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OCR for page 40
ho
IE~ ECTRIC BRE,AKDO~M
:By
E. J. Nurphy
Be:l ~ Telephone [~.bc~ra-tor..es
~,larr`ay T1:~l, No J.
A digest of the papers on dielectric breal~-do~.'n published in 194~-3 is
given in Volume X of this series under the subtitle ''High Voltage Phe:~omenati . At
a symposium on dielectrics held in 1946 at Br~stc>] IJniversi.ty by the Faraday
Society, Prcf. A. Ron Hippel contributed a paper st~mmar.zing the resets cot previ-
ous work on dielectric breakdown in solids, and indicating the nature of exiling
prctlems2. The following paragraphs are concerned essentially with the cont~ribu-
t~'ons to this subject published ire 1947, but it Bill be convenient to describe
the background very briefly.
Solids
__ _
a the orb of breakdown; Which went intc
Consider an electron mooring in a or'~stal having ~ given set of thermal
vibrations. The electron can achieve a speed such thaws it gives up energy to the
crystal lattice less rapidly than it acquires it from the field. This conclusion
is based on the general form of the function giving the dependence of the probe-
bility of quantum mechanical transitions on the speed. of the electron this
function has a maximum. The existence of this maximum, though not its position,
is independent of the nature of the c~iy-sta]. The existence of this maximum nosy
be regarded as the core of three of the present theories Qua tre~k~o~no ~t WBS
first proposed by A. Ron Hippel :in 1932. This theory enabled him to Bed ate break-
do~n strength to the Reststrahien frequencie.s~of the alkali halides, ire first
quantitative success in the theory of breakdo~n24. In 1937 H. Frthlich published
much more detail With regain to the motion
of electrons in a crystal under the influence of an applied field . It yielded
the same general result as the von H;.ppel theory in the sense that it sh`::wed that
above a certain [held strength the electron could not dissipate its energy' to the
lattice as rapidly as it acquired it from the f~e3.d,o for field st,rengt'r~s higher
than this the electron Is speed Would increase indefinitely. Later on
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~1
The objection has been raised against Frohlich's theory that tile high
energy electrons upon Which it depends word not be found ire a crystal, i.e., that
there are processes Which would prevent electrons from attaining these energies2.
An adequate derivation of the function g:~vir~g the number of electrons as a function
of energy in a crystal With an external field applied Would answer this question.
._. , Aim_ it, - _ ~
This is attempted by Frohlich in the pacer "Energy distribution and stabllit;y of
electrons in electric fields).
,; Starting With the Bloc h theory of electronic conduction in crystals,
Prohlich arrives at a distribution function for the energies of the electrons which,
for low energies, reduces to the Max~ell-Boltzmann distribution but for large
energies approaches as;7mptotical~y a finite value instead. of zero. An infinite
supply of electrons would be required to satisfy this condition. Therefore no
physically satisfactory solution is possible in a system depending only on the
exchange of energy With thermal vibrations in the lattice tr: take away the energy
of the electrons.
The same concision can 'ce reached by a non-mathematical argument. An
electron gains energy from the field and ~ie]~.s it to the lattice at rates such
that after a certain speed has been exceeded it should continue to gain energy
indefinitely in ~ system in Which it c`an only lose energy by exchange With crystal
vibrations. In this system an electron Lehigh achieves ~ high energy w~11 rearer
lose it and there Bill be an indefinitely continued increase in the popu~at on of
high energy electrons - an impossible condition.
The fai.luxe of this system to give ~ physically satisfactory solution
implies that £~ditiona]. means of di mi nishing the energy cuff the electrons need to be
sought Ionizing collisions (i.e., collisions -which put electrons in the conduc-
tion band) 2nd also collisions bet`-Tee;~ electrons may be necessary in order for a
stationary distribution to exist. The theory for ~ s`-sten~ In Which ionizing
co]lis~ons contribute to the distribution has not been reorked out. But by consider-
ation of the conditi.or~s under Which ~ stationary distribution is not obtained,
FrahI~ch gives a basis for his assumption that. Then an external field is ailed
there may be many electrons smith energy near the ionization level. Ties analysis
of the energy distribution when ~ field is applied to ~ crystal many lead to further
interesting consequences when it is worked out more fully.
This paper also helps to explain the basis of the cr~tericr~ (or condition)
for breakdown assumed by Froh:lich in his first paper, namely9 that break6G~n
commences Then the applied field attains a value such that electrons Faith energy
equal to or less than the ionization energy vial be accelerated indefinitely. The
reason for this choice of the condition for breakdown has not been entire].`r clear
from Previous capers. The present pacer makes the basis for it more evident by
slowing that there may be a considerable number of electrons in the cryst,&l with
energy near the ionization energy.
The title of the other paper by Froh1ich is: "On the theory of dielectric
breakdown in solids', It refers mainly to the temperature dependence of break`3o,.~n
strength in the higher temperature range. It has been estab].ished that in the lover
range of temperatures the breakdown strength increases with temperature. This is
explained by the earlier Frohlich theory on the basis of the change of relaxation
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Representative terms from entire chapter:
thermal vibrations
42
time With temperature. But at higher temperatures the sign of the temperature co-
efficient is reimmersed, the breakdo~-,tn s~rength.decreades ~,irith increasing temperature.
At first this Ivan attributed to thermal brea,;dovFn. B-ut it s now claimed that this
does not account for it's The extens~ori of Frohlich's theory described In this paper
i s designed to- accc>~t for the negative slope of the brea,kdov!n strength-tam, erasure
curve at high temperatures.
The earlier theory involved the assumption that in dielectrics the pop,'-
~ation c.f electrons in the;conduct~on [eve's is too small for e]ectron-.-e]..ectron .
collisions ,t,o;be important:. the interaction of movi~ng electrons ~h the thermal
vibrations of,the. lattice has the whole basis of.the absorption of~the e2.ectron's
ener.gy,by,the.lattice. In this.pa.pe.r the possibility is examined 'that break6..o~;,n
could,~c,cur,after the,ele.c.tron density in the conduction band becomes great enough
that electron-electron collisions account for a subs-tan- part of '~he energy less
of,a,ny,..elec.tro,n.. The concent,ration.of e.~.=ectrons 'is such that an e].ect-.~onic temper-
ature can be defined for the conduction electrons when the field is alp.'''... ''A
smsIl~.temperatuxe difference exists between the niow ng electrons and the lattice.
This is the way energy is lost by thee set of conduction electrons. 'TIle mathematical
analysis shows that breakdown could occur in such ~ systems that there exists a
temperature To below which the temperature coe.ffic~ent is cos;'ive4v,!n~e ab<.:ve it
is ne,gative, Ad that at this temperature the' energy acquired. from Isle Bleed by the
electron between two Jarge-ang~e collisions Is equal to kT. The vc^'u~- of the
breakdown Strength is not calcu:~.tedl,, the t'neor,~r succeeds one y on ~,rec~ct~ng the
existence of ~ maximum in the breakdown strength a=. a function of temperature.
In the cal.c~.at~..on 'of the energy gain and e..:ergy loss oil the electron
ac-count,.i~ taken.of the fact that there ~,.s a s,.~'ust,an+~al~co~ent.~-ation of ,'i..so:l.ated
levels." due to lattice imperfections at the higher ter;~.`,era,,~;~,'.~< FJect~cns can ne'
trapped6.in,the isolated levels. Me crapped niece.;., moire ~;~~~.~- very slowly lit the
applied field. There~ore.the ele~t-rons, AS ~ set, gall en£:g;,~ On t,he't~eld mainly
in,the con,duct~ion.leve].s aria lose it to the 'later, m=''..n:'; -~re.~.~?~ Ted in' the '
isolated levels. It is sho~.thar On. a.su~ffi~ienCi,~r Ok. ~i.e'~o'stre~gth the elect
tropic temperature A.. grow in~=f-2~ite~y, i.e.9 ttle orysta' bill break domes' ' '
Ti'ith thins extension the :~QU]ich, theory- now corers brea'~dowll by high
eneeiegjJ\ra°n0Sby low energy- ~,~'l1el~a2~.-ere.rgy).el'ectrons. The high et~-cgy el.ectrons are
responsible for bres2~ow,~ at the loper tempe-ratures, the Jo;"er energy electrons
(electrons with them energies.) produce breakdown at. tilde h:.~her +,e.~oera..tu~es.
The high e're~'gy.(lo'~ tem-perature) theory a+'+rib~tes ti.-le e].~.;at~on of'
breakdown st~e.hath in m=~d ~.-f733.aLs lo a prece~s'anal~ogous tic :r,~-u Which explains
th.e.fa:ct that t'ne resinate of an 'Troy _s '-,ig~^'ar than that ~ the pure metals.
The presence of ~imp,~r~'f,i.es o`- a~i7.~ii~YLu~;es In a C'''`rS~..\ Wi97.. S3..8G S7~..~= t the position
of To to lower tem~eratuL es 'by increasing the number 'of isol acted ~ e:, elsO Cn this
theory the addition of impurit;ies would increase t~'b-i?eak~o~~;~n .s~reng~J~ of-some di-
el.ectrics While it wc.~:ld diminish that of others, depending fin ~i.~e',~,er room temnera-
t~re lies
43
A brief paper on breakdown has been published 'oy Halo. and Seitz7. They
franc'. that the breakdown strength of K~)r is independent of temperat~?.re over a con-
side~al'1e range. They propose that the breakdown of solids depends upon the release
of electrons from excitonS 9 -that is, Strom excited (electron-positive hoJe)~pa~rs.
This Mold Scoot i'or the smallness of the temperature coefficient. Froblichts
high-~nerature theory includes some aspects similar to this.
An experimental StU63J of the temperature dependence of the orientation of
breakdown paths in crystals was made by i. W. Dav~-sson4. This type of investigation
may prove useful? in the study of bile motion of high energy electrons in a crystal
lattice.
One of the interesting questions which appears in connection with these
theories arid experiments is whether the directions taken by the breakdown paths
are determined by high energy electrons which initiate breakdown (an implication of
the I'roh~i.ch theory' presumably) or whether flower energy electrons initiate the
breakdown, but the observed paths are those followed by high energy electrons
developed Wafter the offset of breakdown. There is evidence in favor of the Batter
vied. von Fippel and Davison found, a fen years ago9 a peculiar result. the break-
do~n strength of NaCl crystals is -independent of direction, but the breakdown paths
are in (130) directions En the field is applied along a (100N direction. This can
be explained if the breakdown is triggered. off-by the Boa energy (long r.'ave)
electrons which are not mucks influenced by tt,e sym~.etry of the crystal, while the -
breakdown paths are produced by high energy (short Wave length) electrons developed
after breakdown s initiated. which aloe ~'nf7..uenced by the crystal. s~pmmetries2.
Frohlichis expression for the breakdown strength contains the ionization
energy of the crystal (the energy required. to take an electron from the ground level
to some level in the conduction bandy in 'the denominator. The other theories do
not involve the ionization energy. Tt is.introduced by Frohlich's criterion for
bran. It may be that this criterion is unnecessarily strong. in any case,
this is a notable difference between the several theories' and it is avail able for
experimental investigation.
Studies of the breakdown of so]~ids divide themselves naturally into a few
significant sub-~nvestigations9 for example, the relation of breakdown strength to
characteristic frequencies9 such as the Res~st~-ah'en frequencies, the sign of the
t,em~erat~re dependence and the st,ee~ne~s of its slopes the i.nf~uence of ~mpuri:ties ;
car adm~.xtures9 and the orientation of breakdown paths O The caters contributed in
194C' refer mainly to the te~i~cerature dependence. ,
The theories discussed or mentioned above refer to instantaneous break
do~,,:!n. In many practical situations voltages are ar!r:]ied for a long time and the
For example g i r1 the case of paper i.nsu
lated cables it mat' occur by the e].ectrochemica~ process described by the Writer
in 719,~,622
actual brea'<~,vn may occur in other ways.
44
Liqui_
Gases ~ -
No papers Here' found on the break'!dov~n strength of liquids.
A review of the breakdown of gases '~as given by ProfO JUNO 3. octet as the
38th Kelvin Lecture before the Institute of Eieetrica'l`Engir~eers in London on.
April. 24j 1947. ,It is reprinted in Sciencel°. Professor toed revier~s'-the histor:~-
of the subject, explains the present theories, and'ir~dicates' proL3e~.~.s for fu-~re
study. A bibliobrap'ny of 90 papers is given A cti,sc~a,ssio:~ of 'icicle Spark T?~scha.~geti
was also held at a meeting of the Physical Society in Condor. Qua April 239 197trio
This discussion is re~7ier!ecl. in Nature9.
The Townsend theory of breakdowns as Iodized by holists attributes break-
dor,tn to the ejection of electrons from the cathode' boy- tile 'action of positive ion:,
radiatior~ en cl ~neta-stabJe atoms. These' are''gene'rated in the gas blat the electrons
moving in the applied' field. ~hen-these 'products 'just suffice to generate one free
electron at the.cathode for each ' primary e~ectron'in- tine gas ttie condit~on~for
brea~d,'c~n''ex~sts. This theory has prc~ed;, satisfactory When applied to gases at
reduced pressure.' ' ' ' . . '.' ' 2 ''
. . .
. . . . . . .. ..
' At Pressures near'atmospher'ic and for long gap lengths it,has .not,been
sufficient 'to explain observations. A theory of the long spark at atmospheric' .
pressure has been proposed by Loeb and Meek and indere~dentl-)~ by Raether which
depends upon photoionization of the gas by' radiation coming from. prec,.eding parts
of the disc] arge. : This' is sometimes referred to as ti.:e'st',eamer" me~chan:-sm of
breakdown. This is clearly a significant develor~ment, because breakdown processes
at atmospheric pressure should be studied In a different way where photcioniza~icn
of the air (or other gas mixcure) is important than where.it is got important,.
they c 'pressure:
;
The foll.oring papers' have a 'bearing cn the sludgy of the spark `?+ atmos
Zingerman and Nikaevkaia33 have investigated the mechanism of discharges
in long gaps by means of photographs of incomplete breakdowns. They show that the
d~scharge'channel'is not formed by the progress of one avalanche from cath;ode,to
anode but' consists of separate stre~c,hes Which grow together into a Coleman channel.
L. H. Fisher]1 attempted to verify the theory of Jong,-sparks of Loot and
Meek but encountered experimental difficulties which are of interact In connec~..on
. . . .
,.~th the design of such experiments.
Loebl3 has-investigated the mechanism of -the negative point corona at ~
atmospheric pressure in relation 'to the second Tc~nsend c,oef~icient. i, D. Craggs 7
has studied the loca].ized after-gIc~ observed with long sparks in ~:ar~'ous gases.
5raggs and Fo,~ood25 have studied the after-glor~ following start sparks 1~. hydrogen
at one atmosphere pressures They show that recombination of electrons and ions is
apparently the cause of the light em7t-'-ed in the alter-~lo~ ard ca].cu].=Ge t~ereircrn
a coefficient of recombination. They also show that ion concentrations in the
hydrogen spar' channels may be found by observing the Stark broadening of Balmer
lines.
45
The fol.lo~ing papers are also of interest in connection With the break-
do~n of gases. If. Drakarev~4 shovels that, because an electron released by ioniza-
tion gives up its energy during ~ 'arge umber of collisions, the mean-energy of the
electron. is, under certain conditions, larger than the thermal energy of the re-
~ai~;ng gas. The conditions under which the notion of temperature can be applied
to the electron gas are considered and a formula for the electron temperature is
derived.
1.. Sena355 considering that the charge exchange is the basic process of
interaction boatmen ion and atom' shoes that a proportionality exists between mean
velocity of drift Of ions in the field anc! square root of fief 6-strength over
pressure. The distribution of velocities of the ices is of a sharply anisotropic
nature and cannot be associated with the concert of temperature.
Jacobs and I,&RocOIue36~37 have investigated the ~.inimum sparking ~oten-
tia~s of barium-, magnesium and alun~.num. in argon and in helium. They find that the
Ado of electrons emitted from the cathode per bombarding Positive ion (Vm) is
0.1499 O.O8S and. C.045 respectively in argon. }~,Iinimum sparking potentials ~n
lielium are 146 ~ 29 161 ~ 1, and lg7 ~ 2 volts. in general they are higher {lean
argon. ~ graphical method is proposed for ~,redicti.n~, sparl~in=~ potentials for metals
based upon the values of Vm or the work function. Bo M. Gokhterg38 has made
measurements on the first Townsend cceffic:ient (~) for a number of gases of widely
varying dielectric strengths. He `'inds that the brea''do~7n fields are those for
;.Thich. (a) reaches 0.0235 ~ -the Pressure in men Hg. The practical applications of
gaffes smith high breakdown strengths are discussed.
Troop and van der Oraff20 have -estimate the insulation of high
voltages ~n vacuum. They find that t',~e gradient at the electrodes When breakdown
occurs is, for high. voltages (lOQ-700 kV), far beloT.-~? the value for fi.elcl emission.
They suggest cumulative release of secondary e1..ectrons9 positive Ions and photons
as the mechanism.
E. JO Sandbergl9 has studied the breakdown strength of gases and ioniza-
tion coefficients. Hale and H!uxford2 discuss the estimation of ~.inimum sparking
potential from the cathode work func-tio7l0 I. I. t.evintov23 has investigated the
excitati.or~ te~.~erat~re~=, in the ch=nne] of the ;mc~.~lse discharge at atmospheric
pressure. E. Elenbeas~7 leas st~..died the excitation temperature, the gas te~pera-
ture and the electron temperature in the high pressure ~,ercury discharge. Elec-
trodless discharges are discussed by G. I. Labati~9. F. A. ~,nglish30 has studied
corona from-<2ine POSi~iVO poirt,s. Tord Rayleigh32 has considered the surprising
amount of energy vehicle can 'ce collected after the electric discharge has passed.
Fo JO [lev,rellyn ~ di.scusses the incendiary' action of sharks in relation to their
physical routes.
The stupor of brea'
~6
An interesting d.irection of ~.nvest~.gation is that of the influence of
certain gases ~h pclyatomic monocles (such as the ~reons) on c.,rc;~a and br~ak-
dov.~n in air 4 The capture of electrons to form negative Cons is improbable unless
there is some wale of disposing of the energy They collisions would
accomplish these but they are rare. Pol~ratomi~ molecules of suitable types may do
this by dissociating the excess energy is carried Amy as kinetic energy- of tie
products 0.
15 In interesting paper on this subject has been :;ub'.~.sced by fJeleler and
bobs . Their investigation was made in terms of the r~.ega.tlve corona in air. They
measure the corona current arid also eke visua.' observ~ticusO The effect of freon
is to reduce the current in Ache corona at ~ given voltages It also introduces ~
lag or "hysteresis" in the value of voltage at which a portico or type of corona
starts. A second paper gives the results of a study of the positive corona 5~.
The visual characterist,ics of the corona changed markedly with change in the perk
centage of freon in the air9 as did also the c,~rrc:~ts and onset potentials.
Mo V. Blanc28 has studied the ignition of explosi ve gas mixtures by
electric sparks. This. includes minimum ignition energies a:~d quenching d~st=~.~ces
of mixtures of methane, oxygen and inert gas c s.
,
;.,
it.
.,
. , .
~7
B; .LI(~RAPEY
_ ~
D:;~,(-S' Of Literature On Die1OCt1~1CS? X9 (3946-47! ~ 17
''L. VOn Hi3?Pe~ 9 mranS. ?'ara6QY SOC., 42A (1946 SU~11eL1en1) PP 78-87
h. PrOI11iCY-, PrOC. ROY. SAC. A, I609~1937} P 230
tT. lo. Davissong [ih,RSe to 70, (19,!~6N PP 685-698
It ~rolllich, Proc. Roar. SQC. (7 Onion), 1SS, {1947) P 532
lI ~ P,rohlich g P:roc . Roy. Scc . q IS~ 9 ~ 19471 ~ 521
Malmlo~ T and Seitz, Phases O Rev., 71 ., (71.947' ~ 125
Seeger and Teller, Phys. Rc~r. hi, (1938 N P 515
10
2
3.
44 ~
60
70
a O
9. Natures 160 (19471 JUDY 26,, PP 110-112
lGo L. 1~0 LOeb' SCienCe 9 106 (19,!47) SePL. 129 PP 229~236
110 T . 7-, FiSLer, P11_YS. ROV. ~ 729 (~.947) DC) 1~23-428
120 Re.ference deleted
1.3. T-,. P. Ioeb9 rhys. Rev. 719 (191.~7) P 712
14- o
15.
DL5A.
16 0
17.
l.g.
19 0
2~0 0
21.
22 0
23.
FL. Ao Bak and o1:;hers' J. Tech. PLys. USS1? 179 (1947? P 1153
It'~:1~1 =~I' - 61~ 9 1 .~r/~. '~ - v · ~ ~f29 (1047J p 289
I`.~onr an~ ~eissl~,r9 T:;h~rs. RO1T. ~ ~;29 (1947) P 294
R. Coopex., 5,I.~.E49 94 Pt~. 3, (1947J PP 315~325
J. D. Craggs and others, ,T. AP7. PhYS. 189 (19471 P 919
. Franz s Z ~ f. Physik g ~ 607 ~ 1.939)
E. J. Sa:~oberg, JO Tech. PLiys. g USSR9 17 (1947N P 299
Tr~rnp and van der Greaff, J. App. Phy~,. ,, iS (1947N PP 327-332
I~ale and H~uxford, <-, APCO P?1YS. ~ IS {1947) ~ 586
E. J. ~ urpi;y9 191;.6 Im-lual Report 9 Conferenco on Electrica1 Insulatio~l; 1TRG, P 11
I . I ~ I,: ~ri ntov, ~ 0 Tech. Phtys . ., (USSR) 17 ~ (1947) p 781
r.~_." -~' ~-" - ~.~ nn~h ~rh~'c! ~`T
48
24b A. von Hiprcl, 7~. f . Physi>., 75 c ( 1033) P 145
250 Cra~gs and Fopr?ood7 Proo. rhys. SocO (Tondon ~.J7` 947 p 771
.. . .
260 Craggs and F;oprocd, Prc.'cO Pl~ys. ~ocO 593~1947) p 7r5
. . . .
. .. .
270 E. Elenbaas, Phillips Research Bc-cor~s, 29 (]947) F~b. pp 20-41
.. . . . ~.
2ge Fllo V ;,lanc ar~d others, I~. Cham. PhysO g :1 5g (194.7) P 753
· .. ;
290 C;. I. Babat, J. I. EcEo 9 ~.' (1947~) pp 27-37
. - · .
3o o
310
32.
. 11. English5 PhysO Rev. g 71 (~.947) pp 633-639
F. J7 Ilel.!elly~l9 I.R.I. Trans.9 23, (2'947) pp 29-^,4
tord Rayleigh9 Proc. 170yO Soc. g IS99 (1947) 296
~. .
330 Zinger~lan and Nik~e~l-~aia, J. Exp. Theorc Ph,~s. 16, (19i,.~) r' 499~509
(in 8ussian?
34. 00 Dr~arev' J. Pn~'rs. USSR lOg (1946> p 81
350 L. Sena9 u. F,l~ys. USSR 1O, <1946) p I,,rl'9,,,,`
36 0
37 0
38.
TaCObS and ~ C" Rocque ~ J q .AI?P. Ph~rs O la, (~.947J r) ]. 99 ;
JCCQ6S and ~a Rocquc,, Tr~!ns. ElectrocTic~n. .cc,c. 9~9 (1947N P 14
S. I~. Gok}~berg, 74Zlll. ,Acod. Sci. USSR 10, <'9461 p 425
·
.;
