Previous Lecture - - - - Next Lecture

## Plasma Physics

references:

- "Classical Electromagnetic Radiation" M. A. Heald and J. B. Marion
- "Foundations of Electromagnetic Theory" J. R. Reitz, F. J. Milford and R. W. Christy
- "Electromagnetic Fields and Waves" P. Lorrain, D. R. Corson, and R. Lorrain

Plasmas

Plasma:

- dilute ionized gas
- (often at high temperature)
- contains free electrons (light) and positive ions (heavy)
- excellent conductor with current mainly carried by electrons
Usually we concentrate on the behavior of the electrons because they are more mobile.

Creating a plasma:If we start with a gas of neutral atoms, we create a plasma by removing an electron from an atom, leaving a positive ion.Typical ionization energies are shown in the table:

ElementFirst Ionization PotentialSecond Ionization PotentialArgon

15.7 eV

27.76 eV

Mercury

10.3

.

Neon

21.4

.

Oxygen

13.6

34.93

Sodium

5.1

47.0

Chromium

6.7

16.6

Since 1 eV corresponds to about 11,600 K, it is typically not practical to achieve ionization by thermal processes. Instead we rely on electron collisions with atoms.

electrons ionize by collision most effectively for energies around 100 eV

elementnumber of ions formed per cm of travel in 10 mTorr gas for electrons with about 100 eV

He 0.015 Ne 0.025 H _{2}0.040 N _{2}0.100 Ar 0.110 Hg 0.210 electron collisions can also produce excited (but not ionized) atoms,

collisions between excited atoms and ground state atoms can lead to ionization of the ground state atom (Penning ionization)

characterizing a plasma:characterize by temperature (energy), electron density (N_{e}) and particle density or neutral atom density (N)

- cold plasma

- particle energy of a few eV
- typical of most thin film processes
- hot plasma

- particle energy of a few thousand eV
- typical of nuclear fusion and some astrophysics
- electron temperature often > ion temperature

- especially in dilute plasmas

- density

- at pressure of 5 mTorr: total particle density about 10
^{13}particles/cm^{3}- weakly ionized: ion density = electron density is about 10
^{8}ions/cm^{3}- strongly ionized: ion density = electron density is about 10
^{12}ions/cm^{3}These parameters are often grouped as follows:

- Debye length

- distance over which significant charge separation can occur
- l
_{D}(cm) = 743 (T_{e}/ N_{e})^{1/2}

- with density in electrons / cm
^{3}- plasma frequency

- to be derived shortly
- w
_{p}= 56,548.67 N_{e}^{1/2}

- with density in electrons / cm
^{3}- critical degree of ionization

- if N
_{e}/ N is much greater than this critical degree of ionization, the plasma behaves as though it is fully ionized- a
_{c}= 1.73 x 10^{12}s_{eA}T_{e}^{2}

- where s
_{eA}is the electron-atom collision cross section in cm^{2}(typically 10^{-16}- 10^{-15})

Electrostatics

- charged particles in a
**constant**Electric field (**E**) with no magnetic field (**B**= 0)When subjected to Electric field:

- charges redistribute themselves to shield the interior from the fields
- plasma region is field free and approximately neutral
- for T = 2000 K and N = 10
^{18}electrons/meter^{3}, sheath thickness is about 1 micrometer

- electrons in a
**constant**Magnetic Field (**B**) with no electric field (**E**=0)frequency of gyration = w

_{cyclotron}= qB / mnote: electrons have a longer actual path length before reaching one side of the system => more likely to ionize a neutral gas atom.

- electrons in a uniform, constant
**E**and**B**with**E**perpendicular to**B**- motion has three components
- constant velocity v
_{parallel}in direction of**B** - gyration about the
**B**field lines - constant drift velocity v
_{d}= E/B perpendicular to**E**and**B**

note v

_{d}does not depend on mass or charge - so all particles drift together - constant velocity v

- motion has three components

Electrodynamics

apply an oscillator model to electrons in the plasma

- at low frequencies (<50 kHz) ions and electrons both oscillate
- at high frequencies (>50 kHz) heavy ions can not follow switching fields => only electrons oscillate while ions are relatively stationary
Examine forces on electrons:

- driving force from varying
Efield- no restoring force since electrons are not bound (spring constant = 0)

- not true if charge separation in plasma leads to electrostatic restoring forces
- damping term, g, from collisions (this could be large)

- g = collision frequency
- consider effects of electromagnetic wave on plasma (with
nostatic fields)from F = ma we can write down an equation of motion:

Special case: Dilute Plasmas

dilute => few collisions so g is small (<< w)same approximations as before

for g < w < w

_{p}(evanescent domain)k is imaginary => waves are attenuated

When is a plasma dilute ?criteria: g << w ..... to put numbers in, let us say g = 0.01 westimate collision frequency from kinetic theory of gasses:

ąd

^{2}= s_{eA}= electron - atom collision cross sectionusing typical values

- d = 1 Å = 1 x 10
^{-10}m- m = 9.1 x 10
^{-31}kg- T = 10 eV = 116,000 K
then g = 6.65 x 10

^{-14 }N (where N is in particles/m^{3})if the incident frequency, w , is 1000 Hz

- then we want g < 10 Hz which means N < 1.5 x 10
^{14}atoms/m^{3}(or 1.5 x 10^{8}atoms/cm^{3}or 4 x 10^{-9}torr)if the incident frequency is 1,000,000 Hz

- then we want g < 10,000 Hz which means N < 1.5 x 10
^{17}atoms/m^{3 }(or 5 x 10^{11}atoms/cm^{3}or 4 x 10^{-6}torr)Reality check: 1 torr = 3.5 x 10

^{22}atoms/m^{3}. . . . so most plasmas in our processes areNOTdiluteAnother reality check: is the plasma frequency for these conditions greater than the incident frequency ?

Using N = 1.5 x 10

^{17}atoms/m^{3}(and assuming f = 0.1 and q = 1.6x 10^{-19}C), plasma frequency = 7 x 10^{9}Hz which is much greater than anything else.

Special Case: Dense Plasmas

collisions between charged particles are commonelectrons and ions are in thermal equilibriumelectrons and ions move together

equilibrium theory formulation of plasmas

particles maintain a Maxwell-Boltzmann velocity distribution

kinetic properties and transport properties of particles can be calculated from this.

Applications of plasmas

- cleaning / etching of surfaces
- sputter deposition source
- bombardment during deposition to modify film
- activation of reactive gasses

Plasma Sources

- plate electrodes
- low plasma densities (10
^{9}- 10^{10}charged particles per cm^{3}) - common in sputter deposition
- discuss further during sputter deposition

- low plasma densities (10
- Inductively coupled plasma (ICP)
- high plasma densities (10
^{11}- 10^{12}charged particles per cm^{3}) - operates well at lower gas densities (< 50 mTorr)
- can be used up to atmospheric pressures (and beyond)
- couple RF energy inductively into plasma (lossy electrical
conductor)
- produces more efficient ionization

- high plasma densities (10
- Helicon
- high plasma densities (10
^{11}- 10^{12}charged particles per cm^{3}) - operates well at lower gas densities (< 50 mTorr)
- radiates RF energy into plasma for resonant absorption
- produces more efficient ionization

- high plasma densities (10
- Electron cyclotron resonance (ECR)
- high plasma densities (10
^{12}- 10^{13}charged particles per cm^{3}) - operates well at lower gas densities (down to 0.1 mTorr)
- couples microwave energy to electrons by matching frequency
to electron gyration frequency
- w
_{c}= eB / m_{e} - produces more efficient ionization

- w
- control the plasma density with microwave power and gas pressure
- can also control ion species created
(O
_{2}^{+}, O^{+})

- high plasma densities (10