Time lags in the breakdown of NaCl at high temperatures

J. Phys. Chem. So/ids

TIME

Pergamon Press 1970. Vol. 3 I, pp. 253 l-2537.

LAGS

Printed in Great Britain.

IN THE BREAKDOWN HIGH TEMPERATURES

OF NaCl AT

D. B. WATSON Robert Gordon’s Institute of Technology, School of Electrical Engineering, Schoolhill, Aberdeen, Scotland and W. HEYES Electrical Engineering Department, University of Salford, England (Received

29 September

1969: in revisedform

20 February

1970)

Abstract-The relationship between time lag and applied field was investigated at high temperatures for NaCl crystals by applying a single I : 8000 psec impulse to each crystal, of sufficient magnitude to cause breakdown. The observed time lag cannot be. satisfactorily explained in terms of joule heating alone and an ionic space charge mechanism is proposed. 1. INTRODUCTION

THE RELATIONSHIPbetween temperature and the electric strength of alkali halide crystals consists of two regions. At low temperatures breakdown is considered to be electronic in nature and the electric strength increases slowly as the temperature is raised, in qualitative agreement with the theories of Frohlich [ 11 and of von Hippel[2], while at high temperatures the electric strength decreases comparatively quickly. The transition temperature between these two regions is not sharply defined; it is influenced by the waveform of the applied voltage and may be completely suppressed over the temperature range investigated by using steeply rising impulse voltages, in which case the electric strength continues to rise[3-51. Also, for a wave-form the transition given voltage temperature varies widely with the type and degree of impurity content of the dielectric. Cooper, Higgin and Smith [6] found that when O-022 per cent of lead, a divalent impurity, was added to KCI the critical temperature was depressed from about 110°C to - 120°C. Monovalent impurity, however, had little effect. In view of these effects it is not surprising that complete agreement between the results of different studies is difficult to obtain. 2531

The existence of a high temperature region, where the electric strength of alkali halides decreases with rise in temperature, is predicted by Frohlich’s high temperature theory of electronic breakdown[7]. It can also be explained both in terms of impulse thermal breakdown due to the increase in ionic conductivity at high temperatures, or as a consequence of ionic space charge which enhances the internal field locally. Seeking to differentiate between electronic and thermal effects in the breakdown of NaCl and KCI, Cooper, Higgin and Smith[6] applied flat topped impulse voltages and measured the time lags to breakdown. The time lags calculated for impulse thermal breakdown ranged from I to 20 msec at 220°C whereas the measured time lags were of the order of a few microseconds, indicating that at least up to 220°C impulse thermal breakdown does not take place. The effect of divalent impurities on the transition temperature, however, showed the important role of ionic conductivity, and breakdown above the critical temperature was concluded to be conditioned by the onset of ionic space charge. At higher temperatures Heyes and Watson[S] discovered time lags of the order of milliseconds in the impulse breakdown of NaCI. The

2532

D.

variation

of time lags with

H. WA-I-SO&

applied

field was

and W.

HEYES

room temperature

before the specimens

similar to that of impulse thermal breakdown, although at the higher fields the time lags were too short to be directly explicable in terms

the furnace

of energy input alone. Thus the high tempera-

I8 hr before

ture

satisfactorily

when the temperature

the

within 3°C of the required value. A single stage impulse generator

region

explained.

has not yet The

investigation relationship field

in

was

time

high

region of NaCl

of

present

the determination

between

the

been

purpose

of the

lag and

temperature

applied

application

giving a I : 8000 +ec output

allowed

at the operating

relationship

breakdown

in order to throw further light

on the mechanisms

placed in the furnace. The specimens were

voltage

charging

was determined

about

METHOI)

The

were cleaved cubes of NaCl

2 cm side.

drilled

from

two

in-line

recesses.

opposite

A spherical

multiple

determined

faces with a twist drill leaving a gap between the two

was

was used,

voltage wave-form.

3. EXPERIMENTAL

The specimens

for

of the test voltage,

voltage

The and

by means of

sphere gaps.

leading to breakdown.

2. EXPERIMENTAL

to stand in

temperature

of each specimen

between

were

end to

psec

RESULTS

breakdown

by applying

voltage

SO per voltage

impulse

cent and

field was

a series of

impulses,

starting

I : 8000

at

about

of the expected breakdown increasing in increments of

each recess was made by hand with a dentist’s

O-5 kV. The mean value for about 6 specimens

round

at each temperature

burr

was carried

of 064 out

mm dia. This

under

operation

a microscope

which

also

shows

enabled the gap between the recesses to be reduced to 047 mm to an accuracy of + 0.005

breakdown (3). Above

mm.

experimental

To

contact

form with

silver the

electrodes

crystal

in intimate

a colloidal

silver

preparation was painted onto the surface of each recess. and this was allowed to dry at

the held 270°C

is shown in Fig. 1 which

minimum

impulse

and calculated

is quite good. The time lag to breakdown,

25 t

I

I

2Kl

300

2%

3w

Temp. , OC

Electric strength of NaCl as a function of temperature. The vertical lines indicate the range of measured values X Multiple impulse breakdown 0 Single impulse. breakdown near crest of wave. (I) Calculated impulse thermal breakdown field. Fig.

I.

breakdown

field

from the crest

of the impulse wave to the collapse of voltage,

30

I50

thermal

calculated from equation the agreement between the

400

TIME

LAGS

IN

THE

BREAKDOWN

OF

2533

NaCl

was measured to an accuracy of 0.1 psec on a IO MHz counter-timer, and its value was checked against an oscillogram of the impulse voltage wave-form at breakdown. Below 240°C only time lags of a few microseconds were measured, indicating that breakdown had occurred near the crest of the voltage wave. At 240°C some specimens registered time lags as long as 3000psec. and at higher temperatures almost all the time lags were of this order. These long time lags, together with the rapid fall in electric strength, could be considered indicative of impulse thermal breakdown. The relationship between time lag and applied field was investigated at 300 and 350°C by applying to each specimen a single 1 : 8000 psec impulse voltage large enough to cause breakdown. Most specimens broke down on the wave tail and the time lags for these are plotted against the peak value of the applied field in Fig. 2. The calculated time lag for impulse thermal breakdown is also shown for the purpose of comparison. It can be seen that as the field was increased the experimental time lags decreased far more rapidly than the calculated values. At higher fields specimens broke down near the crest of the impulse wave, and breakdown for these was considered to be electronic in nature since time lags of a few microseconds are too short for thermal breakdown. The average values of electric strength of such specimens, included in Fig. I at 300 and 35O”C, indicate that the electronic strength of NaCl continues to rise with increasing temperature when the processes leading to long time lags are inhibited. 4. DISCUSSION

The impulse thermal breakdown strength can be estimated assuming that heat loss by thermal conduction is negligible. The rate of rise of temperature is then $=~exp(-+!)~Oexp(-~)

(I)

I ,

I

6

0

I.0 F8d1

v&m

2.0 of

I”

-. field .MV/cm

applied

x ,

30

Fig. 2. Time lags for single impulse breakdown of NaCl at temperatures (a) 300°C (b) 350°C. (I) Calculated for impulse thermal breakdown; (2) Calculated Ifor space charge controlled breakdown mechanism: x Experimental values.

D. B. WATSON

2534

where Eexp

(

-f

)

is the exponentially decaying applied field, s is the specific heat per unit volume and c+,exp it- b/8) is the law relating electrical conductivity to the absolute temperature 8. If b % 0 equation (I) can be integrated to give approximately (2)

yexp(t)=y[I-exp(-+)I.

Here r, is the time required for the temperature to reach 8,. the value at breakdown, and 8, is the ambient temperature. Since heat losses have been neglected, the lowest value of E at which the temperature rises to 8, is found by putting t, + 03 in equation (2). The lowest impulse thermal breakdown field is then Emin = (&&-)1’2 8, exp ($j-).

(3)

For NaCl u. = O-5 R-r cm-’ and b = 10,000 [9][ 103; s = 2 W cm-“; and putting T = 8,000 psec the following values of Emin are obtained:

and W. HEYES

occurs in a relatively short time[l I]. It may well be that final breakdown takes place before the melting temperature is attained either due to a fall in the electronic strength at high temperatures or to the enhancement of the field by ionic space charge due to the sudden increase in ionic conductivity. Thermal run-away may not be responsible for initiating final disruption of the dielectric, although breakdown must be associated with a significant rise in lattice temperature because of the long time lag involved. At fields higher than Em,,, the impulse thermal time lag is given by

The impulse thermal time lag plotted against the peak value of applied field, in Fig. 2. was calculated using values of E,,, obtained from equation (3). At 2 MV/cm the calculated time lag is of the order of hundreds of microseconds. Such a high field should, however, give rise to electronic breakdown with time lags far too short for thermal breakdown. In fact, in the high temperature region, if break-

Temperature “C

200

225

250

275

300

325

350

E,,, (Mvlcm)

6.1

3.8

2.5

1.7

1.2

0.85

0.64

This characteristic is shown in Fig. 1. In view of the high fields required for impulse thermal breakdown at low temperatures it is most likely that below about 270°C the electric strength of NaCl when determined by applying a series of I : 8000 psec voltage impulses of slowly increasing magnitude will be electronic in nature. Above 270°C the experimental values agree quite well with those predicted by equation (3). This agreement must, however, be viewed with caution. The impulse thermal condition only requires that the temperature is raised sufficiently to produce an order of magnitude increase in the electrical conductivity and about 90 per cent of the pulse time is taken in achieving this. The further rapid rise in temperature

37.5 0.46

400 0.37.

I

down at low fields is due to thermal instability, the relation between time lag and applied field should be described by equation (4) until the field is high enough to cause electronic breakdown when a sharp discontinuity would result as the time lags drop to a few microseconds. In contrast, the experimental time lags fell continuously as the field was increased, from a few thousand microseconds at at &,, to less than one microsecond fields high enough to cause wave-crest breakdown. Unless the electrical conductivity is strongly dependent on held strength it is difficult to see how the impulse thermal breakdown theory could explain the measured time lags. It is possible that the field within the speci-

TIME

LAGS

IN THE BREAKDOWN

men is distorted by the formation of an ionic space charge if the rate at which ions are transported to the electrodes exceeds their rate of discharge. A positive space charge may thus accummulate close to the cathode because of the greatly increased mobility of positive ions at the temperatures of this investigation. The space charge therefore enhances the field in the cathode region causing electronic breakdown when the cathode field reaches some critical value. A possible type of relationship between time lag and applied field, associated with such a breakdown mechanism, may be determined by assuming that the space charge is uniformly distributed within a layer of thickness x adjacent to the cathode. If at any instant the average field throughout the specimen is E,,, the field at the cathode is El, and the field in the neutral body of the specimen is E,, then E,,d=

OF NaCl

2535

is the fraction of the total charge transported to the cathode which is not immediately discharged. Thus

. The fields E, and E2, however, vary with time due to both the build up of space charge and the exponential decay of the applied field, which has the form E,, = Eexp

(

y?

>

where E is the peak value of the applied field. Therefore

thus

E,d+(E,-E,);

(,)

where d is the distance between the anode and the cathode. When the total charge accumulated in the layer of thickness x at the cathode is q, then,

and the cathode field is

E, = E exp E,-E,=$

r

hence

6

( >

=E.v+&- 1-J

(5)

and

(6) These expressions The rate at which charge accumulates the cathode may be assumed to be:-

at

2 = qaEz where v is the electrical

conductivity

and q

show that the charge and and the cathode field rise to maximum values thereafter falling as the specimen discharges. It is now assumed that breakdown is initiated when the cathode field reaches some value EB. Two extreme cases are considered, the first being that the peak value of applied field is almost as great as EB, and the cathode

D.

2536

held rises to the breakdown short time. The lags with

equation

applied

held

B. WATSON

The

linear

is then

short time obtained

by

Iso

series

in equation (8). and

relationship

:

of Fig. 3 between

the reciprocal of applied field and the experimental time lag up to about ISOpsec has. therefore.

0

value in a very

relating

using the first two terms of the Taylor for the exponentials

and W. HEYES

/

-

E

e

=-

,/

D

the gradient

r

m=

The MV

values

Yz wr ( of

1-1.‘~

EI, 1-2

0.3

06

I/E

)hw’

cm

single impulse time lags and reciprocal of applied field at temperatures. (a) 300°C: (b) 350°C. Fig. 3. Relationship

between

respectively,

values of

2.5 MV/cm the

and

2.7 MV/cm.

term

and

E,=+E,exp

E,,, at zero time

I/T

Since

is negligible.

(

-5.

>

Hence

x E’ __=-A.! 2d EB

Thus

(9)

where

1

07

cm

m are 720 and 370psec

the corresponding

T = 8OOOpsec

1

05

l/E ) MV-’

-1’ ) T

cm-r at 300 and 350°C

lag are

04

EH and m are experimentally

(IO)

where

EA = E. exp -5

derived

(

>

.

quantities. In the second case an order of magnitude estimate

of the unknown

by considering

ratio

x/2d is obtained

the lowest applied field

Using

(

>

that will cause breakdown. The total charge is at its maximum q,,, at some time t’ where. by equating to zero the time derivative of equation (71,

Ymax

=e,,e,:EOexp

E, reaches its maximum EB at the same time then, using equation

If it is assumed that value

(5).

of

(9)

and (IO)

equation

lag t and applied field be written

E,, = E. exp - f

equations

relationship

(8)

the general

between

E exp (--r/T)

time

can now

TIME

LAGS

IN THE

The longest time lags t’ are about 3000 psec and the values of E. are 1-OMV/cm and 0.55 MV/cm at 300 and 350°C respectively. Substitution of the experimental values of m, 4, EB and T in equation (1 1) gives the relatronship between time lag and applied field shown in Fig. 2, which compares favourably with the experimental time lag distribution.

5. CONCLUSION

The time lags are not satisfactorily explained in terms of joule heating alone and the proposed ionic space charge mechanism gives results in reasonable agreement with the experimental values. It is concluded that the formation of an ionic space charge leads to breakdown in a time too short to allow the relatively large temperature rise required for impulse thermal breakdown. At the highest breakdown fields very little joule heating takes place, but at the lowest breakdown

JF’CSVd.3lNo.

II

K

BREAKDOWN

2537

OF NaCl

fields the time lags are sufficiently long to allow appreciable heating before the space charge enhanced field reaches the critical between this value, and the distinction space charge mechanism and impulse thermal breakdown becomes less marked. REFERENCES H. hoc. R. Sot. A160.230 (1937). 1. FROHLICH A. Ergebn. exakt. Naturw. 14, 2. VON HIPPEL 79(1935). A. and ALGER R. S. Phys Rev. 3 VON HIPPEL 76, I27 ( 1949). E. A. and SOROKINA L. A. 4. KONOROVA Soviet Phys. solid St. 7, I I86 ( 1965). 5. KUCHIN V. D. Rep. Akad. Sci. USSR 114, 301

( 1957). 6. COOPER

R., HIGGIN

R. M. and SMITH

Proc. phys. Sot. B76.8 17 ( 1960). 7. FROHLICH H. hoc. R. Sot. 188,493

8. HEYES 2200.572

W. and WATSON

W. A.

(1947).

D. B. Nature,

Land.

(1968).

9. SMEKAL A. Handb. Phys. 24.881 (1933). IO. HANSCOMB J. R., KAO K. C., CALDERWOOD J. H.. O’DWYER J. J. and EMTAGE P. R. hoc. phys. Sot. 88,425

(1966).

I I. O’DWYER J. J. The TheoryofDielectric Breakdown ofSolids. Oxford Universities Press, Oxford (1964).