dielectrics in electric fields (9)

8.1 COLLISION PHENOMENA 8.1.1 ELASTIC COLLISION An electron acquires energy in an electric field and during its acceleration elasticcollision occurs between an electron and a molecule..

FUNDAMENTAL ASPECTS OF GASEOUS BREAKDOWN-I

years and the delineation of the various manifestations of discharges hasadvanced in parallel with a better understanding of the fundamental processes

types of discharge one encounters in practice depending upon the combinations ofparameters

The type of discharge is determined by primary factors such as gas pressure, gas density,electrode shape and distance, polarity of the voltage, type of voltage meaning dc, normalfrequency ac, high frequency ac, impulse voltage, etc Secondary factors are theelectrode materials, type and distance to the enclosure, duration of the application ofvoltage, previous history of the electrodes, etc Obviously it is not intended to explainall of these phenomena even in a condensed fashion but the fundamental processes thatoccur are similar, though the intensity of each process and its contribution to the overalldischarge process varies over a wide range In the interest of clarity we limit ourselves tofundamental processes concentrating on the progress that has been achieved during thepast twenty five years However, to provide continuity we recapitulate somefundamental definitions and equations that are relevant to all discharge processes

8.1 COLLISION PHENOMENA 8.1.1 ELASTIC COLLISION

An electron acquires energy in an electric field and during its acceleration elasticcollision occurs between an electron and a molecule During an elastic collision there isvery little exchange of energy with the electron, losing an energy that is proportional to

m/M where m and M are masses of the electron and molecule, respectively The internal

energy levels of the molecule do not change during an elastic collision The mainconsequence of an elastic collision is that the direction of travel of an electron changesdepending upon the angle at which the electron strikes the molecule A more accurate

term for elastic collisions is the momentum transfer collision which is an average

value that takes into account the angle of approach of the electron

DISCHARGES

50 or 60 HZ Impulse High frequency superposed

Fig 8.1 Various manifestations of electrical discharges.

The range of electron energy and the electron density encountered in a wide range of

the electron temperature expressed in units of electronvolts and the electron density Oneelectronvolt (eV) is equal to 11600 degree Kelvin in accordance with T = (e/k) s where

density whereas the fusion plasma has the highest Ionosphere plasma has the lowesttemperature with fraction of an electronvolt energy Fusion reactors, on the other hand,have an energy -100,000 eV Such a wide range of parameters makes the study ofplasmas one of the most interesting.

8.1.2 COLLISION CROSS SECTION

The collision between two particles is described by using a fundamental property calledthe collision cross section, which is defined as the area involved between the colliding

particle and a charged particle, may be considered to a first approximation as if theparticles were hard spheres The effective target area for such collisions is the collision

1Q O

cross section, Q, which has a value of 10" m in air for gas molecules If each particle

has a radius a then the collision cross section is given by 4n a Each inelastic process is

characterized by a corresponding cross section and the total cross section is the sum ofthe momentum transfer and inelastic collision cross sections

8.1.3 PROBABILITY OF COLLISION

The probability of collision is defined as the average number of collisions that an

electron makes with a neutral molecule per meter length of drift The probability is

related to the collision cross section according to

.Interplanetary Space

Magnetic Fusion Experiments

Glow Discharges Plasma Reactors Room

I0 7 I0 8 I0 9 io' 2 io' 3 io' 4 10',16 IO 17 IO 18 I0 lij 10 20 I0 21 IO 22 IO 23 I0 2 4 IO 25 I0 26 I0 27

ELECTRON NUMBER DENSITY n./m 3

Fig 8.2 Electron number density and electron energy in various plasmas (Roth, 1995, with

permission of Institute of Physics.)

P = N Qm where

pressure at 300 K according to the following relationships

1 atmosphere = 760 Torr = 101.33 kPa

v = velocity (m /s)

The probability of collision for electrons in gases is a function of electron energy and isusually plotted against Vs where s is the electron energy

maximum in the range of 10-15 eV For a further increase in energy the probability

the probability of collision is a complicated function due to quantum mechanical effects

In many gases the quantum mechanical wave diffraction of the electron around the atomresults in an increased probability with decreasing energy, as found experimentally byRamsauer during early thirties

Compilation of cross sections for elastic scattering and momentum transfer for common

8.1.4 INELASTIC COLLISIONS

Electrons gain energy from the applied electric field and at sufficiently high energy acollision will result in a change of the internal energy level of the molecule Such acollision is called an inelastic collision Inelastic collisions with atoms or moleculesmainly result in creation of excited species, ionization and metastables (excited

molecules with a long life time) Some common inelastic collisions are given in Table

8.1

8.1 5 MEAN FREE PATH

The mean free path of an electron, A,, is the average distance traveled by an electron

between collisions with gas molecules The concept of the mean free path is general andnot limited to elastic collisions We can refer to a mean free path for elastic collisions asdistinct from mean free path for ionizing collisions, A,j We can also refer to a mean freepath for collisions between gas atoms or molecules even in the absence of an electricfield The mean free path for molecules at atmospheric pressure of 101 kPa isapproximately 60 nm, a very small distance As the pressure decreases the mean freepath increases and the relationship is

attachment e + x y - » x ~ + y + eDissociation e + x y — » x + y + e

Three body

The distance traveled between collisions is a varying quantity due to the random nature

of collisions The probability of having a free path greater than x is an exponentially decaying function according to exp(-x/A) where /I is the mean free path.

8.1.6 IQNIZATION BY COLLISION

When the energy of the electron exceeds the ionization potential of a gas molecule asecondary electron and a positive ion are formed following a collision The ionization

three times the ionization energy For a further increase the ionization cross sectiondecreases slowly Two basic mechanisms for ionization are:

8.1.8 DISSOCIATIVE IONIZATION

X, Y gas atoms or molecules

e = electron

Total ionization cross sections for rare and common molecular gases are available in

o

for several molecular gases

Photo-ionization occurs when photons of energy greater than the ionization potential of

the molecule, s\ impinge on the molecule This reaction is represented by:

XY + hv — > XY^ + e; hv = photon energy

8.1.9 EXCITATION

The first excitation threshold of an atom is lower than the ionization potential and theexcitation cross section is generally higher than the ionization cross section The excitedspecies returns to its ground state after a short interval, -10 ns emitting a photon ofequivalent energy

The direct excitation mechanism is

X + e-»X* -»e + X + /zvWhere X* denotes an excited atom Two other types are

X+ + Y -» X+ + Y*

C THREE BODY ATTACHMENT

Three body attachment occurs in the presence of a molecule that stabilizes and promotescharge transfer

Total cross sections for negative ion formation in several gases (CO, NO, O2, CO2 and

10

I io«

x D

Fig 8.4 Ionization cross sections for several molecules as a function of electron energy (Pejcev

et al., 1979, with permission of American Chemical Society).

(a)A + +e + e—> A*+e Three body recombination

(b) A * +e —>• A + + e + e impact ionization

(c) A*+e—> A** + e Collisional excitation or de — excitation

(d)(AB) + + e —> A * +B * Dissociative recombination

(e)A + + B~ -^A + B or

A*+B or AB

ion — ion recombination

In considering recombination many of these processes have to be taken into accountacting in combination and the decrease of electron density due to recombination has led

to the term collisional radiative decay At low electron densities, 107 < ne < 1012 cm"3,and low electron temperatures ~1 eV the recombination coefficient is relatively constant,

independent of n e In this region two body recombination processes are dominant As the

temperature of electrons increase the recombination coefficient increases with n e This

situation arises in considering recombination in hot spark channels, and three bodyprocesses become increasingly important

8.1.15 SECONDARY IONIZATION COEFFICIENT

There are several mechanisms which yield secondary electrons both at the cathode and

in the gas The secondary electrons contribute to the faster growth of current in thedischarge gap and the important mechanisms of secondary ionization are classified asbelow

A Impact of Positive Ions on the Cathode

Positive ions which impinge on the cathode liberate secondary electrons provided theirenergy is equal to or higher than the work function of the cathode The number ofsecondary electrons liberated per incident ion is dependent on the surface conditions ofthe cathode such as oxidation, adsorbed gas layer, etc The secondary emission is higherfor cleaner and non-oxidized surfaces At low gas pressures the secondary ionization co-

higher pressures (~ 100 kPa.) the influence of secondary electrons due to positive ions

is negligible as the ions do not have sufficient energy

B Impact of Metastables on the Cathode

Under certain conditions an excited molecule loses a fraction of its energy by collisionand the result is a new excited state from which the excited molecule cannot return to the

Some metastables are destroyed by collision with a gas molecule and some are lost byfalling on the anode However, secondary emission can occur when a metastable strikesthe cathode For a given gas in which the metastables are present (the rare gases andnitrogen are examples) the secondary emission due to positive ions will be morepronounced than that due to metastables The reason is that, under any particularcondition, the positive ions are attracted to the cathode due to Coloumb force where asthe metastables, being charge neutral, can only reach the cathode by diffusion Further,the probability of liberation of a secondary electron due to positive ions is higher thanfor metastables

C Photoelectric Action

Emission of electrons from the cathode due to photoelectric action is an importantsecondary mechanism and is effective at moderate gas pressures (-10-100 kPa) and gaplengths of a few centimeters A copious supply of photons of sufficient wave length and

a low absorption coefficient in the gas render this secondary process more effective All

the anode and the number decreases exponentially with gap distance due to photonabsorption according to

where n is the number of photons that survive after a transit distance of jc from the

absorption co-efficient |i is a function of wave length and measurements of absorptionco-efficients in gases using monochromatic beams have been published However thesedata cannot be used in gas discharge studies because the discharge produces photons

several gases using a self sustained discharge as source of photons A corona discharge

intensity of -33% for a transit of 1 cm and the reduction will be greater at higher gaspressures or longer gap lengths

The secondary ionization co-efficient observed experimentally is a combination ofseveral of these effects and the relative contributions have been determined for severalgases Generally speaking at low gas number densities (higher E/N) the positive ionaction predominates whereas at high gas pressures, -100 kPa, the photoelectric actionpredominates The secondary ionization coefficient also increases with E/N as shown in

While these photo-ionization cross sections are of interest from the point of view atomicand molecular physics, it is not possible to apply them directly to electrical dischargesbecause the discharge produces photons of various energies The relative intensity ofphotons generated is also not known Further, in a strongly photon absorbing gas, thephotons generated in the discharge disappear at a very short distance from the detectorand are not available at a distance for measurement Due to these difficulties photonabsorption experiments have been carried out at low gas pressures and the results are

photo-ionizing radiations in several gases

The intensity of photons scattered in a gas is attenuated according to

coefficient is related to the photo-ionization cross section according to

8.1.17 ELECTRON SWARM COEFFICIENTS

literature on gas discharges

Consider a swarm of electrons or ions moving through a reduced electric field E/N andhaving a drift velocity of W m/s The mobility is defined as jo, = W/E and in the literature

on gas discharges mobility is often referred to standard conditions of pressure andtemperature (p = 760 torr and T = 273 K) by expressing

In terms of E/N we have the relationship

Experimental and theoretical values for the swarm parameters for a large number of

practical interest The swarm coefficients are expressed as a function of the parameter

Table 8.2

Photo-ionization cross sections (Meek & Craggs, 1978)

MoleculeOxygenNitrogenCarbon dioxide

Water vaporHydrogenArgon

-18

Wave length (nm) Cross section (x 10 c m )101.9±1 nm

97.947.378.747.388.3 ±1.57098.5 ±0.5654780.3777.0-66.579.0 ± 0.577.0

onset7.04+1.823.1 ±4.18.8 + 1.620.8 ±3.8onset30onset2012onset8onset27

(With permission of John Wiley & Sons)

u** (cm" )

38-250-5502.538-750

~5200-800970400-700

spark

??

Cylindrical corona

*per ionizing collision, ** Normalized to atmospheric pressure

(With permission of Springer-Verlag)

Table 8.4

Electron Swarm Parameters

Parameter Symbol Units

Mean energy s eV

Characteristic energy D/JI eV

77 = ;/!+7/ 2

Recombination coefficient

A Oxygen 17

Three body attachment rate

Neative ion mobility (reduced)

- | 9 2

The actual mobility is given by

60.71.20.030

91.01.70.043

121.42.60.066

151.73.50.086

1824.60.116

212.35.90.149Electron diffusion (longitudinal)

D,

Attachment coefficient: (Fig 8 6)19

N

5 0 x l O ~2 0< £ / A f < 2 0 x l 01 9 Vm2

= 7.0xKT21exp(-2.25xl018x£/AT) m2; El N >2.0xlO~1 9 Vm2

lonization coefficient (Fig 8.6) (Raju and Liu, 1995)

— = 3.4473xl034(£/A02-985 m2; £/7V<4.6xl(T1 9 Vm2

N

= 11.269(£/AOU59 m2; EIN >4.6xl(T1 9 Vm2

Table 8.7 summarizes the investigations on a and r\ in SF6

8.2 ELECTRON GROWTH IN AN AVALANCHE

Electrons released from the cathode due to an external source of irradiation such asultraviolet light multiply in the presence of ionization provided the applied electric field

is sufficiently high The multiplication depends on the parameter E/N according to

«o = number of initial electrons

a = Townsend's first ionization coefficient (m" )

d = gap length (m)

Equation (8.6) is generally adequate at gas pressures greater than about 15 kPa At lowergas pressures the electron has to travel a minimum distance before it acquires adequateenergy for the onset of the ionization process and equation (8.6) then becomes

(8.7)

do = minimum distance for equilibrium (m).

Equations (8.6) and (8.7) apply when the electron multiplication is not large enough togenerate secondary electrons The sources for secondary electrons are photoelectricaction and positive ion action at the cathode The secondary ionization co-efficient isdefined as the number of secondary electrons generated per primary electron and usuallydenoted by the symbol y The contribution due to photoelectric action and positive ion

of secondary ionization is expressed as

_ exp(ad)

I - I Q ~

The electron growth is also influenced by attachment and detachment processes The

-iattachment coefficient, rj, (m~ ), is defined analogous to a as the number of electronslost due to a primary electron during a drift of unit distance

The current growth in an electron attaching gas occurs according to

(a-T])

The current growth shown in equation (8.9) assumes that the secondary processes arenot active To take into account the secondary electrons released from the cathode thecurrent growth equation should be modified as:

a _,_ M^ J //

( a

i — if}

Electron detachment is also a process that occurs in some electron attaching gases such

co-efficient r)* may be defined as r|* = (r| - 8) in moderately detaching gases such as O2.However in the presence of strong detachment the current growth is determined by a

[601 [6SJ [63]

Aicftwandan EdBlton 4McAf(«»

Mailer & Naldu Boyd & Crlcrrton Sldd»gtnuappa «t.al

E 3 b

e e

x Geballe & Harrison [64]

t 9 Dincer & Raju [12]

e + Bhalla & Craggs [59]

e c Raju & Dincer [63,71]

/ el Ascnwanden [77]

_J 1 — , i Oil- Morrow [58] 1 • • '

Table 8.7

Investigations on a AND r| in SF6 (Raju and Liu, 1995) E, Experimental; T, Theory

(©1995 IEEE)Authors

Bhalla and Craggs

Kline et al

Boyd and Crichton

Geballe and Harrison

Mailer and Naidu

Teich and Sangi

Urquij o-Carmona

Yoshizawa et al

Novak and Frechette

Dincer & Govinda Raju

Govinda Raju & Dincer

Itoh et al

Itoh et al

Itoh et al

Itoh et al

Itoh et al

Yousfi et al

Siddagangappa et al

Aschwanden

Edelson and McAfee

Raju et al

Liu & Govinda Raju

IEEE Trans Plasma Sci., 3 (1975) 205-208; Proc IEE, 123(1976)107-108.

Proc Symp on H V Technology, Munich, (1972)391-395

Ph D Thesis, Univ of Manchester, England, (1980)

J Phys D., Appl Phys., 12 (1979) 1839-1853

J Appl Phys., 53 (1982) 8562-8567

J Appl Phys., 54 (1983) 6311-6316

J Appl Phys, 53 (1982) 8562-8567

J Phys D: Appl Phys, 13 (1979) 1201-1209

J Phys D: Appl Phys, 12 (1979) 2167-2172

J Phys D: Appl Phys, 21 (1988) 922-930

J Phys D: Appl Phys, 23 (1990) 299-303

J Phys D: Appl Phys, 23 (1990)415-421

J Phys D: Appl Phys, 18 (1985) 359-375

J Phys D: Appl Phys, 15 (1983) 763-772 Fourth Inter Conf on Gaseous Electronics, Knoxville, Pergamon Press, (1994) 23-33 Rev Sci Instr 35 (1964) 187-190

J Appl Phys, 52 (1981) 3912-3920 IEEE Trans Plas Sci, 20 (1992) 515-514

The coefficients a, TJ, 8 and y are dependent on the applied electric field and the gasnumber density It has been found experimentally that the first three coefficientsexpressed in a normalized way, that is cc/N, Tj/N and §/N, are dependent on the ratio ofE/N only and not on the individual values of E and N The relationship between cc/N andE/N is expressed by the Townsend's semi-empirical relationship

— = Fexp(——) = /(£/TV)

where F and G are characteristics of the gas It can be shown that the ratio G/F is

these parameters for several gases

According to equation (8.6) the current in the gap is a maximum for the maximum value

of a at constant d Differentiating equation (8.11) with respect to N to find the point of

This equation is rearranged to yield the condition for the maximum value of a as afunction of N,

a/N JE\

= f \ — =tan#

Equation (8.14) predicts that the current will be a maximum at the point of intersection

addition to the G/F and the ionization potential The co-efficient r), defined as theionization per volt (cc/E), is sometimes found in the literature in place of a Theexpression for maximum a may be obtained as follows Differentiation of equation(8.11) yields

HC1HeHg

Kr

NeXe

372.7378.9621.1329.2776.456.5621.1400.6450.3329.2124.2689.4

621111335144721086911801155311491897568321062131059627Equating the term in square brackets to zero yields the condition for N at which thecurrent is a maximum as

The Stoletow point corresponds to the minimum of the Paschen breakdown curve forgases, discussed in the next section The ratio G/F is known as the effective ionizationpotential and in every case it is greater than the actual ionization potential due to the factthat the latter is obtained from beam experiments in which an electron beam of thespecific energy passes through the gas The physical significance of the Stoletow point isthat at this value of E/N the energy for generating an ion-pair is a minimum resulting in

a minimum sparking potential of the gas

8.3 CRITERIA FOR BREAKDOWN

Electron multiplication at low gas pressures under sufficiently high electric fields results

in a regeneration of secondary electrons, each primary electron resulting in a secondary

electron This condition is known as electrical breakdown of the gas and the discharge issaid to be self sustaining The current due to the electrons will be maintained eventhough the external agency, which provides the initiating electrons, is switched off.

Mathematically the condition is expressed by equating to zero the denominator of thegrowth equations (8.8) to (8.10)

Paschen discovered experimentally that the sparking potential of a uniform field gap is

dependent on the product Nd rather than, on individual values of N and d According to equation (8.11) a/N is a function of E/N which may be rewritten as a/N = ^(V s /Nd s )