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Chabot Engineering

Chabot Engineering. Semiconductor Machine-Tool Chemical Delivery Chp3 Bubblers-323. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. The Following Presentation Lead to an American Institute of Physics (AIP) Publication in 2001. WJ’s Patented Bubbler.

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Chabot Engineering

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  1. Chabot Engineering Semiconductor Machine-Tool Chemical Delivery Chp3Bubblers-323 Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. The Following Presentation Lead to an American Institute of Physics (AIP) Publication in 2001

  3. WJ’s Patented Bubbler • C. C. Collins, M. A. Richie, F. F. Walker, B. C. Goodrich, L. B. Campbell“Liquid Source Bubbler”, United States Patent 5,078,922 (Jan 1992)

  4. Patent 5 078 922

  5. WJ Bubbler Design Schematic diagram of a the WJ chemical vapor generating bubbler system used in CVD applications. Note the use of the dilution MFC to maintain constant mass flow in the output line. An automatic temperature controller sets the electric heater power level Cut-away view of a WJ chemical source vapor bubbler. The bubbler features a total internal volume of 0.95 liters, and a 25 mm thick isothermal mass jacket with an exterior diameter of 180 mm.

  6. With a 2.2” Liq Level does the WJ bubbler operate HERE? Or HERE?

  7. Microscopic Transient Behavior:Bubble Vapor Saturation • How Well Does the Bubbler “Humidify” the “Dry” Nitrogen Carrier Gas? • Does the Liquid LEVEL in the Bubbler Affect this Humidification (degree of Saturation) • What other Factors affect the Degree of Saturation, and in What Quantity? • What does Bubbling Look like? • Flow Visualization • BT98_VRo.ppt • BT_9806c.ppt

  8. WJ-1999 Bubbler Test; t = 0 Water Surface Bubble Carrier N2 Flow Rate in slpm 6.35 mm Sparger Tube

  9. WJ-1999 Bubbler Test; vr,f Water Surface 9.7 mm Bubble Bubble t = 0 t = 33.3ms 6.35 mm 3.7 mm QN2 = 1 slpm Sparger Tube Sparger Tube

  10. Bubble Saturation Problem Partition • The Bubble Saturation Problem Consists of 3 Loosely Coupled Sub-Processes [2] • Bubble Saturation as a Function of Bubble Size and Vapor Diffusivity • Bubble Size as Function of Sparger Tube Hole-Size, Liquid Density, and Liquid Surface Tension • Residence Time of the Bubble in the liquid by integration the bubble rise-velocity over the liquid height [2] B. Mayer, “Liquid Source Bubbler Carrier Gas Vapor-Saturation Transient Analysis”, WJ-SEG Engineering Library Report, file BM961112.doc, 12Nov96

  11. IntraBubble Vapor Mass TransportPartial Differential Equation • Assume Bubble Diffusion Physics at right • Assume Diffusion of vapor obeys the Fick Eqn • Where • Fv the molar flux in the r-direction in kmol/m2s • Dv the (assumed constant) vapor diffusivity in N2 in m2/s • Cv the molar concentration of the vapor in kmol/m3 • r  the radial coordinate in the bubble in m

  12. Bubble Sat PDEcont.-1 • Molar Flux INTO the Bubble Control Volume • Molar Flux OUT of the Bubble Control Volume • STORAGE Rate of Vapor in the BubbleControl Volume

  13. Bubble Sat PDEcont.-2 • Setting: Influx − Outflux = Storage Rate • This is the 1-Dimensional Diffusion Equation in Spherical CoOrdinates • Now use Perfect Gas Theory to Convert to Vapor Pressure Formulation Taylor series expansion in Appendix-A of JVST-A 2001 paper; Perfect Gas conversion in Appendix-B

  14. Bubble Sat PDEcont.-3 • Comments on the PDE • Linear & Homogeneous • 2nd order in r (need two Boundary Conditions) • 1st Order in t (need one Initial Condition) • BC1: Assume Equilibrium at Bubble Edge • BC2: By Symmetry have No diffusion at r = 0

  15. Bubble Sat PDEcont.-4 • IC: At t=0 bubble is 0% Saturated (trivial IC) • NonDimensionalize • Define the Degree of NonSaturation (a.k.a. Complementary Degree of Sat) Pc

  16. Bubble Sat PDEcont.-4 • PDE Summary

  17. Bubble Sat PDE Solution • Non-Dim Solution for Pc • Dimensional Solution for Pv • See next Slide for Graphical Representation of This (really cool) Solution

  18. 1st 100 Terms of Summation

  19. Bubble Size Determination • Perform Force Balance as shown below • Bubble Breaks free when Buoyant Force just barely exceeds the Surface Tension Force

  20. Bubble Size Determinationcont.-1 • The Buoyant Force • Where • FB the the buoyant force in newtons • g  the acceleration of gravity, 9.8 m/s2 • rl the density of the liquid in kg/m3 (936 kg/m3 for TEOS) • g the density of the carrier gas in kg/m3 (1.01 kg/m3 for N2 at 65 °C) • ro The outside radius of the bubble in m

  21. Bubble Size Determinationcont.-2 • The Surface Tension Force • Where • Fs the surface tension force in newtons • Dh the diameter of the vent hole in the sparger tube in meters (0.508 mm, or 0.02”, from WJ bubbler dwg 986595) •  the liquid surface tension in N/m (0.022 N/m, the value of ethanol at 30 °C) • Thus the Bubble Radius Equation

  22. Rising-BubbleLiquid Residence Time • Assume rough Equivalence for Fluid-Mechanical Drag between: • light bubble rising through a liquid • heavy sphere falling through the same liquid • Position-varying drag forces determine the velocity of a bubble rising in a liquid

  23. Bubble Residence Time, trcont.-1 • The Drag Force • Where • FD the drag force in newtons • CD the the coefficient of drag, a dimensionlessnumber • vr the rise velocity of the bubble in m/s • Apply Newton’s Law of Motion to Rising Bubble

  24. Bubble Residence Time, trcont.-2 • Where • Fy the sum of the forces, in the y-direction, acting on the bubble in newtons • ar the rise acceleration of the bubble in m2/s • mB the “mass” of bubble in kg • Effective Bubble Mass is the Liquid Displaced • Thus the Expression for Bubble Acceleration

  25. Bubble Residence Time, trcont.-3 • Comments on Acceleration Equation • Ordinary Differential Equation (ODE) for vr in terms of y or t • NONlinear & NONhomogeneous • 1st order in y or t (need one BC or IC) • BC/IC: Assume velocity is ZERO at the instant the bubble breaks away from the tube • BC/IC: y = t = 0  vr = 0 • Note: the Bubble Reaches Terminal Velocity • vr,f when: ar = dvr/dt = dvr/dy = 0

  26. Bubble Residence Time, trcont.-4 • tr Solution Strategy (see JVST-A paper) • If we know vr(t) at every instant in time, then simply integrate vr over liquid height H. • Implicitly evaluate vr(t) at any arbitrary time, tA using ODE

  27. Bubble Residence Time, trcont.-4 • Using the “H” and “vr(tA)” Equations • Almost Done. Find CD in Idelchik Text Ref.

  28. Bubble Residence Time, trcont.-5 • Collapse constant expressions into “K” Terms • This eqn can be solved numerically as described in JVST ppr, eqns 2529 • Table on the next slide shows a typical result • The 2mm diameter bubble reaches a terminal velocity of 0.214 m/s (0.48 mph) • This is consistent with the literature • Bubble rises the WJ std 2.2” liq Height in 280 ms

  29. Bubble Residence Time, trcont.-6 • Example Calc: ro = 1 mm,  = 7.4x10-7 m2/s 2.2” = 0.0559m

  30. Degree of Saturation • We (finally) have all the tools to determine the degree of saturation, Sv, for the rising bubble • Conceptually • Note • Dh and H are DESIGN-controlled • Well known liquid properties = rl • Poorly Characterized Liquid properties = Dv, s, n

  31. Degree of Saturationcont.-1 • Estimate Properties for TEOS, Etc. • Saturation Safety Factor, Nt

  32. Degree of Saturationcont.-2 • Validation Testing Performed in Jun98 by MSWalton, B. Mayer, C. Koehler • Water used as Benign Surrogate • See next slide • Calculated • ro = 1.45 mm • vr,f = 0.274 m/s (0.61 mph) • Min Saturation height = 6-7mm (0.25”) • Actual • ro = 1.5-2 mm • vr,f = 9.7mm/33.3ms = 0.29 m/s (0.65 mph) • Fully Humidified

  33. Validation Testing

  34. Degree of Saturation - Conclusions • The standard WJ bubbler liquid level of 2.2” more than assures 100% saturation of the N2 carrier gas with the source chemical vapor. • The 2.2” liquid height results in saturation time factors of safety of 3.8 for all source chemicals. • The liquid level can drop about 1.5” (to 0.7” above the sparger tube) before non-saturation becomes a potential problem • The 1.5” depth equates to a 460 ml working volume for post-dep fill applications

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