Vol. XVII, 1 REVISTA MEXICANA DE FISICA

ABSORPTION AND REABSORPTION CURRENTS IN NaCI

SINGLE CRYSTALS

H.G. R iveros * and L. RosasInstituto de Física, Universidad Nacional de México

(Recibido: 23 enero 1968)

AIlSTRACT

1968

'[h~ presen/ paper at/emp/s to ddl'rminl' the mechanism responsib/l' IQTthe decay 01 the e/~ctric CUTT~ntin a/kali ha/Mes under constant e/ectric lie/d,

taking into account /he /wo mechanisms proposed previous/y: dipole-QTientation

and accumulation 01 space eharge. '[he WQTkwas done wi/b oysta/s 01 NaCl.

some 01 thf'm u'itb Jtn ++ impuri/ies. R~ctangulOT vo/tage pulses were app/ied lo

cr)'sta/s IQTdillerent duration (JOs -3600s) and at dillerent tf'mpera/uus (J000 c-2000 e). with /he lo//owing resu//s: a) /he magnitude 01 diseharge current and

its decay ro/e depends 011 tbe pU/Sf' dura/ion, b) the diseharge current do no/

obe)' Ohm 's law, e) tbe decay ol/he diseharge eurrent is s/CAl'er a/ higher tempera.

/[4rt's, d) the t'xp/anation ol/he lime deeay 01 the curren/ requires bo/h dipo/e-

Facultad de Ciencias, Universidad Nocionol de México.

33

ori~Tztation and spoce-ciJarge occumulatiOTl. Consequently. the conduc/ivity must

he measurf'd a/ter the dípole-orif'ntation current transi~nt and he/ore the accumu-

latiofl o/ space charge.

RESU.lfE.V

En 1'1pr¡os¡ont¡otrahajo se trata d~ d¡oferminar ~l m~canismo r("sponsahl¡o del

decaimiento dI' la corriente f'léctrica ¡onel tiempo (~n halogenuro alcal¡'w a campo

eléctrico constante), tomando como hase los do.'; mecaTzismos propuestos para su

explicación: orieTztacióTl de dipolos y acumulación dI' carga ~spacial. Para e/l'c.

tuar este trahajo, a varios cristales dl' NaCI, algunos dI' ellos con impurezas de

Mn++. SI' les aplicaron pulsos rec/angularl's df' voltajl' durante tiempos diluentes

(J0-3600s~g) ya distintas t~mperaturas (lOO-200° e) obteniéndose como resul.

todos: a) la magnitud de la corriente de descarga y la rapidf'z de d~caimien/o de.

/Jenden dI' 1 ti¡ompo de do/ación del pulso, b) las corrien/~s dí' descarga no obede.

cen la ley de Ohm. c) la rapidez de decaimiento de la corrien/~ de descarga dismi.

nuye conforme aum('Tlta la temperatura, d) el decaimiento de la corrierzt(' ~n el

tiempo se debe a la orientación de dipolos yola acumulación de carga espacial.

En consecuencia. la conductividad Sf' dl'bf' medir despues del traTlSitorio dl' orif'n-

tación dipolar y antes de qu{' se produzca la acumulación d{' carga l'spacial.

INTRODUCTION

It hos long been known thot the conductivity in insulotors ond particulorly

in olkoli holides is time dependent1•2• The experiments to be described were per-

formed in on ottempt to determine the mechonism responsib/e for the decoy with

time of the current which flows upon opplicotion of e steady direct voltage. Two

mechcnisms hove been proposed previous/y: (a) orientotion of dipolor imper.

fections3•4 I ond (b) cccumulotion of space chorge2.

When the current decay is due to the orientotion of dipolor imperfections

34

such os divolent imp•...•..ities Iinked with vaconcies, etc., the interna I electric field

is not modHied and the true ionic conductivity is obtained after sufficient time has

elapsed for the transient to die away and the current to become constant. It is

then expected that Ohm's law will be obeyed because the number of dipoles ori.

ented at time t, 11¡(t), is described by a monomolecular low5:

~ 1 - ex p {- t!T. } ],

with

I'¡E!kT « 1

where

Ti is the reloxotion time,

¡; the e lectric fie Id,

Pi the dipole moment of the dipole type j, and

Si the total number of j.type dipoles.

According to the second mechanism, o spCIce charge occumulotes at one or

both electrodes, due to the finite discharging rote of the current carriers. Thus,

the internal electric field is modified, and so the interpretotion of conductivity

meosurements is rendered difficult, except ot the instant opplying the voltoge

(t = O) when the space charge has not hod time to occumulote. In this cose devi-

otions from Ohm's low ore to be expected4•6 if observotions ore mode ot ti O, as

is normolly the case. Also the durotion of the re-obsorption current transient,

which occurs when the voltage is removed and the specimen is short circuited,

shoutd depend on the chorge tronsported during the preceding period of voltoge

opplication.

P.H. Sutter ond A.S. Nowick4 showed that the polarizotion effects in NaCI

were due to orientotion of dipolor imperfections. They define the dischorge conduc.

35

tivity as the ratio of current dens ity at an instant after the voltage has been re-

moved to the applied mean electric field. They showed that for corresponding

instants in the absorption and re-absorption transients (see Fig. 1) the conduc.

tivity and the discharge conductivity obey Ohm's law. They also found that the

current flow as a function of time during the re-absorption transient was the same

as that during the absorption transient minus the stationary current. Moreover

they found that the re-absorption current transient was independent of the applied

voltage duration provided this was such that the absorption transient could achieve

the steady va lue.

Sutter and Nowick used rectangular voltage pulses and, in general,

currents were measured in the interval extending from 20x 10-3 sto 105 aÚer

applying the voltage. The temperature range extended from 500 C to 200° C and

nomina Ily pure Harshaw crys ta Is were used.

In the present investigatior. "pure" single crystals of NaCI and single

crystals of NoCI containing the divolent impurity Mn were used. The crystols were

grown from the melt in oir by the method of CzochrolskiJ• The NoCI wos obtained

from lYrollinckrodt Chemicol Works. The crystals were cleaved into lOxlOxl mm,

plotes, ond colloidol grophite electrodes were painted on opposite 10x10 mm faces.

The sample was held in o metollic container witnout ony insulator, except thot of

the electrometer input (teflon). Rectangular volge pulses were applied for times

from 30s to 3600s in the temDerature interval from 100°C to 200°C. The experi-

ments were performed using 0408 B Fluke power supply and o 417 Keithley pico-Ommeter.

As a typicol result, Fig. 2 shows how the re.absorption currents voried in

the present experiments ofter the opplicotion of voltage pulses 011 having the sarne

amplitude but with different duration. In every case the steody current while the

voltage pulse lasted wos 10.10 A. Extrapolotion af the curves seems to shO'N

thot the initiol current (t == O) is the SOrne far 011 cases, in ogreement with Sutter

a nd Now ick 's res u lts 4; neverthe le s s, it ca n be see n that the rate of c urrent decay

c1early decreases with increase in the durotían of the voltage pulse. This abser-

vation moy be explair'!ed if o space chorge occumulotes, since o Jorger S¡::xJce

chorge needs more time for re-obsorption. In terms of dipolor orientotion only one

curve ís expected, except if the reloxotion times Ore greoter thon the pulse width.

36

In po-actice it was found irnpossible to wait until the re~obsorption current

becorne zero. Consequently it connot be said that the crystol is in e)(octly the

SOrne conditions ot the instont of applicotion of eoch of a succession of voltoge

impulses, ond it is necessory to odopt some method of normalizing the observotions.

The method adopted is illustroted by Fig. 3. This shows the dischorge current in

o crystol to which o pulse of 1000 V ornplitude wos applied for 30s (curve A). It

can be seen thot opprecioble current wos still flowing ofter 600s; ofter 630s the

voltoge pulse wos ogoin opplied for 30s. The resulting dischorge CLXrent is shONn

in curve B of Fig. 30. It can be seen thot o difference exists between the two

curves. Theyore plotted on o log-Iog base in Fig. 3b ond it is cleor thot the

relotionship between log i ond 10g t is olmost linear. Consequentlyextropolation

is relotively eosy ond corrections can be made to any discharge curve for the ef-

fects rernoining from ony previous opplicotion of voltoge (see insert in Fig. 30).

The curve A'B' in Fig. 30 is a curve obtoined by correcting curve A and curve B

by the obove method.

To enhance the eHect, Sorne of the rneosurements were mode on crystols

doped with divolent impurities. It is well known that the effect of these impurities"

is to increase the conductivity, because they increase the positive vaconcy densi-

ty, ond olso the mognitude of the dischorging current. Fig.4 shows the influence

of odd ing divo lent Mn (1 .5x 10-1~ otomic) to NoC l. The eHect of Mn impurities on

the current I during the opplication of the electric field is greater thon the effect

On the dischorge current, but the rote of current decoy is slower for the NoCI(Mn)

crystal. This result can be accounted for by the accumulotion of sJXlce chorges.

In terms of dipolar orientation the same decay rote is expected.

Fig.5 shows curves af re-absorption conductivity following the opplication

of voltage impulses of the same duration (1205) but with different amplitudes os

indicated on the curves. It can be seen t¡'ot Ohm's low is not obeyed, and also

thot the rote of current decay decreases with increase in the omplitude of the

voltage pulse. In this connection it must ~ borne in mind that the quantity of

ch(lrge transported by the absorption current increoses proportional!y with the

37

opplied field. If the chorge is occumuloting ond the volue of the dischorge current

does not ¡ncrease linearly with the applied field, then the dischorging time should

be 10nger ot higher fields. In terms of dipolor orientation only one curve is ex-

pected, beca use of the proportionolity between field and number of oriented

dipoles.

Fig.6 illustrates the influence of temperoture on the absorption ond re-

obsorption current flowing through a crystal of NoCI, with o voltoge of 1000 V

applied for 305. At ony instant in this period the obsorption current ot 1820 eexceeded the corresponding current at 92° C by o factor of 104• It can be seen

thot the rate of decay of the re-obsorption current ot 920 C greotly exceeded that

ot 1820 C, but the re-absorption current ot the latter temperoture exceeded thot ot

the lower temperatlJre by o factor between 10and 102, depending on the absorption

time. This result COnnot be accounted for in terms of dipolar orientation, beco use

this process should occur more rapidly ot higher temperature.

The experiments show that the re-absorption current transient which flows

after removing the voltage depends on the magnitude ond durotion of the applied

voltoge, on the impurity content, and the temperature.

One of the NoCI (Mn) crystol showed a decreose of 30% in conductivity

after being under 1000 V at 1550 C for 40 hours. This is in opposition to the

time-independent current expected from the dipole orientation mechonism when the

time is ver y lorge.

The experiments hove brought to Iight o smolJ but systemotic deviotion

from Ohm's low for both pure crystols ond crystals contoining Mn impurities. It

can be seen from Fig. 7 that the effect increoses with temperature.

CONCLUSIONS

The present observotions show thot the toil of the re-obsorption current

does not obey Ohm's low, that it depends on the durotion of the opplied field and

thot the decoy is slower ot higher temperotures. These effects con be occounted

for by the mechonism of spoce-chorge occumulotion. It seems evident thot both

38

mechonisms must be involved to explain the current decoy with time, ond the;r

relative importance depends on the temperoture. At low temperatures the domi~

nant term is the dipolor orientationJ ond at high temperatures, the dominant term

is the occumulotion of space chorgeó• This last conclusion is in agreement with

the results of Bucci and Rivosin KCI crystols.

Therefore the conduct;vity must be meosured ot some intermediate time,

after the dipole orientation current tronsient and before the accumulat;on of s pace

chorge, this corresponds to the knee of the curve clearly seen between 1000 C ond

200t> C. Experiments are under way to determine the best procedure for higher

temperatures. The opplied field must be high enough in order to hove o negligible

circulating current before the application of the field.

ACKNOWLEDGEMENTS

The authors wish to thank ProL R. Cooper of Manchester University

for his discussion of the work and help in the ~ep::lrotion of the manuscript, and

to the members of the Sol id Stote Group at Mexico University fer their suggestions.

REFERENCES

1. J. Curie, and P. Curie, Ann.Chim. Phys. 17, 385 (1889); lB, 203 (1889).

2. A.F. Joffé, The Physics of Crystals McGrow-Hill Book Company, Inc.,

New York (1928).

3. R.W. Dreylus, Physical Review 121,1675 (1961).

4. P.H. Suller and A.S. Nawick, J.Appl.Phys. 34,734 (1963).

5. C.A. Buccl and S.c. Riva, J.Phys.Chem.Salids 26, 363 (1965).

6. A.R. Allnatt, P.W. M. Jacobs and J.N. Maycack, J. al Chem. Phys. 43,

2526 (1965).7. J.Z. Czochralskl, Phys.Chem. 92,219 (1917) 144,131 (1925).

39

G(I) =J/Eao

-t

3<D

lT111

lT1Q

IC)-8

C)8

lT111

o

Fig.l Schemotic diogrom showing the voriation of conductivity with time underOn applied electric f¡eld Ea (the -The chorging curve"), and the cfter

effect when the field is abruptly dropped to zero (the discharging curve).After P.H. Sufter and A.S. Nowick

40

o.. -12E 10t.'

-1310

1000 volls-lO

1 : 10 amp.

NaCI (92 OC)

3600 seco1200 seco

300 seco

60 seco

30 seco

O 120 240 360 480 t sec.Fig.2 Discharge current vs. time for a síngle crystal. 1 is the current circulating

during the opplication of electric field.

41

-1010

ci.Ee

BA

a

-1110

50 200 400 600

Ae

100010010

-1010

-1110

t(sec. )

Fig. 30 and 3b Discharge currents, aher having opplied 1000 V during 3D secoCurve B was obtoined aher the application of onother pulse at the end ofcurve A. The insert shows the relationship between e, A', A, S' ond B.

42

1000 V.107 oC

300 seco

60 seco

N o C I ( P u re )-10

I=4.7xI0 A

No CI (Mnl-8

1 = 6.8 x lOA

-1210 60 120 180 240 300 360 420 480 540

t (sec.)

Fig.4 The discharge current os a function of time showing the influence of impurity

oddition (Mn) ond pulse width.

-1110

-1010

Q.

Eo

43

'- 100 volts

volts

Crystol 2'g

'0= 2 minoT = 1860 C.

0;j-10

10

- 1110

Eu,E

..c::o

-1210

-1310

10 100 1000 t ( sed

Fig.5 Typicol voriation of dischorge conductivity with time at different voltagesin NaCI (Mn).

44

-14'0

-11(j (182 'C) = 8xl0

(j(92 'C) =8x1015

60 seco

30 seco-17

10

-1510

60 seco1

E 30 secou

E-'=o

-1610

1200 seco300 seco

10 100 1000 t (sec.)

Fig.6 The dischorge conductivity as o function of time showing the influence oftemperoture and pulse width.

45

,-Eu,E

..c::o

-+-+-+-+-+_---+-+ +-+- 236 oC+

-910

-1010

-+ +-+---+--_+_+-+-+-'1--+-+ 1 8 1 ° C

+-++-+-+-~+-+-+ +--+,--- 162 ° C

+-+-+ +-+-+--+-+-+-+- 147 oC+

..•. +--+-+ +--+--+--+-+--+ - 122 oC

-1110 -+----+--+--++--+--+--++-+--+-

99 oC

-/210

10 100 1000 -1E (V cm )F ig. 7 Typica I res ults obta ined for a v. s. E lec trie fie Id. (J was meas ured cher the

opplication of the field.

46