chapter-2 Breakdown in Gases (part-1)

12/12/2017High Voltage Engineering 1
Chapter 1
Electrical Breakdown in Gases

Contents
1. Ionization Processes
2. Cathode Processes
3. Decay Processes
4. Townsend’s 1st and 2nd Coefficeints
5. Townsend’s Mechanism of Spark
6. Streamer Mechanism of Spark
7. Paschen’s Law
8. Penning Effect
9. Partial Breakdown-Corona Discharges
10. Applications of Corona

Cathode Processes
Electrodes, in particular the cathode, play a very
important role in gas discharges by supplying electrons
for the initiation, for sustaining and for the completion of a
discharge.
Under normal conditions electrons are prevented from
leaving the solid electrode by the electrostatic forces
between the electrons and the ions in the lattice.
The energy required to remove an electron from a Fermi
level is known as the work function (𝑊𝑎) and is a
characteristic of a given material.

There are several ways in which the required energy
may be supplied to release the electrons.
1. Photoelectric emission
2. Electron emission by positive ion and excited atom impact
3. Thermionic emission
4. Field emission
Cathode Processes

Photoelectric emission
Photons incident upon the cathode surface whose energy
exceeds the work function (ℎ𝑣 > 𝑊𝑎) may eject electrons
from the surface. For most metals the critical frequency 𝑣0
lies in the u.v. range.
When the photon energy exceeds ℎ𝑣 the work function 𝑊𝑎,
the excess energy may be transferred to electron kinetic
energy according to the Einstein relation:
where m is the electron mass, 𝑢 𝑒 its velocity and ℎ𝑣0 is the
critical energy required to remove the electron and ℎ𝑣0= 𝑊𝑎
the work function. 12/12/2017High Voltage Engineering 5

The following Table gives the work functions for several elements.
The work function is sensitive to contamination which is indicated
by the spread in the measured values.
The spread is particularly large in the case of aluminum and
metals which readily oxidize.
In the presence of a thin oxide film, the positive ions may gather
at the oxide layer without being neutralized, giving rise to a high
field strength leading to augmented secondary emission.
The effect is known as the Malter effect.
1. Photoelectric emission

2. Electron emission by positive ion
and excited atom impact
Electrons may be emitted from metal surfaces by bombardment
of positive ions or metastable atoms.
In order to cause a secondary emission of an electron, the
impinging ion must release two electrons, one of which is utilized
to neutralize the ion charge.
The minimum energy required for a positive ion electron
emission is twice the work function 𝑊𝐾 + 𝑊𝑝 ≥ 2𝑊𝑎, since the
ion is neutralized by one electron and the other electron is
ejected.
 𝑊𝐾 and 𝑊𝑝 are the respective kinetic and potential energies of
the incident ion.

 The electron emission by positive ions is the principal secondary
process in the Townsend spark discharge mechanism.
 Neutral excited (metastable) atoms or molecules incident upon the
electrode surface are also capable of ejecting electrons from the
surface.
2. Electron emission by positive ion
and excited atom impact

In metals at room temperature, the conduction electrons
will not have sufficient thermal energy to leave the surface.
If we consider the electrons as a gas at room temperature,
then their average thermal energy is
which is much lower than the work function (Table 5.8).

 If, however, the metal temperature is increased to some
1500– 2500 𝐾, the electrons will receive energy from the violent
thermal lattice vibrations sufficient to cross the surface barrier and
leave the metal. The emission current is related to the temperature of
the emitter by the Richardson relation for thermionically emitted
saturation current density:
 where e and m are the electronic charge and mass respectively, ℎ is
Planck’s constant, 𝑘 Boltzmann’s constant, 𝑇 the absolute
temperature and 𝑊𝑎 the surface work function.

Putting
---------------- (1)
which shows that the saturation current density increases with
decreasing work function and increasing temperature.

On substitution of the constants 𝑚, 𝑒, 𝑘 and ℎ ,
𝐴 = 120 × 104 𝐴/𝑚2 𝐾2.
The experimentally obtained values are lower than
predicted by eqn (1).
This discrepancy is attributed to the wave nature of the
electrons.
Although electrons may possess the required escape
energy, some of them may be reflected back into the solid
from the surface atoms or surface contaminants such as
adsorbed gases.

The effect may be taken into account by inserting the effective
value 𝐴 𝑒𝑓𝑓 = 𝐴(1 − 𝑅) in the current density expression
(1), where 𝑅 is the reflection coefficient.
In the presence of a strong electric field there will be a
reduction in the work function as the Schottky effect and the
thermionic emission will be enhanced.

4. Field Emission
 Electrons may be drawn out of a metal surface by very high
electrostatic fields.
 It will be shown that a strong electric field at the surface of a metal may
modify the potential barrier at the metal surface to such an extent that
electrons in the upper level close to the Fermi level will have a definite
probability of passing through the barrier.
 The effect is known as ‘tunnel effect’. The fields required to produce
emission currents of a few microamperes are of the order of 107 –108
V/cm.
 Such fields are observed at fine wires, sharp points and
submicroscopic irregularities with an average applied voltage quite low
(2–5 kV). These fields are much higher than the breakdown stress
even in compressed gases.

 To derive an expression for the emission current let us consider an
electron as it leaves the surface in the direction 𝑥 as shown in Fig.
5.13.
 Its electric field can be approximated as that between a point charge
and the equipotential planar surface.
 The field lines here are identical to those existing when an image
charge of +𝑒 is thought to exist at a normal distance of 𝑥 on the
other side of the equipotential metal surface.
 Applying Coulomb’s law, the force on the electron in the x-direction is
given by
4. Field Emission

4. Field Emission

The potential energy at any distance 𝑥 is obtained by integrating the
above equation from∞ to 𝑥.
𝑊𝑒1 =
−𝑒2
16𝜋𝜀0 𝑥
which gives a parabola shown by curve 1 of Fig. 5.13. The effect of the
accelerating external field when applied at right angles to the cathode
surface gives the electron a potential energy
𝑊𝐸 = −𝑒𝐸𝑥
which is a straight line shown by Fig. 5.13 (curve 2). The total energy is
then
𝑊 = 𝑊𝑎 + 𝑊𝐸 = −
−𝑒2
16𝜋𝜀0 𝑥
− 𝑒𝐸𝑥 ------ (2)
which is shown by the resultant curve 3 (Fig. 5.13).
4. Field Emission

Thus a marked reduction ∆𝑊 in the potential barrier is obtained. The
maximum reduction at 𝑥 𝑚 is obtained by differentiating eqn (2) or
𝑑𝑊
𝑑𝑥
=
𝑒2
16𝜋𝜀0 𝑥 𝑚
2 − 𝑒𝐸 = 0
𝑥 𝑚 =
𝑒
16𝜋𝜀0 𝐸
Inserting this value into eqn (2) the lowering in the work function
becomes
∆𝑊 = −𝑒
𝑒𝐸
4𝜋𝜀0
4. Field Emission

Hence, the effective value of the work function is
𝑊𝑒𝑓𝑓 = 𝑊𝑎 −
𝑒𝐸
4𝜋𝜀0
and the saturation current due to electron emission using Eq (1) in the
presence of field 𝐸 becomes
𝐽𝑠 = 𝐴𝑇2 𝑒𝑥𝑝 −
𝑒
𝐾𝑇
𝑊𝑎 −
𝑒𝐸
4𝜋𝜀0
4. Field Emission

Decay or De-ionization Processes
1. Deionization by recombination
2. Deionization by attachment – negative ion formation
3. deionization by diffusion

1. Deionization by recombination
Whenever there are positively and negatively charged particles present,
recombination takes place.
The potential energy and the relative kinetic energy of the recombining
electron–ion is released as quantum of radiation. Symbolically the
reaction may be represented as
𝐴+ + 𝑒 → 𝐴 + ℎ𝑣
𝐴+ + 𝑒 → 𝐴 𝑚 + ℎ𝑣
𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
𝑟𝑒𝑐𝑜𝑚𝑏𝑖𝑛𝑎𝑡𝑖𝑜𝑛
Alternatively a third body C may be involved and may absorb the excess
energy released in the recombination.
The third body 𝐶 may be another heavy particle or electron.
Symbolically
𝐴+ + 𝐶 + 𝑒 → 𝐴∗ + 𝐶 → 𝐴 + 𝐶 + ℎ𝑣
Or
𝐴+ + 𝑒 + 𝑒 → 𝐴∗ + 𝑒 → 𝐴 + 𝑒 + ℎ𝑣

1. Deionization by recombination (cont..)
At high pressures, ion–ion recombination takes place. The rate of
recombination in either case is directly proportional to the concentration
of both positive ions and negative ions. For equal concentrations of
positive ions 𝑛+ and negative ions 𝑛− the rate of recombination
𝑑𝑛+
𝑑𝑡
=
𝑑𝑛−
𝑑𝑡
= −𝛽𝑛+ 𝑛− (1)
where 𝛽 is a constant known as the recombination rate coefficient.
Since 𝑛+ ≈ 𝑛− = 𝑛𝑖 and if we assume at time 𝑡 = 0: 𝑛𝑖 = 𝑛𝑖0 and
at time t: 𝑛𝑖 = 𝑛𝑖(𝑡)then eqn (1) becomes
𝑑𝑛𝑖
𝑑𝑡
= −𝛽𝑖
2

The variation of the recombination rate coefficient 𝛽 with pressure in air
is shown in Fig. 2. The recombination process is particularly important at
high pressures for which diffusion is relatively unimportant.
1. Deionization by recombination (cont..)
Figure 2 Recombination coefficient (ion-ion) in air at 𝟐𝟎° 𝑪

2. Deionization by attachment-Negative ion formation
Electronegative Gases
Certain atoms or molecules in their gaseous state can readily acquire a
free electron to form a stable negative ion.
Gases, whether atomic or molecular, that have this tendency are those
that are lacking one or two electrons in their outer shell and are known
as electronegative gases.
Examples:
halogens (𝐹, 𝐶𝑙, 𝐵𝑟, 𝐼 𝑎𝑛𝑑 𝐴𝑡) with one electron missing in their outer
shell, and 𝑂, 𝑆, 𝑆𝑒 with two electrons deficient in the outer shell.

Electron Affinity
For a negative ion to remain stable for
some time, the total energy must
be lower than that of an atom in the ground
state.
The change in energy that occurs when an
electron is added to a gaseous atom or
molecule is called the electron affinity of
the atom and is designated by 𝑊𝑎.
This energy is released as a quantum or
kinetic energy upon attachment.
Table 5.4 shows electron affinities of some
elements.

There are several processes of negative ion formation:
1. The simplest mechanism is one in which the excess
energy upon attachment is released as quantum known as
radiative attachment.
This process is reversible, that is the captured electron can
be released by absorption of a photon known as photo
detachment. Symbolically the process is represented as:
𝐴 + 𝑒 ↔ 𝐴−
+ ℎ𝑣 (𝑊𝑎 = ℎ𝑣)

2. The excess energy upon attachment can be acquired as kinetic
energy of a third body upon collision and is known as a third body
collision attachment, represented symbolically as:
𝑒 + 𝐴 + 𝐵 → 𝐴−
+ 𝐵 + 𝑊𝑘 (𝑊𝑎 = 𝑊𝑘)
3. A third process is known as dissociative attachment which is
predominant in molecular gases. Here the excess energy is used to
separate the molecule into a neutral particle and an atomic negative
ion, symbolically expressed as:
𝑒 + 𝐴𝐵 ↔ 𝐴𝐵−
∗↔ 𝐴−
+ 𝐵

4. In process (3) in the intermediate stage the molecular ion is at a
higher potential level and upon collision with a different particle this
excitation energy may be lost to the colliding particle as potential
and/or kinetic energy. The two stages of the process here are:
𝑒 + 𝐴𝐵 ↔ 𝐴𝐵− ∗
𝐴𝐵− ∗ +𝐴 ↔ 𝐴𝐵 − + A + 𝑊𝑘 + 𝑊𝑝
Other processes of negative ion formation include splitting of a
molecule into positive and negative ions upon impact of an electron
without attaching the electron:
𝑒 + 𝐴𝐵 ↔ 𝐴+ + 𝐵− + 𝑒
and a charge transfer following heavy particle collision, yielding an
ion pair according to:
𝐴 + 𝐵 → 𝐴+ + 𝐵−

All the above electron attachment processes are reversible, leading to
electron detachment. The process of electron attachment may be
expressed by cross-section for negative ion formation & 𝜎𝐴 in an
analogous way to ionization by electron impact.
Typical examples of the variation of attachment cross-section with
electron energy for processes (2) and (3) measured in 𝑆𝐹6 and 𝐶𝑂2 are
shown in Figs 3 and 4 respectively.

Figure 3 Variation of attachment cross-section with electron energy in SF6 .
1. Radiative attachment 2. Dissociative attachment
Figure 4 Variation of electron attachment cross-section with electron energy in CO2
(both peaks O-)

3. Deionization by Diffusion
In electrical discharges whenever there is a non-uniform concentration
of ions there will be movement of ions from regions of higher
concentration to regions of lower concentration.
The process by which equilibrium is achieved is called diffusion. This
process will cause a deionizing effect in the regions of higher
concentrations and an ionizing effect in regions of lower concentrations.
The presence of walls confining a given volume augments the
deionizing effect as the ions reaching the walls will lose their charge.
The flow of particles along the ion concentration gradient constitutes a
drift velocity similar to that of charged particles in an electric field.

Space Charge
Accumulation of charged particles in a specific space within gap
(insulation) is called space charge.
Space charge is a concept in which excess electric charge is treated as a sequence of charge
distributed over a region of space rather than distinct point-like charges.
Space charge usually only occurs in dielectric media (including vacuum) because in a
conductive medium the charge tends to be rapidly neutralized or screened.
The sign of the space charge can be either negative or positive.
This effect was first observed by Thomas Edison in light bulb filaments, where it is sometimes
called the Edison effect, but space charge is a significant phenomenon in many vacuum
and solid-state electronic devices.

Streamer or ‘𝐾𝑎𝑛𝑎𝑙’ mechanism of spark
The growth of charge carriers in an avalanche in a uniform field
𝐸0 = 𝑉0/𝑑 is described by the exponent 𝑒 𝛼𝑑
.
This is valid only as long as the electrical field of the space charges of
electrons and ions can be neglected compared to the external field 𝐸0.
Raether observed in his studies of the effect of space charge of an
avalanche on its own growth, 𝑑 in such as way that when the charge
concentration was 106 − 108 the growth of an avalanche was weakened.
When the ion concentration exceeded 108, the avalanche current was
followed by a steep rise in current and breakdown of the gap followed.
Both the under-exponential growth at the lower concentration and rapid
growth in the presence of the high concentration have been attributed to
the modification of the originally uniform field 𝐸0 by the space charge field.

Figure 6 shows diagrammatically the
electric field around an avalanche as it
progresses along the gap and the
resulting modification to the original field
𝐸0.
For simplicity the space charge at the
head of the avalanche is assumed
concentrated within a spherical volume,
with the negative charge ahead because
of the higher electron mobility.
The field is enhanced in front of the
head of the avalanche with field lines
from the anode terminating at the head.
Streamer or ‘Kanal’ mechanism of spark
Figure 6 Diagrammatic representation
of field distortion in a gap caused by
space charge of an electron avalanche.

Further back in the avalanche, the field between the electrons and the ions
left behind reduced the applied field (𝐸0).
Still further back the field between the cathode and the positive ions is
enhanced again. The field distortion becomes noticeable with a carrier
number 𝑛 > 106.
For instance, in nitrogen with 𝑑 = 2 𝑐𝑚, 𝑝 = 760 𝑡𝑜𝑟𝑟, 𝛼 ≈ 7 and
𝐸0 𝑝0
≈ 40𝑉 𝑡𝑜𝑟𝑟 𝑐𝑚, the field distortion is about 1%, leading to 5%
change in 𝛼.
If the distortion of ≅ 1% prevailed in the entire gap it would lead to a
doubling of the avalanche size, but as the distortion is only significant in the
immediate vicinity of the avalanche head it has still an insignificant effect.

However, if the carrier number in the avalanche reaches 𝑛 ≈ 108
the space
charge field becomes of the same magnitude as the applied field and may
lead to the initiation of a streamer.
The space charge fields play an important role in the mechanism of corona
and spark discharges in nonuniform field gaps.
In the Townsend spark mechanism, the gap current grows as a result of
ionization by electron impact in the gas and electron emission at the cathode
by positive ion impact. According to this theory, formative time lag of the
spark should be at best equal to the electron transit time 𝑡𝑖.
In air at pressures around atmospheric and above 𝑝𝑑 > 103 𝑡𝑜𝑟𝑟 − 𝑐𝑚
the experimentally determined time lags have been found to be much
shorter than 𝑡𝑖.

Furthermore, cloud chamber photographs of avalanche
development have shown that under certain conditions the space
charge developed in an avalanche is capable of transforming the
avalanche into channels of ionization known as streamers that
lead to rapid development of breakdown.
From measurements of the pre-breakdown current growth and the
minimum breakdown strength it has been found that the
transformation from avalanche to streamer generally occurs when
the charge within the avalanche head (Fig. 1) reaches a critical
value of 𝑛0 𝑒 𝛼𝑥 𝑐 ≈ 108
or 𝛼𝑥 𝑐 ≈ 18 − 20, where 𝑥 𝑐 is the
length of the avalanche path in field direction when it reaches the
critical size.

In the models developed by Raether and Meek it has been
proposed that when the avalanche in the gap reaches a certain
critical size the combined space charge field and externally
applied field lead to intense ionization and excitation of the gas
particles in front of the avalanche head.
Instantaneous recombination between positive ions and
electrons releases photons which in turn generate secondary
electrons by the photoionization process.

These electrons under the influence of the electric field in the gap
develop into secondary avalanches as shown in Figure 7. Since photons
travel with the velocity of light, the process leads to a rapid development
of conduction channel across the gap.
Figure 7 Secondary avalanche formation by photoelectron

On the basis of his experimental observations and some simple assumptions
Raether developed an empirical expression for the streamer spark criterion of the
form
𝛼𝑥 𝑐 = 17.7 + ln𝑥 𝑐 + ln
𝐸𝑟
𝐸
where 𝐸𝑟 is the space charge field strength directed radially at the head of
avalanche as shown in Fig. 8, 𝐸 is the externally applied field strength.
Fig. 8 Space charge field (𝐸𝑟) around avalanche head

The resultant field strength in front of the avalanche is thus (𝐸 + 𝐸𝑟)while in the
positive ion region just behind the head the field is reduced to a value (𝐸 − 𝐸𝑟).
It is also evident that the space charge increases with the avalanche length 𝑒 𝛼𝑥
.
The condition for the transition from avalanche to streamer assumes that space
charge field Er approaches the externally applied field 𝐸𝑟 ≈ 𝐸 hence the
breakdown criterion equation becomes
𝛼𝑥 𝑐 = 17.7 + ln 𝑥 𝑐
The minimum breakdown value for a uniform field gap by streamer mechanism is
obtained on the assumption that the transition from avalanche to streamer occurs
when the avalanche has just crossed the gap (𝑑). Then Raether’s empirical
expression for this condition takes the form
𝛼𝑑 = 17.7 + ln 𝑑
Therefore the breakdown by streamer mechanism is brought about only when the
critical length 𝑥 𝑐 ≥ 𝑑. The condition 𝑥 𝑐 = 𝑑 gives the smallest value of 𝛼 to
produce streamer breakdown.

Paschen’s Law
An analytical expression for breakdown voltage for uniform field gaps as
a function of gap length and gas pressure can be derived from the
threshold equation ( 𝛾𝑒(𝛼−𝜂)𝑑 = 𝛾𝑒 𝛼 𝑑 = 1 ) by expressing the
ionization coefficient 𝛼 𝑝 as a function of field strength and gas
pressure.
Substitute 𝛼 𝑝 = 𝑓 𝐸 𝑝 in the criterion equation we obtain
𝑒 𝑓 𝐸 𝑝 𝑝𝑑 =
1
𝛾
+ 1
Or
𝑓 𝐸 𝑝 𝑝𝑑 = ln
1
𝛾
+ 1 = 𝐾

For uniform field 𝑉𝑏 = Ed, where 𝑉𝑏 is the breakdown voltage,
𝑒 𝑓 𝑉 𝑏 𝑝𝑑 𝑝𝑑
= 𝐾 = 𝑒 𝐾
(1)
Or
𝑉𝑏 = 𝐹(𝑝𝑑)
which means that the breakdown voltage of a uniform field gap is a unique function
of the product of pressure (𝑝) and the electrode separation (𝑑) for a particular
gas and electrode material.
Eq(1) is known as Paschen’s law, and was established experimentally in 1889.
Eq(1) does not imply that the sparking voltage increases linearly with the product
𝑝𝑑, although it is found in practice to be nearly linear over certain regions.
The relation between the sparking voltage and the product 𝑝𝑑 takes the form
shown in Fig. 9 (solid curve).
The breakdown voltage goes through a minimum value 𝑉𝑏𝑚𝑖𝑛at a particular value
of the product 𝑝𝑑 𝑚𝑖𝑛.
Paschen’s Law

Paschen’s Law
Figure 9 Sparking Voltage-𝒑𝒅 relationship (Paschen’s curve)

Penning Effect
Paschen’s law is not applicable in many gaseous mixtures. The
outstanding example is the neon–argon (Ne-A) mixture.
A small admixture of argon in neon reduces the breakdown strength
below that of pure argon or neon as shown in Fig. 10.
The reason for this lowering in the breakdown voltage is that the lowest
excited state of neon is metastable and its excitation potential (16 eV) is
about 0.9 eV greater than the ionization potential of argon.
The metastable atoms have a long life in neon gas, and on hitting argon
atoms there is a very high probability of ionizing them.
The phenomenon is known as the Penning effect.

Figure 10 Breakdown voltage curves in neon-argon mixtures
between parallel plates at 2cm spacing at 0°
𝐶
Penning Effect

chapter-2 Breakdown in Gases (part-1)

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