Vacuum Technology and film growth
p-channel
Poly Gate pMOS
Metal-Oxide-Semiconductor (MOSFET)
Polycrystaline Silicon
Source Gate Drain
ion-implanted
n-Si
polysilicon
Diffusion
Resistor
Poly Si
Resistor
Field oxide grown in steam, gate oxide made by CVD
p-regions ion-implanted, Al sputter deposited or evaporated
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1
Why cover vacuum science?
• Oxidation
Sept. 14
Key advantage of Si: stable uniform oxide
How control its growth, thickness, quality
• Ion implantation and diffusion
Sept. 28
How semiconductor surfaces are doped
• Chemical vapor deposition (CVD)
Oct 12
Most widely used method for growth of high-grade
semiconductor, metals, oxide films,
• Physical vapor deposition (PVD)
Oct. 19, 26
Growth of quality films by sputter deposition or evaporation
These processes done in vacuum or controlled environment.
Therefore, need to understand
vacuum technology,… gas kinetics.
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Gas Kinetics and Vacuum Technology
How far does a molecule travel between collisions?
m ≈ 5 x 10-26 kg
Consider a volume V of gas (e.g. N2)
L
velocity
“Snap shot”
molecule
d
number N,
=>
n=
N N
=
V L3
impact parameter, scattering
cross section = π d 2
d
“Movie”
Mean free path ≡ λ
λ
π d2
Volume swept out by 1 molecule
between collisions = λπd 2
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Volume swept out by 1 molecule
between collisions = λπd 2
Total volume of sample
λ
L3 = V ≈ Nλπd 2
π d2
V
1
∴λ ≈
=
2
Nπd
nπ d 2
Use Ideal
gas:
nn==N/V
N/V==p/k
p/kBBTT
2 kB T
∴λ =
2πd 2 p
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More accurately:
λ=
2
2nπd 2
p
λ (cm)
1 atm
10-5
1 Torr
10-2
1 mT
10
4
What is flux of atoms hitting surface per unit time?
vx
area
# / vol.
nvx
J ( # / area time) =
2
JJ==nv
nv
Show
ShowJJ
analogous
analogoustoto
current
currentdensity,
density,
We need vx , v
related
relatedtoto
pressure
pressure(elec.
(elec.
field)
field)
Calculating gas velocities
P(v)
Maxwell speed distribution:
3/2
⎡ mv 2 ⎤
⎡ m ⎤
2
v exp⎢−
P(v) = 4 π ⎢
⎥
⎥
⎣ 2πkT ⎦
⎣ 2kT ⎦
v=
Generally:
v vvms
speed
∫ vP (v)dv
1 2 3
mv ≈ kBT
2
2
Do
Dodimensional
dimensional
analysis
analysison
on
vx =
2kT
πm
v=
v x = v /2
8kT
3kT
, v rms =
πm
m
vrms ≈ 500 m/s
TT<=>
<=>molecular
molecularvelocity
velocity
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So flux of atoms hitting surface per unit time
vx
area
# / vol.
nvx n 2kT
Jx =
=
2 2 πm
p
= Jx
2πmkT
ideal
gas
Compare:
Dimensional analysis: (force/area = en/vol.):
mv
E kin
=n
p=
2
Vol
λ=
2 kB T
2πd 2 p
2
= Jmv
Pressure
Pressure==(Molecular
(Molecularmomentum)
momentum)xxflux,
flux,JJ
Numerically, Jx = 3.5 ×10 22
p(Torr)
(atoms /cm 2 sec)
MT(g /mole ⋅ K)
This gives a flux at 10-6 Torr of 1 monolayer (ML) arriving per sec
Why
Whynot
notper
perunit
unitarea?
area?
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Diffusivity
∆G
⎡ ∆G⎤
D = D0 exp⎢−
⎥
⎣ kT ⎦
Recall diffusion
in solids:
Debye ν ≈ 1013 s-1
For gas, no energy barrier, just collisions.
n J
n
dc
Jgas = −Dgas
dx
≅ −D
nvx
2
recall
λ
Dgas ≈
λ
λvx
2
(cm2/s)
2 kT
λ=
2πd 2 p
vx ∝ T
T 3/2
∴ Dgas ∝
p
Figure removed for copyright reasons.
or Dgas ∝ T1/ 2
Figure 2-2 in Ohring, M. The Materials Science of Thin Films.
2nd ed. Burlington, MA: Academic Press, 2001. ISBN: 0125249756.
much
muchweaker
weakerT-dep.
T-dep.than
than
in
solid
(which
is
exponential)
in solid (which is exponential)
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10-6 Torr => 1 monolayer/ sec
7
Review
2kB T
∴λ =
2πd 2 p
Ideal gas: pV = NkBT,
Generally:
1 2 3
mv ≈ kBT
2
2
nvx n 2kT
=
Jx =
2 2 πm
J gas = Dgas
≈ 10 cm at p = 1 mT
100 m at 10-6 Torr
n
dc
≅D
dx
λ
ideal
gas
Dgas ≈
λv x
2
(cm2/s)
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p
= Jx
2πmkT
mv
E kin
=n
p=
2
Vol
2
= Jmv
Weak temperature dependence
relative to solid state diffusion
8
Knudsen number
L = dimension of chamber or reactor
Recall:
2kB T
λ=
2πd 2 p
λ/L < 1
Knudsen
number, N0 = λ/L
λ/L > 1
p
λ (cm)
1 atm
10-5
1 Torr
10-2
1 mT
10
Flow is viscous; p > 1 mT
Pump power must be > viscosity;
Must transport large # of molecules
Molecular, ballistic flow;
p < 1 mT
Pump efficiency is critical;
Must attract and hold molecules
What does this imply for pumping?
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Gas flow and pump speed
Gases are compressible, unlike liquids.
∴ express flow as number of molecules/time,
not volume/t.
dN
1 ⎛ dp
dV ⎞
Q=
=
+p
⎜V
⎟
dt kB T ⎝ dt
dt ⎠
Conductance of
vacuum component:
p1
p2
Using
Usingideal
ideal
gas
gaslaw
law
Pump throughput, Q:
dp/dt
dp/dt==vv∇∇pp
pp
pump
⇒ Q = C(p − pp )
Units of conductance = 1/(sec-Pa)
C ∝ area/length
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Q ≡ pS
Ohm:
Ohm:I I==V/R
V/R
S=Q/p
S=Q/punits
units
#/(sec*Pa)
#/(sec*Pa)
Pump speed units, S = V/(kBT t)
sccm
Std. cc/min
or
L/s
Liters/sec
10
Gas flow and pump speed
Conductance of vacuum component:
System throughput:
p
⇒ Q = C (p − p p )
Q ≡ pS,
eff
Q
p = eff
S
(pp is pressure
nearer pump)
pp =
Q
Sp
⎛ Q
CS p
Q⎞
1
Q = C⎜⎜ eff − ⎟⎟ ⇒ S eff =
=
Sp ⎠
C + Sp 1 + 1
⎝S
C Sp
chamber
pp
pump
Sp
Like
Likeparallel
parallelresistors
resistors
Series
Seriesconductances:
conductances:
1/C
1/C==1/C
1/C11++1/C
1/C22
SS==Q/p
Q/pand
andCC==Q/dp
Q/dp
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Seff
C
Effective pump speed, Seff, never exceeds conductance
of worst component or pump speed, Sp.
11
Vacuum technology: Generating low pressure
Two classes of vacuum pumps:
1) Molecules physically removed from chamber
a) mechanical pump
S=
1 dV
kT dt
b) Turbo molecular pump
c) Oil diffusion pump
p
2) Molecules adsorbed on a surface,
or buried in a layer
a) Sputter/ion pump (with Ti sublimation)
b) Cryo pump
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1) Molecules physically removed from chamber
a) Mechanical pump
b) Oil diffusion pump
c) Turbo molecular pump
1 atm
Oil contamination,
Vibrations.
But pumps from
1 atm to mT.
S ≈ 2 x 104 L/s
Hot Si oil vaporized,
jetted toward fore pump,
momentum transfer to gas,
which is pumped out.
S = 12A L/s
Rotating (25 krpm) vanes (760 Torr)
impart momentum to gas,
pres’re incr’s away from chamber,
1 Torr
gas pumped by backing pump.
No oil. S = 103 L/s
1 milliT
Figure removed for
copyright reasons.
10-6 T
Figure 2-9 in Ohring, 2001.
Figure removed for copyright reasons.
Figure 2-8 in Ohring, 2001.
10-9 T
Figure removed for copyright reasons.
Figure 2-7 in Ohring, 2001.
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2) Molecules adsorbed on a surface, or buried in a layer
a) Sputter/ion pump (with Ti sublimation)
b) Cryo pump
1 atm
(760 Torr)
Gas is ionized
by hi-V,
ions spiral in B field,
1 Torr
embed in anode,
Figure removed for copyright reasons.
Coated by Ti.
Figure 2-10 in Ohring, 2001.
No moving parts,
no oil.
Figure removed for copyright reasons.
1 milliT
S depends on
Very clean,
Figure 2-11 in Ohring, 2001.
pump size and
molecules condense
S(H) >>S(O,N,H2O)
on cold (120 K) surfaces,
No moving parts. S ≈ 3A (cm2)L/s
10-6 T
v
B
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10-9 T
14
PUMP SUMMARY
Two classes of vacuum pumps:
1) Molecules physically removed from chamber
a) mechanical pump
Pumps from 1 atm; moving parts, oil
b) Turbo molecular pump
c) Oil diffusion pump
Clean, pumps lg. M well, from 1mT;
low pump speed, moving parts
No moving parts; oil in vac
2) Molecules adsorbed on a surface,
or buried in a layer
a) Sputter/ion pump
Clean, pumps reactants, no moving parts;
(with Ti sublimation)
pumps from 10-4 T down.
b) Cryo pump
Clean, no moving parts;
pumps from 10-4 T down.
Most systems use different pumps
for different pressure ranges…
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Vacuum technology: Deposition chambers
Standard vacuum, p ≈ 10-5 -10-6 Torr
Glass or stainless steel,
usually diffusion pumped,
CVD, thermal evap. or sputter dep.
=> polycrystalline films
Ultrahigh vacuum, p ≈ 10-8 -10- 11 Torr;
Stainless steel (bakeable);
Ion and/or turbo pumped
thermal evap. Sputter deposition
=> better quality films, epitaxial
1. Get
p < 1 mT;
close valve
Figure removed for copyright reasons.
Figure 2-12 in Ohring, 2001.
2. Open
backing valve,
Turn on diff’n
pump
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Vacuum technology: Deposition chambers
Ultrahigh vacuum, p > 10-11 Torr;
Stainless steel (bakeable);
Ion and/or turbo pumped
thermal evap. Sputter deposition
=> better quality films, epitaxial
Baking a stainless-steel uhv system
(T up to 200 C for 10’s of hrs)
desorbs water vapor, organics
from chamber walls;
these are ion-pumped out;
pressure drops as T returns to RT.
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Thin film growth general
Bonds on 3 sides
3 bonds with substrate
More bonds
R
≡
Rate of arrival
Diffusion rate
Arrival, sticking,
surface diffusion,
bonding
Bonds on 1 side
arrival
Film growth
competes with gas arrival.
diffusion
growth
1)
R > 1 ⇒ Non-equilibrium, fast growth, many misaligned islands form, leading to
defective (high-surface-en), polycrystalline film, columnar grains, This 3-D growth
is “Volmer-Weber” mode; Can ⇒ amorphous film.
2)
R < 1 => Slower, more equilibrium, layer-by-layer growth, larger grains (raise
surface temperature to ↑ mobility ⇒ ↑ g.s. ). If film and substrate have same
crystal structure, film may grow in perfect alignment with substrate (“epitaxy”).
This 2-D growth is “Frank-van der Merwe” mode.
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Thin film growth details (R < 1)
R
≡
1) Arrival rate,
physical
adsorption
3) Chemical
reaction
Diffusion rate
5) Growth
4) Nucleation
2) Surface
diffusion
Rate of arrival
6) Bulk diffusion
Better quality films;
layer-by-layer growth
If R > 1, processes 2) - 6) have reduced probability;
=> poor quality, rough films
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Knudsen number
L = dimension of chamber or reactor
λ/L < 1
Knudsen
number, N0 = λ/L
λ/L > 1
p
λ (cm)
1 atm
10-5
1 Torr
10-2
1 mT
10
Flow is viscous; p > 1 mT
Deposited species “thermalized”;
Growth is from all directions,
good step coverage
Molecular, ballistic flow;
p < 1 mT
Deposited species arrives “hot”;
Growth ballistic, shadow effects,
poor step coverage
What does this imply for film growth?
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Looking ahead…
Thin films made by a variety of means:
thermal vapor deposition (evaporation)
- for metals
Physical vapor deposition
(PVD)
sputter deposition
DC-magnetron- for metals
-RF for oxides
chemical vapor deposition
- for metals, semiconductors
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Chemical vapor deposition
(CVD)
21