University of California, Berkeleylieber/plasmaproc21cent.pdfUniversity of California, Berkeley P L...
Transcript of University of California, Berkeleylieber/plasmaproc21cent.pdfUniversity of California, Berkeley P L...
University of California, Berkeley PLASMA
PLASMA PROCESSING IN THE 21ST CENTURY
M.A. Lieberman
Department of Electrical Engineering and Computer SciencesUniversity of California
Berkeley, CA 94720
icpig23May05 1
University of California, Berkeley PLASMA
OUTLINE
• The nanoelectronics revolution
• Plasma etching
• Dual frequency capacitive discharges
• Decoupling high and low frequencies
• Standing wave and skin effects
• Conclusions
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University of California, Berkeley PLASMA
THE NANOELECTRONICS REVOLUTION
• Transistors/chip doubling every 2 years since 1959• 500,000-fold decrease in cost for the same performance• In 20 years one computer as powerful as all those
in Silicon Valley today
EQUIVALENT AUTOMOTIVE ADVANCE
• 4 million km/hr• 1 million km/liter• Never break down• Throw away rather than pay parking fees• 3 cm long × 1 cm wide• Crash 3× a day
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THE INVENTION OF THE TRANSISTOR
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FIRST INTEGRATED CIRCUIT AND MICROPROCESSOR
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University of California, Berkeley PLASMA
MOORE’S LAW
• “Transistors/chip double every 18 months” — Gordon Moore (1965)(Transistor size shrinking; chip size growing)
• Now a self-fulfilling prophecy
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 201510
2
103
104
105
106
107
108
109
1010
Year
Tra
nsis
tors
/Chi
p
4004
8086
80286 i386
i486 Pentium
Pentium Pro Pentium II
Pentium III
Pentium IV
Itanium
2 yr doubling
Montecito
• “No exponential is forever. . .but we can delay ‘forever”’(Gordon Moore, 2003)
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University of California, Berkeley PLASMA
DOUBLE/TRI GATE TRANSISTORS
• Both structures can be built with current ic fabrication techniques• CMOS can be scaled another 20 years!• State of the art (2005):
– In manufacture:50 nm (200 atoms) gate length1.5 nm (5 atoms) gate oxide thickness
– Smallest fabricated CMOS transistor (FinFET, UC Berkeley):12 nm (48 atoms) gate length
– Limiting gate length from simulations (desktop ic):4 nm (16 atoms) gate length
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University of California, Berkeley PLASMA
LOW TEMPERATURE INDUSTRIAL DISCHARGES
Lighting,Radiationsources
Electricity
Mechanicalenergy
HeatChemistry
Low temperatureplasma discharges
Plasma displaysGas lasersFluorescent lampsArc lightingElectron and ion beam sources
Electric power switch gearMHD power generation
Plasma thrusters
p < 1 Torrp > 1 Torr
Plasma-assisted materials processing
Microelectronics etching, deposition, oxidation, implantation, passivationLiquid crystal display and solar cell depositionsAerospace and automotive ceramic and metal coatings, films, paintsMetallurgical melting, refining, welding, cutting, hardeningCeramics synthesis, ultrapure powders, nanopowdersFood packaging permeability barriersTextile adhesion treatmentsMedical materials bio-compatibility treatments, sterilization, cleaningArchitectural and automotive glass coatings
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ANISOTROPIC ETCHING
︷ ︸︸ ︷ ︷ ︸︸ ︷Wet etching Ion-enhanced plasma etching
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University of California, Berkeley PLASMA
RECIPE FOR PLASMA ETCHING
1. Start with inert molecular gas CF4
2. Make discharge to create reactive species:CF4 −→ CF3 + F
3. Species reacts with material, yielding volatile product:Si + 4F −→ SiF4 ↑
4. Pump away product5. Source of anisotropy:
Energetic ions bombard trench bottom, but not sidewalls:(a) Increase etching reaction rate at trench bottom(b) Clear passivating films from trench bottom
Mask
PlasmaIons
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University of California, Berkeley PLASMA
EVOLUTION OF ETCHING DISCHARGES
FIRST GEN-ERATION
SECONDGENER-ATION
THIRD GEN-ERATION ? ?
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WHY DUAL FREQUENCY CAPACITIVE DISCHARGES?
• Motivation for capacitive discharge– Low cost– Robust uniformity over large area– Control of dissociation (fluorine)
• Motivation for dual frequency– Independent control of ion flux and ion energy
High frequency voltage controls ion fluxLow frequency controls ion energy
• A critical application for dielectric etch
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University of California, Berkeley PLASMA
TYPICAL OPERATING CONDITIONS
• R ∼ 15–30 cm, L ∼ 1–3 cm• p ∼ 30–300 mTorr, C4F8/O2/Ar feedstock• High frequency fh ∼ 27.1–160 MHz, Vh ∼ 200–500 V• Low frequency fl ∼ 2–13.56 MHz, Vl ∼ 500–1500 V• Absorbed powers Ph, Pl ∼ 500–3000 W
~
~
Vl
Vh
+
–
+
–
~
~
Vl
Vh
+
–
+
–
Diode (2 electrodes) Triode (3 electrodes)
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University of California, Berkeley PLASMA
CONTROL OF PLASMA DENSITY
• Particle balance =⇒ electron temperature Te
(independent of plasma density)=⇒ Te ∼ 2–6 eV
• Electron power balance =⇒ plasma density n(once electron temperature Te is known)
n ∝ Pe
• In these dischargesPe = power absorbed by electrons ∝ ω2Vrf
=⇒ n ∝ ω2Vrf
• Make ω2hVh � ω2
l Vl
Vh controls plasma density (ion flux)
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University of California, Berkeley PLASMA
CONTROL OF ION ENERGY
• Ion bombarding energy is total dc bias voltage across sheath
Ei ∼ |Vh + Vl|• Make Vl � Vh
Vl controls ion energy
• Combined condition for independent control of ion flux and energy
ω2h
ω2l
� Vl
Vh� 1
1. M.A. Lieberman, J. Kim, J.P. Booth, J.M. Rax and M.M. Turner,
SEMICON Korea Etching Symposium, p. 23 (2003)
2. H.C. Kim, J.K. Lee, and J.W. Shon, Phys. Plasmas 10, 4545 (2003)3. P.C. Boyle, A.R. Ellingboe, and M.M. Turner, J. Phys. D: Appl. Phys.
37, 697 (2004)
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University of California, Berkeley PLASMA
GLOBAL MODEL OF DISCHARGE
• Asymmetric diode (plate areas Aa and Ab)
~ Vl+
–
~ Vh
+
– Lsalsah
sbhsbl
Ab
Aa
(ωh)
(ωl)
• Low frequency Child law sheaths• High frequency homogeneous sheaths• Ion particle balance, and electron and ion power balance• All high and low frequency heating terms
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University of California, Berkeley PLASMA
RESULTS FOR 27.1/2 AND 60/2 MHz
• Aa = 544 cm2, Ab = 707 cm2, L = 1.6 cm, p = 190 mTorr argonfh = 27.1 MHz fh = 60 MHz
0 100 200 300 400 5000
5
10
15
x 1016
Ph (W)
n0 (
m-3
)
Vl = 900 VVl =1200 VVl =1500 VVl =1800 V
0 100 200 300 400 5000
200
400
600
800
1000
1200
1400
Ph (W)
Eia
(V
)
0 100 200 3000
0.5
1
1.5
2
x 1017
n0 (
m-3
)
Vl = 900 VVl =1200 VVl =1500 VVl =1800 V
0 100 200 3000
200
400
600
800
1000
1200
Eia
(V
)
Ph (W)
Ph (W)
The high/low frequencydecoupling is goodbut not perfect
The high/low frequencydecoupling is betterbut not perfect
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University of California, Berkeley PLASMA
1. DUAL FREQUENCY STOCHASTIC HEATING?
• High frequency sheath oscillates over nearly uniform ion density
Bulk plasma
High frequency homogeneoussheath motion Ions
Electrons
Wall
Stochasticheating
Bulk plasma
High frequency Child lawsheath motion
Ions Electrons
Wall
Stochasticheating
Bulk plasma
High frequency step modelsheath motion
Ions
Electrons
Wall
Stochasticheating
(Lieberman, 1988) (Lieberman, 1988) (Kaganovich, 2002)Sstoc = 0 Sstoc ≠ 0 Sstoc ≠ 0
Dual frequencysheath
Bulk plasma
High frequencynear-homogeneous
sheath motion
Ions Electrons
Stochasticheating???
Wall
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University of California, Berkeley PLASMA
2. COUPLING OF VOLTAGES?
• Additive assumption?Ei ≈ 0.41 (Vl + Vh)
• Current-driven homogeneous model gives
Ei =38
Vl + Vh − 23
VlVh
Vl + Vh︸ ︷︷ ︸
cross termWorst case for crossterm is 1
6 (Vl + Vh) when Vl = Vh
• Cross term for Child law sheaths?Voltage-driven discharges?Real systems driven through matching networks?
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University of California, Berkeley PLASMA
3. ION POWER SUPPLIED BY SOURCES?
• For single frequency capacitive discharges
Electron power =Pe ∝ ω2Vrf ∝ n
Ion power =Pi ∝ ω2V 2rf ∝ nVrf � Pe
⇒ RF power source supplies Pe and Pi
• For dual frequency discharges
Electron power =Pe ∝ ω2hVh ∝ n
Ion power =Pi ∝ ω2Vh (Vl + Vh) � Pe
High frequency source supplies Pe
Which sources supply the ion power? Is Pil/Pih = Vl/Vh?
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University of California, Berkeley PLASMA
TRIPLE FREQUENCY RF DISCHARGE
• IEDF depends on rf bias period/ion transit time across sheath
~
~
Vl1
Vh
+
–
+
–
~ Vl2
+
–
Power
Bias
(60–160 MHz)
(13.6 MHz)
(1 MHz)
Ions
f(E)
E 1
∆
EE 2
E i
Coburn and Kay (1972)
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University of California, Berkeley PLASMA
WIDTH OF ION ENERGY DISTRIBUTION
(Argon, 600 V rf bias, 1011 cm−3 density)
0.0 0.5 1.0 1.5 2.0 2.5
0.00
0.25
0.50
0.75
1.00
1.25
theory
simulations
theo
ry
x
x
13.56 MHz
1 MHz
RF bias period/ion transit time across sheath
Ion
ener
gy w
idth
Ion
ener
gy m
axim
um
1. V. Georgieva, A. Bogaerts, and R. Gijbels, Phys. Rev. E 69, 026406 (2004)
2. J.K. Lee, O.V. Manuilenko, N.Y. Babaeva, H.C. Kim, and J.W. Shon,
Plasma Sources Sci. Technol. 14, 89 (2005)3. S. Shannon, D. Hoffman, J.G. Yang, A. Paterson, and J. Holland,
submitted to Journal of Applied Physics (May 2005)
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University of California, Berkeley PLASMA
HIGH FREQUENCY ELECTROMAGNETIC EFFECTS
• High frequency and large area ⇒ standing wave effects
• High frequency ⇒ high density ⇒ skin effects
• Previous studies of capacitive discharges mostly based on electro-statics, not full set of Maxwell equations
=⇒ no standing wave or skin effects
M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, and M.M. Turner,
Plasma Sources Sci. Technol. 11, 283 (2002)
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University of California, Berkeley PLASMA
CYLINDRICAL CAPACITIVE DISCHARGE
Consider only the high frequency source
~+–
2R
s
s
2d 2lPlasma
Vh
z
r
Sheath
Sheath
Fields cannot pass through metal plates
(1) Vs excites radially outward wave in top vacuum gap(2) Outward wave excites radially inward wave in plasma
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University of California, Berkeley PLASMA
BASIC PHYSICS
• Plasma is (weakly) lossy dielectric slab
κp = 1 −ω2
p
ω(ω − jνm)where
ωp = (e2ne/ε0m)1/2 = plasma frequencyνm = electron-neutral collision frequency
• TM modes with Hφ ∼ ejωt
• Maxwell’s equations∂Hφ
∂z= −jωε0κpEr (inductive field)
1r
∂(rHφ)∂r
= jωε0κpEz (capacitive field)
∂Er
∂z− ∂Ez
∂r= −jωµ0Hφ
• Choose some uniform density ne and sheath width s
• Solve with appropriate boundary conditionsicpig23May05 25
University of California, Berkeley PLASMA
SURFACE WAVE MODE
• Power enters the plasma via a surface wave mode:
PlasmaStandingwave
Decay(weak)Decay
Surface Wave Mode
λδ
s2ds
• Radial wavelength for surface wave (low density limit):
λ ≈ λ0√1 + d/s
∼ λ0
3
with λ0 = c/f the free space wavelength• Axial skin depth for surface wave:
δ ∼ c
ωp
• There are also evanescent modes leading to edge effects near r = R
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University of California, Berkeley PLASMA
POWER DEPOSITION VERSUS RADIUS AT 13.56 MHz
• R = 50 cm, d = 2 cm, s = 0.4 cm (λ ≈ 9–10 m)• Pcap (dash), Pind (dot) and Ptot (solid) as a function of r
ne = 109 cm−3
δ = 16.7 cmne = 1010 cm−3
δ = 5.3 cm
Pow
er/a
rea
r (cm)0 25 50
0.5
1
0
Total
Capacitive
Inductive
Edgeeffect
Pow
er/a
rea
r (cm)0 25 50
0.5
1
0
Total
Capacitive
Inductive
Edgeeffect
Small stand-ing wave andskin effects
Large skin ef-fect
icpig23May05 27
University of California, Berkeley PLASMA
POWER DEPOSITION VERSUS RADIUS AT 40.7 MHz
• R = 50 cm, d = 2 cm, s = 0.4 cm (λ ≈ 3 m)• Pcap (dash), Pind (dot) and Ptot (solid) as a function of r
ne = 109 cm−3
δ = 15.9 cmne = 7×109 cm−3
δ = 6.3 cm
Pow
er/a
rea
r (cm)0 25 50
0.5
1
0
Total
Capacitive
Inductive
Edgeeffect
Pow
er/a
rea
r (cm)0 25 50
0.5
1
0
Total
Capacitive Inductive
Edgeeffect
Large stand-ing wave ef-fect
Standing waveand skin ef-fects cancel
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University of California, Berkeley PLASMA
EXPERIMENTAL RESULTS FOR STANDING WAVES
20×20 cm dischargep = 150 mTorr50 W rf power
The standing wave ef-fect is seen at 60 MHzand is more pronouncedat 81.36 MHz
(A. Perret, P. Chabert, J-P Booth, J. Jolly, J. Guillon and Ph. Auvray,
Appl. Phys. Lett. 83, 243, 2003)
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University of California, Berkeley PLASMA
TRANSMISSION LINE MODELS
• Parallel plane transmission line model with local (in x) particle andenergy balance to determine density ne(x) and sheath width sm(x)
x = x0x = 0
~ Vrf
+
–
EdgeMidplane
+
–
V
I
Z' = jωL'
Y'=G'(V)+jωC'(V)
Sheath capacitance Ion energy loss
Stochastic heating
Ohmic heating
Plasma inductance
+
–
V(x)
dxλ/λ0 ≈ 40V1/10rf L−1/2f−2/5
P. Chabert, J.L. Raimbault, J.M. Rax, and M.A. Lieberman,
Phys. Plasmas 11, 1775 (2004)
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University of California, Berkeley PLASMA
SUPPRESSION OF STANDING WAVE EFFECTS
• Shaped electrode (and diel plate) eliminate standing wave effects
• Increased overall thickness in center compared to edge keeps voltageacross discharge section constant
• The electrode shape is a Gaussian, independent of the plasma prop-erties
L. Sansonnens and J. Schmitt, Appl. Phys. Lett. 82, 182 (2003)
P. Chabert, J.L. Raimbault, J.M. Rax, and A. Perret, Phys. Plasmas 11, 4081 (2004)
icpig23May05 31
University of California, Berkeley PLASMA
EXPERIMENTAL CONFIRMATION
• 5–250 mTorr argon, 50–300 W
H. Schmitt et al, J. Appl. Phys. 95, 4559 (2004)
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University of California, Berkeley PLASMA
SKIN EFFECTS?
• Skin effects =⇒ radial nonuniformities at high densities when
δ <∼ 0.45√
d R
δ ∝ 1√n
= collisional or collisionless skin depth
d = bulk plasma half-thicknessR = discharge radius
• Control of skin effects?
1. M.A. Lieberman, J.P. Booth, P. Chabert, J.M. Rax, and M.M. Turner,
Plasma Sources Sci. Technol. 11, 283 (2002)
2. P. Chabert, J.L. Raimbault, P. Levif, J.M. Rax, and M.A. Lieberman,
submitted to Physics of Plasmas, May 2005
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University of California, Berkeley PLASMA
CONCLUSIONS
• Transistors will scale to nano-sizes — 4nm–12nm gate lengths
• Nanoelectronics drives the development of processing discharges
• Dual frequency capacitive reactors are increasingly important fornext-generation dielectric etching
• The high and low frequencies can be well-decoupled
• Standing wave effects can be controlled
• Plasma processing has a bright future in the 21st century!
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