W A T K I N S - J O H N S O N C O M P A N Y Semiconductor Equipment Group

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Chabot Engineering
Semiconductor Machine-Tool Chemical Delivery
Chp3Bubblers-323
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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The Following Presentation Lead to an American
Institute of Physics (AIP) Publication in 2001
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WJs Patented Bubbler

• C. C. Collins, M. A. Richie, F. F. Walker, B.
  C. Goodrich, L. B. CampbellLiquid Source
  Bubbler, United States Patent 5,078,922 (Jan
  1992)

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Patent 5 078 922
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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.
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With a 2.2 Liq Level does the WJ bubbler operate
HERE? Or
HERE?
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Microscopic Transient BehaviorBubble 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

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

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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

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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
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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

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Bubble Sat PDEcont.-4

• IC At t0 bubble is 0 Saturated (trivial IC)

• NonDimensionalize

• Define the Degree of NonSaturation (a.k.a.
  Complementary Degree of Sat) Pc

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Bubble Sat PDEcont.-4

• PDE Summary

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Bubble Sat PDE Solution

• Non-Dim Solution for Pc

• Dimensional Solution for Pv

• See next Slide for Graphical Representation of
  This (really cool) Solution

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1st 100 Terms of Summation
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Bubble Size Determination

• Perform Force Balance as shown below

• Bubble Breaks free when Buoyant Force just barely
  exceeds the Surface Tension Force

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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

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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

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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

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Bubble Residence Time, trcont.-1

• The Drag Force

• Where
• FD ? the drag force in newtons
• CD ? the the coefficient of drag, a dimensionless
  number
• vr ? the rise velocity of the bubble in m/s

• Apply Newtons Law of Motion to Rising Bubble

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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

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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

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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

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Bubble Residence Time, trcont.-4

• Using the H and vr(tA) Equations

• Almost Done. Find CD in Idelchik Text Ref.

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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

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Bubble Residence Time, trcont.-6

• Example Calc ro 1 mm, ? 7.4x10-7 m2/s

2.2 0.0559m
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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

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Degree of Saturationcont.-1

• Estimate Properties for TEOS, Etc.

• Saturation Safety Factor, Nt

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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

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Validation Testing
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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