01/11/23

SIF2019
Gas Discharge Physics

General Properties of plasmas

(Ionised Gas)

1
 01/11/23

Plasma

Discharge of Gas, forming ionised gas

— Lets take a static example: a box of gas, upon ionisation

turns into a box of ionised gas or plasma.

2
 01/11/23

Questions on the existence and

continuation..
— How ?
— When ?
— What ?
— Why ?

— How to generate plasma

— Plasma dynamic
— Plasma diagnostics
— Plasma application

Definition of a plasma
— A wide variety of macroscopically neutral substances
containing many interacting free electrons and ionised
atoms or molecules, which exhibit collective behaviour
due to the long range coulomb forces.

— For the collection of interacting charged and neutral

particles to exhibit plasma behaviour it must satisfy
certain conditions or criteria, for plasma existence.

3
 01/11/23

• Sufficient energy provided to gaseous state:

molecular gas dissociate into atomic gas
(result of collision)

• Increasing fraction of the atoms posses

enough kinetic energy to overcome binding
energy of orbital electrons (result of
collision)

• ⇒ ionised gas or plasma

— Transition from gas to plasma occurs

gradually with increasing temperature ⇒ Not
phase transition in thermodynamic sense.

— Since thermal decomposition breaks inter

atomic bonds before ionizing, most
terrestrial plasmas begin as gases. In fact, a
plasma is sometimes defined as a gas that is
sufficiently ionized to exhibit plasma-like
behaviour.

— Gas particles are ionized, the composition

remain electrically neutral in macroscopic
scale.

4
 01/11/23

— There are many examples of plasma in the

nature.

— It is recognized that 90% of all observable/

visible matter in the universe is in the plasma
state

— The universe is made of up of space plasma

— There are a wide range of plasma on earth

— Laboratory plasma from micron to m length

— Potential application of plasma is unlimited

5
 01/11/23

— At extreme temperatures (exceeded atomic

ionization energies), atoms decompose into
negatively charged electrons and positively
charged ions.
— Nevertheless, because the charges are no
longer bound, their assemblage becomes
capable of collective motions of great
complexity.

— These charged particles are by no means

free: in fact, they are strongly affected by
each others’ electromagnetic fields.

Observations

6
 01/11/23

Related answers from these questions

— How does universe evolve ?
— How does milky way formed into a disk and
create planets?
— How does it disperse once the planet-
formation process has ended?
— By combining observations of the early
universe with those of the births of stars and
galaxies, space observation shall be the
premier tool in the quest to understand our
origins.

7
 01/11/23

Questions

— Charge distribution inside plasma ?

— Collective behavior, how to realized ?

— So what is the properties of plasma ?

8
 01/11/23

— Equilibrium
— Space Potential
— Debye Shielding
— Plasma Sheath
— Plasma Frequency

Space potential (or plasma potential)

— Charge distribution inside plasma – expected
to be at equilibrium
ρ = 0 (no net charge everywhere)
E = 0 (no electric field)
— The potential as it exists within a plasma (in
the space between charged particles), in the
absence of any probes, is called the "plasma
potential", or the "space potential".

9
 01/11/23

— The good electrical conductivity of plasmas

causes their electric fields to be very small.
(quisineutrality)

— the length-scale associated with such

shielding is the Debye length. Within the
Debye length there can be charge imbalance.

— Outside φ = 0 or constant
— Inside the plasma, φ = φs (constant)

Debye Shielding
— The most important static property of plasmas is that
they shield out electric fields.

— The shielding of an external electric field can be viewed

as a result of high plasma conductivity, or shielding as a
dielectric phenomena (polarization of the plasma
medium, and the associated redistribution of space
charge, which prevents penetration by an external
electric field.)

10
 01/11/23

Stray Charge in plasma

— Consider a positive point charge Q at the origin
of coordinates and let it be immersed in a plasma
in which the ions and electrons have the same
temperature T and the same number density n
(particles per unit volume) before the point
charge showed up.
— Also suppose that the ions have only lost one
electron so that the electrons have charge −e and
the ions have charge e.

— Now think about what the stray charge + does. It

will attract the electrons and repel the ions,
making a cloud of net negative charge around
itself, reducing (shielding) the electric field the it
makes.

— But the electrons can’t just collapse onto the

point charge to completely neutralize it because
they have too much thermal energy.

11
 01/11/23

— If we wait for interparticle collisions to allow this competition

between Coulomb attraction and thermal motion to come to
equilibrium we have the situation first studied by Peter Debye
and called Debye shielding.

Debye Length
— The Debye Length is a parameter having units of
length that characterizes the thickness of the
diffuse layer.

12
 01/11/23

— Consider in a 1-D case, plasma with number density n0 = ni = ne.

— At the vicinity of a stray charge, the potential is φ(x) = φ0

— A plasma in which the particles are, to a first approximation, stationary

(very small thermal motion) and suppose that the ions and electrons do
not recombine to form neutral atoms: the result is a equilibrium
(stationary) state: the positive and negative charges are distributed
alternately and almost uniformly
Idealized distribution of
particles in plasma (almost)
at rest.

— if a hypothetical perturbation occurs, displaces one charge, all the

neighboring charges will react to the local deviation from equilibrium
thus created. This demonstrates that a plasma consists of particles which
may behave collectively.

Thermal equilibrium
— The first key idea is that in thermal equilibrium
the probability of a particle being in a state with
energy E is proportional to the Boltzmann factor

where k is Boltzmann’s constant,

k = 1.38 °x10−38J/K and where T is the
temperature in kelvins.

13
 01/11/23

— Since probability and number density are

proportional to each other in a gas (if there is a high
probability of a particle being at a certain point in
space then the particle density will be high there)

— and since the energy of a particle is simply

E = qV
we may immediately write for the electron and ion
densities

— At infinity V = 0 and there is no applied field to

disturb the equilibrium between ions and
electrons, so we have A = B = n0, where n0 is the
density of both ions and electrons before the
point charge arrived.
— To determine the potential V (r) we just use
Poisson’s equation:

14
 01/11/23

— Potential V appears on both sides of the equation,

giving us a second-order non-linear differential
equation to solve.

— We will follow Sir Peter Debye and consider only

the case in which the potential energy of the
particles in the applied field ±eV is much smaller
in magnitude than the kinetic energy of the
particles 3/2kT.

— This simply requires that the plasma be really hot,

which is usually the case, so it’s a pretty good
approximation.

— We exploit this approximation by using the Taylor

series for the exponential function ex = 1 + x +
x2/2 + ..., keeping only the first two terms to
obtain a new approximate version of Poisson’s
equation.

15
 01/11/23

— Poisson’s equation

— Where

Debye Length
— So now we can see the physical meaning of the Debye
length is the “screening” distance.

— or the distance over which the usual Coulomb field is

killed off exponentially by the polarization/
redistribution of charge carriers in the plasma.

— This is the most important length in plasma physics.

16
 01/11/23

Applying
— particles in which this length is larger than the size of the
gas (a low density particle beam in an accelerator, for
instance) you don’t have to do plasma physics.

— But if the Debye length is smaller than the size of the gas,
as occurs in flames, the solar wind, fusion experiments,
the sun, the accretion disk around a black hole, etc., then
you have to worry about the fact that electric fields,
applied to such plasmas don’t penetrate into them any
deeper than a few Debye lengths.

Plasma Properties
— Neglecting boundary effects, equilibrium is
represented by the Maxwell—Boltzmann distribution
of particles in energy.

— The Debye length, or Debye screening distance,

gives an estimate of the extent of the influence of a
charge fluctuation.

17
 01/11/23

Example
— In Fusion plasmas
— ne = 1020 m−3 Te = 1keV
— λD = 2 ×10−5m = 20 μm
— λD is typically small.

— plasma at 1 eV and 1 cm−3 (say the solar wind)

has a Debye length of 740 cm.

plasma sheath
— The boundary layer of charged particles between a
plasma and its surrounding walls, electrodes, or other
plasmas.

— The sheath is generated by the interaction of the plasma

with the boundary material.

— Current flow may be in only one direction across the

sheath (single sheath)

18
 01/11/23

— When a plasma is in contact with a solid, the solid acts as

a "sink" draining away the plasma. Recombination of
electrons and ions occur at surface.

— Plasma is normally charged positively with respect to the

solid.

— There is a relatively thin region

called the "sheath", at the
boundary of the plasma, where
the main potential variation
occurs.

— Reason for potential drop:

Different velocities of electron
and ions.

19
 01/11/23

— Because of mass difference electrons move faster

and hence would drain out of plasma faster.

— Hence, plasma charges up enough that an electric

field opposes electron escape and reduces total
electric current to zero.

The Plasma sheath

— The layer in a plasma with charge imbalance.
— It has a greater density of positive ions, that balances an opposite negative
charge on the surface of a material with which it is in contact.
— The thickness of such a layer is several Debye lengths thick, depends on the
characteristics of plasma (eg. temperature, density, etc).

20
 01/11/23

In the plasma, electrons are smaller than the ions, they move quickly
relative to the ions. At a sample surface (wafer), the electrons quickly
strike the wafer and are depleted. A steady-state electric field known
as the sheath is formed to balance the current losses.

This boundary layer plays important roles for in surface processing,

such as deposition, plasma ashing (to remove the photoresist), and
plasma etching.

Plasma etching - dry etching, made good a breakthrough for

anisotropic etches alowing deep features. In operation, the input gas
type and volume, the applied voltage amplitude and waveforms, and
the reactor geometry can all be varied to give considerable flexibility in
plasma etching reactors.

Common reactor types are capacitive coupled, more variation like

multiple electrodes can be for selective etching, or an inductively
coupled uses higher frequencies to enable higher densities and a faster
etch rate.

21
 01/11/23

— The sheath is the usually due to the

transition from a plasma to a solid surface.

— Similar physics is involved with two

plasma, both regions that have different
characteristics.
— The transition between these regions is
known as a double layer, and features one
positive, and one negative layer.

Double sheath
— Current flow in both directions across the sheath (double
sheath), or when the plasma is immersed in a magnetic field,
it may flow along the sheath surface at right angles to the
magnetic field (magnetic current sheath).

— The dynamics of plasmas interacting with external and self-

generated magnetic fields are studied in the
magnetohydrodynamics.

22
 01/11/23

— In spaceflight, an envelope of ionized gas, or plasma,

that surrounds a body moving through an atmosphere
at hypersonic velocity.
— When entering the atmosphere, the plasma sheath
forms around the spacecraft may interrupts or
interferes with communication with the ground.

A plasma behaves as a collective medium

— Consider, as an example, a plasma in which the particles are, to a first
approximation, stationary (very small thermal motion) and suppose that
the ions and electrons do not recombine to form neutral atoms: the
result is a equilibrium (stationary) state: the positive and negative
charges are distributed alternately and almost uniformly

Idealized distribution of
particles in plasma (almost)
at rest.

— if a hypothetical perturbation occurs, displaces one charge, all the

neighboring charges will react to the local deviation from equilibrium
thus created. This demonstrates that a plasma consists of particles which
may behave collectively.

23
 01/11/23

A plasma behaves as a collective medium

— If a plasma, with dimensions much greater than the Debye length λD,
experiences a local perturbation from neutrality (resulting, for example,
from the random movement of particles), this equilibrium will be re-
established by a collective movement of charges. If there are few or no
collisions, this return to equilibrium will take the form of a oscillation
about the point where the initial disturbance occurred.

Idealized distribution of
particles in plasma, heavy
particle (ion) at rest.

A plasma behaves as a collective medium

— During these oscillations, the ions, which are

much heavier than the electrons, remain
practically immobile: they barely start to move
in one direction, under the influence of the
space charge field, when they are forced to
move in the opposite direction.
— a slight non-uniformity in the distribution,
resulting from a displacement of electrons by a
distance x, creates an electric field in this
region (referred to as the space charge field).
The return of the displaced electrons to their
initial positions, due to the electric field, leads
to an oscillatory motion about their
equilibrium position.

24
 01/11/23

Plasma Frequency

— This is a simple harmonic motion, with the angular frequency :

25
 01/11/23

Physical meaning of plasma frequency

— Plasma respond to em wave

26
01/11/23

27