chabot engineering
DESCRIPTION
Chabot Engineering. Semiconductor Machine-Tool Chemical Delivery Chp3 Bubblers-323. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]. The Following Presentation Lead to an American Institute of Physics (AIP) Publication in 2001. WJ’s Patented Bubbler. - PowerPoint PPT PresentationTRANSCRIPT
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt1
Bruce Mayer, PE Chabot College Engineering
Chabot Engineering
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Semiconductor Machine-Tool Semiconductor Machine-Tool Chemical Delivery Chp3Chemical Delivery Chp3
Bubblers-323Bubblers-323
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt2
Bruce Mayer, PE Chabot College Engineering
The Following Presentation Lead to an American Institute of Physics (AIP) Publication in 2001
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt3
Bruce Mayer, PE Chabot College Engineering
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)
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt4
Bruce Mayer, PE Chabot College Engineering
Patent 5 078 922
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt5
Bruce Mayer, PE Chabot College Engineering
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.
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt6
Bruce Mayer, PE Chabot College Engineering
CONCEPTUAL Degree of Saturation vs Liquid Level
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
0 20 40 60 80 100 120
Liquid Level (Arbitrary Units)
De
gre
e o
f S
atu
rati
on
file = Vap_Prss.xls
With a 2.2” Liq Level does the WJ bubbler operate HERE? Or HERE?
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt7
Bruce Mayer, PE Chabot College Engineering
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
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt8
Bruce Mayer, PE Chabot College Engineering
WJ-1999 Bubbler Test; t = 0
Carrier N2 Flow Rate
in slpm
Bubble
6.35 mm
Sparger Tube
Water Surface
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt9
Bruce Mayer, PE Chabot College Engineering
WJ-1999 Bubbler Test; vr,f
Bubble
6.35 mm
Sparger Tube
Water Surface
Sparger Tube
Bubble
t =
0
t = 33.3m
s
9.7 mm
3.7 mm
QN2 = 1 slpm
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt10
Bruce Mayer, PE Chabot College Engineering
Bubble Saturation Problem Partition
The Bubble Saturation Problem Consists of 3 Loosely Coupled Sub-Processes [2]1. Bubble Saturation as a Function of Bubble Size
and Vapor Diffusivity
2. Bubble Size as Function of Sparger Tube Hole-Size, Liquid Density, and Liquid Surface Tension
3. 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
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt11
Bruce Mayer, PE Chabot College Engineering
IntraBubble Vapor Mass TransportPartial Differential Equation
Assume Bubble Diffusion Physics at right
Assume Diffusion of vapor obeys the Fick Eqn
r
trCDtrF v
vv
,,
– Whereo Fv the molar flux in the r-direction in kmol/m2s
o Dv the (assumed constant) vapor diffusivity in N2 in m2/s
o Cv the molar concentration of the vapor in kmol/m3
o r the radial coordinate in the bubble in m
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt12
Bruce Mayer, PE Chabot College Engineering
Bubble Sat PDEcont.-1
Molar Flux INTO the Bubble Control Volume
2
,,, 4 rr
CDAFn
r
vvinsidesurfoutvoutv
Molar Flux OUT of the Bubble Control Volume
2,,, 4 drr
r
CDAFn
drr
vvoutsideCVsurfinvinv
STORAGE Rate of Vapor in the BubbleControl Volume
drrt
Cn
r
vstorv
2, 4
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt13
Bruce Mayer, PE Chabot College Engineering
Setting: Influx − Outflux = Storage Rate
Bubble Sat PDEcont.-2
t
C
D
1
r
Cr
rr
1
t
Cdrr
r
Cdrr
r
Crdr2D v
v
v22
v2
r
2v
22
r
vv
This is the 1-Dimensional Diffusion Equation in Spherical CoOrdinates
t
P
Dr
Pr
rrv
v
v
11 2
2
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
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt14
Bruce Mayer, PE Chabot College Engineering
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
Bubble Sat PDEcont.-3
timeallforPtrP satvov .),( BC2: By Symmetry have No diffusion at r = 0
timeallforr
P
r
v 00
011 2
2
t
C
Dr
Cr
rrv
v
v
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt15
Bruce Mayer, PE Chabot College Engineering
IC: At t=0 bubble is 0% Saturated (trivial IC)
Bubble Sat PDEcont.-4
Define the Degree of NonSaturation (a.k.a. Complementary Degree of Sat) c
rallforrPv 0)0,( NonDimensionalize
orr 2ov rtD
satvvv PP ,
satv
vsatv
satv
v
satv
satvvc P
PP
P
P
P
P
,
,
,,
,1
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt16
Bruce Mayer, PE Chabot College Engineering
PDE Summary
P a r a m e t e r P r o b l e m F o r m u l a t i o n
P v ( r , t ) v ( , )
c ( , )
P D E 1 12
2
r r rPr D
Pt
v
v
v
12
2
v v
12
2
c c
B C - 1 P r t Pv o v s a t( , ) . v ( , )1 1 c ( , )1 0 B C - 2 . 1 P r t f i n i t ev ( , ) v f i n i t e( , ) c f i n i t e( , ) B C - 2 . 2
Pr
v
r
0
0
v
0
0
c
0
0
I C P rv ( , )0 0 v ( , ) 0 0 c ( , ) 0 1
Bubble Sat PDEcont.-4
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt17
Bruce Mayer, PE Chabot College Engineering
Bubble Sat PDE Solution
Non-Dim Solution for c
1
1 22sin12,
n
nn
c en
n
Dimensional Solution for v
1
1 222sin121,
n
rtDn
o
on
vove
rrn
rrntr
See next Slide for Graphical Representation of This (really cool) Solution
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt18
Bruce Mayer, PE Chabot College Engineering
Liquid Source Vapor Bubble Saturation Transient
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0 2.3 2.5
Radial Position Inside Bubble, r (mm)
Va
po
r S
atu
rati
on
Fra
cti
on
, v
Pv(r,t) (t=0.01 s)Pv(r,t) (t=0.04 s)Pv(r,t) (t=0.10 s)Pv(r,t) (t=0.15 s)Pv(r,t) (t=0.25 s)Pv(r,t) (t=0.35 s)Pv(r,t) (t=0.50 s)
file = BubPv(t)1.xls
• Bubble Diameter = 5 mm
• D for TEOS in N2 = 0.05 cm2/s Increasing Time
P r t
n r rn r r
evn o
o
n Dt r
n
o,sin
1 2 1 1
1
2 2 2
1st 100 Terms of Summation
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt19
Bruce Mayer, PE Chabot College Engineering
Bubble Size Determination Perform Force Balance as shown below
Bubble Breaks free when Buoyant Force just barely exceeds the Surface Tension Force
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt20
Bruce Mayer, PE Chabot College Engineering
Bubble Size Determinationcont.-1
The Buoyant Force
33 3434 olgloB rggrF – Where
o FB the the buoyant force in newtons
o g the acceleration of gravity, 9.8 m/s2
o l the density of the liquid in kg/m3 (936 kg/m3 for TEOS)
o g the density of the carrier gas in kg/m3 (1.01 kg/m3 for N2 at 65 °C)
o ro The outside radius of the bubble in m
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt21
Bruce Mayer, PE Chabot College Engineering
Bubble Size Determinationcont.-2
The Surface Tension Force
– Whereo F the surface tension force in newtons
o Dh the diameter of the vent hole in the sparger tube in meters (0.508 mm, or 0.02”, from WJ bubbler dwg 986595)
o the liquid surface tension in N/m (0.022 N/m, the value of ethanol at 30 °C)
hDF
Thus the Bubble Radius Equation31
4
3
l
ho g
Dr
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt22
Bruce Mayer, PE Chabot College Engineering
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
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt23
Bruce Mayer, PE Chabot College Engineering
Bubble Residence Time, rcont.-1
The Drag Force
222rloDD vrCF
– Whereo FD the drag force in newtons
o CD the the coefficient of drag, a dimensionless number
o vr the rise velocity of the bubble in m/s
Apply Newton’s Law of Motion to Rising Bubble
dt
dvmamFFF r
BrBDBy
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt24
Bruce Mayer, PE Chabot College Engineering
Bubble Residence Time, rcont.-2
– Whereo Fy the sum of the forces, in the y-direction, acting on the
bubble in newtons
o ar the rise acceleration of the bubble in m2/s
o mB the “mass” of bubble in kg
Effective Bubble Mass is the Liquid Displaced
logloB rrm 33 3434
Thus the Expression for Bubble Acceleration
o
rDr
rrrr r
vCgv
dy
dv
dtdy
dy
dv
dt
dva
8
3 2
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt25
Bruce Mayer, PE Chabot College Engineering
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
Bubble Residence Time, rcont.-3
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt26
Bruce Mayer, PE Chabot College Engineering
r Solution Strategy (see JVST-A paper) If we know vr(t) at every instant in time, then simply
integrate vr over liquid height H.
Bubble Residence Time, rcont.-4
dtvHdydtdy
vr
r
H
r
00
Implicitly evaluate vr(t) at any arbitrary time, tA using ODE
dt
r
tvCgdtatvdv
AAAr t
o
rDt
rAr
tv
r
0
2
00 8
3)(
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt27
Bruce Mayer, PE Chabot College Engineering
Bubble Residence Time, rcont.-4
Using the “H” and “vr(tA)” Equations
Almost Done. Find CD in Idelchik Text Ref.
A
t
Do
rH
dtdtCr
tvgHdy
r A
0 0
2
0 8
3
21313 2
491.0
2
565.4299.23
Re
491.0
Re
565.4Re
99.23
ororor
Drvrvrv
C
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt28
Bruce Mayer, PE Chabot College Engineering
Bubble Residence Time, rcont.-5
Collapse constant expressions into “K” Terms
This eqn can be solved numerically as described in JVST ppr, eqns 2529
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
A
t
o
rrrH
dtdtr
vKvKvKgHdy
r A
0 0
233
3521
0
375.0
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt29
Bruce Mayer, PE Chabot College Engineering
Bubble Residence Time, rcont.-6
Example Calc: ro = 1 mm, = 7.4x10-7 m2/s
TimeStep, n
a(m/sq-s)
Re del-v(m/s)
v(m/s)
del-y(m)
H(m)
Time(ms)
1 9.8 n/a 0.0098 0.0098 9.8E-06 9.8E-06 1
2 9.715655 26.48649 0.009716 0.019516 1.95E-05 2.93E-05 2
3 9.570822 52.74501 0.009571 0.029086 2.91E-05 5.84E-05 3
4 9.382618 78.6121 0.009383 0.038469 3.85E-05 9.69E-05 4
5 9.159834 103.9705 0.00916 0.047629 4.76E-05 0.000145 5
6 8.909038 128.7268 0.008909 0.056538 5.65E-05 0.000201 6
7 8.635705 152.8053 0.008636 0.065174 6.52E-05 0.000266 7
276 1.55E-08 579.3578 1.55E-11 0.214362 0.000214 0.055772 276
277 1.44E-08 579.3578 1.44E-11 0.214362 0.000214 0.055986 277
2.2” = 0.0559m
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt30
Bruce Mayer, PE Chabot College Engineering
Degree of Saturation We (finally) have all the tools to determine the
degree of saturation, Sv, for the rising bubble
dre
rrn
rrndrrrS
oorv
o r
n
rDn
o
onr
rvov
01
1
0
222sin121,)(
Conceptually
),,,,,( HDDSS lhvvv Note
Dh and H are DESIGN-controlled
Well known liquid properties = l
Poorly Characterized Liquid properties = Dv, ,
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt31
Bruce Mayer, PE Chabot College Engineering
Estimate Properties for TEOS, Etc.
Degree of Saturationcont.-1
Saturation Safety Factor, N
Chemical Temperature(K)
ro
(mm)vr,f
(m/s)
r,99
(ms)
r,tot
(ms)N
TEOS 338 (65 °C) 0.9996 0.233 67 257 3.8
TMB 297 (24 °C) 0.9873 0.220 60 273 4.6
TMPi 297 (24 °C) 1.001 0.169 57 343 6.0
Chemical Temperature(K)
Mw(kg/kmol)
l
(kg/m3)Dv
(m2/s)
(N/m)
(m2/s)
TEOS 338 (65 °C) 208.3 936 7.27x10-6 0.0240 5.11x10-7
TMB 297 (24 °C) 103.92 915 7.87x10-6 0.0226 6.58x10-7
TMPi 297 (24 °C) 124.08 1005 8.42x10-6 0.0259 19.3x10-7
Ethanol 303 (30 °C) 47.06 789 13.7x10-6 0.0220 12.7x10-7
Water 298 (25 °C) 18.01 998 23.9x10-6 0.073 9.13x10-7
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt32
Bruce Mayer, PE Chabot College Engineering
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
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt33
Bruce Mayer, PE Chabot College Engineering
Validation Testing
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt34
Bruce Mayer, PE Chabot College Engineering
TEOS Liquid Source Vapor Bubble Saturation v. Liquid Height
0%
20%
40%
60%
80%
100%
0.0 0.2 0.4 0.6 0.8 1.0
Liquid Level Inside Bubbler, y (inch)
Inte
gra
ted
Bu
bb
le S
atu
rati
on
, S v
0
30
60
90
120
150
Bu
bb
le R
ise
Tim
e,
r (m
s)
Integrated Saturation (%)
Rise Time (ms)
file = Sv(t)_01.xls
• Bubble Diameter = 1.999 mm
• Dv for TEOS in N2 = 0.0727 cm2/s
• Kinematic viscosity,, = 0.00511 cm2/s
99% Saturation after 67 ms, or 0.46"
Linear portion of r curve indicatesterminal velocity of ~0.23 m/s
[email protected] • Applied_Math-Physics_Vapor-Gen_Transient_Behavior.ppt35
Bruce Mayer, PE Chabot College Engineering
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
Degree of Saturation - Conclusions