1. 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

2. Part 1: Basic Plasma Technology

3. Plasma: an ionized gas consisting of atoms, electrons, ions, molecules, molecular fragments, and electronically excited species (informal definition)

4. Plasma: the “fourth state of matter”
energy
plasma
(electrons+ions)
gas
(steam)
energy
solid
(ice)
liquid
(water)
energy

5. DC Plasma (AC Fluorescent Lamp…why AC?)
”sputtering”
Argon + ~0.01 atm. - + - + + - - + - - + - - + + + - +
Argon
Electron
Argon ion
lamp endcap
Also, this is the heart of high powered gas lasers.

6. Fluorescent Lamp Spectrum The strong peaks of light emission are due to excited Hg: Hg + e- (hot)  Hg* + e- (cold)  Hg + light + e-
photon

7. Integrated Circuit Fabrication and Plasma Technology

8. Microfabrication deposit-pattern-etch-repeat
(g)
Copper metallization
on the PowerPC chip
(d)
(h)

9. Basic Plasma Technology Sputtering MagnetronDC
Pulsed RF S N S
Target N S N
Substrate
to pump

11. Basic Plasma Technology Capacitively Coupled Plasma
0.4 – 60 MHz
Hopwood and Mantei, JVST A21, S139 (2003)

12. Plasma Etching Cl2 Cl+ SiCl2 Cl S Simplified anisotropic etching
Cl2 + e-  Cl + Cl+ + 2e-
Si(s) + 2Cl(g)+ ion energy  SiCl2(g)

13. Anisotropy is 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)
wafer
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.

14. Trenches: etched and filled with copper
Jason M. Blackburn, David P. Long, Albertina Cabañas, James J. Watkins
Science 5 October 2001: Vol no. 5540, pp

15. Plasma Deposition SiH4 SiHX+H2 SiH H2 SiH2 S
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)

16. Hopwood and Mantei, JVST A21, S139 (2003)
Basic Plasma Technology Electron Cyclotron Resonance Plasma: Etch and Deposition
Hopwood and Mantei, JVST A21, S139 (2003)

17. Hopwood and Mantei, JVST A21, S139 (2003)
Basic Plasma Technology Inductively Coupled Plasma: Etch and Deposition
0.4 – MHz
Hopwood and Mantei, JVST A21, S139 (2003)

18. Other applications: Xenon Ion Propulsion
Deep Space 1 encounter with Comet Borrelly

19. Plasma Display Panels (PDPs)
Other Applications :
Plasma Display Panels (PDPs)
Structure
red
green
blue
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).

20. Plasma Display Panels (PDPs)
Basic Operation
sustain plasma
(~ 180 volts)
surface
initiate breakdown
(~ 300 volts)
Sustain Electrode
Bus Electrode
h ~ 200 m
l ~ 400 m
d ~ 60 m
From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).

21. Part 2: Basic Vacuum Concepts

22. 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

23. Vacuum (units) Typical High Pressure Plasma Ultrahigh Vacuum
Rough Vacuum
Typical Low Pressure
Plasma Processing
1 atm.
1.3x10-3
1.3x10-6
1.3x10-9
760 Torr
1 Torr
1 mTorr
1x10-6 Torr
1 Torr =
1 mm-Hg
101,333 Pa
133 Pa
0.133 Pa
0.133x10-3 Pa
1 Pascal =
1 N/m2

24. Rough Vacuum
“Mechanical Pumps” typically create a base pressure of 1-10 mTorr or Pa
Warning:
Certain process gases are incompatible with pump fluids and pose severe safety risks!
Rotary Vane Pump
(Campbell)

25. High Vacuum Pumping
Cryopumps condense gases on cold surfaces to produce vacuum
Typically there are three cold surfaces:
Inlet array condenses water and hydrocarbons ( Kelvin)
Condensing array pumps argon, nitrogen and most other gases (10-20 K)
Adsorption is needed to trap helium, hydrogen and neon in activated carbon at 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

26. High Vacuum Pumping Process chamber Turbomolecular 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

27. High Vacuum Pumping Process chamber Diffusion Pump
The process gas is entrained by the
downward flow of vaporized pumping
fluid.
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.
Not recommended for “clean” processes.
Water-
cooled
walls
Foreline
-to mech pump
Heater/Pumping Fluid
adapted from Lesker.com

28. 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 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

29. 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 = 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)

30. 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)
Ion Gauge:
Sensitive to gas composition, but
a good choice for base pressures
Ionization of Gas
RGA:
A simple mass spectrometer
Vacuum Gauge Selection adapted from Lesker.com

31. 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

32. 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

33. Gas Kinetics Maxwellian Distribution Average speed of an atom:
Flux of atoms to the x-y plane surface:
Very important!
(Campbell)

34. 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 = cm/s
Gz = (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.

35. 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
 lAr(cm) ~ 8 / P (mTorr) Ar

36. Part 3: Plasma Basics

37. Electron energy<ionization energy
Paschen Curve
VDC d
F. Paschen, Ann. Phys. Chem., Ser. 3 37, 69 (1889).
Too many collisions
Electron energy<ionization energy
Too few ionizing
collisions: l>d

38. What do we need to know about plasma?
excited atoms
and molecules
light
electrons
ne, Te
Power
gas
(ng)
Gas flow
pumping
Wall
Wall
PLASMA
ions
radicals,
molecular fragments
secondary
electrons
reaction
products
substrate

39. Power Absorbed excited atoms and molecules light Power gas (ng)
Gas flow
pumping
Wall
Wall
PLASMA
electrons
ne, Te
ions
radicals,
molecular fragments
secondary
electrons
reaction
products
substrate

40. Power Absorbed: DC DC power
General electrical mobility and conductivity
Mobility: me = 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 = qneme = q2ne/nmme
DC power absorbed:

41. Power Absorbed: RF RF/microwave power Ohmic Heating
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 = MHz * 2p = 85.2Mrad/s
ngas = 0.1*85.2x106/5x10-8(2)1/2 = x1014 cm-3 = 3.7 mTorr
VRF
f=13.56 MHz
An electron oscillates in a rf electric field without gaining energy
unless
electron collisions occur
Hopwood and Mantei, JVST A21, S139 (2003)

42. Reflecting Boundary (plasma sheath)
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

43. Wave/Resonant Heatingx
-Ex - t1 t2 t3 k
Electron cyclotron frequency:
wce = qB/me = 1.76x107 B(gauss)
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
ERF
W/cm3
BDC x y v
F = q(vxB)
E=0
Hopwood and Mantei, JVST A21, S139 (2003)

44. Electron Collisions excited atoms and molecules light Power gas (ng)
Gas flow
pumping
Wall
Wall
PLASMA
electrons
ne, Te
ions
radicals,
molecular fragments
secondary
electrons
reaction
products
substrate

45. Electron Collisions Elastic Collisions: Excitation 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)

46. 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.
becomes
(cm3s-1)

47. The RATE CONSTANT: Kiz(Te)  Kizoexp(-Eizo/Te)
Graphically
f(E)
f(E) or s(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

48. Graphically The RATE CONSTANT: Kiz(Te)  Kizoexp(-Eizo/Te)
Hot electrons – more ionization
f(E)
f(E) or s(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

49. Examples of Numerically Determined Rate Constants (Lieberman, 2005)

50. 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

51. 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

52. Transport to Surfaces excited atoms and molecules light Power gas (ng)
Gas flow
pumping
Wall
Wall
PLASMA
electrons
ne, Te
ions
radicals,
molecular fragments
Gn = ¼ n<v>
secondary
electrons
reaction
products
substrate

53. Electron and Ion Loss to the Substrate and Walls - the plasma sheath -
neni
r  0 -
neni
r  0
chamber
electrons are much more mobile than ions
me = q<t>/me >> q<ti>/mi = mi

54. Electron and Ion Loss to the Substrate and Walls - the plasma sheath -
r(x) x +
ne = ni
ne<<ni
(sheath)
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

55. (this is the ion speed at the edge of the sheath)
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 Gi = uBni (cm-2s-1)
(this is the ion speed at the edge of the sheath)

56. Electron Flux
Only the most energetic electrons can overcome the sheath potential, Vs.
Ge = ¼ ne<ve> exp (qVs/kTe)
flux to surface
Boltzmann factor
f(E) Te
qVs
Electron energy, E

57. 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
Ge = Gi
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.

58. 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
Ei = 4.7 Te = 14 eV
Ion mean free path:
li = 1/ngassi ~ 3/p (cm) for Ar+
…where p is the pressure in mTorr
Here li = 3/100 cm or torr
NOTE: s>>li  Ei << 1014 eV!
(after Mahan, 2000)
-1kV s x V
0 v

59. 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
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

60. The electron temperature (Te) is a unique function of
gas density, ngas (pressure)
chamber size, deff = V/Aeff
gas type: Kiz, Eiz
Ar+eAr*+e
Ar* + e  Ar+ + 2e
Ar + e  Ar+ + 2e
Example:
Two large parallel plates separated by 2 cm are used to sustain an argon plasma at 25 mTorr. Find Te.
deff = V/Aeff ~ pR2d / (pR2 +pR2) = 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)

61. 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 = [nizEiz + nexEex + ndissEdiss + nm(3me/mi)Te]/niz
Pion
Pelectron
qVs
2Te

62. Collisional Energy Loss

63. 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 eV)
 ne = 2.3 x 109 cm-3

64. Example (cont’d)  ne = 1.7x109 cm-3
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]}
 ne = 1.7x109 cm-3
anode
cathode

65. Secondary Electrons Ge = gsec Gi , where gsec~0.1-10 and Ee ~ qVs
excited atoms
and molecules
light
Power
gas
(ng)
Gas flow
pumping
Wall
Wall
PLASMA
electrons
ne, Te
secondary
electrons
ions
radicals,
molecular fragments
reaction
products
secondary
electrons
substrate

66. Summary excited atoms and molecules light electrons ne, Te Power gas
(ng)
Gas flow
pumping
Wall
Wall
PLASMA
ions
radicals,
molecular fragments
secondary
electrons
reaction
products
substrate

67. Conclusion Basics of Vacuum Plasma Generation and Simple Models
ng, <v>, Gn,, l
Plasma Generation and Simple Models
Te, ne, ni, Gi
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