Low temperature space charge polarization in alkali halide crystals

f Pkw. Chm.

Soiid~. lYl8. Vol. 39. pp. 21%219.

f’rrgsmon Press.

Priarcd

in Grea(B&in

LOW TEMPERATURE SPACE CHARGE POLARIZATION IN ALKALI HALIDE CRYSTALS S.

W. S.

and D. M. MJCHES Bangor, GwyneddLLS7IUT. Wales

MCKEEVERt

School of Electronic Engineering Science. U.C.N.W.. (Receioed

5 Aprii

1977: accepted

in raked

form

10 August

1977)

Abstract-Evidence is presented to indicate the presence of linear space charge polarization in single crystals of KCI and NaCI in the temperature range between liquid nitrogen temperature and 350 K. Polarization phenomena, both dipolar and space charge, were studied by means of TSPC, ITC and by the testing of Ohm’s law and the Superposition principle. The results are interpreted in terms of the formation of a linear space charge, possibly caused by the trapping of ionic charge carriers within the bulk of the material.

When a constant d.c. voltage is applied to a dielectric material at time t =O, the observed current density is seen to be time dependent; in particular, it decays from an initial value of j. at t = 0 to a final steady value of j_, at f = m (Fig. 1). Shorting of the electrodes at t = t, produces a reverse current flow, the magnitude of which is also seen to decay with time. This dielectric “after effect” has intrigued experimenters for many years since it was first observed by Hopkinson in the 1870s (see Ref.[l]). The fundamental problem has been to determine the physical mechanisms responsible for this effect and it has been to this end that most research has been carried out, p~icuiarly on the alkali halides, in the past 40-50 yr. 2BACKCROUND

space

of the main points of contention concerning the dielectric “after effect” is whether the mechanism responsible, at a given temperature, can be described by linear or non-linear equations. Dipolar polarization (atomic, electronic or orientationat) involves the microscopic displacement of bound charges, either in atoms, molecules or in the crystal lattice, under the influence of an applied electric field. The current density arising from such polari~tion is seen to be linear with the applied field. On the other hand, free charges that can migrate over macroscopic distances exist within the solid and the displacement of these charges under the influence of the applied electric field can give rise to a second type of polarization. When these charge carriers are impeded in their motion by becoming trapped in the bulk (at dislocations, for example) or because they cannot be freely discharged or replaced at the electrodes, a space charge results. If this space charge is large enough, it may result in a large scale field distortion which may appear to an outside observer as an increase in capacitance of the material and thus may be difficult to distinguish from a real rise in ~rmittivity. Much work has been directed towards the study of a

1

Fig. 1. Current transients following the application and removal of an external field.Field appliedat I = 0 and removedat t = t,. j,(t) = charge current; j,,(t) = discharge current; j_ = steady state current. charge

electrodes

One

tNow at University of Birmingham, Department Edgbaston, Birmingham 915 2TT, England.

-iI I)

caused

by the build

up of charge

at the

due to an inability of the carriers to be discharged theref2-61 with gradual progress being made until a good a~eement with theory was obtained; however, observed capitance values were lower than those predicted[7-91. A suggested source of error was in ignoring the possibility of a space charge existing within the bulk of the material, trapped there at dislocations and internal surfaces. Such a space charge was suggested by Gerson and RohrbaughI~O] and Parker and Schneiderl Ill. This type of space charge may give rise to a field distortion which is too small to detect and hence the polarization will have a linear dependence on field. Perlman has ably demonstrated the existence of this linear type of space charge in carnauba wax electrets[I2]. Much disagreement is evident in the literature concerning the type of polarization which plays a dominant role in the alkali halides. High temperature, non-linear polarization in NaCl crystals has been observed[t3]. Sutter and Nowick, however, produce detiiled evidence to suggest that non-linear electrode polarization does not occur in NaCl and that the polarization can be described by totally linear equations[l]. Bucci and Rival141 attempt to solve the conflict by producing evidence for both linear and non-linear space charge polarization in KCI crystals.

of Physics,

211

212

S. W.

S. MCKEEVER

3. THEORY

The experiments of Sutter and Nowick[l] and of Bucci and Rival 141proceed along similar lines with both groups of experimenters using the Superposition principle and Ohm’s law to detect the presence of a nonlinear space charge. 3. I Superposition principle The essence of the Superposition principle is that the residual charge stored by a dielectric medium following the application of a constant electric field is totally redelivered during the discharge process. The time dependence of the charging conductivity is due to the building-up of a state of polarization within the dielectric and the discharge is the elimination of this state of polarization. In order for this condition to hold true, the internal field over the discharge cycle must be equal to the internal field over the charge cycle. If this is so, then, referring to Fig. I, /omjJr)=[(jJt)-jJ

(1)

where ja(f) = the current density during the discharge cycle; j,(t) = the current density during the charge cycle; jm= the steady-state current density following the build up of polarization during the charge cycle. In the case of linear polarization, the condition expressed in eqn (I) will hold; for non-linear polarization this condition is not obeyed. (Care has to be taken with this type of measurement, particularly at high temperatures, because the current density may be seen to be still decaying even several hours after the application of the field. Uncertainty in j_ influences the testing of equation I ).

and D. M. HUGHES

The build up of polarization, at temperature T, can be described by the equation P(r)=P,,(I-exp(-5)) with respect to time. Here, POis the maximum amount of polarization possible at temperature T and can be expressed, to a first approximation, by Langevin’s equation p = 0

NDP’EP 3kT

where ND = concentration of Z-V dipoles; Ep = local held; p = dipole moment (assumed independent of temperature)[ 181. In eqn (2), 7 is the time taken to polarize the dipoles at temperature T and may be represented by the Arrhenius equation 7(T) = 7,exp

H 8

(>

where 70-1 is the characteristic frequency factor for a vacancy jump from one lattice site to another for the orientation of the I-V dipole and H is the associated activation energy. Making use of the linear heating programme T= T,+@

dT + P=;iT

3.2 Ohm’s law For linear polarization, the final current density j.. will be seen to be linearly dependent upon the applied voltage V. A In (jm) vs In(V) plot will thus be seen to produce a straight line of slope +I. Non-linear polarization will produce a curve of slope > I. 3.3 TSPC and ITC Recently an experimental method was described for observing the orientation of I-V dipoles in alkali halides [ IS]. The method, known as Thermally Stimulated Polarization Current (TSPC) analysis, is in fact the inverse of the well known Ionic Thermocurrent (ITC) method, introduced by Bucci et al.[l6,17]. It was found that by comparing the TSPC and ITC signals produced in alkali halide crystals, it is possible to gain further information about the formation of an ionic space charge in these materials. The two techniques are compared in Fig. 2. The TSPC signal is produced by firstly cooling the sample to To (- 100K) under short-circuit conditions. The sample is then heated linearly with a bias field (d.c.) applied. A current-temperature spectrum is monitored in which current peaks appear due to the polarization of any I-V dipoles present in the material.

Fig. 2. Comparison of TSPC and ITC. For the TSPC measurement, the field is applied at TO and a TSPC peak is produced when the sample is heated at rate 8. For the ITC measurement. the field is applied at TP > T, > TO, and removed at TO. An ITC peak is then produced when the sample is heated at rate 8.

Low temperature

we

can obtain the following TSPC signal

expression

for

space charge

polarization

the observed

3T,kT

I. Quantitative

impurity analysis samples

of the NaCl

and KCI

-i-

Ns2& exp

j,(T) = - -

Table

213

in alkali halide crystals

(-$-&/TIev(-&)dr>

7

IMPURITY

(5) Using this equation, the activation energy for the dipole orientation (H) can be found from a plot of In (j,(T)T) vs T-’ for the initial part of the TSPC curve. 7 can be evaluated from the equation (6) where T,,, = temperature of the peak maximum. The values of H and T obtained can be seen to be independent of the polarizing field Ep The equation quoted by Bucci and Fieschi[lll] to describe the observed ITC peak is jATT)=d Ns’E 3r,kT

exp ( -$-p$/=Iev

(-$)dT)

Ca

12.0

a.2

1.1

CO.1

0.4 Sr

0.6

Cd

1.1

co.1

Pb

co.2

Cr

co.2

Impurity

content

expressed

in

parts

?er

million

(ppm).

(7) Comparison of eqns (5) and (7) reveals that the ITC method will give a peak at the same temperature T,,, and produce the same calculated values for H and T” as the TSPC method; however, the peaks will be of opposite sign. Furthermore, the expression for jb(T) contains the applied field E,, not the local field Ep This latter point needs examining in more detail. In the ITC method the sample is polarized at a high temperature, usually greater than 300K. If an ionic space charge is being formed at this temperature it will have the effect of reducing the local field (which polarizes the dipoles) such that Ep < E,. Equation (7) ought then to contain the term Ep not E,. In contrast, in the TSPC method the field is not applied until temperature To. Because of the reduced mobilities of the ions at this low temperature, an ionic space charge is not built up, thus, as the sample is heated, the dipoles become polarized by a field which has not been reduced by the presence of a space charge; hence, Ep = Ea. In practice, this will produce the result j,,(T) > jAT). Thus, a comparison of TSPC and ITC peaks ought to reveal the presence of a space charge. (Here we have assumed that the temperature at which the TSPC peak appears (T,,,) is low enough to inhibit the formation of an appreciable space charge). 4.EXPERMENTALDETAILS

The alkali halide samples used in the experiments were single crystals of NaCl and KCI purchased from Koch Light Laboratoriest. An analysis of the crystals by flame emission spectrophotometry$ showed divalent metallic impurities to be present in concentrations from 0.1 to IOppm. The full quantitative analysis is given in Table I. tKoch Light Laboratories, Colnbrook, Bucks., England. *The analysis was performed by Rooney and Ward Blackwater Station Estate, Camberly, Surrey, England.

Ltd..

When received from the manufacturer, the samples were large unpolished discs, 2.5 cm dia. and 2 mm thick. Four or five smaller crystals were cleaved from each of the large crystals, then ground and polished to the required size. The grinding and polishing procedure was performed using a glass lap, polishing rouge and dry methanol; the crystals were then thoroughly cleaned in acetone and methanol and finally stored in a dry atmosphere. In the nomenclature used in this paper, NaCl (2.5) will refer to crystal number 5 from original crystal number 2, and so forth. The final crystals were of typical dimensions 5 x 5 x 0.5 mm3. (Allied work on cleaved samples gave no observable differences between the cleaved, and the ground and polished crystals). Electrical contact was provided via gold electrodes evaporated onto opposite sides of the crystals. Evaporated electrodes were used in an effort to prevent air gaps being trapped between the electrode and sample. The currents (as low as 10-14A) were measured by means of a Keithley 602 electrometer, and the temperature was monitored using a chromel-alumel thermocouple. Heating rates of <6”/min were uskd as we found that values of /? greater than this gave rise to misleading peaks in the current-temperature spectrum owing to the presence of large temperature gradients within the sample. All measurements were carried out in a vacuum of 10m5torr. Figure 3 shows a schematic representation of the measuring equipment. 5.RESULTSANDDlSCUSSION

5.1 TSPCIZTC In order that a genuine comparison can be made of the relative sizes of the TSPC and ITC peaks, it is necessary that no change in the concentration of Z-V dipoles occurs between the two measurements. The samples

214

S.

W. S. MCKEEVEI

and D. M. HUCHE~

Keithky 602

t_IThermocor

r

P-5

DVM

suPPlY

-II=

Fig. 3.

Schematic

representation of the measuring measuring circuit. the temperature

circuits, showing measuring circuit

used in the experiments had been stored at room temperature for many months prior to the measurements and so it was thought unlikely that appreciable aggregation of the I-V dipoles into higher-order complexes would take place during the course of the experiments. Furthermore, dissociation of any higher-order complexes into I-V dipole form was inhibited by ensuring that the samples were never heated above 300K. (Although long-term storage usuaIly results in a high concentration of aggregates, all that is required in the present experiments is that a sufficient number of I-V dipoles exist in order to produce a measurable TSPC or ITC signal). Figure 4 shows the results obtained for KC1 (1.6). The experimental procedure was to cool the sample to liquid nitrogen temperature (7’,) and then to apply the field. The sample was then heated (at rate 8) and the TSPC specp

p1

INSET 1

Temperature,

40

K

the vacuum chamber and sample, and the heater control circuit.

trum monitored. At a temperature near 300K the heating was stopped and the sample re-cooled to To. The sample was then short-circuited through the electrometer and the ITC spectrum monitored as the sample was re-heated (at rate 8) back to ambient temperature. From Fig. 4 we can see the following; (i) the TSPC peak is much larger than its ITC equivalent; (ii) two peaks appear in the TSPC spectrum-the main peak at 250 K and a shoulder at 267 K-whilst the ITC spectrum only contains the main peak, at 244 K; (iii) both the ITC and TSPC peaks ,appear at approximately the same temperature (any shght differences can perhaps be explained by the non-reproducibility of the heating rate which could not be kept perfectly linear during the course of the ex~riments): (iv) the inset shows a very small TSPC signal between 130 and 170K-there is no corresponding ITC signal. The activation energies and pre-exponential factors for the ITC and TSPC peaks were calculated according to the theory. The results for KC1 (1.6) are summarized in Table 2. The difference in size between the two peaks in Fig. 4 is postulated as being due to the formation of an ionic space charge which is built up during the polarizing

Tables

2. Summary

of the TSPC

r,,,iQ TSPC

0

1, 1

ITC I’ 1, , _-__, 220 240 2so 280 Temperature, K

250

and ITC

results on

HlsYi 0.76

KCI(1.6).

@SCr) 5 x IO-l4

to.05

-,TegUt’

Fig. 4. Comparison of TSPC and ITC in “as received” KCI (I .6). Note that the TSPC and ITC currents are of opposite sign. they peak at the same temperature and that TSPC > ITC. Note also that the TSPC spectrum contains an “extra” peak appearing on the high temperature side of the TSPC curve. The inset shows a small TSPC signal at - 130-l70K; there is no corresponding ITC signal.

the current

Fig. 4 ITC

244

0.76

3 x lo-l4

to.05 TSPC

242

0.74

5 x 10-14

'0.05 Fig. 5

I

ITC

244

0.75 to.05

-14 4 x 10

Low temperature

space charge

polarization

Temperature, Fig. 5. Second TSPC/ITC

measurement

on KCI (1.6). Here the TSPC peak of Fig. 4.

period near 300 K. The internal field which polarizes the dipoles is thus reduced by this space charge and this accounts for the smaller current observed in the ITC measurement, i.e. it is found that jr,(r) > jAT). After obtaining the curves of Fig. 4, the space charge must still exist within the sample. (Bucci et al.[16] have reported that ionic space charges are not released until temperatures greater than 420K are reached in KCI.) Thus, a TSPC measurement taken now should reveal a peak of approximately the same size as the ITC peak of Fig. 4. This is illustrated in Fig. 5. Here the TSPC curve was monitored immediately after the spectra of Fig. 4. The peak produced is much smaller than the first TSPC peak and is approximately equal in size to the first ITC neak. Following this measurement, another ITC spectrum was taken. Again we see that the TSPC peak is larger than the ITC peak; both appear at approximately the same temperature (242 and 244K) and, in addition to the main peak, the TSPC peak has a shoulder at 255 K. Values of activation energies and pre-exponential factors obtained from Fig. 5 are also listed in Table 2. The results obtained from similar measurements on NaCl (1.2) are shown in Figs. 6 and 7. Two sets of ITC/TSPC peaks are observed in a current-temperature spectrum for NaCl (1.2). The low temperature set (Fig. 6) confirms the observations noted in the measurements on KCI (1.6), namely that the TSPC peak is larger than its

215

in alkali halide crystals

K peak is approximately

equal in size to the ITC

ITC equivalent and that they both appear at approximately the same temperature. Note that only one TSPC peak is evident. The higher temperature results are a little more complex (Fig. 7). A very large TSPC peak appears which is

(TSPC)

0

L; d 140

1 / /I

180

Temperature,

\ I(,

\

\

220

K

Fig. 6. Low temperature TSPCand ITC peaksin NaCl (I .2) (note scales). There is no evidenceof an “extra” TSPC peak at these low temperatures.

216

S. W. S. MCKEEVER

and D. M. HUGHES

25 -

0

I

LOl

/‘I

240

260

\

‘L

I\

’ I

\

280

1

1

300

90

Tenpemture, K Fig. 7. High temperature TSPC and ITC peaks in NaCl (1.2). The TSPC peak is made up of two components and peaks at a height of - 5 x 10~” A. There is only one corresponding ITC peak.

thought to be made up of two components; one due to I-V dipole orientation and a second peak, the origin of which is unclear at this stage. The corresponding ITC peak is due to the depolarization of the I-V dipoles. Both the ITC and the TSPC peaks appear in the same temperature range (220-280 K) but great difficulty was found in separating the TSPC peak into its two components. For this reason values of T,,,, H and 7” could not be obtained for the I-V dipole peak from the TSPC results of Fig. 7. The NaCl (1.2) results are summarized in Table 3. 5.2 Current-voltage measurements From the observation that TSPC peaks are larger than ITC peaks (jD(T) > id(T)) we conclude that a space charge is formed within the sample when polarized by an electric field near 300 K. Current-voltage measurements were thus employed to determine whether or not the presence of this space charge could be detected by searching for a failure of Ohm’s law. Current-voltage plots taken at different temperatures are shown in Fig. 8 for NaCl (1.3). The electric fields Table

3. Summary

of the TSPC

TSPC

and ITC results on NaCl

T,,,,IKi

HICY,

191

0.62

?J,Y’,

2 x

10

2 x

10

8 x

10

-14

10.05 Fig.

6 ITC

196

0.60

-14

to.05

Fig.

TSPC

-

ITC

257

7 0.9 to.05

-14

(1.2)

IO

Id Voltage, volts

I03

Fig. 8. Current-voltage characteristics of NaCl (1.3) for fields ranging from 2.8 kV/m to 1.3 x IO2 kV/m and temperatures: 0. 299 K; 0, 308 K; A, 314 K; 0. 325 K. Note the straight lines of slope t I; there is no indication of a significant deviation from Ohm’s law.

used ranged from 2.8 kV/m to 1.3x IO3kV/m, and, as can be seen, the curves do not significantly depart from a slope of + 1. The plots of Fig. 8 were taken by applying a field at t = 0 and waiting for the current transient to die away before obtaining the value j_,. The value of j_ was taken typically I hr after the application of the field. 5.3 Further evidence for low temperature space charge formation It was felt that further experimental evidence was necessary to attempt to solve the apparent conflict between the ITC/TSPC results and the current-voltage results. Bucci et a/.[ 161, in their work on ITC in KCI, observed current peaks at temperatures higher than that at which the sample was originally polarized (i.e. referring to Fig. 2, T, > Tp). These signals were given the name “Dielectric Chaos” (DC.) peaks by Bucci et al. The D.C. peaks were shown to obey linear theory up to fields of IO3kV/m. Furthermore, by polarizing the samples at slightly higher temperatures, another peak exhibiting non-linear characteristics would appear in the spectrum at a temperature higher than the DC. peaks. This peak was attributed to the release of a (non-linear) ionic space charge. To determine whether similar peaks could be observed in the present samples, NaCl (1.2) was heated above 3OOK. after the appearance of the ITC peaks of Figs. 6 and 7. The result is a third peak (Fig. 9) appearing at a temperature in excess of 300 K, and yet the sample had not previously been polarized above 300K, nor indeed had it ever been heated above 300K. The charge responsible for this peak had obviously not been released during the ITC warming cycle when monitoring the

Low temperature

space charge polarization

5

04/

I

1

320

340

360

Temperature, K Fig. 9. Release of an ionic space charge in NaCl (1.2)in the range 342-346 K. This has predominantly linear characteristics.

peaks of Figs. 6 and 7. Instead, the charge had become “trapped” within the sample. This trapped charge is possibly responsible for the space charge which reduced the internal field sufficiently to produce the result j&t) > j&J. Examination of Fig. 9 reveals that the peak has the following properties; (i) a reasonably definite T,,, of 342-346K; (ii) a shape described by the linear equation relating to dipolar orientation-applying this linear theory gives an activation energy of 0.92eV; (iii) it appears in the same region as the D.C. peaks of Bucci et al. (though their work was on KCI, not NaCI); (iv) T,,, > Tp (in this case Tp = 300K); (v) an “area” of - 3 x lo-” cs. Properties (i)+(iii) indicate that the peak is due to a dipolar (linear) phenomenon; property (iv) implies that it is due to a space charge phenomenon. The NaCl (1.3) sample was now returned to the measuring chamber. The sample was polarized at room temperature and the resultant current transient monitored (j=(r)). When a steady state had been reached the value of jm was noted and the sample short-circuited and the discharge current (jJf)) was monitored. In accordance with the Superposition principle a comparison was then made of jd(t) with (jc(t) - j_). The two curves were identical, within experimental error. When the current transient following the short-circuiting of the sample had died away, the sample was heated and a current-temperature spectrum was monitored. The resultant peak is shown in Fig. 10. The “area” under the curve is = lo-” cs. From these observations it is postulated that the peak of Fig. IO corresponds to the release of a trapped space charge. It is of the same form as the peak of Fig. 9, occurs at the same temperature as this peak (343 K) and is similar to Bucci’s D.C. peaks in KCI. Adopting the nomenclature of Bucci et al. [ 161,we shall now refer to

I

I

1

320

340

Temperature,

t

Ok

21-l

in alkali halidecrystals

360

K

Fig. IO. The “D.C.” peak in NaCl (1.3) at 343 K. This appears in the same temperature region as the peak in Fig. 9 and is postulated as being due to the release of a linear ionic space charge.

the peaks of Figs. 9 and IO as the D.C. peaks. The space charge involved in the production of the DC peaks cannot be observed by Superposition experiments and the current-voltage plots have the appearance of ohmic characteristics. Some space charge phenomena are known to obey linear theory for fields < IO3kV/m[7]. This is consistent with Bucci and Riva’s observation[ 141 that the D.C. peaks in KCI exhibit linear behaviour only for fields < IO3kV/m. An activation energy of 0.92eV for the D.C. peak of Fig. 9 is consistent with the activation energies for ionic movement in this temperature range. Measurements on CdF*[ 191and CaF,[20] have revealed that the activation energy for the release of an ionic space charge at a particular temperature will be the same as the activation energy for ionic conduction in the same temperature range. These facts suggest that the space charge under observation here is ionic in origin. Owing to the ohmic behaviour of the electrodes and to Bucci and Riva’s observation[ 141 that charge accumulation at the electrodes does not decay until temperatures higher than that of the DC. peaks, it is suggested that the ionic space charge producing the D.C. peak is not an electrode effect. Rather, it is believed to be a bulk effect caused, perhaps, by trapping of ionic charge carriers at dislocations within the bulk of the material. A space charge of this form, having linear characteristics, has been suggested by Gerson and Rohrbaugh[lOl and by Parker and Schneider[ I I], and has been observed in carnuaba wax by Perlman[ 121.We suggest that this is the type of space charge which gives rise to the observed difference in size between the TSPC and ITC peaks. Sutter and Nowick[l] have observed that samples which have undergone a grinding/polishing procedure, similar to that carried out on the present samples, have electrodes which have the characteristics of blocking contacts. This, they suggest, is due to the trapping of air pockets between the electrode and the rough crystal

218

S.

W. S. MCKEEVER and D. M. HUGHES

surface. This, however, is not thought to be the case with the present samples because the electrodes were evaporated on in a vacuum environment. In addition, the peaks observed in this work only exhibited linear characteristics: a non-linear peak would be expected if the electrodes formed blocking contacts. Furthermore, Bucci and Riva[l4] observed a non-linear space charge (in KCI) only when the sample was polarized at high temperatures ( - 500K), and that when polarized at near 300 K (as in the TSPC/ITC work on NaCI (1.2)) the KCI samples exhibited only the linear, D.C. space charge. This point is further illustrated by Superposition experiments carried out in the present work on KCI (1.2). Here, Fig. 1I, deviations from linearity are only observed at high temperatures (411 K) and at low temperatures (298 K) the Superposition principle holds. This implies that the difference in the TSPC and ITC peaks must only be due to the linear (D.C.) space charge. 5.4 The “extra” TSPC peak The other main question arising from the TSPC and ITC comparisons concerns the origin of the “extra” peak observed in the TSPC spectra. This extra peak appears as a shoulder on the TSPC peak near room temperature for both the KCI (1.6) and the NaCl (1.2) samples. It seemingly appears whenever a TSPC spectrum is taken but becomes smaller on repeated measurements (Figs. 4 and 5). Some further experiments were performed at this stage in an attempt to determine the origin of this peak. A TSPC measurement was performed on NaCl (1.1) (Fig. 12a). After producing the TSPC peaks. the sample was re-cooled to T,, but with the field still applied. This has the effect of freezing the I-V dipoles in their polarized positions so that when the sample is heated

Temperature, K Fig.

12. Removal of the “extra” TSPC peak in NaCl (1.1). and c is the order in which the curves were taken.

a. b

again the contribution to the TSPC signal from I-V dipole orientation is removed. The resultant spectrum (Fig. 12b) contains only the unknown peak, though it is now somewhat smaller than before. Repeated heating and cooling in this manner suppresses, and, in some cases, completely removed the peak, as indicated in Fig. 12. If, after the peak has been removed by this process, the sample is short-circuited at 300K and a TSPC measurement again taken, only the signal due to I-V dipole orientation is observed. From this it is evident that although the process by which the unknown peak is formed takes place below 300 K, simply short-circuiting at 300 K does not allow the system to return to its original state. If the process is one of polarization, then shorting the electrodes at 300 K does not allow relaxation back to the random state. If the sample is now heated above 300K whilst under short-circuit, a current peak at 343 K, identical to the D.C. peak of Fig. 9, is obtained. These observations suggest a strong correlation between the formation of the linear space charge and the extra TSPC peak. Bucci and Riva[ 141have observed that polarizing a sample at a temperature Tp < T,,, (in this case T,,, = 343 K) does not induce saturation, i.e. the space charge is not completely formed. If the peaks of Fig. 12 represent the formation of a space charge, then the gradual disappearance of the peak with repeated thermal cycling might represent an approach to saturation. 6. CONCLUSIONS

Comparison of the TSPC and ITC signals suggests that a space charge is being formed within the crystal when polarised by a d.c. electric field near 300K. Further measurements indicate that this space charge is released at - 343 K (in NaCl) and the testing of Ohm’s law and of the Superposition principle has shown that the space charge obeys linear theory. An “extra” peak appearing in the TSPC spectra has been related to the formation of this space charge. Time, sets Fig. 1I. Charge (0, A) and discharge (0, A) currents in KCI (1.2) at two temperatures (298 and 411 K). Deviations from the Superposition principle are only evident at 411 K.

Acknowledgement-One of the authors (SWSM) is grateful for the award of a research studentship from the Science Research Council (U.K.) during the course of this work.

Low temperature

space charge polarization

REFERENCES 1. Sutter P. H. and Nowick A. S., 1. Appl. Phys. 34, 4, 734 (1963). 2. Joffe A., Physics of Crystals. McGraw-Hill, New York (1928). 3. Jaff.4 G., Phys. Rev. 85, 354 (1952). 4. Jaff6 G. and Chang H., J. Chem. Phys. 20, 1071 (1952). 5. Friauf R. J., /. Chem. Phys. 22, 1329 (1954). 6. Macdonald J. R.. Phys. Rev. 92, 4 (1953). 7. Allnant A. R. and Jacobs P. W. M., J. Phys. Chem. So/ids 19, 281 (1961). 8. Jacobs P. W. M. and Maycock J. N.. J. Chem. Phys. 39, 3. 757 (1963). 9. Beaumont J. H. and Jacobs P. W. M. 1. Phys. Chem. So/ids 28,657 (1%7).

in alkali halide crystals

219

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