(PVD) LiquidVaporGas
(CVD) Supply rateDeposition rate and the ratio of elements
(compound) Transport VacuumSourceSubstrate(PVD) Fluid(CVD)
PlasmaVacuumFluid Deposition Substrate condition
Reactivity of source material
Energy input
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Analysis StructureCompositionProperties Properties Hardness of tool
coatingbreakdown voltage of an isolatorthe index of refraction of
an optical film
Vapor phase thin-film techniques(Liquid phase) 1.
2.
3.
Chapter 2. Gas Kinetics (T)
Vapor
a (Vapor) V↓, p↑ b (Liquid-Vapor)
V↓ c (Liquid) p↑, V↓ d (Solid-Liquid)
V↓ e (Solid) p↑, V↓ f (Solid)
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Fig. 2.1p-T
3.
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The pressure in a gas based on kinetic theory: xΔP
N
xvlt /2=Δ
random
2222 zyx vvvv ++= v
22222 3 xzyx vvvvv =⇒==
Maxwell-Boltzmann Distribution
Let c=vMaxwell distribution of speeds f (v)
(Mean speed)
ArMaxwell-Boltzmann
(or Pa .m3/ mol.K) NA=Avogadro’s number
=6.02x1023 mc/mol (mc = molecule)
M RT
mN TNk
m Tkc
Molecular Impingement Flux () random
vx(θ)1/2
(mc/m2.s)n(mc/m3)
A(r = 1)
( ) ( )( )
Ideal-Gas Law
(STP01 atm)22,400 cm3/mol
( ) ( ) ( ) 2 xxxxii nmv2mvnv
Molecular translational energy: εt
⇒
εr εv
(cp) >(cv)
Ummole
SI1 Pa (Pascal) = 1 Nt/m2
cgs1 dynes/cm2 = 1/10 Pa = 10-6 bar (1 bar = 750.06 mmHg)
1 psi (pound/in2) = 51.715 mmHg
1 mmHg = 101,325/760 N/m2 (Q 1 atm = 101,325 N/m2) 1 torr = 1 mmHg
= 133.322 Pa 1 micron = 1 μ =10-3 mmHg 1 Pa = 7.5 mTorr (Mass Flow
Rate) sccm (s: standard, cc: cm3, m: minute), sccs (s: second), slm
(l: liter) Q 1 sccm = 4.48×1017 (mc/s) ∴pumpmass flow rate torr⋅l/s
Pa ⋅l/s
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Knudsen Equation ()
For example: M = 40 g, T = 25 , p = 10-3 Pa,
= 0.3 nm(Monomolecular LayerML)1015Accumulation rate =
2.4×1015/1015
= 2.4 (ML/s) 2.4×0.3×10-9/(1/60 ×1/60) = 2.6 μm/h 10-3 Pa ≈ 10-8
atm10-6Pa 99.9%( )
The linear deposition rate:dh/dt (h:film thickness, t:deposition
time) In SI units: Jr = (mc/m2·s)
ρm= (kg/m3)
(: ρmNA/M ≈ 5×1022 mc/cm3)
Mean Free Path ()
(a) a ( « a) σm=π(a/2)2 = πa2/4 (cm2) n (mc/cm3)nσm
(b) a
(Gas Flow)
Def. Knudsen numberKn = l / L l
LSourceSubstrate
⇒
⇒ ( p < 10-2 Pa) 2. Kn < 0.01 ⇒(viscous flow regionfluid flow
region)
( p) ⇒
⇒
3. 0.01 < Kn < 1 ⇒(transition region)Plasma process ⇒
Knudsen numberReynold’s number ()
(ρ)(v)(η) (d)
Def. Reynold’s numberRe = v ρd / ηη/
Kn <0.01continuum flow continuum flowReynold’s number
1. Re <1200 ⇒() 2. Re >2200 ⇒() 3. 1200 < Re < 2200
⇒
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Transport Properties: Mass (diffusion), Momentum (viscous shear)
and Energy (heat conduction)
Transport is always described by an equation of the form: (flux of
A) = − (proportionality factor) × (gradient in A)
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Diffusion: AB Diffusion flux JA(net) = J (down at x) − J (up at
x+l) =
AB
(cf. Table 2.1) p ↓ ⇒ DAB ↑p
Kn>1 ()
Viscosity: u
= (J) ×()
η(viscosity) kg/m·s = N·s/m2 = Pa ·s (SI) g/cm ·s = Poise
(cgs)
( ) dx du
dx dumcn
4 1umJ η==Δ×=τ∴ l
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⇒1. T ↑ ⇒ η ↑ () 2. p (Kn>1η)
Heat conduction: Heat flux () Φ (J/s·cm2 = W/cm2)
(Thermal conductivity)
1.
2.
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Pump selection: 1. Process vacuum level. 2. The properties of the
vapors to be handled. 3. The pump operate well at the desired
process pressure. 4. The cost (depend on pumping speed,
liter/s).
1.
2.
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Vacuum pump
()
Sputtering ion pump
The unthrottled case: (cf.Fig.3.3 & Eq.3.3) Qi:pi= Qi/Co
The throttled case: (fixed pressure p2 with a throttle)
⇒ Qsp2p2throttle (C2)pi
⇒p2
)QQ( Q Q
⇒Let t=0p2= p2o
V/Co
Exp: For a typical case of a 100 l chamber and a 10 l/s roughing
pump, the time constant is 10 s. This means that evacuation of the
air from 1 atm to 10-5 Pa would take place in a mere 4 min.
Contamination Source:
(Au)
=
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Oil backstreaming (backstreaming) (pv)
⇒ For example, a typical rotary pump oil has a pv of 10-4 Pa at 25
but a pv of 10-1 Pa at a pump operating temperature of 85.
⇒
⇒
⇒Oil backstreaming behavior in molecular flow and fluid flow:
Kn>1 process chamber
()
() ()
⇒Cooled baffle
Process chamberValve
⋅ =−
2) 2
A = tube cross-sectional area, cm2
Q = gas mass flow rate, Pa·cm3/s (at 25⇒ Q = sccm × 1837)
p = total pressure in the tube (Pa)
Ar⇒ cf: Table 2.1D(Ar-Ar) (p.26)
⇒ D = 0.19×105/p (cm2/s)
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Gas evolution () (Outgassing) Source(Bulk)
⇒
1. Oil( )(ACETCE IPA)
2. Water Baking() Desorb()
[(CH3-CH2)4Pb] 2,2,4-()100 92%(95%)92%(95%) 92(95)92(95)()
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⇒1 monolayer 1 monolayer1015 mc/cm21 m2
1019 mc:
( ) ( ) ( ) ( )s4000
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⇒40 Pa·l1 atm (~105Pa) 10 slm (l/m)1 ppmPump
=10(l/m)/106=10×103(cm3/m)/106=10−2 cm3/m:
)m(40 )Pa(10)m(10
)Pa(40 )atm(1)mcm(10
)Pa(40t 55-32- = ⋅ ⋅
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⇒ (O-rings) O-rings O-rings 10−6 Pa (O-rings 10−8 Pa)
⇒ (Zn)(Cd)(Pb)(Sb) (P)303(S)(Se)
⇒304(L)316(L)(Fe-Ni-Cr )SSe L(Carbon)
⇒450 (Mn) MBEMnTrapGaAs (W)(Ta) (Mo)Ta WmpPv()
⇒Virtual-leak problemcf: Fig. 3.5