EE-194-PLA
Introduction to Plasma Engineering
Part 1: Plasma TechnologyPart 2: Vacuum Basics
Part 3: Plasma Overview
Professor Jeff HopwoodECE Dept., Tufts University
Part 1:Basic Plasma Technology
Plasma: an ionized gas consisting of atoms, electrons, ions, molecules,
molecular fragments, and electronically excited species (informal definition)
www.geo.mtu.edu/weather/aurora/
Plasma: the “fourth state of matter”
solid(ice)
gas(steam)
energy
energyplasma(electrons+ions)
liquid(water)
energy
DC Plasma (AC Fluorescent Lamp…why AC?)
+
- + --
-
+
ArgonElectronArgon ion
Argon + Mercury @ ~0.01 atm.
lamp endcap
--+
--+
--+
--+
--+
- +
”sputtering”
Also, this is the heart of high powered gas lasers.
Fluorescent Lamp SpectrumThe strong peaks of light emission are due to excited Hg:
Hg + e- (hot) Hg* + e-
(cold) Hg + light + e-
http://en.wikipedia.org http://www.chemcool.com
photon
Integrated Circuit Fabricationand Plasma Technology
Microfabricationdeposit-pattern-etch-repeat
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Copper metallizationon the PowerPC chip
Basic Plasma TechnologySputtering Magnetron
Magnetron
N
S
N
SN
STarget
Substrate
DC
Pulsed
RF
to pump
Basic Plasma TechnologyCapacitively Coupled Plasma
0.4 – 60 MHz
Hopwood and Mantei, JVST A21, S139 (2003)
Plasma Etching
Cl2Cl+
Cl SiCl2
Cl2 SiCl2
Simplified anisotropic etching
Cl2 + e- Cl + Cl+ + 2e-
Si(s) + 2Cl(g)+ ion energy SiCl2(g)
S
Anisotropyis due to directional ion bombardment
Cl+
Cl
Si(s) + 2Cl(g)+ ion energy SiCl2(g)
The directional ion energy drives the chemical reaction only at the bottom of the microscopic feature.
Dry or Plasma Etching Wet Etching (in acid)
In wet chemistry, the chemical reaction occurs on all surfaces at the same rate. Very small features can not be microfabricated since they eventually overlap each other.
wafer wafer
Jason M. Blackburn, David P. Long, Albertina Cabañas, James J. Watkins
Science 5 October 2001: Vol. 294. no. 5540, pp. 141 - 145
Trenches: etched and filled with copper
Plasma Deposition
SiH4
SiHSiH2
H2
SiH4 SiHX+H2
Simplified plasma deposition
SiH4 + e- SiH3 + H + e-
SiH3 + e- SiH2 + H + e-
SiH2 + e- SiH + H + e-
SiH + e- Si + H + e-
SiHx+ surface+ ion energy Si (s) + Hx(g)
S
Basic Plasma TechnologyElectron Cyclotron Resonance Plasma: Etch and Deposition
Hopwood and Mantei, JVST A21, S139 (2003)
Basic Plasma TechnologyInductively Coupled Plasma: Etch and Deposition
0.4 – 13.56 MHz
Hopwood and Mantei, JVST A21, S139 (2003)
Other applications:Xenon Ion Propulsion
Deep Space 1 encounter with Comet Borrelly
http://nmp.nasa.gov/ds1/images.html
Other Applications :Plasma Display Panels (PDPs)
Structure
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).
red
green
blue
Plasma Display Panels (PDPs)Basic Operation
h ~ 200 ml ~ 400 md ~ 60 m
Sustain Electrode
Bus Electrode
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).
initiate breakdown(~ 300 volts)
+ + + + + +
+ + + +
sustain plasma(~ 180 volts)
surface
Part 2:Basic Vacuum Concepts
Goals
• To review basic vacuum technology– Pressure, pumps, gauges
• To review gas flow and conductance
• To understand the flux of vapor phase material to a substrate
• To understand mean free path,
Ultrahigh Vacuum High Vacuum Rough Vacuum
Typical HighPressure Plasma
Typical Low PressurePlasma Processing
Vacuum (units)
1 atm.1.3x10-31.3x10-61.3x10-9
760 Torr1 Torr1 mTorr1x10-6 Torr
1 Torr =1 mm-Hg
101,333 Pa133 Pa0.133 Pa0.133x10-3 Pa
1 Pascal =1 N/m2
Rough Vacuum
• “Mechanical Pumps” typically create a base pressure of 1-10 mTorr or 0.13-1.3 Pa
Rotary Vane Pump(Campbell)
Warning:
Certain process gases are incompatible with pump fluids and pose severe safety risks!
High Vacuum PumpingCryopumps condense gases on cold
surfaces to produce vacuum
Typically there are three cold surfaces:
(1) Inlet array condenses water and hydrocarbons (60-100 Kelvin)
(2) Condensing array pumps argon, nitrogen and most other gases (10-20 K)
(3) Adsorption is needed to trap helium, hydrogen and neon in activated carbon at 10-12 K. These gases are pumped very slowly!
Warning: all pumped gases are trapped inside the pump, so explosive, toxicand corrosive gases are not recommended. No mech. pump is needed until regen.
adapted from www.helixtechnology.com
(Campbell)
High Vacuum Pumping
Process chamberTurbomolecular Pump
High rotation speed turbine imparts momentum to gas atoms
Inlet pressures: <10 mTorr
Foreline pressure: < 1 Torr
Requires a rough pump
Good choice for toxic and explosive gases –
-gases are not trapped in pump
All gases are pumped at approx. the same rate
Pumping Speeds:
20 – 2000 liters per sec
foreline
adapted from Lesker.com
High Vacuum PumpingProcess chamber
Heater/Pumping Fluid
Foreline -to mech pump
Diffusion Pump
The process gas is entrained by the downward flow of vaporized pumpingfluid.
Benefits:Low cost, reliable, and rugged.High pumping speed: ~ 2000 l/s
Caution:The process chamber will becontaminated by pumping fluid.A cold trap must be used between thediffusion pump and the process chamber.
Not recommended for “clean” processes.
Water-cooledwalls
adapted from Lesker.com
Flow Rate
Typically gas flows are cited in units of standard cubic centimeters per minute (sccm) or standard liters per minute (slm)
“Standard” refers to T=273K, P = 1 atm.
Example:Process gas flow of 50 sccm at 5 mTorr (@300K) requires
50 cm-3min-1(760Torr/5x10-3Torr)(300/273)(1min/60sec)(1/103) = 140 liters/sec of pumping speed at the chamber pump port
Conductance Limitation50 sccm
5 mTorr
140 l/s
= Q/(P1 – P2)
Fixed Throughput, Q:Q = 0.005 Torr x 140 l/s = 0.7 Torr-l/s
> 140 l/s …since P2<P1
Conductance depends on geometry and pressure (use tabulated data)
Corifice = ¼ (a2)<v> l/s
Ctube = a2 (2a<v>/3L)
…if mean free path >> a, L
(see Mahan, 2000)
Pressure Measurement
Vacuum Gauge Selection adapted from Lesker.com
Convectron Gauge:Initial pumpdown from
1 atm, and as a foreline monitor
Thermal Conductivity of Gas
Baratron:Insensitive to gas
composition,Good choice for
process pressures
True Pressure (diaphragm displacement)
Ion Gauge:Sensitive to gas composition, buta good choice for base pressures
Ionization of Gas
RGA:A simple mass spectrometer
Residual Gas AnalysisLow pressure systems are dominated by water vapor as seen in this RGA of a chamber backfilled with 4x10-5 torr of argon
Why? H2O is a polar molecule that is difficult to pump from the walls --> bake-out the chamber
Source: Pfeiffer vacuum products
Leak?
Gas Density (n)Ideal Gas Law
PV = NkT
Gas density at 1 Pascal at room temp.
N/V = n = P/kT = (1 N/m2)/(1.3807x10-23J/K)(300 K)= [1 (kg-m/s2)/m2]/[4.1x10-21 kg-m2/s2]= 2.4x1020 atoms per m3
= 2.4x1014 cm-3 …at 1 Pa
Rule of Thumb
n(T) = 3.2x1013 cm-3 x (300/T) …at a pressure of 1 mTorr
Gas Kinetics
kT
mv
kT
m
v
vPvf
2exp
24
)()(
22/3
2
0
2_ 8
4)(m
kTdvvvfvcv
vndvvfvnvnZv
zzz 4
1)( 3
0
Maxwellian Distribution
Average speed of an atom:
Flux of atoms to the x-y plane surface:
(Campbell)
Very important!
Example
A vacuum chamber has a base pressure of 10-6 Torr. Assuming that this is dominated by water vapor, what is the flux of H2O to a substrate placed in this chamber?
n = 3.2x1013 cm-3/mTorr * 10-3 mTorr = 3.2x1010 cm-3
<v> = (8kT/M)1/2 = 59200 cm/s
z = (¼)n<v> = 4.74x1014 molecules per cm2 per sec!
This is approximately one monolayer of H2O every secondat 10-6 Torr base pressure.
Collisions and Mean Free Path
Gas Densityn = P/ kT
n
Cross-section~ d2
d
Rigorous Hard Sphere Collisions: = kT / 2 d2P
Arcm8 / P (mTorr)15 22.6 10 cm Ar
Part 3: Plasma Basics
Paschen Curve
http://www.duniway.com/images/pdf/pg/Paschen-Curve.pdf
F. Paschen, Ann. Phys. Chem., Ser. 3 37, 69 (1889). VDC
d
Too few ionizingcollisions: >d
Too many collisionsElectron energy<ionization energy
What do we need to know about plasma?
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
Power Absorbed
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
Power Absorbed: DC
• DC power– General electrical mobility and conductivity
– Mobility: e = q<t>/m = q/mme
Where <t> is the average time between collisions
and m is the collision frequency (collisions per second)
– Electron Conductivity: DC = qnee = q2ne/mme
– DC power absorbed: 3)( dvEEP
vol
DCabs
Power Absorbed: RF• RF/microwave power
– Ohmic Heating
– Generic electron-neutral collision frequencym ~ 5x10-8 ngasTe
1/2 (s-1)
… ngas (cm-3), Te(eV).
– Example: Find the pressure at which rf ohmic heating becomes ineffective: m = 0.1 Te = 2eV
= 13.56 MHz * 2 = 85.2Mrad/s
ngas = 0.1*85.2x106/5x10-8(2)1/2 = 1.2x1014 cm-3 = 3.7
mTorr
VRF
An electron oscillates in a rf electric field without gaining
energy
unless
electron collisions occur
3222
2
||2
1dvEP
vol m
mDCabs
f=13.56 MHz
Hopwood and Mantei, JVST A21, S139 (2003)
Stochastic Heatingan electron enters and exits a region of high field for a fraction of an rf cycle
t0 << 2
Reflecting Boundary (plasma sheath)
-
Emax
E ~ 0
ERF
x
z
vx(t0) > vx(0)
The usual mechanism for heating electrons using RF electric fields at low pressures
Wave/Resonant Heating
x
-Ex
- - -
t1 t2 t3
k
BDC
x
yv
F = q(vxB)
E=0
Electron cyclotron frequency:
ce = qB/me = 1.76x107 B(gauss)
If ce and ERF is perpendicular to BDC, then the electron gains energy from Ex in the absence of collisions.
Ex. f=2.45 GHz --> B=875 G
ERF
W/cm3
Hopwood and Mantei, JVST A21, S139 (2003)
Electron Collisions
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
Electron Collisions• Elastic Collisions:
– Ar + e Ar + e– Gas heating: energy is coupled from e to the gas
• Excitation Collisions– Ar + ehot Ar* + ecold, Ar* Ar + h – Responsible for the characteristic plasma “glow”– Eelectron>Eexc (~11.55 eV for argon)
• Ionization Collisions:– Ar + ehot Ar+ + 2ecold
– Couples electrical energy into producing more e_
– Eelectron > Eiz (15.76 eV for argon) • Dissociation:
– O2 + ehot 2O + ecold or O2 + ehot O + O+ + 2ecold
– Creates reactive chemical species within the plasma– Eelectron > Ediss (5.12 eV for oxygen)
Collision Cross Sections
• Unlike the hard sphere model, real collision cross sections are a function of electron kinetic energy (E), or electron velocity (v).
• We must find the expected collision frequency by averaging over all E or v.
gasgasinelastic nwherenvcm
cmv
t
/1...
)(
sec)/(1
vK
dvvfvvnvn gasgasinelastic
0
)()(
becomes
(cm3s-1)
Graphicallyf(
E)
or
(E
)
Electron energy, E
Ar(E)f(E)
Te Eiz
Note: the exponential tail of energeticelectrons is responsible for ionization
The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te)
curve fitting
Graphicallyf(
E)
or
(E
)
Electron energy, E
Ar(E)f(E)
Te Eiz
Note: the exponential tail of energeticelectrons is responsible for ionization
The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te)
curve fitting
Hot electrons – more ionization
Examples of Numerically Determined Rate Constants (Lieberman, 2005)
Generation Rate of Plasma Species by Electron Collisions
y + e x + e
dnx/dt = Kxneny
For example,
Ar + e Ar+ + e + e
dne/dt = Kiznengas
is the number of electrons (and ions) generated
per cm3 per second
Electron-Ion RecombinationThree-Body Problem:
e + Ar+ + M Ar + M
the third body is needed to conserve energy and momentum in the recombination process
-
+
MM
-
+M
wall recombination dominates at low pressure because three body collisions are rare
wall recombination volume recombination
Transport to Surfaces
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
n = ¼ n<v>
neni
0
Electron and Ion Loss to the Substrate and Walls- the plasma sheath -
electrons are much more mobile than ionse = q<t>/me >> q<ti>/mi = i
neni
0neni
0
-
-
- - --
-
-- --
chamber
Electron and Ion Loss to the Substrate and Walls- the plasma sheath -
(x)
x
+ +
ne = ni
ne<<ni
(sheath)
x
V(x) e
(after Mahan, 2000)
-1kV
s
x
V
0 v
+
low energy electrons are trapped within the plasma, but ions are accelerated by the sheath potential to the chamber walls and substrate
Ion FluxThe ion flux to a solid object is determined by
the Bohm velocity (or sound speed) of the ion:
uB = (kTe/mi)1/2 = 9.8x105 (Te/M)1/2 cm/s
=9.8x105 (3 eV/40 amu)1/2 ~ 2.5x105 cm/s
…and the ion flux is given by i = uBni (cm-2s-1)
(this is the ion speed at the edge of the sheath)
Electron Flux• Only the most energetic electrons can
overcome the sheath potential, Vs.
• e = ¼ ne<ve> exp (qVs/kTe)
f( E)
Electron energy, E Te qVs
flux to surface Boltzmann factor
Sheath Potential, Vs
In the steady state, the electron and ion fluxes to the chamber/substrate must be equal, if there is no external current path
e = i
¼ ne<ve> exp (qVs/kTe) = uBni = (kTe/mi)1/2 ne
giving
Vs = -Teln(mi/2me) ~ -5Te
This is often called the floating potential: Isolated surfaces have a negative potential relative to the plasma.
Ion Energy
(after Mahan, 2000)
-1kV
s
x
V
0 v
Ex: Assuming argon with Te = 3 eV,
the ion energy at the cathode is
Ei = q(1 kV + 4.7Te) = 1014 eV
ignoring ion-neutral collision within s,
and the ion energy at the anode is
Ei = 4.7 Te = 14 eV
Ion mean free path:
i = 1/ngasi ~ 3/p (cm) for Ar+
…where p is the pressure in mTorr
Here i = 3/100 cm or 0.3 mm @ 0.1 torr
NOTE: s>>i Ei << 1014 eV!
Particle Conservationand Electron Temperature
A simple model for electron temperature can be found for a steady state plasma:
# of ions created/sec = # of ions lost/sec
KizngasneV = uBniAeff
Kiz/uB = Kizoe-Eiz/kTe /(kTe/mi)1/2 = Aeff/(V ngas)
=1/deffngas
(V=plasma volume, Aeff = effective chamber area, deff = V/Aeff)
ne=ni
The electron temperature (Te) is a unique function of
1. gas density, ngas (pressure)
2. chamber size, deff = V/Aeff
3. gas type: Kiz, Eiz
Single-step vs. Two-step Ionization
ngdeff (m-2)
1e+18 1e+19 1e+20 1e+21 1e+22
Te
(eV)
0
1
2
3
4
5
6
7
n0 = 1 x 1011 cm-3
single-step
two-step
Ar+eAr*+eAr* + e Ar+ + 2e
Ar + e Ar+ + 2eExample:
Two large parallel plates separated by 2 cm are used to sustain an argon plasma at 25 mTorr. Find Te.
deff = V/Aeff ~ R2d / (R2 +R2) = d/2
ngasdeff ~ (25*3.2x1019m-3)(0.01m) =0.8e+19 m-2
Te = 3 eV
(Note: we have assume that the plasma density is uniform)
Power Conservation and Electron Density, ne
Power Absorbed by the Plasma = Power Lost from the Plasma
Pabs = [qniuBEion+q(¼ne<ve>eVs/kTe )Eelec]Aeff +(Pheat+Plight+Pdiss)
≡ qneuBAeff(Eion + Eelec + Ec)
where EC is the collisional energy lost in creating an electron-ion pair due to ionization, light, dissociative
collisions, and heat:
EC = [izEiz + exEex + dissEdiss + m(3me/mi)Te]/iz
qVs2Te
Pion Pelectron
C
Collisional Energy Loss
Electron Density ExampleContinuing with the previous example
A plasma is sustained in argon at 25 mTorr between two parallel plates separated by 2 cm. The radius of the plates is 20 cm and the power absorbed by the plasma is 100 watts. Find ne.
100 W = qneuBAeff(Eion + Eelec + Ec)= (1.6x10-19C)ne(2.5x105cm/s)(2x202 cm2) x
(5Te + 2Te + 35 eV)
ne = 1.3x1010 cm-3
Find ne if the gas is N2, assuming that Te ~ 3 eV
100 W = (1.6x10-19C)ne(2.5x105cm/s)(2x202 cm2)(5Te + 2Te + 400 eV)
ne = 2.3 x 109 cm-3
Example (cont’d)
Repeat the previous example using argon, BUT include an electrode voltage of 1000v that is applied to one plate to sustain the plasma.
100 W = qneuBAeff(Eion + Eelec + Ec)
= (1.6x10-19C)ne(2.5x105cm/s)(x202 cm2) x
{(5Te + 2Te + 35 eV)+[(1000 eV+5Te) + 2Te + 35 eV]}
ne = 1.7x109 cm-3
anode cathode
Secondary Electronse = seci , where sec~0.1-10 and Ee ~ qVs
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
secondaryelectrons
Summary
substrate
radicals,molecular fragments
ionsWall Wall
gas(ng)
Gas flow
pumping pumping
electronsne, Te
Power
excited atomsand molecules
light
reaction products secondary
electrons
PLASMA
Conclusion
• Basics of Vacuum– ng, <v>, n,,
• Plasma Generation and Simple Models– Te, ne, ni, i
• Basic Plasma Generation– DC (sputter deposition systems)– AC < 400 kHz (plasma displays, lighting)– Radio Frequency 0.4<f<900 MHz (etching and
deposition)– Microwave > 900 MHz