ON THE MECHANISM OF DIELECTRIC BREAKDOWN
IN GLASS AND lTS RELATION TO
ELECTRICAL CONDUCTION
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD V AN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECHNISCHE HOGESCHOOL TE DELFT, OP GE-ZAG VAN DE RECTOR MAGNIFICUS DR. O.BOTTEMA, HOOGLERAAR IN DE AFDELING DER ALGEMENE WETENSCHAPPEN, VOOR EEN COM-MISSIE UIT DE SENAAT TE VER-DEDIGEN OP WOENSDAG 29 APRIL 1959 DES NAMIDDAGS TE 4 UUR
DOOR
JACOBUS VERMEER
NATUURKUNDIG INGENIEUR, GEBOREN TE ROTTEIWAM
BIBLIOTHEEK DER
TECHNISCHE NOGESCHOOl
DELFTDRUK: V.R.B. KLEINE DER A ·1 - GRONINGEN -TEL. 31000
~~~
~r
Dit proefschrift is goedgekeurd door de promotoren
prof. dr. M.
J.
Druyvesteyn
en
The research work described in this thesis was carried out during the years 1951-1957 in the physical laboratory of the N. V. tot Keuring van Electrotechnische materialen (KEMA) at Arnhem under the direction of prof. dr. J. J. Went, Head of the Research Department of the KEMA. The author is indebted to prof. dr. ir. J. C. van Staveren, director of the N. V. KEMA, for the permission to publish the results in the present form.
CONTENTS
Chapter I General Introduction
1. Introduction to the problem 1
2. Survey of earlier work on dielectric breakdown
2.1 The earlier work up to about 1930 3 .2.2 Review of theories concerning the mechanism of
intrinsic breakdown 8
2. 3 Comments on results of some recent
experimen-tal investigations 13
2.4 Conclusions and objects of the present research, 23 3. Th~ scope of the investigations
3. 1 Measurements of intrinsic breakdown strengths 25
3. 2 Thermal breakdown 25
3. 3 Electrical conduction in glass 27 3. 4 The kinds of glass used for the experiments 29 Chapter 11 Experimental Methods
1. Breakdown measurements
1. 1 The shape of the test specimens 32 1. 2 Measurement of specimen thickness 33
1.3 Electrodes 34
1. 4 ·High voltage p~lse generators 34
1. 5 Measurement of voltage 39
1. 6 Variation of temperature 40
1. 7 Reproducibility of results ; reduction of scatter 40 1. 8 Accuracy of the measurements. 45 2. Conductivity measurements
2. 1 The test samples 46
2. 2 Measurement of the dimensions 46
2.3 Electrodes 48
2.4 Voltage source; current and voltage
measure-ment 48
2. 5 Time effect 48
2. 6 Reproducibility and accuracy of results 49 Chapter III Results of Breakdown Measurements
1. Systematic investigation of glass BSI
1. 1 Intrqduction 50
1. 2 The effect of thickness 50
1. 3 The electrode effect 51
1. 4 The effects of temperature and of voltage
duration 54
Chapter IV
Chapter V
2. Results for other glasses 2. 1 Introduction 2.2 Glass AS 2. 3 Glass ABS 2.4 Glass BSII 2.5 Glass BSIII 2.6 Glass S
3. Comparison of the results 4. Conclusions
Results of Conductivity Measurements 1. Introduction
2. The time effect for glass S
3. The effect of temperature for low field strength 4. Measurements at high field strengths
5. Analysis of the results 6. Relation to glass structure
Thermal Breakdown in Glass
58 59 60 61 63 63 64 67 69 69 70 71 72 77 1. Introduction 80
2. Calculation of thermal breakdown strengths 80 3. Comparison between calculated and experimental
values for different glasses 83
3. 1 lntroduction 83
3. 2 The temperature region of thermal breakdown 84
3. 3 The effect of voltage duration 86
3.4 Transition to intrinsic breakdown 87
4. Conclusions. 87
Summary 89
Samenvatting 90
Bibliography 92
1012.
1593
ERRATA.
blz. 1. 11 de regel: thecelectrodes moet zijn the electrodes blz. 11. Onderaan de blz. komt fig. I. 2
1
Ta T, T, Tm
- ELECTRON TEMPERATURE
Fig. 1. 2. Energy gain (A) for different field strengths and energy 10ss (B) of e1ectrons in arporphous solids (or imperfect crystals) according to Fr ö hl i c h [12) .
1
CHAPTER I
GENERAL INTRODUGTION 1. 1. Introduction to the problem.
Just like gaseous and liquid dielectrics, solid insulating materials exhibit the phenomenon of dielectric breakdown. It is a fact that it is not possible to raise the field strength within asolid dielectric up to an unlimited high value. Depending on the kind of dielectric and on the experimental conditions spark-br.eakdown occurs at field st:rengths ranging' from ab out O. 1 x 106 V/cm up to about
10 x 10liÏ V / cm*). The dielectric is pierced by adischarge:between thecelectrodes leaving a narrow channel where the m.aterial is destroyed by melting or decomposition.
Because of the need for insulating ' materials in electrical engineering practice, especially in high voltage engineering, it is obviously of great interest that the physical mechanism .of this phenomenon is understoodas completelyas possible.As a part .of the physics of the solid state it offers man~r difficulties to the in-vestigator.s, both theoretical and experimental.
The breakdo.wn strength of a dielectric may dep end on various factors, e. g. specimen thickness, rate of rise ofthe field strength, temperature and electrode mate rial. Moreover annealing of the specimens may influence the electric strength. The specimens must be of such a shape and the electrodes must be applied in such a way that secondary effects which would initiate breakdown of the specimen, such as field concentrations and discharges in the ambient medium, are avoided or rende red harmIess. Finally the stock of the dielectric material to be investigated must be as homogeneous in cOI!I:position as possible and the material must be free fr om local inhom'ogeneities, as such inhomogeneities form weak spots where breakdown is promoted.
In view of the above it is not surprising that considerable differences exist amongst the results of comparable investigations and that most experimenters have experienced difficulties in obtaining reproducible results. These difficulties have persisted up to recent years, although the investigation of the breakdown of solids has been taken up Ip.ore than fifty years ago, when the young technics of electrical engineering became interested because of insulationp~oblems in electrical machines and powertransmission at high voltage.
It is evident that this lack in reproducibility means a se,rious impediment for the study of the influence on the electric strength of the various ~actors summed 'up above. Also the comparison of the results of theoretical', calculatioris with experimental data becomes somewhat premature if the latter are subject to uncertainty owing to scatter. ,A first condition for a justifiabIe experimental study is to find out the, causes of eventual .spread and if possible to *) Ignoring recent recommendations the unity l06'V / ~~ or MV / cm is used
I-i
take measures in order to reduce it within the limits of experimental errors.
In some of the earliest investigations scatter of results was regarded as inherent to the phenomenon. But later experiments
, learned that various secundary effects may fnfluence and modify the real phenomenon. In this connection the paper of V 0 n Hippel and Alger*) may be cited, which clearly showed the difficulties in investigating the breakdown of alkali-halide single crystals. It was this publication, together with the fa ct that his colleague Dr. K. J . KeIl eralso experienced trouble in_ getti,ng reproducible results for glass at lowtemperature and with metallic electrodes**), that gave rise to the author' s investigations.
The initial aim was to study the causes of spread in dielectric breakdown, as was experienced by KeIl er. Since the investigation of glass promised to give less trouble than that of simple crystals like alkali-halides, the work was started with glass. It appeared possible to reduce the scatter in comparable values of electric strength to within ab out 2t%, which is within the limits of known experimental errors. A necessary condition al;>peared to be thorough cleanliness. of the specimens immediately before the application of the electrodes. Thus it beca~e possible to make an accurate study of the various factors, e. g. specimen thickness, electrode material, temperature, duration of test voltage, that may influence the electric strength of glass.
This was done extensively for a glass of the Pyrex type. The results gave rise to the investigation of glasses of different chemical cömposition. Comparison of the results of these glasses with those of the Pyrex glass and with those obtained previously by KeIl er for a Thuringian glass demonstrated that under certain experimental conditions arelation existed between the breakdown strengths and the electric conductivities of the glasses. In order to be able to study this relation in detail, the conductivities were measured up to high field strength and as
a
function of 'temperature. The results were used for a quantitative calculation based on the assumption that the heat dissipated by the pre-breakdown current is the cause of thermal destruction of the test specimen (thermal breakdown, cf. the next section). ,:,,~,~ ..Successive results have already been published ) and the present thesis offers an extended survey of the results of this research.
All experiments were performed usmg stationary or approximately linearly rising direct voltages. Alternating voltages have not been used. This would have involved the study of the dielectric losses of the investigated glasses as a function of
tem-*)A. von Hippel and R. S. Alger, Phys.Rev.76 (1949)127. Itmay be stressed' that V 0 n Hip pel has been engaged during almost 20 years
with breakdown, of alkali-halides at the time publication of this paper. **) K. J. Kelle r, Physica 17 (1951) 5ll, fig. 3; also, Electrotechniek 31
(1953) 1.
1-2-1 3
perature and of field strength; a rather complicated phenomenon. !\lthoughin particular the investigation 'of the. influenc~.:.of fielq'
,strengfh on tne power Tactor oÎ glasses seems to be of great interest, we had to restrict ourselves to the use of 'unindirectiona~
voltages in order to limit the extent of this research. We believe however that this does not set any restriction with regard to a fuU comprehension of the fundamental breakdown mechanism.
It must be stressed that the review of experimental and theoreticaL
studies given
m
the following sections is far from, complete. It was given with the aim to elucidate the state of knowledge concerning dielectric breakdown of glass at the time when the present research was started (1951).1. 2. Survey of earlier work on dielectric breakdown.
1. 2. l.The earlier work up to about 1930. After the appearance of the recent compliation of Fr a n z in the new edition of the Handbuch der Physik, Bd. XVII (Encyclopedia of Physics, Vol. XVII), an extensive historical survey might seem to be of little use. However, the author is of opinion that a review given from an experimental point of view still may be of suffi'cient value. Moreover , in order to arrive at a right judgement of the research presented here, a review of the results of earlier work and of the conclusions drawn from it can not be omitted. Since we onlydeal with the physical
mechanism of dielectric breakdown. we may pass many of the
investigations of a technical nature which were carried out inlorder to gather data with a view to practical applications. In view of the object ofthe present investigation it is obvious that some emphasis will be given to the research on glass.
A more or less systematic investigation of dielectric breakdown was started about the turn of the century maiply by electrical
engineers. They became interested because of the important
technical problem ofproviding adequate insula,tion for hIgh voltage. Objects of research were mainly the materials at that time used for technical insulation: Mica, dry and impregnated paper, ebonite, glass and porcelain, paraffin and waxes, oils [132][38][41][139].
The first experiments we re all done at ambient temperature and they were carrie<,i out rather primitively, mostly in incomparable ways, so that the different investigatorscame to'different -results,
both as to the absolute values and as to the dependence on specimen thickness. In most .cases it was found that with increasing thickness
the 'breakdown voltage increased slower than proportional to
thickness. Very frequently the re sults showed considerable spread. Mos cic ki [108] was the first who studied - with a view to the manufacture of high voltage condensors - the dielectric breakdown
of glass in homogeneous fields. These investigations are of
particular interest, since he showed with the aid of careful experiments that, without special precautions, the field concen-trations at the edges of the electrödes always initiate breakdown at a much lower voltage than wh en these field concentrations were made harmiess by a suitable shape of the test samples. His test specimens were made by drawing and blowing up thick-waUed tubes. The field at the thin part could be considered to be sufficiently
homo-4 1-2-1
geneous whereae the edges of the electrodes were laid on the thick part of the tubes, which eventually were thlCkened by a suitable chosen land of wax. For an alkali glass Mos cic ki found that the breakdown voltag-e measured in this way was propor-tional to the thickness for specimens between 0 05 mm and 0.5 mmo However, in the case of edge breakdown, the breakdown vo~ta~e
increased slowe r than proportional to specimen thickness, with about the square root of thickness. where.as much lower values were found than wlth homogeneous fields.
Later these experiences were confirmed by Sc hw a i ge r [142]. He emphatically pointed out that in investigating flat specimens between flat electrodes or between a plate and a ball as electrodes , discharges at the edges in the ambient air may lower considerably the breakdown voltage. Sc h w a i g e r stated that when these discharges were suppressed by a suitable chosen immersion liquid, a breakdown strength independent of thickness was found at least for homogeneous materiais. He stated that when a decrease of breakdown strength with increasing specimen thickness was found, the breakdown should be always influenced by discharges. Spread in the results should be an accompanying phenomenon.
Real progress in the interpretation was made in the year 1922. Previously it was already found that the breakdown strength of
di~lectrics may be influenced by temperature in such a way that at higher temperatures lower breakdown voltages were found [60] and that there appeared to be a certain relation to dielectric loss
[ 138] . G ü n t her - S c h u I z e [62] , H a y. den and St e i n met z [651. but parlicularly Wagner [136, 137J recognized that in these cases breakdown was caused by a thermal instability. This instability is essentially associated with the fact that the electrical conductivity of insulating materials increases strongly with in-creasing temperature. Consequently, if the high field strength causes a conduction current that generates a perceptible Joule- heat, the resulting temperature rise in its turn causes an increase of the conduction current with cumulative heat generation and further increase of temperature. The heat will be removed by conduction towards the surroundings, but if the field is high enough the rate of heat generation may surpass the rate of heat removal and consequently the temperature wiU rise to infinity.
It is Wa g ne r 's merit to have given a first mathematical treatment of this phenomenon, whicn was called thermal break-down. Ris calculation was based on the assumption of the existence of a weak spot between the electrodes, where a channel of higher conductivity is formed. Very soon almost the total current is carried by this channel. If the conductivity within this channel is assumed to be an exponential function of temperature, it can be shown that only below a certain critical field strength the heat production within the channel is balanced by heat conduction towards the surrounding medium. This is illustrated in fig. I. 1: A balanee between heat production and heat removal is only possible of the field strength is lower than E • For fields above this critical value an equilibrium is impossiblFand, due to an infinite temperature rise, destruction of the mate rial takes place af ter a certain finite time. This time is the shorter the higher the field strength above
1-2-1 5
T, T. Tm
_ TEMPERATURE
Fig. 1.1. Heat production (.t) for different field strengths and heat removal towards the surroundings (D) for a dielectric material exhibiting astrong increase of electrical conductivity with temperature; T 0: initia! temperature (temperature of the surroundings), Em: field strengthfor which thermal instability begins.
the critical value. The characteristics of Wagn er' s channel breakdown are:
The breadkown strength is the higher the higher the specific resistance of the material.
The breakdown strength decreases with increasing temperature at the same rate as the square root of the specific resistance. The breakdown strength decreases with increasing time of
application of the voltage.
The breakdown strength is independent of specimen thickness. Apart from the last one these conclusions were in good agree-ment with experiagree-mental results.
The succes of Wa g ne r 's theory initiated a lot of experiments by different investigators on various insulating materiais. In Germany at first the electrical engineers gave guidance to the research, but in this stage also physicists became interested in this aspect of solid-state physics. The name of A. Jo f f é especiaUy may be mentioned as the promotor of a group of Russian investigators in Leningrad.
The calculations of Wa g n -e r were extended by Rog 0 w ski
[121], Von Kármán [92] and Dreyfus [55] andcomplctedby the work of F 0 c k [56] . These authors dealt with the case where
the dielectric remains homogeneous up to the moment of break-down. The heat pf'oduced within tbe dielectric is not carried away
from a hot channel towards the surrounding dielectric mate rial. but towards the electrodes and from the electrodes towards thc ambient medium. All parameters, such as thickness, thermal
and electrical conductivity and specific heat of the dielectric material and thickness and thermal conductivityof the electrodes as wel! as the coefficients of heat transfer from the electrocles to
the ambient medium were taken into consideration. The
cal-culations were set up for flat as weU as for cylindrical (cabie ) configurations and for direct current as weU as for alteEnatin~~
current (complex electrical conductivity of thc dielectricr').
6 1-2"-1
A dependence on thickness more in acco:rdance with experiment was predicted by these calculations. It appeared that for th in specimens the critical breakdown voltage is proportional to the square root ofthe thickness, whereas in the limit of great thickness the breakdown voltage tends to a constant value independent of thickness.
Just as was established by Wa g ne r the critical field strength decreases with increasing temperature as the square root of the specific resistance. Besides the temporal development of break~ down, if a field strength above the critical value is applied, could be predicted. The relaxation time appeared to be of the order of seconds or minutes.
The conclusions of these theoretical calculations we re com-pletely confirmed by the results of experiments of different investigators, among which particularly those of In ge and Wal th er may be mentioned. In order to investigate "the break-downphenomenon in its purest state these experimenters observed it for homogeneous crystalline dielectric materials of the most simple structure, namely mono-cry"stals ofthe alkali-halides [76 , 77,79] but also for " glass [78, 81J and porcelain [80].
At the same time, however, it was recognized that the thermal theory could not account for the breakdown phenomenon under all circumstances. Thermal breakdown can only occur when the electrical conductivity of the material at the test temperature is sufficiently high, so that the amount of heat dissipated at high field strengths indeed causes a rise in temperature during the time of application of the voltage. It was found that at lower temperatures, when the dissipation of heat is negligible, there is no longer a correlation between electrical conductivity and break-down strength. In contrast to the experience for the region of thermal breakdown, the electric strength appeared to be independent of temperature or even to increase with increasing temperature. Moreover , the rate of rise of the voltage was no longer significant :[82] , indicating that in these cases the break
-down occurred within very short times. With the aid of the high-speed cathode ray oscillograph, at that time developed by co-operators of Rog 0 w ski, it was found that for instance the break-down of mica at room temperature takes place within a time less than 1O-? sec without any perceptible previous energy consumption 124 . In ge and Wal th e r observed the breakdown of glass and rock salt crystals ininhomogeneous fields with the aid ofvery rapid impulse voltages. With the shortest voltage surges used (about 3 x 10-8 sec) partial breakdowns were obtained within specimens of some millimeters thickness, indicatin~ that the breakdown proceeded with a velocity of about 107 cm/ sec {84, 85] .
This phenomenon was called "rein-elektrischer Durchschlag", "disruptivbreakdown" or intrinsic breakdown. Investigations with electrodes producing inhomogeneous fields within glass showed that this kind of breakdown always started in the region of maximum field strength and th at breakdown occurred if the field strength in this region exceeded a certain value [83 ]. In accordance with this fact it appeared that the intrinsic electrlc strength was independent of specimen thickness. In this conneXIon it may be mentioned that
· 1-2-1 7 it was regarded as a further characteristic of intrinsic breakdown that the breakdown strength measured with d. c. voltage cor-responds with the peak value measured with a. c. voltage, whilst thermal breakdown would give rise to a .correspondance between the d. c. value and the a. c. -r. m. s.value. Of course this will only be the case if the dielectric loss of the tested material is wholly to be ascribed to conductance [ 110 ] .
Knowledge of the characteristiCs of intrinsic breakdown was gathered step by step during the course ofa great number ofyears by the work of different investigators. It is therefore not surprising that in some of these investigations wrong conclusions were drawn due to faulty experimental techniques and that there·was disagree-ment between different authors as well as concerning the experimental results as concerning the theoretical interpretation. It is not useful to cite and comment all the work done in this field. However, certain results, especially for glass, will be mentioned here.
In the first place the experiments of Werner 1141],
G Ü lln e r [61] and Ing e and Wu 1 [87] established that with flat specimens it is practically impossible to determine correct values of electric strength, since, even with the aid of ambient dielectric liquids with high permittivity"'or of ambient semi-conducting liquids, stress concentrations at the electrode edg,ws and discharges in the ambient medium cannot wholly be avoided ). Therefore· the use of special-shaped specimens (cf. section U. 1. 1) is absolutely necessary in order to be sure that these effects will not affect the realphenomenon. But even in the investigations we re this precaution was taken many of the results showed such a spread that conclusions could not be drawn with great certainty.
E. g. the a. c. measurements ofRocho w [120] with bi-concave specimens of flint glass exhibited a spread of by more than a factor 2 : He found (peak) values between 2.1 and 5.2 MV / cm. His conclusion that up to 90°C the breakdown strength of flint glass is independent of temperature was therefore rather optimistic.
Likewise the measurements of In ge and Wal th e r with glass bulbs showèd a considerable spread ~81, 82] .. Nevertheless the different characteristics ofthermal and intrinsic breakdown could be distinghuished. In the light ofthe results presented in this thesis, however, it is doubtful whether the rather low value of about
2 MV / cm they f ound for "Duranglas" and "Russiches Geräteglas" indeed represents the intrinsic breakdown strength of these kinds of glass (cf. section UI. 2.6).
TheworkofMoon andNorcross[104,105] , partly with glass bulbs, partly with flat plates surrounded by semi-conducting liquids, was critü.edby Inge andWalther [88], whoquestioned that the results would give rise to the supposition of the existence of an intermediate region between thermal and intrinsic breakdown.
In fact this work ~oo exhibited such a scatter that an exact decision about the nature of the temperature dependence of the breakdown *) Cf. also the considerations about this problem in the monographs of·
8 1-2-2
strength of the investigated glasses was riot justified.
The existence of spread in results of breakdown measurements with glass,even when recessed or bulb- shaped specimens were used in order to avoid edg~ effects, is- according to We r n er [141'J-likely to be ascribed for a good deal to an insufficient adherence of the electrode material to the surfaces of the specimens. In particular the fact that spread was observed with .mercury elec-trodes (R 0 c ho w ; M 0 0 n and Nor c ros s) supports this
suppo-sition. We may refer to section Il. 1. 7, where it is demonstrated that, provided the stock material is sufficiently homogeneous, it is possible to avoid spread if a perfect adherence' of the electrode mate rial is ensured.
In contrast to thermal breakdown an acceptable explanation of the mechanism of intrinsic breakdown accounting for the different characteristics was not yet given. It is of no use to give:a dis-cussion of the different attempts that have been undertaken before about 1930. As will appear in the next section it was mainly V 0 n Hip pel who gathered evidence in favour of the conception
that intrinsic breakdown .was an electronic phenomenon. The
previous theories - such as R 0 ~ 0 w ski' s "elektrostatische
Zerreissung" [122, 123L J 0 ff é' s'collision-ionizationby positiv
ions"[91], Rogowski's.and Horowitz's 'd-ischargesinsub-,
mi'O-roscopic cracks" [123][75] - were unable to account for the whole of the characteristic phenomena.
I. 2.2. Review of theories concerrliri the mechanism of intrinsic break-down. About 1930 Rogowski 125 as weIl as Von Hippel 661, recognizing the characteristics of intrinsic breakdown collected owing to the investigations of the preceding years, put forward the interpretation that appeared to be fruitful in the future. They stated that the phenomena could only be explained bythe :assumption that free electrons, accelerated bl the field, multiplicate by collision-ionization into avalanches ). In particular the partial breakdowns in single crystals of rock salt, oriented along crystallo-graphic directions and depending on the pola,rity of the point-electrode , which were observed by In ge' and Wal th e r using pulse voltages ofvery short duration and a point-to-plane electrode arrangement [84,85] formed strong support for this view. Further experimental evidence of this kind, also in homogeneous fields, was gathered by Von Hippel [66], Lass [100] andbylnge and Wal th er [86] . The latter tried however to maintain the theory of Jo f f é [89] . As a conclusive experimental proof V 0 n Hip pel
adduced the fact that copper-ions, diffused within an alkali-halide crystal, become visible as a result of breakdown [70] .
Meanwhile the modern theoretical treatment of the problem of
intrinsicbreakdown incrystals begins with Von Hippel[16~,69,
17] . He realized that the possibility of ionization by collision and the formation of electron-avalanches are determined by the fact that the energy transfer frorp accelerated free electrons to the lattice vibrations does not steadily increase with increasing velocity of the electrons. Above a certain value of the kinetic energy,
1-2-2 9 mostly lower than the ionization energy, the probability of energy transfer decreases with increasing electron energy. So if the field is sufficiently high, free electrons surpassing this region of "maximum friction" will be accelerated with ever increasing ease, up till they reach the ionization level. Then electron-avalanches wiU be formed leading to breakdown.
The first applications ofthe wave-mechanisms ofthe solid state of Bloch [1] and Brillouin [2,3] to thebreakdownproblemdate from Zener [36], Frö,hlich [7,8] and Seeger and Teller
[29].Fröhlich aswellasSeeger andTeller gave a first wave-mechanical treatment of the ionization by collision in ionic crystals; Zener introduced anew element in thetheory, as he recognized that the transition of electrons from the valence band into the conduction band is possible by a sort of tunnel- effect. This internal field-emission, which is quite analogous to the field emission from a free metal surface under the action of a st rong electric field, forms another possible cause of breakdown and it remained to be examined whether in a given case this eff~ct or impact-ionization will be the real cause of intrinsic breakdpwn.
In view of the very complicated nature of the problem ;.Jt is not surprising that between the different authors, who tried go give a further development of the theory, a vivid discussion broke out about the physical principles, the right way of approximation as weU as about the breakdown criterion. This discussion has been continued ~p, till recent years: Since the au thor does not presume on being competent in this fi~ld, he wil! refer here to the Encyclopedia-article of Fr a n z >i). This is a survey ofthe develop-ment of the ionization theory and of the theory of internal field-emission with reference to the work of the different authors who have contribut~d to this development [4 - 36
J
.
'IFranz also gives asummary ofthe present state ofthe theory. He calculates the dependences on field strength of the. mean probability for ionization by col!ision and of the probability for field-emission from the valence band as wel! as from impêrfection levels. These appear to be rather complicated functiohs of the parameters of the crystal considered, in particular the ionization energy and the energy difference between valence band and con-duction band. For the different possible cases sets of formula are derived determining the relation between the critical field strength necessary for breakdown, the formative time lag, specimen thickness, temperature and the crystal parameters. As to the alkali-halides, which show rather low breakdown strengths (about 106 V/cm or less), internal field-emissiondoes notplay apart; for, in view of the fact that the ionization energies of these materials amount to ti to 10 eV, this: effect alone would lead to field strengths of the order of 107 V/cm. The same wil! be the case for most dielectric materials.
The applicability of band-structure considerations is restricted to the region of low temperatures. The electrons are treated as subinitted only to the external fieldand to the forces originating from the periodic potential field of the crystal lattice and are
10 1-2-2
assumed not to interact with one another.Some: qualitative features.
of the low-temperature avalanche breakdown theory will be remarked up on below.
With risingtemperature, the mean free path of the free electrons within the lattice will diminish due to the increasing frequency of interaction with lattice vibrations. Consequently the rate of energy gain from the field wiU be reduced and a higher field strength wiU be necessary for the electrons to reach the ionization level. 50 in this temperature region an increaseof intrinsic breakdown strength with rising temperature may be expected*). The same effect, viz. a diminution of the mean free path, is caused byan increase of the number of disturbances of the ideal crystal structure. Hence an increase of the number of lattice defects as weU as admixture of foreign atoms wiU result in a higher breakdown strength [10] .
Consequently, if amorphous substances, in particular glasses, might be considered as crystals with a very great number of imperfections**), it may be expected that the intrinsi.c electric strength of amorphous materials in the considered low temperature region wiU be higher than that of comparable crystaUine substances. Moreover , it is eviçlent that the mean free path of electrons wiU hardly be influenced by temperature, so that the effect of tem-perature on the intrinsic breakdown strength of these materials wiU be very small.
As to the formative time lag and the effect of thickness, the following simplified reasoningmay elucidate what may be expected
. on the basis of the avalanche theory.
The theory predicts a certain minimum field strength Et"
necessary for breakdown. Now it may be assumed that at this field strength the formation of avalanches of a certain minimum size
{no electrons) is necessary in order that disruption occurs. These avalanches require a certain formative length 10' If the thickness of the test specimen is greater than this length it is evident that breakdQwn will take place as soon as the field strength reaches the value independent of the specimen thickness. On the other hand, if the specimen thickness is less than 10, avalanches of magnitude no
can be formed provided the field strength is greater than E*.
So, it may be expected th at beyond a certain specimen thick-ness the intrinsic electric strengthof dielectrics is independent of thickness, whereas below this thickness the electric strength increases with decreasing thickness. Since now the energy loss per unit length of accelerated free electrons in ideal crystals is less than in imperfect crystals or amorphous dielectrics, it is evident that avalanches wiU grow easier in the more perfect crystals, so that for these crystals the intrinsic breakdown strength wiU remain independent of thickness down to smaller thicknesses than for comparable amorphous substances.
Whitehead[147]estimated that the average time tJfor a free electron to reach the ionization energy ] and to create another free electron tbr. collision-ionization amounts to at most 10-10 sec. (tJ = toe oïTwhere to is the time to accelerate an electron which
.mal<;esnocollisions up to theenergyJandTis theaverage time *) The increase of the resistivity of metals with temperature arises from
the same effect.
11
interval between successive conisions). The formation time lag for
an avalanche of no electrons (see above) thenamounts to tE
=
kotj'where no .= 2ko. It may be supposed with certainty that ko does not
surpass 100, so that the formative time lag amounts to at most 10-8
sec, but likely win be much less*). This implies that when intrinsic breakdown measurements are done with impulse voltages of different shapes, the breakdown strength win be independent of the steepness of the voltage wave front down to front times of about 10-7 sec at least.
The above considerations fail when the electrons become so
numerous that interactions cannot be neglected. Fr ö h l i c h [12}
has given a theory of intrinsic breakdown of imperfect crystals and amorphous substances particularly at such high temperatures th at the electrons in the imperfection levels, intermediate between the valence band and the conduction band, exchange energy with each other and with the electrons in the conduction band more rapidly thanwitheitherthefield or the latticevibrations. In this case these electrons can be treáted as to form a kind of "electron gas". When an extemal electric field is applied, the transfer of energy to this ?ras by the acceleration of the free electrons win re sult iri an 'electron temperature" exceeding that of the lattice. The electron temperature will rise to such an extent that the energy transfer
.from the electron gas towards the crystal lattice balances the
energy gain from the field. Fr ö h l i c h showedthat the energy loss
of the electrons rises less and less rapidly with increasing electron témperature, whereas on the other hand the energy gained rom
the field rises more and more rapidly with rising electron
fem-perature. Above a certain maximum field strength E m (breakdown
strength) an equilibrium between gain and loss is no longer possible: fig. 1. 2.
*) According to Se i t z [31] the value of n o ' the minimum number of free electrons in an avalanche capable to cause disruption for a field strength of ab out 106V/cm, amounts to about 1012 =
240 ; thus ko is certainly smaller than 100.
12 1-2-2 The situation is somewhat analogUus to .thát ofthermal breakdown (cf. fig. 1.1): Fröhlich's high-temperature theoryalso predicts an exponential decrease of breakdown strength with
in-creasing temperature. This is caused by the fact that with rising t.emperature a growing number of electrons are liberated by thermal exitation from the imperfection levels. In the latter case however the primary cause of the instability is of electrical nature: when thecritical field strength "L'm is exceeded, the distribution function of the electrons becomes unstable owing to 1:he fact that the electrons gain more energy from the field than they can transfer to the lattice. Thermal breakdown, on the contrary, is caused by pure thermal effects; the progressive increase of joule heat due to a - mostly exponential - increase of the electrical conductivity with rising temperature cannot be balanced by a sufficiently rapid heat con-duction towards the medium surrounding tl1e dielectric. As we have seen in the pr.eceding section, the time lags of thermal breakdown are of the order of thermal relaxation tiIJ:?,es, viz. seconds or minutes. As to the delay times of the high-temperature intrinsic breakdown according to Fr ö h 1 ic h, Sim ps 0 n [32] deduced an
expression for the formative time lag as a function of overvoltage. With the aid of this expression Whi t e h e a d [147] estimated that for soda-lime glass at room temperature the time for breakdown for an overvoltage of 0.50/0 should lie between 5xl0-10 and 5x10-12
sec.
lt is. evident that in view of the great difference in time lags it will be ràther easy to distinghuish between thermal breakdown and high-temperature intrinsic breakdown according to F röh lic h.
In both cases the breakdown strength of amorphous dielectrics wil! decrease rather rapidly with rising temperature. How:~ver, thermal breakdown shows a characteristic dependence on voltage duration which is absent when the breakdown is intrinsic.
Se i t z [31] has pointed out that breakdown due to electron avalanches in the low-temperature region wiU be subjected to statistical fluctuations inherent in phenomena where elementary particles play a part. These fluctuations give rise to a certain spread in breakdown strength measured with rapid impulse voltages and to a statistical time delay in addition to the formative time lag mentioned above. The generation o~ an avalanche may be retarded owing to lack af sufficient primary electrons. If per'
second vo primary electrons are supplied within the specimen, the statistical time lag wil! be cif the order of 1/0-~ sec. On ' the other
hand if the breakdown can be described as a coUective mechanism e.g. theinstabilityof the "electron gas"accordingto Fröhlich' s high-temperature theory for amorphous solids, a statistical time lag does not occur and the only delaytime is formed bythe build-up time of the instability of the electron gas.
We also mention here the effect, observed by St ark and Garton [131] , who supposed that the breakdown ofpolyethylene above about 600C is caused byan electro-mechanical effect. These
authors assumed that for very high field strengths the strong attractive farces acting on theelectrodes may compress the material and' thus cause breakdown as a result of the mate rial being squeezed from between the electrodes. This effect also is
1-2-3 15 [84,85, 86].The latterphenomenon was also observed by L as s [100].
As we mentioned previously, the fact that oriented breakdown depended on the polarity of the point electrode in experiments with point-to-plane electrodes, was regarded byVon Hippel [66, 67] as a st rong support in favour of his views concerning the electronic nature of intrinsic breakdown. In the foUowing years V 0 n Hip pel developed his theoretical considerations and tried to confirm them experimentaUy [68, 69] . A first summary was given in 1935 [17]. His experiments showed, in accordance with the electronic theory'*) that the electric strengths of the alkali-halides decreased,with increasing lattice constant,viz. from ~.IMV/cm for LiF to 0.5 MV/cm
for RbJ.
Later, Buehl and Von Hippel [43J, Austen arid Whitehead [39] Von Hippel and Maurer f721 and Von Hip pel and Alg e r [74] published meásurements of the temperatu-re dependence of the btemperatu-reakdown sttemperatu-rengths of alkali - halides, mainly carried out with d. c. voltage. In contract with I n ge and Walt her it appeared that at lower temperatures the breakdown stI'ength increased with increasing temperature - in accordance· with avalanches theories [17
J
'
(7, 8] - then, however, traversed a maximum and feU rather steeply towards higher temperatures. However, as is seen from fig. I. 3, the agreement between the results of different investigations for one and the same substance was far from satisfactory. Especially the resultsof V 0 n Hip pel and Alg e rare striking by the fact that the temperature of the maximum was 1000C higher. At the same time said investigations Clearly showed that the results may beinfluenced by a number of secondary effects connected with the method of preparation and eventual special treatments ofthe specimens, the type of electrodes used etc. In most cases the.reproducibilitywas rather bad: in some cases a maximum spread of about 1.5 was found at room temperature. In the light of the above it is obvious that at that time a comparison of theoreticaUy calculated absolute values of the electric strengths of the alkali-halides with experimental results was rather premature. All that could be said was that the dependence on tem-perature predicted by the avalanche .. theory is in reasonably good qualitative agreement with' the experhnental results in a region below about 400 oK. In fig. I. 3 the theoretical values for KBr according to Fr.ö hl ic h 's avalanche theory are indicated by a dashed line. It may be stressed that these values were derived merely with the aid of known crystal parameters and without any arbitrary constants in the formulae.Meanwhile Fr ö h l i c h dev~loped his theory of intrinsic break-down in the high-temperature region [12] in order to be able to account for the decrease of breakdown strength at higher
16 f·i 1I cm
'
.
,
)
r
I
"" ~<)'"
~ ~8~---~---~----~~--~~~---~----~ ;;; <: ~ Cl Cl .", « "-' Cl: Ol1
0.6I
0.4 o 8UEHL ~n v.HIPPEL 1939 • v.HIPPEL en MAURER 1941 0.21 -· -- - - 1 - - - - -- - - ,.HIPPEL en ALGER 1949 x AIJSTEN en WHITEHEAD 1940 ---AVALANCHE THEORY } FRÖHLlCH . ---AMORPHOUS THEORY ! - - - .. ~ fEHPERATURE 1-2- 3Fig. 1. 3 _ The dependenee on temperature of the breakdown strength of KBr found by different experimenters compared with the predictions
of Fr ö h 1 i eh' s theories (the figure has been taken from
KeIler [97].
tures. For KBr the theoretical curve has also been given in fig.!. 3, but here we may bear in mind that the absolute values were adapted to the experimental results by disposing of arbitrary constants. The width of the energy region b. V immediately below the conduction band where electrons are trapped in closely spaced imperfection levels can be calculated by using the experimentally determined temperature coefficient. The fact, however, that in this way too small values were found for the ground states of electron traps due to usual defects in alkali-halides - Calderwood and Cooper [46] found 0.12 eV and 0.072 eV for NaCI and KCI respectively, fig. 1.3 yields O. 16 eV for KBr - may give rise to some doubt whether this theory is applicable'~) and if not possibly above the transition temperature real thermal breakdown gradually begins to play a part.
*) For this re as on 0' D lil' Y er [26, 26a] proposed very recently a modification of the "amorphous " theory_
1-2-3 17
In favour ofthis supposition it may be quoted that V 0 n Hip pel
and Alg e r found a dependenee on the rise time of the voltage in the high-temperature region. With voltage pulses rising to break-down in 10-6 sec the breakdown strength of KBr crystals showed
no transition temperature and continued to increase with rising temperature up to 3600C. With impulses of longer duration ~ transition to a decrease exists at about 2200C, the curves for 10-4 sec, 10-3 sec and for d. c. faillng increasingly steeper above this temperature as is shown in fig. I. 4. It may be remarked thatthese
Hvlcm o_~ r - - - - r - - - - r - - - - r - - - - r - - - - r - - - - , 0.21-- --1---l---lf---lf--- -If--"._-I and 60-OL-_ _ _ L -_ _ ~~ _ _ ~~ _ _ ~~ _ _ ~~ _ _ ~ - 200 -100 0 100 200 JOO .oo·e _ TEMPERATURE
Fig. I. 4. The dependenee on temperature of the breakdown strength ofKBr for different voltage rise times, according to V 0 n Hip pel and
Alger [74].
results are in disagreement with the supposed existence of a region of amorphous breakdown according to the ideas of Fr ö h 1 ic h [12], for as we have seen in the preceding section the formative time lag of this type of intrinsic breakdown is so small that it cannot possibly account for the great difference between the results obtained with the given different rates of rise of the voltage. In fact in the regionabove 2200C there is a close analogy to the results of the measurements on glasses presented in this thesis (cf. chapter lIl). As will be seen we interpret these results as to be caused by the fact that ionic conductivity begins to play a part, resulting in space charge distortion ofthe field and at higher temperature -thermal breakdown, which effects are the more dominant the longer the rise time of the voltage.
Indeed we are in agreement with V 0 n Hip pel and Alg ~ r in
the belief that the increasing reduction of the breakdown strength of KBr with increasing temperature and with increasing impulse duration could be attributed to migration of positive ions which are mobilized with increasing temperature to form a positive space charge and raise the field strength in front of the cathode. With increasing transient speed the positive space charge has less and
18 1-2-3 less time to develop, for the shortest impulses used (10-§ sec)
its influence being negligible a,nd the real avalanche breakdown strength is found also at high temperatures.
The difference's in breakdown strength below the transition temperature (fig. I. 4) were ascribed by V 0 n Hip pel and A I g e r
to the formation of a negative space charge owing to field emission. of electrons from the cathode. By supposing the electron emission to require a formative period, ,it is argued by the authors that again the fastest transients showed the highe st breakdown strength. However, it is difficult to see why in this temperature region the breakdown strength measured with d. c. could be tound to lield higher values than wh en using impulses of 10-~ and 10- , sec duration. We wil! suppose the differencies to be not essential and to lie within the limits of spread, which was rather great at lower temperatures (see above).
Among other substances P les sn e r [113] studied the'breakdown of very thin evaporated layers of NaF and KBr and found that the electric strength measured with impulses of 10-4, sec duration was
a factor 2 to 3 higherthanfor 10-sec pulses at room temperature. Probably these results may'not be compared with those of V 0 n
Hip pel and A I ge r, because the specimens were certainly not monoc rystalline.
In contrast to the above, 'C a I der w 0 0 d and C 0 0 per [46] ,
investigating the effect of temperature on the electric strength' of NaCI and KCI crystals, did not find a difference between results for d. c. and for standard 1/50 /-l,sec pulses. In these experiments a number of subsequent pulses of increasing magnitude but with alternating polarity were applied until breakdown occurred on the crest of the wave. This procedure was chosen in an attempt to avoid space charge formatic;m. Within the limits of spread the authors found 'no effect of voltage duration up to about 1500C and both
sub-stances showed a transition temperature of about 500C, above
which Fröhlich IS high-temperature theory was assumed to
apply.
These authors also started an extensive research into the possible causes of spread in measurements of alkali-halide crystals [44~ 45] as experienced by Von Hippel and Alger. They showed by means of statistical experiments that an increase of breakdown strength was caused by the presence of accidental or artificial mechanical stresses in the specimens*), that careful annealing by heating the crystals slightly below their melting points reduced the scatter byeliminat.ing higher breakdown values, and that the mechanicalpressures developed between the electrodes by the mere application of high electrical stress on alkali-halirle specimens mayalso influence the breakdown strength 149, 50]. These experiments seem to support the suggestion that for alkali-halides the significant value of electric strength lies amongst the
,lower values and ,is not the maximum value.
V 0 n Hip pel [17] studied tlie dielectric strength of mixed
crystals of KCI and RbCI and found that it was higher than those of the pure components, The temperature dependence of NaCl
1-2-3 19
crystals with admixture of AgCI was investigated by V 0 n Hip pel
and Lee [731. At low temperatures the breakdown strengths of pure NaCI and of mixed crystals increased with rising temperature, the characteristics having about the 'same slope; increasing silver content displaced the 'curves to higher values. The higher the silver concentration the sooner the dielectric strength reached a maximum and the steeper the negative slope hereafter.U has been pointed out by Fr ö h I ic h [11] that thls behaviour is in general accordance with the predictions of hls avalanche theory [10] (cf. the preceding section). In the same paper V 0 n Hip pel and Lee made an
attempt to explain the drop of the breakdown strength beyond the maximum on the basis ofthe avalanche theory. They assumed that though the motion of electrons in ionic crystals is impeded by temperature vibration disordering the lattice structure, at higher temperatures the number of electrons that will be liberated fr om traps, especially formed by the foreign silver atoms in the NaCl crystal, may increase at such a rate that breakdown bec'Jmes facilitated. Fr ö h l i c hlS hlgh-temperature theory [12] accounts for the same effe-èt.
Very few measurements have been done about formative length and time lag of avalanches in alkali-halide crystals. The experi-m'ents of Ryu and Kawamura [126] showed that the electric strength of KCI crystals at room temperature is indepenrlent of specimen thickness down to about 10 IJ Since the preparation of still thinner monocrystalline specimens of these mechanically poor materials seems to become practically impossible, a check,
whether the thlckness effect found by PI e s sn e r [113] for evaporated films of 10-5 to 10-4 cm exists also for monocrystals,
cannot be expected to be realized. U may be mentioned that for mica [39] [126] and aluminiumoxide films [102] an increase of breakdown strength with decreasing specimen thickness was found iildicating,that the formative length may be of the order of 10-5 cm,
perhaps 10-4 cm. From the experiments of Inge and Walther
[85] and of Kawamura, Ohkura and Kikuchi [93J , who used impulses of very short durations - down to 3 x 10-8 sec - it
may, be concluded that both the formative and the statistical time lagsarevery short, likelylessthan 10-7 sec.The results of recent
investigations of Co 0 per and G ros sar t [51] ; who applied
impulses with a - rather long - rise time of 10-6 sec, seem to be
somewhat less reliable.
A discus sion of the investigations about the orientation of break-down paths in alkali-halide crystals will not be given here. As we saw in the preceding section, the experimental fact, that break-down in inhomogeneous fields in mono-crystals proceeds along preferential crystallographic directions, was the starting point of the modern views concerning the electronic nature of intrinsic electric breakdown. The explanation of all observed phenomena is based upon the conception of impact-ionization. Comprehensive investigations of Davisson ,[53, 54]and Caspari [47] showed that with short impulse voltages, electronic breakdown occurs up to. more than 3000C, in accordance with the experiences of V 0 n
Hippel and Alger cited above [74].
20 1-2- '3
the conclusion seems to be justified that indeed at low temperatures
(:li~lectric breakdown is caused by avalanche formation owing to impact-ionization. lIowever, due tO.the fact that it is practically impossible to avoid a rather great scatter caused by irreproducible mechanical effects, it can hardly be hoped that sufficiently reliable values of the different alkali-halides wUI become avaUable for a quantitative comparison with theoretically predicted values. In any case the general trend of the phenomena is undeniable that predicted by the avalanche theory, although there are fairly great differences between the results of different investigators. On the other hand there is some doubt about the applicability of Fr ö h 1 ic h ' s high-temperature theory to alkali-halides in the high-high-temperature region. More systematic experiments are needed, especially con-cerning the effect of voltage duration, in order to be able to clude with certainty if this theory does apply under certain con-ditions and where iönic mobility begins to play a part.
2. Glasses and quar tz. Contrary to the situation for the alkali -halides, which as we saw we re the object of rather extensive investigations aimed at finding evidence for the intrinsic breakdown theories, very few and rather fragmentary investigations have been devoted to the breakdown of glass in the years after about 1930. We agree with the statement of'W hit e h e a d [147] that a great deal of the work before that time was inconsistent and uncertain owing to the factO
that essential test conditions we re not mentioned. In those cases where intrinsic breakdownstrengths of the investigated glasses·:were stated to be independent of temperature, the values were all about
3 to 4 MV/ cm [120] [78, 81, 82, 88] [104, 105] [110]. In some of these investi!bations an independence of temperature was quoted up to 600 to 100 C.
In contrastto theseresults, Von Hippel andMaurer [72], investigating soda-lime glass with d. c. voltage between liquid air temperature and 130°C, found no range in which the electric strength ~as independent of temperature. Between -1900C and about -60°C disrupti ve breakdown was observed with a slight decrease of breakdown strength from 5. 0 to 4. 5 MV / cm. Above -60o C a steep decrease with increasing temperature occurred: at room temperature a value of about 0.9 MV / cm was found. In this region thermal breakdown was mentioned to be the cause of failure since it 'was preceded by a creeping increase of the current at constant voltage. It is therefore rather curious that Fr ö h 1 ic h cited these results as giving experimental evidence for his high-temperature theory [12] . However, as we have pointed out in the preceding section, since the temperature dependences of thermal breakdown and of high-temperature intrinsic breakdown are alike, it is impossible to distinguish between them if no other charac-teristics, e. g. the dependence on voltage duration, are considered simultaneously. Nevertheless the results of V 0 n Hip pel and
M a ure r showed that within a glass with a rather good ionic con-ductivity thermal breakdown can occur under homogeneous d. c. stress down to' temperatures far below OOC.
The d. c. measurements, made at room temperature, by
A us ten and Wh i te h e a d {39
J
on flat specimens of a certain lead glass in an immersion liquid yielded about 5 MV / cm as mean value.1-2- 3 21
The ionic conductivity of this glass, containing no sodium, was certainly much lower than that of the glass of V 0 n Hip pel and
M a ure r. The rather great spread in the results could be an indication that discharges in the am bi ent medium we re not prevented, so that little value can be attached to such a figure.
Measurements with short impulse voltages were made by Lehmhaus [101] and Standring [130], but also only at room temperature. L e h m h a us studied the influence of the steepness of the wave front upon the electric strength of cover glass and found the breakdown strength to be cOI}stant about 6 MV / cm -between some J.lsec and about 10-1. sec; below this value an in-crease with rising steepness set on suggesting ihtrinsic breakdown with a formative time delay of at most ab out 10-7 sec. The results of St a n d ring, who used standard 1/50 IJsec surges, are hardly worth mentioning as his glass obviously showed macroscopic defects. The low values - e. g. for "pyrex" glass an ave rage value of 1. 7 MV / cm was found - and the great scatter - up to
400;0-render these results suspect. Noteworthy is the use of distilled water as an immersion medium for flat specimens by both authors:
Stand ring obtained on mica the highe st electric strength ( 15 MV / cm) hitherto observed.
G 1 ase r [58] investigated the electrical conductivity and break-down strength of very thin glass foils «4t) of "Gunde lach Apparate-glas GC 29" with self-healing evaporated metal electrodes. At 230C
this glass showed a d. c. breakdown strength of 3. 7 MV / cm, at -1500C a value of 6.8 MV/ cm was found. Although the author {mentioned his values to be independent of specimen thickness down to O. 07 IJ , the breakdown at room temperature can certainly not be expected to have been "rein-elektrisch" as the author stated. The experiments of Von Hippel and Maurer showed that thermal breakdown may occur at temperatures far below 800
e
which temperature was mentioned by G 1 ase r to be the lower limit of thermal breakdown,As we see, all investigations cited above give merely incidental information about the breakdown of a certain kind of glass. Only the work of Von Hippel and Maurer 1:-72] gives some insight as to the different mechanisms of breakdown. In this connecti0r.
their meoasurements of the breakdown strengths of quartz and silica glass as a function of temperature are of great interest. The authors found th at the electric strength of crystalline quartz rises with increasing temperature, from almost 4 MV / cm at -800C up to ab out 7 MV / cm at 700C. The breakdown strength of
silica glass at -800
e
is about twice that of quartz, viz. 7 MV / cm,and it remains practically independent of temperature up to about 300C, where a steep fall with rising temperature sets in, ~o that
at 700
e
quartz on its turn is twice as st rong as silica glass ). Forthe low temperature region this picture is quite in accordance with the predictions of the avalanche theory. As we have discussed in the preceding section, it may be expected that the intrinsic electric strength of an amorphous material in this region will be higher
*) Unpublished d. c. measurements of KeIl er on sillca glass are in good _ agreement with these results. Cf. also the note on page 29..
,22 1-2-3
than that of a comparable crystalline substance. Moreover we saw that the intrinsic strength of a crystal will increase with rising temperature but that the effect of temperature will bE: very small for amorphous materiais. The behaviour of quartz and silica glass is therefore in good qualitative agreement with the theory of breakdown due to impact-ionization avalanches. Without further study it can not be decided whether the decrease of the breakdown strength of silica glass beyond 300C can be explained in terms of
Fr ö h l i c hlS high-temperature theory for amorphous substances or that thermal breakdown, which V 0 n Hip pel and M a ure r
found in soda-lime glass to be the cause ofthe negative slope, begins to play" ,.d. part. It may be regretted that these authors have restricted themselves to the use of d. c. voltages only.
Considering the above mentioned results we' may doubt if actually intrinsic breakdown strengths of glasses have been observed hitherto. We again agree with Whitehead [147] that the value of 7 MV / cm found by V 0 n Hip pel and M a ure r for quartz and
silica glass would suggest still higher values for glass. The modifying ions, non-bridging oxygen ions and network-formers other than silicon *) provide additional scattering centers for free electrons in comparison with fu~ed silica, so that higher field strengths would be. necessary in order to accelerate them up to the ionization level. In this connection we may already refer to the results of our own measurements on different kinds of glass (chapter lIl), which indeed confïrm the expectation expressed here.
A really extensive research into all factors possibly influencing the dielectric breakdown of glass was started by K e 11 er [94,95, 96] . Thuringian glass - a soda -lime glass with some percent A1203 - was used for the experiments. In order to avoid edge discharges and field concentrations bulb-shaped specimens were blown from tubes. Several types of electrodes were used: mercury, aqueous solutions of electrolytes, chemically deposited silver layers and thin aluminimum layers evaporated in high vacuum. In the first tests [94] the voltage was increased at such a rate that breakdown occurred after about half a minute. A dependence on temperature, in general agreement with the results of V 0 n Hip pel
and M a ure r, was found. The results were affected by the choice of the kind of electrodes, this leading to the conclusion, again in accordance with V 0 n Hip pel and M a ure r, that the specimens
were heated by the pre-breakdown ion current. In order to avoid these thermal effects measurenients with impulse voltages we re made [95] . It appeared that the breakdown strength of Thuringian glass at room temperature increased with decreasing voltage duration down to the shortest impulses used (about 10 Jolsec). Though very high values, up to 9 MV/ cm, were found, it was not possible, due to the large scatter especially at low temperatures, to conclude whether the intrinsic breakdown strength has actually been measured. However these measurements' provide already a first confirmation with regard to the above expectation.
Breakdown measurements on very 'thin layers of glass have been done by Alexandrow and Joffé [37] - down to 0.7 IJ. - and by G I ase r [58] down to 0.07 Jol . For the given test conditions
