experimental verification (2) translational oscillation Challenge the future 31

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 Challenge the future 32

Experimental verification (3) rotational oscillation Challenge the future 33

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 Challenge the future 34

Experimental verification (4) explanation of the difference • In real system not all the flow contributes to the lateral stiffness of the wafer. Challenge the future 35

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. Challenge the future 36

Experimental verification (2) translational oscillation Challenge the future 37

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