Electrical phenomena in barium titanate ceramics

J. Phys. Chem. Solids, 1973,Vo|. 34, pp. 573-S81. Pe~gamonPress, PrintedinGreatBritain

ELECTRICAL PHENOMENA IN BARIUM T1TANATE CERAMICS* L. BENGUIGUIt ELA, 98 Rue Maurice Arnoux, Montrouge, France (Received 30 N o v e m b e r 1970; in revised f o r m 3 August 1971)

A b s t r a c t - We have studied the current voltage curves of BaTiO3 ceramics, with fired silver electrodes, between 110-400~ We have observed a current controlled negative resistance between low conductivity and high conductivity states, The passage from the low to the high conductivity state is accompanied by a brown coloration starting from the anode. Once the high conductivity state is reached it is impossible to return to the low conductivity state unless one anneals the sample for several hours at 400~ We have measured the voltage distribution along the sample and the short circuited currents after applying a voltage. We interpret our results, assuming carriers injection, by means of the Rose and Lampert models of injection. In the low conductivity state the conduction is ohmic or due to electron injection, and in the high conductivity state there is a double injection regime. However the agreement of the results with the theoretical prediction is good only qualitatively. We think that a more elaborate model is necessary. 1. INTRODUCTION

IN STUDYING the electrical resistivity of barium titanate ceramic[I,2], we observed that it was easy to obtain deviations from Ohm's Law. If the voltage V is low enough, we have proportionality of the current I with V and L -~ (L thickness of the sample). If V increases, the I(V) relation is non-linear and depends on the nature of the electrodes, the temperature, the impurities, and the thickness. In the last case we have I GoL-", n > 1. Tredgold and his co-workers [3] described such behavior in single crystals of BaTiO3 and SrTiOz. They attributed them to injection of electrons from metallic electrodes. They also observed that when using gold electrodes there is an increase of the current with the time up to saturation, and they attributed this phenomenon to a modification with the time of the metal-insulator interface (comparable with the so-called 'forming process'). Koikov et al. [4] also observed such an increase of the current in BaTiO3 ceramics as well as an irreversible change of the resistivity. Annealing in air *Work supported by contract with D.R.M.E. tPresent Address: Department of Physics, TechnionIsrael Institute of Technology, Haifa, Israel.

restored the properties of their samples. They tried to interpret their experiments by injection of carriers. Recently Kunin et a/.[5] related, in a single crystal of SrTiO3, the increase of the current with time to the coloration of the crystal which starts from the anode. The same kind of coloration was observed in a single crystal of BaTiO3 by Kosman and Bursian [6]. We have also observed these phenomena in BaTiO3 ceramics (an increase of the current and coloration from the anode), but only between 115-400~ and when we used fired silver electrodes. We have also shown their connection with the non-linearity in the I-V curve, in particular, that the increase in the current is due to the presence of a negative resistance in the I-V curve, and that the advance of the coloration ends when the current reaches saturation. We have investigated in detail all the electrical phenomena only with fired silver electrodes. The following measurements have been carried out: (a) Determination of the I-V curves between 115-400~ (b) In the region where 1 and V are not pro573

JPCS Vol.34, No.4-- A

574

L. BENGUIGUI

portional to each other the voltage distribution was m e a s u r e d along the sample, in o r d e r to detect space charges. (c) T h e time of the current increase up to its saturation was measured during the coloration of the sample, as well as its variation with the voltage, the temperature, and the thickness of the sample. (d) After voltage is applied to the sample, there is a short circuit current which persists for a very long time. W e have studied this short-circuit current which c o r r e s p o n d s to a release of charges. W e shall first present the experimental results and then discuss t h e m in the light o f the injection theory. It seems to us that all the described p h e n o m e n a can be v e r y well explained by assuming injection of holes and electrons from metallic electrodes. But it is difficult to achieve quantitative results, using the existing models of the injection. 2. EXPERIMENTAL PROCEDURES

T h e samples are made by ceramic techniques b y the firm ' L a C e r a m i q u e Ferroelectrique'. T h e purity o f the sample is 99-9 per cent and their Curie point is 120~ T h e thickness of the sample is between 1 and 1 0 m m . T h e samples used to determine the I - V curves w e r e short discs with a surface of 1-5 m m 2 and for m e a s u r e m e n t of the voltage distribution, h a v e the f o r m o f a parallelpiped 5 • 10• 10mm. In all cases the g e o m e t r y corresponds to a planar flow. T h e m e a s u r e m e n t of the voltage distribution along the sample was done with a metallic p r o b e and a capacitive voltage divider.

[A A

10 -5

lO-S

10-7

116"C

10"e

I

I

10

10

Fig. 1. I-V curve exhibiting a negative resistance, measured when the current is kept constant by the external circuit (L = 1 mm, S = 1.5 cm2).

IA/cm

10-~ 10-4

10-5

10-6

3. EXPERIMENTAL RESULTS

(a) The l - l / c u r v e s T h e detailed shape of the curve depends on the external circuit. I f the current is kept constant b y the external circuit, we obtain the curve of Fig. 1 showing the negative resistance. Conversely, if the voltage is constant, the 1-V curve has a discontinuity (Fig. 2). Figure 3 presents schematically an I - V

10-7 lO-e

10-1

1

10

10 z

lO 3

v

Fig. 2. I-V curves at different temperatures measured when the voltage is kept constant. The discontinuity of each curve corresponds to the negative resistance of the Fig. 1 (L = I mm, S = 1-5 cm2).

BARIUM T1TANATE CERAMICS Log I,

F

/ 11

-

I0

_

.

G

D

~_

IC

Bi v,

Log~

Fig. 3. Schematic I-V curve, defining the different conduction regimes: ABC, low conductivity state. CD, current increase or negative resistance. DEF, high conductivity state. curve. T h e AB part is ohmic, independent of the nature of the electrodes, so that we can define the conductivity o- o f the sample. T h e o- is proportional to exp (--Ec/kT) with Ec ~0 . 8 e V up to 350~ and Ec ~ 1.1 eV a b o v e 350~ In the part BC, we note a deviation from O h m ' s law such as I o~ V 2, which can be seen in Fig. 2 on the curve for 150~ T h e other curves show only the beginning o f this part. At point C, at the threshold voltage Vt, we obtain the turnover of the c u r v e (part CG) if the current is kept constant. I f we maintain the voltage constant, we o b s e r v e the increase of the current f r o m the value I0 (point C) to the value 11 (point D). T h e b r o w n coloration from the anode starts with this increase. T h e rise time tl (from C to D) is several hours as seen in Fig. 9. This is in agreement with the published values [3-5]. tl depends strongly on the t e m p e r a t u r e as discussed in detail below. F o r the time being we note that the coloration and the current increase can be o b s e r v e d only for V ~ Vt. As is shown in Fig. 2, Vt decreases with the temperature, approximately as exp(+O.4eV/kT), Vt depends also on the

575

thickness and is proportional to LL I f L = 1 mm, Vt decreases f r o m 1 5 0 V at 150~ to 3 V at 350~ A b o v e point D, there is a region w h e r e I oc V 2 (part D E ) and a region w h e r e I oc V a (part E F). We did not o b s e r v e these two parts in all the samples. In s o m e samples both can be seen (Figs. 1 and 2, curves for 200 and 300~ in others we o b s e r v e only one part (I ~ V ~ or I oc V3). In the V 2 part, the current is proportional to L -3 if the voltage is fixed (Fig. 4). So we can write I = AV~L -3 with A 0c exp (-- 1 eV/kT). We did not suceed in measuring the dependence of I on L in the V 3 part because the observation of the V 3 part is erratic. Sometimes the V 3 part disappears after the sample has been annealed. W h e n V and L are fixed, I varies with T, as e x p (-- 1.3 eV/kT). I f V decreases f r o m the point F, we pass again through the path EDGH. A n d if we increase V again, we obtain the path HGEF. T h e negative resistance or the increase of the current can be o b s e r v e d only once. When the sample is heated several hours at 400~ in air, the original properties of the sample are restored.

A/cm t 9

V = 50V I

10 ~ =20V

10 .4

lO-S

1 0 "s - ,,,

0.1

I

1

10

Lrn m

Fig. 4. I vs L, if V and T are fixed. I is proportional to L-a, in the Vz part of the high conductivity state.

576

L. B E N G U I G U I

(b) Voltage distribution along the sample We measured the voltage distribution V(x) in each part of the I-V curve. In accordance with the linear relation between I and V, in the part AB V(x) curve is a straight line. (a) Part B.C. This part is seen most clearly in the Fig. 2, curve at 150~ We succeeded in drawing the curve V(x)/V versus x/L of such a sample (Fig. 5). The curve shows an upward concavity. This is proof of the presence of a net negative charge in the sample. (b) Part D.E. In this part, where I 0c V 2, the V(x) has the shape shown in Fig. 6. The downward concavity indicates a net positive charge in the sample. The curve is independent of V and T, and can be described by the following expression: VV ( x ) = 1-- ( l - - L ) 3/z

(1)

(c) Part E.F. We show in Fig. 7 two curves V(x) at 151 and 180~ There are two concavities: downward near the cathode, and upward near the anode. The inflexion point is

o

Experimental point v =. _.-_ x.3J2

112

0

I 112

., x L

Fig. 6. V(x/L)/V curve in t h e V 2 part of the high conductivity state. T h i s conduction regime is characterized by the presence of a net positive charge, which appears during the passage from the point C to the point D (L = 10ram, T = 180~

V

v., V

v. o 18&C o

Experimentalpoints

/

112 I/2

0

I

0

1/2

L

Fig. 5. V(x/L)/V curve in the V 2 part of t h e low conductivity state. T h e upward concavity s h o w s the p r e s e n c e o f a net negative charge in the sample (L = 1 0 r a m , T = 150~

I 112

x L

Fig. 7. V (x/L)/V c u r v e s in the V 3 part o f the high conductivity state at 150~ and 180~ T h e curves exhibit two concavities, and there are a net negative charge near the cathode and a net positive charge near the anode (L = 10 ram).

BARIUM TITANATE CERAMICS

located in the vicinity of the middle of the sample, in some samples nearer to the cathode, in others nearer to the anode. As the temperature increases, the curve is flattened and the concavities are less marked. At constant T, the curves do not depend on V. (d) Blocking anode. We have already said that the current instability can be observed only with fired silver electrodes. T o check the electrode influence we used a blocking contact at the anode. We evaporated a film of silicon oxide of 1/, thickness and deposited the silver electrode on the silicon oxide. At voltage greater than Vt, the V(x) curve is a straight line with a voltage drop near the anode (Fig. 8), and the current is in accordance with the conductivity of the sample although the part o f V which is on the sample is greater than Vt. This result shows the importance of the m e t a l dielectric contact in these experiments. (c) Current increase T o learn about the transition from the low conductivity state to the high conductivity state, we determined the properties of the rise time t~ when a voltage equal or greater than

v v~ 1 192"C

9

577

Vt was applied to a virgin sample (Fig. 9). Before reaching its final values, the current passes through a maximum. When we reverse the voltage, the variation of the current versus time is also given in the same figure. T h e coloration regresses toward the new cathode, and a new coloration appears at the new anode. After reversal, the magnitude of the current does not change very much. This is not so after the first application of the voltage. As is seen in the first part of Fig. 9, I1/I0 is greater than 10. It seems that there is a relation between the simultaneous values of the current and of the colorated volume of the sample. Figure 10 shows that there is a linear relationship between tl and the inverse of the voltage. Before each measurement (i.e. each point on the graph), the sample was annealed to restore its original properties. We measured tl, when V = Vt at 250~ for a sample o f various thicknesses L = 5 mm, 2.3 mm and 1-78mm. W e obtained respectively tl = 170min, 173 and 165 min. We can state that t, is independent of L if V = Vt. Since t~ oc V-~ and Vt oc L 2, we deduce that t~ o~ L2/V (V >i Vt). T h e proportionality coefficient has the dimension o f an inverse mobility. So t~ = L2/I,V. M e a s u r i n g / z at different temperatures, we f o u n d / ~ = 2 . 10 -5 exp ( - 0-56 e V / k T ) ( m 2 /

0

10-4

1/2 0

0 1

2

I

2

-[7"XF-q~+

10-5

o

1/2

=. x

L Fig. 8. V (x/L)/V curve with a blocking anode. The curve is a straight line with a voltage drop in the blocking contact. (L = 10 ram, V = 1000 V).

10-6

I 60

I 120

I 180

I 240

I 300

Fig. 9. Variation o f current vs t, at the threshold voltage. (a) First application of the voltage. (b) After reversal of the polarity. We show also the colored regions and the direction of advance.

578

L. B E N G U I G U I 1

iA

/

"~ volt-1 T=250"C

10-1 10-6

0

I

I

I

I

I

1

1

2

8

4

5

6

t (-hours)

Fig. 10. Linear variation of the rise time with the inverse of the voltage V(V >/Vt). tl is the time necessary for the current to increase from the point C to the point D of Fig. 3.

Vsec). Thus, at 150~ -- 7.4.10 -aa m2/Vsec and /~ becomes equal to 1.5.10-1~ sec at 350~

I

100

200

500

I

,

4 0 0 T *C

Fig. 11. Short circuit current after application slightly lower than the threshold voltage Vt(T,~ = 250~ L = 1 mm, S = 1.5 era2).

which we applied V, was greater than 300~ the current i was very low. (b) We applied V greater than Vt, and waited for complete stabilization of the current (point D, Fig. 3). The curve i(T) exhibits two peaks when the terpperature Tv is lower than 300~ and one peak if Tv > 300~ (Fig. 12(a) and (b)). The peak near 250~ is lower than the 400~ peak.

(d) Short circuit currents After a voltage has been applied in a nonlinear region of the I-V curve and the sample was short circuited, a current through the sample could be observed. At constant T the current persists for a very long time (several days at 120~ The measurement of this current i vs the time is a lengthy process [7, 8]. 4. DISCUSSION AND INTERPRETATION OF RESULTS We adopted the procedure used in the glow The experimental results are very reminiscurve and in the thermally stimulated conduccent of the predictions of the injection theory. tivity, as proposed by Devaux and Schott [9]. The following points give strong support to We applied a voltage V at a fixed temperature Tv. After removing the voltage we cooled an interpretation by assuming carriers injecthe sample quickly to room temperature. After tion from metallic electrodes: that we recorded the short circuit current (a) The dependence of I and Vt on the thickwhile heating the sample at the constant rate ness of the sample shows that there is a of 2~ We performed the following ex- volume effect. periments varying V and Tv. (b) The nature of the electrodes strongly (a) We applied voltages in the non-linear influences the experimental results. With a part of the low conductivity state (region B C). blocking anode, but with a voltage across the In recording the current i as explained above, sample (V minus voltage drop in silicon oxide) we obtained the curve i(T) of Fig. 11; the greater than Vt, there is neither current incurve shows a peak near 300~ If Tv, at crease nor non-linearity.

BARIUM T1TANATE CERAMICS

579

(c) The space charge in the sample is always iA. associated with deviations from Ohm law. The net negative space charge is greater near the 3.1o-e cathode, and the net positive charge is greater near the anode. Such a situation can exist only if the charges come from outside the sample (positive charges from the anode and 2.10"6 negative charges from the cathode.) It is usual to assume that the injected charges are electrons and holes. However the very slow current increase and the corresponding advance of the color may suggest that an lo-e ionic process is involved[10]. But we think that we can discard ion injection on the basis of the results of Branwood et al.[ll]. They observed the current increase and the deviation from Ohm law in their BaTiO3 single ~ o 200 300 4 0 0 "l'~*C crystals with gold electrodes. They showed, (a) using radio tracers, that the gold ions do not enter the sample. They do not mention the 9IA coloration, but is likely that it occurred. They may not have observed it because the electrodes were placed over the wide area of thin samples. We propose to give an interpretation of our results in the light of Rose and Lampert l~ models [12, 13]. In the low conductivity state (part A B C , Fig. 3), the conduction is ohmic at very low field and in the part B C there is electron injection giving the quadratic dependence I oc V 2 and the negative space charge with V ( x l L ) / V = (x/L) 3/2 (Fig. 5). If further we assume the presence of an electron trap, we can explain the 300~ peak in the short circuit current and the o 200 300 400 T ~C rapid variation of the current with temperature loo ~) in the non-linear part. At Vt, the hole injection begins and is re- Fig. 12. Short circuit current after application of voltage sponsible for the sample coloration. This sort greater than Vt, i.e. the sample was in the high conducof coloration is used currently to form color tivity state ( L = l mm, S = 1.5cmZ). (a) T v = 150~ V = 200 V (b) Tv = 370~ V = 3 V. centers[14]. The slow advance of the color is due to occupation by holes of centers which act as hole traps and recombination centers. model of negative resistance[13] can be apThe 400~ peak of the short circuit current plied for the following reasons: (a) The injection takes place in two steps, (Fig. 12(a) and 12(b)) is due to holes released from a recombination center, since it is ob- first the electron and then the holes injection. (b) The mechanism which delays the hole served in all cases. We think that the Lampert

580

L. BENGUIGUI

injection is a volume effect since the threshold voltage depends on sample length (Vt oc L2). (c) T h e negative resistance is associated with o c c u p a n c y change of center (which controls the recombination), as can be seen f r o m the short circuit current. In the high conductivity state, there is a double injection-regime. A further reason for thinking that the Rose and L a m p e r t models can be used is that, to the knowledge of the author, only in these models, is it possible to explain double injection regime with I ~ V 2, and afterwards I oc V 3. T h i s interpretation seems very satisfactory. But when we try to give a quantitative analysis, we obtain too high values of carrier lifetimes. We call /z, and /xp, the electron and hole mobilities, r , and zp their lifetimes, 0n and 0p, that ratios of free and trapped charges. It is possible to show that, when shallow traps are present, we can use the results of the double injection theory without traps, using effective mobility (O,,p,n, Opl~,) and effective cross sections (0,o-,, 0~,trp). In our case it is also necessary to take into account the diffusion as done by Baron[15]. T h e details of the calculation are given in the reference[16]. W e obtain TnOp[d,nldbp ~- 10-14 M K S Onl.ll, n

~

4 . 1 0 -8 m2/Vsec

Using the value o f ~ , = 0 . 5 . 1 0 -4 m2/Vsec[17], we get

5. CONCLUSION W e have shown in our e x p e r i m e n t s that the p h e n o m e n a reported in detail here and observed by different r e s e a r c h e r s (non-linearity in I - V curve, increase of the current and negative resistance, irreversible change of the resistivity, coloration f r o m anode) are all related. T h e y h a v e their origin in the injection o f electrons and holes from metallic electrodes. W e have used the Rose and L a m p e r t model of injection and have found that qualitatively the experimental results agree well with the theoretical predictions H o w e v e r , by a straightf o r w a r d application of the theory we have found a large and unrealistic value of the lifetime of a free pair. We conclude that s o m e other m e c h a n i s m acts and contributes to the o b s e r v e d phenomena. W e want to note that although it seems very easy to inject charges in BaTiO3[3, 4, 10, 18], the p h e n o m e n a are far from being well understood. S o m e authors[10, 18] think it is necessary to include ionic motion (oxygen vacancies), but it is not clear if this is justified in all cases. It seems necessary to undertake new experiments, (for example, optical injection) in order to understand the electrical properties of Barium titanate. Acknowledgement--We wish to express our thanks to

Prof. LeCorre and Coelho of the University of Paris for their suggestions and encouragements, to Prof. Many of the Hebrew University of Jerusalem for his interest in this work and to Prof. Pollak of the University of California for his careful reading of the manuscript. We should also like to thank M. Hervet, for calculating on a computer the V(x) curves of the Baron model, and Mlle. Berrehar for his assistance in the measurements.

"rn ~ 5 . 10-3 sec

REFERENCES

W e can show also that ~-p = 0.1 sec. It is unlikely that the lifetime o f a free pair (equal to the shorter of the two lifetimes) has so great a value. We arrive at the conclusion that the R o s e and L a m p e r t theories explain the results v e r y well, but only qualitatively. T h u s it is necessary to develop a m o r e elaborate model, but our experiments are not sufficient to provide it.

i. BENGUIGUI L., C.R. Acad. Sci. Paris 262B, 642 (1966). 2. BENGUIGUI L., Proc. Int. Meeting of Ferroelectricity of Prague, Voi. II p. 326 (1966). 3. TREDGOLD R. N., Space Charge Conduction in Solids, Elsevier, Amsterdam (1966). 4. KOIKOV S. N., TSIKIN A. N. and SHAKIROV A.~oviet Phys. solid St. 9, 2777 (1969). 5. KUNIN V. YA, TSIKIN A. T., SHTURBINA N. A.~ovietPhys.-solidSt.ll, 598 (1969). 6. KOSMAN, M. S. and BURSIAN E. V., Soviet Phys.-Dokl.Z 354 (1957). 7. LINDMAYER J., J. appl. Phys. 36, 196 (1965).

BARIUM TITANATE CERAMICS 8. H A Y N E S M. E. and C A R E Y - R E A D , Brit. J. appl. Phys.1, 1257 (1968). 9. D E V A U X P. and S C H O T T M.,Phys. Status Solidi 20,301 (1967). 10. G O T O Y. and K A C H I S., J. Phys. Chem. Solids 32, 889(1971). 11. B R A N W O O D A., H U G H E S O. H., H U R D J. D. and T R E D G O L D R. H., Proc. Phys. Soc. Lond. 79, 1161 (1962). 12. L A M P E R T M. A. and ROSE A., Phys. Rev. 121, 26 (1961).

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13. L A M P E R T M. A.,Phys. Rev.125, 126 (1962). 14. S C H Y L M A N J. H. and C O M P T O N W. D., Color Centers in Solids, Chap. 2, p. 38, Pergamon Press, Oxford (1963). 15. B A R O N R., Phys. Rev. 137A, 272 (1965). 16. B E N G U I G U I L., Thesis (1969), University of Paris. 17. R E I K M. G. and H E E S E D. N., Phys. Status Solidi 24, 281 (1967). 18. L E H O V E C K. and S H R I N G. A., J. appl. Phys. 33, 2036 (1962).