EE-194-PLA
Introduction to Plasma
Engineering
Part 1: Plasma Technology
Part 2: Vacuum Basics
Part 3: Plasma Overview
Professor Jeff Hopwood
ECE 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”
plasma
energy
(electrons+ions)
gas
(steam)
solid
(ice)
energy
energy
liquid
(water)
DC Plasma
(AC Fluorescent Lamp…why AC?)
”sputtering”
-
Argon + Mercury @ ~0.01 atm.
+
-
-
+
-
++-
-
-
-
+-
-
+-
-
+
+
-
+
Argon
Electron
Argon ion
lamp endcap
Also, this is the heart of high
powered gas lasers.
Fluorescent Lamp Spectrum
The strong peaks of light emission are due to excited Hg:
Hg + e- (hot)  Hg* + e- (cold)  Hg + light + ephoton
http://en.wikipedia.org
http://www.chemcool.com
Integrated Circuit Fabrication
and Plasma Technology
Microfabrication
deposit-pattern-etch-repeat
(a)
(b)
(c)
(e)
(f)
(g)
Copper metallization
on the PowerPC chip
(d)
(h)
Basic Plasma Technology
Sputtering Magnetron
DC
Magnetron
Pulsed
RF
S
N
Substrate
to pump
Target
N
S
S
N
Basic Plasma Technology
Capacitively Coupled Plasma
0.4 – 60 MHz
Hopwood and Mantei, JVST A21, S139 (2003)
Plasma Etching
Cl2
Cl2
SiCl2
SiCl2
Cl
S
Cl+
Simplified anisotropic etching
Cl2 + e-  Cl + Cl+ + 2eSi(s) + 2Cl(g)+ ion energy  SiCl2(g)
Anisotropy
is due to directional ion bombardment
Dry or Plasma Etching
Wet Etching (in acid)
Cl+
Cl
wafer
Si(s) + 2Cl(g)+ ion energy  SiCl2(g)
The directional ion energy drives the
chemical reaction only at the bottom
of the microscopic feature.
wafer
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.
Trenches: etched and filled with copper
Jason M. Blackburn, David P. Long, Albertina Cabañas, James J. Watkins
Science 5 October 2001: Vol. 294. no. 5540, pp. 141 - 145
Plasma Deposition
SiH4
SiH4
SiHX+H2
SiH
SiH2
S
Simplified plasma deposition
H2
SiH4 + e-  SiH3 + H + eSiH3 + e-  SiH2 + H + eSiH2 + e-  SiH + H + eSiH + e-  Si + H + eSiHx+ surface+ ion energy  Si (s) + Hx(g)
Basic Plasma Technology
Electron Cyclotron Resonance Plasma: Etch and Deposition
Hopwood and Mantei, JVST A21, S139 (2003)
Basic Plasma Technology
Inductively 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
blue
red
green
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).
Plasma Display Panels (PDPs)
Basic Operation
initiate breakdown
(~ 300 volts)
Sustain Electrode
sustain plasma
(~ 180 volts)
surface
++++
++++++
Bus Electrode
h ~ 200 m
l ~ 400 m
d ~ 60 m
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).
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, l
Vacuum (units)
1.3x10-9
1x10-6 Torr
0.133x10-3 Pa
1.3x10-6
1 mTorr
0.133 Pa
1.3x10-3
1 Torr
133 Pa
Typical High
Pressure Plasma
1 atm.
760 Torr
101,333 Pa
1 Torr =
1 mm-Hg
1 Pascal =
1 N/m2
Typical Low Pressure
Plasma Processing
Ultrahigh Vacuum
High Vacuum
Rough Vacuum
Rough Vacuum
• “Mechanical Pumps” typically create a base
pressure of 1-10 mTorr or 0.13-1.3 Pa
Warning:
Certain process gases
are incompatible with
pump fluids and pose
severe safety risks!
Rotary Vane Pump
(Campbell)
High Vacuum Pumping
Cryopumps 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!
(Campbell)
Warning: all pumped gases are trapped inside the pump, so explosive, toxic
and corrosive gases are not recommended. No mech. pump is needed until regen.
adapted from www.helixtechnology.com
High Vacuum Pumping
Turbomolecular Pump
Process chamber
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 –
foreline
-gases are not trapped in pump
All gases are pumped at approx.
the same rate
Pumping Speeds:
20 – 2000 liters per sec
adapted from Lesker.com
High Vacuum Pumping
Process chamber
Diffusion Pump
The process gas is entrained by the
downward flow of vaporized pumping
fluid.
Watercooled
walls
Foreline
-to mech pump Benefits:
Low cost, reliable, and rugged.
High pumping speed: ~ 2000 l/s
Caution:
The process chamber will be
contaminated by pumping fluid.
A cold trap must be used between the
diffusion pump and the process chamber.
Heater/Pumping Fluid
adapted from Lesker.com
Not recommended for “clean” processes.
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 Limitation
50 sccm
Conductance depends on
geometry and pressure (use
tabulated data)
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
Corifice = ¼ (pa2)<v> l/s
Ctube = pa2 (2a<v>/3L)
…if mean free path >> a, L
(see Mahan, 2000)
Pressure Measurement
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)
Ionization of Gas
RGA:
A simple mass
spectrometer
Ion Gauge:
Sensitive to gas
composition, but
a good choice for
base pressures
Vacuum Gauge Selection adapted from Lesker.com
Residual Gas Analysis
Low 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
Leak?
Source: Pfeiffer vacuum products
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
Maxwellian Distribution
P (v )  m 
f (v ) 


2
2
p
kT
4pv


3/ 2
  mv 2 

exp 
 2kT 
Average speed of an atom:
_

8kT
 v   c   v f (v)4pv dv 
pm
0
2
Flux of atoms to the x-y plane surface:
z  n  v z  n  vz f (v)dv 3 
vZ  0
1
nv
4
Very important!
(Campbell)
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/pM)1/2 = 59200 cm/s
z = (¼)n<v> = 4.74x1014 molecules per cm2 per sec!
This is approximately one monolayer of H2O every second
at 10-6 Torr base pressure.
Collisions and Mean Free Path
Gas Density
n = P/ kT
Cross-section
s ~ pd2
l  1/sn
d
Rigorous Hard Sphere Collisions: l = kT / 2 pd2P
sAr 2.6 1015 cm 2 
lAr(cm) ~ 8 / P (mTorr)
Part 3: Plasma Basics
Paschen Curve
F. Paschen, Ann. Phys. Chem., Ser. 3 37, 69 (1889).
VDC
d
Too many collisions
Electron energy<ionization energy
http://www.duniway.com/images/pdf/pg/Paschen-Curve.pdf
Too few ionizing
collisions: l>d
What do we need to know about
plasma?
light
Power
Gas flow
PLASMA
gas
(ng)
Wall
electrons
ne, Te
excited atoms
and molecules
ions
Wall
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
Power Absorbed
Power
light
Gas flow
PLASMA
gas
(ng)
Wall
electrons
ne, Te
excited atoms
and molecules
ions
Wall
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
Power Absorbed: DC
• DC power
– General electrical mobility and conductivity
– Mobility: e = q<t>/m = q/nmme
Where <t> is the average time between collisions
and nm is the collision frequency (collisions per second)
– Electron Conductivity: sDC = qnee = q2ne/nmme
– DC power absorbed:
Pabs   (s DC E  E )dv 3
vol
Power Absorbed: RF
• RF/microwave power
– Ohmic Heating
VRF
f=13.56 MHz

1
2
3
Pabs   s DC 2
|
E
|
dv
2
2
w


m
vol
2
m
– Generic electron-neutral collision
frequency
nm ~ 5x10-8 ngasTe1/2 (s-1)
… ngas (cm-3), Te(eV).
– Example: Find the pressure at
which rf ohmic heating becomes
ineffective: nm = 0.1w, Te = 2eV
w = 13.56 MHz * 2p = 85.2Mrad/s
ngas = 0.1*85.2x106/5x10-8(2)1/2 =
1.2x1014 cm-3 = 3.7 mTorr
An electron oscillates in a rf
electric field without gaining
energy
unless
electron collisions occur
Hopwood and Mantei, JVST A21, S139 (2003)
Stochastic Heating
an electron enters and exits a region of high field for a fraction of an rf cycle
t0 << 2p/w
Reflecting Boundary (plasma sheath)
Emax
ERF
z
x
-
E~0
vx(t0) > vx(0)
The usual mechanism for heating electrons using RF electric fields at low pressures
Wave/Resonant Heating
-Ex
t1
t3
t2
-
-
x
k
Electron cyclotron frequency:
BDC
wce = qB/me = 1.76x107 B(gauss)
ERF
E=0
x
v
F = q(vxB)
y
If w  wce 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
W/cm3
Hopwood and Mantei, JVST A21, S139 (2003)
Electron Collisions
Power
light
Gas flow
PLASMA
gas
(ng)
Wall
electrons
ne, Te
excited atoms
and molecules
ions
Wall
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
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 + hn
– 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 s(E), or
electron velocity s(v).
• We must find the expected collision frequency by
averaging over all E or v.
1
v(cm / sec)
inelastic 

 vsngas ...where l  1 / sngas
t 
l (cm)
becomes

inelastic  ngas  s v   ngas  s (v)v f (v)dv 
0
K  sv 
(cm3s-1)
Graphically
f(E) or s(E)
f(E)
sAr(E)
Note: the exponential tail of energetic
electrons is responsible for ionization
Te
Eiz
Electron energy, E
The RATE CONSTANT: Kiz(Te)  Kizoexp(-Eizo/Te)
curve fitting
Graphically
f(E) or s(E)
Hot electrons – more ionization
f(E)
sAr(E)
Note: the exponential tail of energetic
electrons is responsible for ionization
Te
Eiz
Electron energy, E
The RATE CONSTANT: Kiz(Te)  Kizoexp(-Eizo/Te)
curve fitting
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,
e  Ar+ +
Ar +
e+e
dne/dt = Kiznengas
is the number of electrons (and ions) generated
per cm3 per second
Electron-Ion Recombination
Three-Body Problem:
e + Ar+ + M  Ar + M
the third body is needed to conserve energy and momentum in the
recombination process
wall recombination
volume recombination
-
-
M
M
M
+
+
wall recombination dominates at low pressure because three body collisions are rare
Transport to Surfaces
Power
light
Gas flow
PLASMA
gas
(ng)
Wall
electrons
ne, Te
excited atoms
and molecules
ions
Wall
radicals,
n = ¼ n<v>
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
Electron and Ion Loss to the Substrate and Walls
- the plasma sheath -
-
-
-
chamber
neni
r0
-
-
-
-
-
-
electrons are much more mobile than ions
e = q<t>/me >> q<ti>/mi = i
Electron and Ion Loss to the Substrate and Walls
- the plasma sheath s
ne<<ni
n e = ni
(sheath)
-1kV
r(x) +
+
0v
V
x
x
V(x)
+
e
x
(after Mahan, 2000)
low energy electrons are trapped within the plasma, but ions are
accelerated by the sheath potential to the chamber walls and substrate
Ion Flux
The 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)
Boltzmann factor
f(E)
flux to surface
Te
qVs
Electron energy, E
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/2pme) ~ -5Te
This is often called the floating potential:
Isolated surfaces have a negative potential relative to the plasma.
Ion Energy
Ex: Assuming argon with Te = 3 eV,
s
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
-1kV
0v
Ei = 4.7 Te = 14 eV
V
Ion mean free path:
x
li = 1/ngassi ~ 3/p (cm) for Ar+
…where p is the pressure in mTorr
Here li = 3/100 cm or 0.3 mm @ 0.1 torr
NOTE: s>>li  Ei << 1014 eV!
(after Mahan, 2000)
Particle Conservation
and 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
ne=ni
Kiz/uB = Kizoe-E /kT /(kTe/mi)1/2 = Aeff/(V ngas)
=1/deffngas
iz
e
(V=plasma volume, Aeff = effective chamber area, deff = V/Aeff)
Single-step vs. Two-step Ionization
The electron temperature (Te) is a
unique function of
7
1. gas density, ngas (pressure)
2. chamber size, deff = V/Aeff
6
11
n0 = 1 x 10 cm
3. gas type: Kiz, Eiz
-3
5
Example:
Two large parallel plates separated by
2 cm are used to sustain an argon
plasma at 25 mTorr. Find Te.
Te (eV)
single-step
Ar + e  Ar+ + 2e
4
3
two-step
deff = V/Aeff ~ pR2d / (pR2 +pR2) = d/2
2
ngasdeff ~ (25*3.2x1019m-3)(0.01m)
=0.8e+19 m-2
1
Ar+eAr*+e
Ar* + e  Ar+ + 2e
0
Te = 3 eV
1e+18
1e+19
1e+20
ngdeff (m-2)
(Note: we have assume that the plasma density is uniform)
1e+21
1e+22
Power Conservation
and Electron Density, ne
Power Absorbed by the Plasma = Power Lost from the Plasma
Pion
Pelectron
Pabs = [qniuBEion+q(¼ne<ve>eV /kT )Eelec]Aeff
+(Pheat+Plight+Pdiss)
≡ qneuBAeff(Eion + Eelec + Ec)
s
qVs
e
2Te
where EC is the collisional energy lost in creating an
electron-ion pair due to ionization, light, dissociative
collisions, and heat:
EC = [nizEiz + nexEex + ndissEdiss + nm(3me/mi)Te]/niz
Collisional Energy Loss
EC
L (eV)
104
103
N2
102
Ar
101
1
2
3
4
Te (eV)
5 6 7 8 910
Electron Density Example
Continuing 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)(2px202 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)(2px202 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)(px202 cm2) x
{(5Te + 2Te + 35 eV)+[(1000 eV+5Te) + 2Te + 35 eV]}
anode
cathode
 ne = 1.7x109 cm-3
Secondary Electrons
e = gsec i , where gsec~0.1-10 and Ee ~ qVs
Power
light
Gas flow
PLASMA
gas
(ng)
Wall
excited atoms
and molecules
secondary
electrons
electrons
ne, Te
ions
Wall
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
Summary
Power
light
Gas flow
PLASMA
gas
(ng)
Wall
electrons
ne, Te
excited atoms
and molecules
ions
Wall
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate
pumping
pumping
Conclusion
• Basics of Vacuum
– ng, <v>, n,, l
• 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