The effect of high fields on the conduction of glasses containing iron

JOURNALOF NON-CRYSTALLINESOLIDS 4 (1970) 220--230 © North-Holland Publishing Co., Amsterdam

THE EFFECT OF HIGH FIELDS ON THE CONDUCTION OF GLASSES CONTAINING

IRON

J. L. BARTON Recherche Fondamentale, Laboratoires Seientifiques Saint-Gobain, 52 Boulevard de la Villette, Paris X I X , France

Electronic conduction in iron-containing glasses has been studied at high fields and compared with high-field ionic conductivity in glasses containing alkali. Both processes show a Poole-Frenkel effect at fields greater than 2 × 105 V cm -1. The combined effects of field and temperature are in agreement with an expression of the form log i ~ a -- (b -- cEO/T. Dielectric constants calculated from e range from 16 to 26 and do not appear to be directly related to the dielectric properties of the bulk materials. The two types of conduction may be distinguished by the values of a and b but not of e. It is suggested that the similarity between electronic and ionic conduction is basically due to the importance of the Coulomb forces which explain not only the high-field effects but also the dielectric relaxation observed in both systems.

I. Introduction It has been f o u n d 1) that at high fields glasses k n o w n to be ionic c o n d u c t o r s d i s p l a y a c u r r e n t - v o l t a g e r e l a t i o n s h i p o f the P o o l e - F r e n k e l type. Such beh a v i o u r h a d previously been o b s e r v e d only in the c o n d u c t i o n o f thin films o f s e m i c o n d u c t o r s or dielectrics a n d might have been a s s u m e d to be c h a r a c teristic o f electronic c o n d u c t i o n . It has been noted, however, that there is a certain similarity between electronic c o n d u c t i o n in glasses c o n t a i n i n g transition metal ions a n d the m o r e c o m m o n ionic c o n d u c t i o n in glasses containing alkali. B o t h o f these c o n d u c t i o n processes are associated with the same type o f low frequency dielectric r e l a x a t i o n 2, 3) which is c h a r a c t e r i z e d by a t o t a l dispersion p r o p o r t i o n a l to ( a n d in a b s o l u t e units r o u g h l y equal to) the p r o d u c t o f the c o n d u c t i v i t y m u l t i p l i e d b y the m e a n r e l a x a t i o n time. In view o f this similarity a n d o f the fact that glasses c o n t a i n i n g transition metal ions are electronic c o n d u c t o r s one w o u l d expect t h e m to show a P o o l e - F r e n k e l effect. The present w o r k has been u n d e r t a k e n to confirm the existence o f such an effect in glasses c o n t a i n i n g a transition metal oxide a n d to c o m p a r e their high-field b e h a v i o u r with that o f glasses which are ionic conductors. 220

221

EFFECT OF H I G t l FIELDS ON CONDUCTION OF GLASSES

2. Experimental For this preliminary investigation three electronically conducting glasses were selected whose resistivities in the ohmic region have been shown to be quite high 4, 5). High fields could thus be applied at readily accessible temperatures. The compositions of these glasses are given in table 1 along with those of some of the glasses containing alkali with which they have been compared. Samples 0.1 to 0.3 m m thick are obtained by grinding and polishing. Thickness measurements made with a precision micrometer show the sample faces to be parallel to within _ 3/~m. The experimental arrangement is indicated in figs. 1 and 2. The sample is fixed between two supporting tubes with an epoxy resin which can be used up to 120°C (the lower temperature limit, imposed by the refrigeration system, is about - 4 0 °C). The supporting tubes are of a high resistivity glass (P25o --- 101° ohm cm) having a wall thickness of 1.4 mm. The guard electrode is silver paint applied to the upper surface of the sample just outside the epoxy seal. When possible, thermal and electrical contact with both faces of samples with ionic conduction is made with aqueous or water/alcohol solutions of a sodium salt. At higher temperatures, the upper solution is replaced by mercury and the lower solution by a layer of silver paint. The latter arrangement is generally used for electronically conducting samples. The temperature of the sample is taken to be that of the thermostatic liquid as measured with mercury thermometers. The difference between the TABLE 1 Compositions of glasses (mol %)

SiO2 TiO2 Fe2Oa Al2Oa B203 PbO BaO CaO MgO K20 Na20

MS a

7336

Pyrex

EHF b

68.58 1.76 0.04 2.89 3.33

72

82.70

61.56

0.06 1.38 11.62 32.97

1.05 6.85 3.14 1.50 10.80

a Microscope cover slide. b Extra heavy flint.

20 8

0.75 3.48

5.29

49314~

495I~) 49615)

60

40

45

8

10 10 10

5 10 10

30

30

32

222

J.L. BARTON h TensionConnection

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EpoxyResinSeals

Tube ~---

=

Teflon Rubber Fig. 1.

Connection

Cell for high-field conductivity measurements.

Screened

Enclosure

!

r- . . . . . . . . . . . . I

106 =

I I I I

,

} /

To Stobilised High Tension Supply

.10e

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J~

Electrometer and Recorder

Electrical circuit.

EFFECT OF HIGH FIELDS ON CONDUCTION OF GLASSES

223

temperatures at the inlet and outlet sides of the enclosure is never more than one or two tenths of a degree. A Keithley 610 B electrometer is used for the current measurements. The voltage dividing network used in the high tension measurement is made up of precision wire-wound resistors. For a given sample the lower limit of the temperature range is determined by the relaxation time rather than the sensitivity of the electrometer. In practice, measurements are usually made down to a temperature giving a resistivity of the order of 10 ~5 ohm cm. Under these conditions several hours are required for electrical equilibrium to be reached after each change in field. The upper limit of temperature or field is imposed by the appearance of a slight upward drift in current. The measurements of ohmic conduction are made at a field of 104 V cm -~ while in the exponential region currents are generally measured under fields ranging from 0.2 to 0.6 MV cm -1. 3. Results

The glasses containing iron show the same current-field relationship as that already observed in glasses with ionic conduction. The slopes of the log i versus E ~ curves are also quite similar as can be seen from the two examples shown in fig. 3. It may be noted that the data are sufficiently precise and have been obtained over a wide enough range to show quite clearly that it is the current rather than the conductivity which is the exponential function of E ~. This is illustrated in fig. 4. The two types of conduction may be distinguished by the pre-exponential terms in the expression for ohmic conductivity and by the activation energies, the electronically conducting glasses showing the lower values. (These characteristic differences have been pointed out previously by Zertsalova, Fainberg and Grechanik6).) Another distinguishing feature of the glasses containing iron is that their activation energies tend to decrease at lower temperatures. If, as in the model proposed by Frenkel7), the effect of the field is to lower the activation energy by an amount proportional to E ~, the combined effects of temperature and field on the current should be represented by an equation of the type: log i = a - ( b - c E ½ ) / T . (1) A simple way of testing this expression is to carry out the measurements at regular temperature intervals A T and to plot Tlog i as a function of E ~.

224

J.L. BARTON

-Z5 Iog,oi [Arnp.cm"

.....~~

40o

6bo

7;0 p01tV~Crfi'/2]

Fig. 3.

Examples of high-field behaviour; comparison of electronic and ionic conduction. i

GLASS 4 9 6

O*C

-13,

-8

IOgtoi lAmp.era -T]

IOgloO" [ohm

cm]-'

-9

-14

-10

-15

-11 4o0 Fig. 4.

s~o

8~o

1~ [Vo,~cn~]

, ~oo

C o m p a r i s o n of log i versus E t and log a versus E t plots.

225

EFFECT OF HIGH FIELDS ON CONDUCTION OF GLASSES

2000 GLASS M.S (127~)

~/-

2200

..

~oC

2400 -Tlogt

2600

280C

300

400

500

600

700

800

[vo,t '/2 cr~'/2] Fig. 5.

Typical Tlog i versus Et plot for a glass with ionic conduction.

2:500

2400

GLASS 496

.,k~G

2500 -TlogL 2600

2700

2800

400

Fig. 6.

5;0

i

600

7~0

800

Typical T l o g i versus g ~ plot for a glass with electronic conduction.

226

J.L. BARTON

I" GLASSES CONTAINING Fe ~Effect of Field on Activation Energy I

~

rLine, d. . . . .

ith

,10pe]

,61 \ 15'

x,~9 6

~1\1 \

14

4,576 ( ~ ) E

[K,Co,.Mo,-]

........

l I\t

11

10 0

l

]\l [ . , ~

200

400 600 [voltV~cn~'']

800

Fig. 7. Comparison of activation energies at high and low fields. If (1) holds, the points should all fall on a series of equidistant parallel straight lines (of slope c and separation aA T). Glasses with ionic conduction give data which follow this pattern throughout the temperature range investigated as can be seen from the example given in fig. 5. Diagrams of this type provide a convenient means of calculating a and c. Electronically conducting glasses show similar behaviour only in the upper part of the temperature range. At the lower temperatures, the distance between the isotherms decreases progressively, a reflection of the decrease in the parameter a which accompanies the slight decrease in activation energy. The slope of the isotherms also decreases slightly: in the example shown in fig. 6, c is 0.9I at 60°C and 0.87 at 15°C. The effect of field on the activation energy may be seen more directly when D log i/8 (l/T) is plotted against E ½. The precision of the apparent activation energies measured at different fields is not sufficient to define the relationship with much accuracy. However, as shown in fig. 7, the data can be represented quite well by a line with the slope - T ( D log i/DE½). Such diagrams can be used to estimate the parameter b.

227

EFFECT OF HIGH FIELDS ON CONDUCTION OF GLASSES

TABLE2 Parameters for the equations logi=a--(b--c~E)/T (E.-->2×105Vcm-1) log a T = A -- B I T (E <<.104 V cm-1)

a 4.576 b ( × 103) ±0.3 c ~ 1.5 ~

MS

7336

Pyrex

EHF

6.1

6.9

6.0

6.9

2.5

2.0

1.7

21.9

25.2

23.7

(32.6)

14.3

13.0

16.6

0.87

0.88

0.95

A 4.576 B

4.2

( >( 10 7)

21.8

23.9

23.0

19.4

18.9

16.2

0.87

3.7

493

0.77

495

0.75

496

0.89

-- 0.4

-- 0.5

-- 0.9

(32.6)

13.0

12.0

15.4

19.4

24.6

26.1

18.5

~0.2 (14.65/c2)

Measured values of a, b and c are shown in table 2 together with the parameters for the ohmic region.

4. Discussion The essential feature of Frenkel's 7) explanation for what is known as the Poole-Frenkel effect is the existence of a purely coulombic potential barrier around a charged site from which a carrier may be excited thermally. With an applied field E, the potential barrier in the field direction is lowered an amount A U given by: A U = ( q 3E/rreeo) ~ , (2) where e is the high frequency dielectric constant of the medium and eo the permittivity of vacuum. The case originally treated by Frenkel was that of field-assisted thermal excitation of electrons into the conduction band where their mobility is considered independent of field. The current is thus a product of a velocity term linear in E and a free-carrier concentration term exponential in E ~. The conductivity at high fields is therefore an exponential function of E ~. In glasses containing transition metal oxides however, conduction may be considered to take place by electrons jumping from one transition metal ion to another. This process is formally similar to that proposed by Jonscher a) for conduction in amorphous dielectrics: a carrier liberated thermally from one charged centre is retrapped by another centre nearby. In both cases the distance travelled by the carrier is considered independent of the field strength. The field therefore influences only the probability of escape.

228

J.L. BARTON

If the potential energy barrier opposed to jumping is coulombic, the jumping probability in the field direction will at high fields become an exponential function of E ½ and, to a first approximation, so will the current. Thus the essential difference between thermally activated jumping and thermal excitation into a conduction band can explain why log i rather than log ~ is a linear function of E ~ in the systems under investigation. (Jonscher has taken into account the effect of field on the escape probability in directions other than that of the field and showed that log i E ~ should be a linear function of E ~. In practice, he found that multiplying i by E ~ changes the slope of the curve but hardly modifies its linearity. The same is true of the data given in fig. 4.) A Poole-Frenkel mechanism supposes an overall jump of considerable length. Under a field of 105 V/cm for example, the maximum in the electrostatic potential barrier will be at a distance of some 30 A from the centre from which the carrier is moving so that the distance between charged centres must be greater than this. It may also be supposed that in the absence of a field, the potential barrier is formed by the superposition of the coulomb potentials of two adjacent centres. Unless the centres are very far apart the magnitude of the potential maximum could be significantly less than the depth of an isolated potential well (the potential corresponding to the parameter b in (1)). A difference between the energy of activation in the ohmic region and the value extrapolated to zero field from the high field values may be explained in this way. Although the energies of activation at high fields are not obtained with great precision, the results shown in fig. 7 are consistent with a difference of about 1 kcal. This corresponds to a distance between centres of the order of 60 A. As mentioned by Jonscher, dielectric constants calculated from the slopes of log i versus E ~ curves are often found to be greater than the high frequency dielectric constants of the bulk materials. In the systems investigated here this tendency is very pronounced. The values of e calculated from the relation d log i

qk

dE ~ = (rCeeo)½ k T

(3)

range from 18 to 26 in the glasses containing iron and from 16 to 19 in the glasses containing alkali, whereas the square of the refractive index does not exceed 3 in either group. The highest dielectric constant at radio frequencies is about 12 so that at least part of the dielectric dispersion at very low frequencies would have to be added to reach the values calculated from (3). It is thus seen that there is no obvious relationship between the parameter c and any of the known dielectric properties of the glasses which have been

EFFECT OF HIGH FIELDS ON CONDUCTION OF GLASSES

229

investigated here. Further work will be undertaken to determine the factors influencing c. It may be noted that the range of values of c for the glasses with ionic conduction overlaps the values found in the electronically conducting systems so that it is impossible to establish a criterion distinguishing the two types of conduction on the basis of the slopes of the log i versus E ~ curves. Thus, as already found in the relationship between dielectric relaxation and ohmic conduction, the similarity between the electronic and ionic charge transport mechanisms in glasses is not only qualitative but, in some respects, quantitative. This lends some support to the idea that in both mechanisms long-range Coulomb potentials are of primary importance since for electrons and monovalent cations their magnitude is the same. These Coulomb potentials, evoked to explain the field effect, could also provide the basis of a mechanism for the dielectric relaxation; we need only introduce neutral traps between the charged centres in order to create the necessary dipoles. In the ionic case such traps would be provided by interstitial sites and the charged centres by cation vacancies. In the detailed model recently proposed by Drake, Scanlan and Engelg) to account for dielectric relaxation and high-field conduction in glasses containing transition metal oxides the same essential features are found: the Coulomb potential, the donor-like centres (low-valence ions) and the neutral traps (high-valence ions).

Conclusion The Frenkel model of field assisted thermal excitation can explain the general form of the high-field results but fails to predict the slope of the log i versus E ~-curves. The importance of Coulomb forces in this model can explain why ionic and electronic processes give rise to similar phenomena at high fields and in alternating fields.

Acknowledgement The author wishes to thank M. Leblond and J. P. Dehaene for their assistance in the experimental work and in treating the data.

References 1) J. L. Barton and M. Leblond, Paper presented at the meeting of the Union Scientifique Continentale du Verre, Paris 28-29 October 1968. To be published in Verres et R6fractaires. 2) J. L. Barton, Compt. Rend. (Paris) 264 (1967) 1139. 3) H. Namikawa and K. Kumata, J. Ceram. Assoc. Japan 76 (1968) 64.

230

J.L. BARTON

4) L. A. Grechanik, E. A. Fainberg and I. N. Zertsalova, Fiz. Tverd. Tela 4 (1962) 454. 5) O. V. Mazurin, G. A. Pavlova, E. Ya. Lev and E. K. Leko, Zh. Tekhn. Fiz. 27 (1957) 2702. 6) I. N. Zertsalova, E. A. Fainberg and L. A. Grechanik, in: Structure o f Glass, Ed. O. V. Mazurin (Consultants Bureau, New York, 1965). 7) J. Frenkel, Phys. Rev. 54 (1938) 647. 8) A. K. Jonscher, Thin Solid Films I (1967) 213. 9) C, F. Drake, I. F. Scanlan and A. Engel, Phys. Status Solidi 32 (1969) 193.