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

2 Challenge the future 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

3 Challenge the future 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

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

5 Challenge the future 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.

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

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

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

9 Challenge the future Mathematical background of the model(2) g gap above the wafer g gap below the wafer L w ---- length of the wafer in lateral direction L y ---- length of the wafer in transporting direction μ ---- viscosity coefficient m ---- mass of wafer D w ---- thickness of wafer b ---- slope of the curve"average pressure difference---- lateral displacement" (to be determined) dynamic equation x ΔP b o

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

11 Challenge the future 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 P1P1 P2P2 x ΔP b o

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

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

14 Challenge the future Inlet boundary condition numerical implementation

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

16 Challenge the future 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

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

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

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

20 Challenge the future supply pressure supplying pressure (pa) stiffness coefficient (N/m) Ratio of stiffness coefficients

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

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

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

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

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

26 Challenge the future supply pressure supplying pressure (pa) stiffness coefficient (N/m) Ratio of stiffness coefficients

27 Challenge the future Parameter study (2) configuration updated initial configurationsupdated configurations width of chamber (mm) diameter of exhaust holes (mm)

28 Challenge the future Parameter study (2) configuration updated

29 Challenge the future Part IV Experimental verification

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

31 Challenge the future Experimental verification (2) translational oscillation

32 Challenge the future Experimental verification (2) translational frequency supplying pressure (pa) analytical frequency (Hz) experimental frequency (Hz) ratio

33 Challenge the future Experimental verification (3) rotational oscillation

34 Challenge the future Experimental verification (3) rotational frequency supplying pressure (pa) analytical frequency (Hz) experimental frequency (Hz) ratio

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

36 Challenge the future 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.

37 Challenge the future Experimental verification (2) translational oscillation

38 Challenge the future