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Determination of the potential barrier height in barium titanate ceramics
Soluh’lare Electronics Vol. 27, No. 11, pp. 929-935. Printed in the U.S.A.
1984
003x-1101/x4 $3.00 + .oo Pergamon Press Ltd.
DETERMINATION OF THE POTENTIAL BARRIER HEIGHT IN BARIUM TITANATE CERAMICS M. KUW~BARA Kyushu Institute of Technology, Tobata, Kitakyushu, 804 Japan (ReceivedAugust 1983; in revisedform 21 December 1983) Abstnw-The
height of potential barriers formed at the grain boundaries in porous semiconducting barium titanate ceramics have been determined on the basis of the Heywang model using both the resistivity-temperature and the dielectric constant-temperature characteristics. All the porous barium titanate ceramics used here showed the PTCR effect of more than seven orders of magnitude, and the experimental results obtained showed a good fit with the Heywang model. The present study gives a strong support to the validity of the Heywang model in conjunction with a description of the nature of surface acceptor states, the existence of which was assumed in the Heywang model to be necessary for the formation of grain boundary potential barriers in barium titanate ceramics. An investigation made of the ambient gas dependence of the resistivity-temperature characteristic revealed that oxygen adsorbed on the grain surface formed a surface acceptor state necessary for the appearance of the FTCR effect. 1. INTRODUCIION
There have been many experimental and theoretical approaches[l-161 to the mechanism of the PTCR (positive temperature coefficient of resistivity) effect in semiconducting barium titanates since the ceramic materials were tirst found to exhibit remarkable resistivity anomalies above the Curie point [ 171. It has been shown that the mechanism of the PTCR effect could be described most appropriately by a grain boundary barrier model proposed by Heywang [2,5], which has been extended by Jonker[6], who took into account of the influence of the spontaneous polarization on the resistivity below the Curie point and further extended by Daniels et ~I.[161 who postulated that barium vacancies highly concentrated in the region near the grain surfaces caused the formation of grain boundary potential barriers. Several ambiguities with the model have, on the other hand, also been argued especially in relation to both the type of the potential barrier formed at the grain boundaries[ 181 and the nature of surface acceptor states assumed in the model[l6]. The following two things may be the main difficulties with the Heywang model in explaining the PTCR characteristics which have appeared in the literature. (a); There have been observed various types of the resistivity-temperature characteristics which do not seem to be described by the equation representing the Heywang model P = p. exp (4/W
= p. exp (~N,2/2e~ONdW
(1)
where p is the resistivity at temperature T(“K), pO is a constant, e+ is the height of a potential barrier, N, is the density of surface acceptor states, N,, is the density of ionized donor states, E, is the dielectric constant of the grain boundary barrier layers, and others have the usual meaning, respectively. (b) There has been no definite experimental evidence supporting the assumption that surface acceptor states are inevitably required for the PTCR effect, and further
the precise nature of the surface states assumed in the model has never been made clear experimentally. An observation of the PTCR characteristics which exactly follow eqn (1) seems to provide a clue to solve problem (a), where the agreement between the observed characteristics and the model must of course be consistent in itself. As to problem (b), on the other hand, an investigation of the ambient gas dependence of the PTCR characteristic may be expected to provide significant information about the nature of the surface acceptor states. The aim of this paper is to provide solutions for the above two problems by analyzing the resistivitytemperature characteristics with large PTCR effects of more than seven orders of magnitude and their ambient gas dependence on the basis of the Heywang model, which were both obtained for porous semiconducting barium titanate ceramics. 2. EXPERIMENTAL Porous semiconducting barium titanate ceramics having porosities in the range of 20-30x were prepared using commercial barium titanyl oxalate, BaTiO(C,O,), .4H,Ot, and Sb203$ as a doping substance. A conventional method for preparation of ceramics was used, but special attention was directed at control of porosity and the grain size to have a value between 2 and 5pm[l9]. The porosity in the sintered bodies was changed by changing the density of the “green” bodies which were formed at various pressures. Sintering was conducted at 1350°C for 2 hrs in air, where the heating and cooling were both performed at a rate of lO”C/min. The cooling rate TShin-Nippon Metal Chemical Co., Ltd., Kyoto, Japan; manufacturer’s analysis (in wtW) BaO 34.16, TiO, 17.83, Fe,O, 0.0005, Cl 0.003, purity as BaTiO, 99.58, Ba/Ti ratio 0.998. $E. Merck AG, Darmstadt, Federal Republic of Germany; purity 299%. 929
M. KUWABARA
930 Table
1. Compositions
and relative
densities
of the present Relative
Sample
Composition
samples
density
(%)
G?Zeel-l Sintered
Ba0.898Sb0.002S'0.1Tio
46.3
78.0
44.4
75.1
51-3
41.6
71.1
S2-2
Ba0.798Sb0.002S'0.2Tio
44.4
72.7
B -3
Ba0.998Sb0.002Ti03
45.0
77.7
Sl-1
3
51-2
after sintering has been considered to influence the magnitude of the observed PTCR effect appreciably[l2], but, for porous barium titanate ceramics here concerned, the cooling rate has been confirmed to cause no significant influence on the observed PTCR characteristics[20]. In the present study, semiconducting barium titanate ceramics having the compositions described by the formulae Ba, ,Sr,,,TiO, and Ba, &,,TiO, were also prepared. They had the Curie point at about 80 and 57”C, respectively[21]. Chemical compositions and the relative densities of the ceramic materials prepared are given in Table 1. Electrical measurements were conducted on the porous materials with In-Ga electrodes rubbed on both surfaces of the pellets (= 8 mm dia. x e 2 mm thick) at room temperature up to -400°C. A d.c. bias in the ohmic region (< 10.0 V) was employed for the resistivity measurements, and the capacitance was measured at 1 kHz. All the electrical data reported here were taken during heating (3”Cjmin) in air. To confirm the role of oxygen adsorbed on the grain surfaces in determining the feature of the PTCR characteristic the ambient gas dependences of the resistivity-temperature characteristics were also investigated using ambient gases having various reducing powers. Details of the experimental procedure used here have been described elsewhere[22]. All the resistivity measurements under the ambient gases, except for measurements under air and oxygen atmospheres, were made on the material which had undergone a heat treatment in oxygen at 350°C for 30 min prior to respective measurements. Turning the ambient gases from one to another was carried out at 350°C after evacuating the previous ambient gas down to N 140 Pa within 10 set, and the resistivity measurements were conducted first on cooling and then on heating at a rate of 3”C/min. The ambient gases were flowed at a rate of 35 ml/min in the present experiment.
3
barium titanate ceramics with a certain porosity and a small grain size can exhibit such a large PTCR effect as shown in this figure without the addition of acceptor elements such as Mn or Cr[23], while the usual barium titanate ceramics without the additional acceptor elements can exhibit small PTCR effects of only 2-4 orders of magnitude. This may be attributed to such a distinguishable grain structure as is shown in Fig. 2, which was obtained for sample A-3 and which exhibited almost the same electrical properties as those of sample B-3. It can be considered that porous, small grain-sized barium titanate ceramics do not contain degraded grain boundaries having very small potential barrier heights at the grain boundaries above the Curie point which often exist in the materials with large grain structures caused by exaggerated grain growth[24]. Before attempting to confirm whether the resistivity-temperature characteristic shown in Fig. 1 can be described by the Heywang model, which is represented by eqn (l), we should make a small modification on the equation to enable it to be expressed using the observed dielectric constant ?, (referred to as the apparent one) instead oft. used in
I
Il-
IO9-
43
3. RESULTS AND DISCUSSION
In Fig. 1 are shown typical examples of the resistivity-temperature and the dielectric constanttemperature characteristics of porous semiconducting barium titanate ceramics. The data shown here are those obtained for sample B-3. It is interesting that
prepared
t 21 0
I
I 100
I
I 200
I 2
T (“C) Fig.
1. Resistivity and perature
dielectric constant for sample 8-3.
against
tem-
Barrier
height
in barium
titanate
ceramics
Fig. 2. Scanning electron micrograph of a typical fracture surface of porous barium titanate ceramics showing large FTCR effects, which was obtained for sample A-3 which exhibited almost the same PTCR effect as that of sample B-3. Bar = 10 pm.
931
Barrier height in barium titanate ceramics eqn (1). The apparent dielectric constant 5 can be calculated from the capacitance, F, measured, using the equation P, = Fd/.&,, where d is the thickness of a sample and S, is the area of the electrode. The relationship between cr and e, may be given as 2, = c,/2b, where r is the average grain size of a sample and b may in turn be given as N,/N,. Equation (1) can thus be rewritten, using the above relations, as
,, 10 9 E,e 5 ? o q6 ;5
p = p. exp( e2Nsr/4ircokT).
(2)
4
Since the present materials examined have, however, considerable porosities, eqn (2) should be further revised into a form which allows for the influence of porosity on the effective contact area between grains prior to the analysis of the results obtained for the present porous materials. When the ratio of the effective sectional area, S, of a material to S, is given by f(p), i.e. S/S, =f(p), we obtain a revised form of eqn (2)
3
~=~~exp(e’hT,~f(p)/4~,~~kT).
(3)
Unfortunately, the exact form off(p) as a function of porosity p can not be known because of its complexity, but we can at least assume that the value off(p) increases monotonically as the porosity decreases in the porosity region here concerned. If the resistivity-temperature characteristics obtained for the present samples are described by eqn (3), one may expect linear relationships in the log p against IIF,T plot because N,, r and f(p) are all considered to be temperature independent constants. Figure 3 shows the log p against l/C,T plots of the resistivity-temperature characteristics obtained for the present samples, in which good linear relationships can be clearly seen. This shows that the resistivity-temperature characteristics of the porous materials above the Curie point can be described completely by the Heywang model. From this figure the value of p,,, which corresponds to the bulk resistivity of the ceramic grain, can be obtained by the extrapolation of the straight line to l/E;T = 0, and the value of NJ(p) can as well be obtained from the slope of the straight line. In addition, one may also calculate the height of a potential barrier by applying
21”““““““” 0
15 IO 10e/2.3~rT ( K-’)
5
Fig. 3. Logp against l/cJ plots for the present porous barium titanate ceramics. T, denotes Curie point.
eqn (1) to the straight
line in the plot. The values of
p. , IV,f ( p) calculated for r = 2 pm and 5 pm. and e+ both at the Curie point (T,) and at the maximum resistivity temperature (T,,), as well as slopes of the respective straight lines, from which the value of Nsf( p) was calculated, are given in Table 2. The height of the potential barriers at T,,, obtained for the present porous barium titanate ceramics, which was assumed to be nearly equal to the activation energy of the surface acceptor states in the Heywang model, is found to be nearly the same as the value estimated by him[S]. He estimated the activation energy of the surface acceptor states to be -0.9 eV and explained the PTCR effects of only 24 orders of magnitude. However, according to eqn (1) an increase in the potential height by a factor of S-10 over the temperature range from T,-T,,, seems to be enough to explain the PTCR effect of 7-8 orders of magnitude, and this has been successfully confirmed in the present study. The value of N,, on the other hand, cannot be determined unless the exact form of f(p) is known, but a set of data of N,!(p) obtained for samples Sl-1, Sl-2 and Sl-3 may enable one to make it possible to estimate the value of N,. The values of iV,f( p) calculated for samples Sl-1, Sl-2 and Sl-3, which have the same composition, are found to de-
Table 2. Results obtained for the present porous PTCR materials, where the slopes of the straight lines drawn in Fig. 3 are given in the third column N,f(p) Sample
P, (ohmcm)
A ("K)
20
b-2)
r=2pm-5um
e6 (@o at T, T,
Sl-1
2.5x103
4.0x107
3.8-1.5~101~
0.06
0.69
Sl-2
.2.5x103
3.0x107
2.9-1.2x1013
0.06
0.67
Sl-3
2.5x103
2.3~10~
2.2-O.9x1O13
0.08
0.69
52-2
2.5~10~
2.8x107
2.7- 1.1~101~
0.09
0.66
B -3
3.2~10~
2.6~10~
2.4- 1.0~101~
0.11
0.88
934
M.
KUWABARA
crease almost linearly with increasing porosity, and this seems to be successfully described by eqn (3) on the assumption that the value of f(p) increases with decreasing porosity. If the assumption is allowed, but without a theoretical basis, that f(p) can be given as l-p in the porosity region of interest, the value of N, can be obtained by the extrapolation of the straight line in the N,f( p) against p plot to p = 0. The value of N, estimated in this manner to be in the region of 1 X 1Or4 cm-’ seems to be reasonable in comparison with those which have been estimated by previous investigators[5, 6, 141. Figure 4 shows the Arrhenius plots of the resistivity obtained for the present samples. Since the height of the potential barrier is considered to be unchanged at temperatures above T,, the Arrhenius plot of the resistivity above T, is expected to give an activation energy nearly equal to the value of the potential barrier e4 at T,,,, and this can in fact be seen. Another experiment has been made to investigate how the adsorption of oxygen influences the magnitude of the PTCR effect, where the resistivity measurements were carried out under ambient gases having various reducing powers. The results are shown in Fig. 5. It is clearly seen that the magnitude of the PTCR effect can be easily degraded by exposing the material to a reducing gas, where the degree of degradation of the PTCR effect seems to proceed with an increase in the reducing power of the gases. In this figure a drastic degradation of the PTCR effect in CO gas is seen, and this may suggest that CO gas can significantly reduce the height of the potential barrier at the grain boundaries by eliminating the adsorbed oxygen from the grain surfaces. The adsorption of CO gas on the surfaces of n-type semiconductors is, on the other hand, usually considered to provide surface donor states which reduce the
IO
I air 2 02
9
3 N2 4 co2
F6
5 CH4
0
6 Co
0
T(T) Fig. 5. Ambient gas dependences of the resistivitytemperature characteristic for a RTCR material with the same composition as that of sample B-3.
resistivity of the materials, and this may also be the case for the data obtained in the present experiment. The rate of the resistivity change when the ambient gas was turned from O2 to CO, and vice versa, was measured at several temperatures. The results are shown in Fig. 6. From this figure the height of grain boundary potential barrier is found to be lowered very quickly at temperatures above 250°C in the CO atmosphere, and it is also found that the lowered potential barrier heights can be raised again very quickly by exposing the sample to O2 gas at those temperatures. This clearly indicate that twodimensional acceptor states formed by the adsorption of oxygen, the existence of which was postulated by Heywang, generate potential barriers at the grain
250.C
300
2-
2 103/T (K-l)
Fig. 4. Arrhenius plots of the resistivities present porous barium titanate ceramics. Curie point.
3
obtained for the Arrows indicate
0
I
2
3 t
4
5
6
7
(min)
Fig. 6. Response characteristics of the resrstivity for the FTCR material used in the experiment of the ambient gas dependence when the atmosphere was turned from 0, to CO, and vice versa, at several temperatures.
Barrier height in barium titanate ceramics
boundaries. From this experiment the assumption, proposed by Daniels et al., that three-dimensional acceptor states form potential barrier layers at the grain boundaries may be discarded in the present samples because the concentration of barium vacancies do not seem to change so quickly as seen in this figure at such low temperatures as those used in the present experiments. 4. CONCLUSION
In the present study, the resistivity-temperature characteristics of barium titanates in the FTCR region have been definitely confirmed to follow eqn (1) proposed by Heywang, and it has also been confirmed that the nature of acceptor states forming potential barriers at the grain boundaries is not barium vacancies concentrated in the region near the grain boundaries, but oxygen species adsorbed near the grain boundary interfaces. It is concluded that the mechanism of the PTCR effect can be described completely, at least from a phenomenological point of view, on the basis of the Heywang model. Acknowledgement-The
financial support of the Ministry of
Education, Science and Culture of Japan in the form of a Grant-in-Aid knowledged.
for Special Research, No. 57116001, is ac-
REFERENCES
1. 0. Saburi, J. Phys. Sot. Jpn. 14, 1159 (1959). 2. W. Heywang, Solid-St. Electron. 3, 51 (1961).
935
3. W.T. Peria, W. R. Bratshun and R. D. Fenity, J. Am, Ceram. Sot. 44, 249 (1961). 4. G. Goodman, J. Am. Ceram. Sot. 46, 48 (1963). 5. W. Heywang, J. Am. &ram. SW. 47, 484 .( 1964). 6. G. H. Jonker. Solid-St. Electron. 7. 895 (1964). 7. J. B. MacChesney and J. F. Potter, j. Am: Ceram. Sot. 48, 81 (1965). 8. G. T. Mallick, Jr. and P. R. Emtage, J. Appl. Phys. 39, 3088 (1968). 9. H. Schmelz, Phys. Status Solidi 35, 219 (1969). 10. B. M. Kulwicki and A. J. Purdes. Ferroelectrics 1. 253
(1970). 11. S. A. Long and R. N. Blumenthal, J. Am. Ceram. Sot. 54, 515 (1971). 12. M. Kahn, Am. Ceram. Sot. Bull. 50, 676 (1971). 13. P. Gerthscn and B. Hoffman, Solid-St. Electron. 16, 617 (1973). 14.
A. M. J. H. Seuter, Philips Res. Repts. Suppl. No. 3, (1974).
H. Ihrig, Phys. Status Solidi (a), 17, 437 (1978). 16. J. Daniels, K. H. Hardtle and R. Wemicke, Philips
15.
Tech. Rev. 38, 73 (1978/74). 17. P. W. Haaiiman. R.W. Dam and H. A. Klasens. West German Pa;. 924350, June 23, 1955. 18. C. A. Miller, J. Ph_vs. D. 4, 690 (1971). 19. M. Kuwabara, J. Am. Ceram. Sot. 64, 639 (1981). 20. M. Kuwabara, Jpn. J. Appl. Phys. 20, (1981) Suppl.
20-4, pp. 131-34. 21. B. Jaffe, W. R. Cook Jr. and H. Jaffe, Piezoelectric Ceramics, pp. 91-102. Academic Press, London (1971). 22. M. Kuwabara and H. Inoue, Proc. Int. Meeting on Chem. Sensors, Fukuoka, pp. 182-86, 19-22 September (1983). 23. T. Matsuoka, Y. Matsuo, H. Sasaki and S. Hayakawa, J. Am. Cerum. Sot. 55, 108 (1972). 24. H. Nemoto and I. Oda, J. Am. Ceram. Sot. 63, 398 (1980).
1984
003x-1101/x4 $3.00 + .oo Pergamon Press Ltd.
DETERMINATION OF THE POTENTIAL BARRIER HEIGHT IN BARIUM TITANATE CERAMICS M. KUW~BARA Kyushu Institute of Technology, Tobata, Kitakyushu, 804 Japan (ReceivedAugust 1983; in revisedform 21 December 1983) Abstnw-The
height of potential barriers formed at the grain boundaries in porous semiconducting barium titanate ceramics have been determined on the basis of the Heywang model using both the resistivity-temperature and the dielectric constant-temperature characteristics. All the porous barium titanate ceramics used here showed the PTCR effect of more than seven orders of magnitude, and the experimental results obtained showed a good fit with the Heywang model. The present study gives a strong support to the validity of the Heywang model in conjunction with a description of the nature of surface acceptor states, the existence of which was assumed in the Heywang model to be necessary for the formation of grain boundary potential barriers in barium titanate ceramics. An investigation made of the ambient gas dependence of the resistivity-temperature characteristic revealed that oxygen adsorbed on the grain surface formed a surface acceptor state necessary for the appearance of the FTCR effect. 1. INTRODUCIION
There have been many experimental and theoretical approaches[l-161 to the mechanism of the PTCR (positive temperature coefficient of resistivity) effect in semiconducting barium titanates since the ceramic materials were tirst found to exhibit remarkable resistivity anomalies above the Curie point [ 171. It has been shown that the mechanism of the PTCR effect could be described most appropriately by a grain boundary barrier model proposed by Heywang [2,5], which has been extended by Jonker[6], who took into account of the influence of the spontaneous polarization on the resistivity below the Curie point and further extended by Daniels et ~I.[161 who postulated that barium vacancies highly concentrated in the region near the grain surfaces caused the formation of grain boundary potential barriers. Several ambiguities with the model have, on the other hand, also been argued especially in relation to both the type of the potential barrier formed at the grain boundaries[ 181 and the nature of surface acceptor states assumed in the model[l6]. The following two things may be the main difficulties with the Heywang model in explaining the PTCR characteristics which have appeared in the literature. (a); There have been observed various types of the resistivity-temperature characteristics which do not seem to be described by the equation representing the Heywang model P = p. exp (4/W
= p. exp (~N,2/2e~ONdW
(1)
where p is the resistivity at temperature T(“K), pO is a constant, e+ is the height of a potential barrier, N, is the density of surface acceptor states, N,, is the density of ionized donor states, E, is the dielectric constant of the grain boundary barrier layers, and others have the usual meaning, respectively. (b) There has been no definite experimental evidence supporting the assumption that surface acceptor states are inevitably required for the PTCR effect, and further
the precise nature of the surface states assumed in the model has never been made clear experimentally. An observation of the PTCR characteristics which exactly follow eqn (1) seems to provide a clue to solve problem (a), where the agreement between the observed characteristics and the model must of course be consistent in itself. As to problem (b), on the other hand, an investigation of the ambient gas dependence of the PTCR characteristic may be expected to provide significant information about the nature of the surface acceptor states. The aim of this paper is to provide solutions for the above two problems by analyzing the resistivitytemperature characteristics with large PTCR effects of more than seven orders of magnitude and their ambient gas dependence on the basis of the Heywang model, which were both obtained for porous semiconducting barium titanate ceramics. 2. EXPERIMENTAL Porous semiconducting barium titanate ceramics having porosities in the range of 20-30x were prepared using commercial barium titanyl oxalate, BaTiO(C,O,), .4H,Ot, and Sb203$ as a doping substance. A conventional method for preparation of ceramics was used, but special attention was directed at control of porosity and the grain size to have a value between 2 and 5pm[l9]. The porosity in the sintered bodies was changed by changing the density of the “green” bodies which were formed at various pressures. Sintering was conducted at 1350°C for 2 hrs in air, where the heating and cooling were both performed at a rate of lO”C/min. The cooling rate TShin-Nippon Metal Chemical Co., Ltd., Kyoto, Japan; manufacturer’s analysis (in wtW) BaO 34.16, TiO, 17.83, Fe,O, 0.0005, Cl 0.003, purity as BaTiO, 99.58, Ba/Ti ratio 0.998. $E. Merck AG, Darmstadt, Federal Republic of Germany; purity 299%. 929
M. KUWABARA
930 Table
1. Compositions
and relative
densities
of the present Relative
Sample
Composition
samples
density
(%)
G?Zeel-l Sintered
Ba0.898Sb0.002S'0.1Tio
46.3
78.0
44.4
75.1
51-3
41.6
71.1
S2-2
Ba0.798Sb0.002S'0.2Tio
44.4
72.7
B -3
Ba0.998Sb0.002Ti03
45.0
77.7
Sl-1
3
51-2
after sintering has been considered to influence the magnitude of the observed PTCR effect appreciably[l2], but, for porous barium titanate ceramics here concerned, the cooling rate has been confirmed to cause no significant influence on the observed PTCR characteristics[20]. In the present study, semiconducting barium titanate ceramics having the compositions described by the formulae Ba, ,Sr,,,TiO, and Ba, &,,TiO, were also prepared. They had the Curie point at about 80 and 57”C, respectively[21]. Chemical compositions and the relative densities of the ceramic materials prepared are given in Table 1. Electrical measurements were conducted on the porous materials with In-Ga electrodes rubbed on both surfaces of the pellets (= 8 mm dia. x e 2 mm thick) at room temperature up to -400°C. A d.c. bias in the ohmic region (< 10.0 V) was employed for the resistivity measurements, and the capacitance was measured at 1 kHz. All the electrical data reported here were taken during heating (3”Cjmin) in air. To confirm the role of oxygen adsorbed on the grain surfaces in determining the feature of the PTCR characteristic the ambient gas dependences of the resistivity-temperature characteristics were also investigated using ambient gases having various reducing powers. Details of the experimental procedure used here have been described elsewhere[22]. All the resistivity measurements under the ambient gases, except for measurements under air and oxygen atmospheres, were made on the material which had undergone a heat treatment in oxygen at 350°C for 30 min prior to respective measurements. Turning the ambient gases from one to another was carried out at 350°C after evacuating the previous ambient gas down to N 140 Pa within 10 set, and the resistivity measurements were conducted first on cooling and then on heating at a rate of 3”C/min. The ambient gases were flowed at a rate of 35 ml/min in the present experiment.
3
barium titanate ceramics with a certain porosity and a small grain size can exhibit such a large PTCR effect as shown in this figure without the addition of acceptor elements such as Mn or Cr[23], while the usual barium titanate ceramics without the additional acceptor elements can exhibit small PTCR effects of only 2-4 orders of magnitude. This may be attributed to such a distinguishable grain structure as is shown in Fig. 2, which was obtained for sample A-3 and which exhibited almost the same electrical properties as those of sample B-3. It can be considered that porous, small grain-sized barium titanate ceramics do not contain degraded grain boundaries having very small potential barrier heights at the grain boundaries above the Curie point which often exist in the materials with large grain structures caused by exaggerated grain growth[24]. Before attempting to confirm whether the resistivity-temperature characteristic shown in Fig. 1 can be described by the Heywang model, which is represented by eqn (l), we should make a small modification on the equation to enable it to be expressed using the observed dielectric constant ?, (referred to as the apparent one) instead oft. used in
I
Il-
IO9-
43
3. RESULTS AND DISCUSSION
In Fig. 1 are shown typical examples of the resistivity-temperature and the dielectric constanttemperature characteristics of porous semiconducting barium titanate ceramics. The data shown here are those obtained for sample B-3. It is interesting that
prepared
t 21 0
I
I 100
I
I 200
I 2
T (“C) Fig.
1. Resistivity and perature
dielectric constant for sample 8-3.
against
tem-
Barrier
height
in barium
titanate
ceramics
Fig. 2. Scanning electron micrograph of a typical fracture surface of porous barium titanate ceramics showing large FTCR effects, which was obtained for sample A-3 which exhibited almost the same PTCR effect as that of sample B-3. Bar = 10 pm.
931
Barrier height in barium titanate ceramics eqn (1). The apparent dielectric constant 5 can be calculated from the capacitance, F, measured, using the equation P, = Fd/.&,, where d is the thickness of a sample and S, is the area of the electrode. The relationship between cr and e, may be given as 2, = c,/2b, where r is the average grain size of a sample and b may in turn be given as N,/N,. Equation (1) can thus be rewritten, using the above relations, as
,, 10 9 E,e 5 ? o q6 ;5
p = p. exp( e2Nsr/4ircokT).
(2)
4
Since the present materials examined have, however, considerable porosities, eqn (2) should be further revised into a form which allows for the influence of porosity on the effective contact area between grains prior to the analysis of the results obtained for the present porous materials. When the ratio of the effective sectional area, S, of a material to S, is given by f(p), i.e. S/S, =f(p), we obtain a revised form of eqn (2)
3
~=~~exp(e’hT,~f(p)/4~,~~kT).
(3)
Unfortunately, the exact form off(p) as a function of porosity p can not be known because of its complexity, but we can at least assume that the value off(p) increases monotonically as the porosity decreases in the porosity region here concerned. If the resistivity-temperature characteristics obtained for the present samples are described by eqn (3), one may expect linear relationships in the log p against IIF,T plot because N,, r and f(p) are all considered to be temperature independent constants. Figure 3 shows the log p against l/C,T plots of the resistivity-temperature characteristics obtained for the present samples, in which good linear relationships can be clearly seen. This shows that the resistivity-temperature characteristics of the porous materials above the Curie point can be described completely by the Heywang model. From this figure the value of p,,, which corresponds to the bulk resistivity of the ceramic grain, can be obtained by the extrapolation of the straight line to l/E;T = 0, and the value of NJ(p) can as well be obtained from the slope of the straight line. In addition, one may also calculate the height of a potential barrier by applying
21”““““““” 0
15 IO 10e/2.3~rT ( K-’)
5
Fig. 3. Logp against l/cJ plots for the present porous barium titanate ceramics. T, denotes Curie point.
eqn (1) to the straight
line in the plot. The values of
p. , IV,f ( p) calculated for r = 2 pm and 5 pm. and e+ both at the Curie point (T,) and at the maximum resistivity temperature (T,,), as well as slopes of the respective straight lines, from which the value of Nsf( p) was calculated, are given in Table 2. The height of the potential barriers at T,,, obtained for the present porous barium titanate ceramics, which was assumed to be nearly equal to the activation energy of the surface acceptor states in the Heywang model, is found to be nearly the same as the value estimated by him[S]. He estimated the activation energy of the surface acceptor states to be -0.9 eV and explained the PTCR effects of only 24 orders of magnitude. However, according to eqn (1) an increase in the potential height by a factor of S-10 over the temperature range from T,-T,,, seems to be enough to explain the PTCR effect of 7-8 orders of magnitude, and this has been successfully confirmed in the present study. The value of N,, on the other hand, cannot be determined unless the exact form of f(p) is known, but a set of data of N,!(p) obtained for samples Sl-1, Sl-2 and Sl-3 may enable one to make it possible to estimate the value of N,. The values of iV,f( p) calculated for samples Sl-1, Sl-2 and Sl-3, which have the same composition, are found to de-
Table 2. Results obtained for the present porous PTCR materials, where the slopes of the straight lines drawn in Fig. 3 are given in the third column N,f(p) Sample
P, (ohmcm)
A ("K)
20
b-2)
r=2pm-5um
e6 (@o at T, T,
Sl-1
2.5x103
4.0x107
3.8-1.5~101~
0.06
0.69
Sl-2
.2.5x103
3.0x107
2.9-1.2x1013
0.06
0.67
Sl-3
2.5x103
2.3~10~
2.2-O.9x1O13
0.08
0.69
52-2
2.5~10~
2.8x107
2.7- 1.1~101~
0.09
0.66
B -3
3.2~10~
2.6~10~
2.4- 1.0~101~
0.11
0.88
934
M.
KUWABARA
crease almost linearly with increasing porosity, and this seems to be successfully described by eqn (3) on the assumption that the value of f(p) increases with decreasing porosity. If the assumption is allowed, but without a theoretical basis, that f(p) can be given as l-p in the porosity region of interest, the value of N, can be obtained by the extrapolation of the straight line in the N,f( p) against p plot to p = 0. The value of N, estimated in this manner to be in the region of 1 X 1Or4 cm-’ seems to be reasonable in comparison with those which have been estimated by previous investigators[5, 6, 141. Figure 4 shows the Arrhenius plots of the resistivity obtained for the present samples. Since the height of the potential barrier is considered to be unchanged at temperatures above T,, the Arrhenius plot of the resistivity above T, is expected to give an activation energy nearly equal to the value of the potential barrier e4 at T,,,, and this can in fact be seen. Another experiment has been made to investigate how the adsorption of oxygen influences the magnitude of the PTCR effect, where the resistivity measurements were carried out under ambient gases having various reducing powers. The results are shown in Fig. 5. It is clearly seen that the magnitude of the PTCR effect can be easily degraded by exposing the material to a reducing gas, where the degree of degradation of the PTCR effect seems to proceed with an increase in the reducing power of the gases. In this figure a drastic degradation of the PTCR effect in CO gas is seen, and this may suggest that CO gas can significantly reduce the height of the potential barrier at the grain boundaries by eliminating the adsorbed oxygen from the grain surfaces. The adsorption of CO gas on the surfaces of n-type semiconductors is, on the other hand, usually considered to provide surface donor states which reduce the
IO
I air 2 02
9
3 N2 4 co2
F6
5 CH4
0
6 Co
0
T(T) Fig. 5. Ambient gas dependences of the resistivitytemperature characteristic for a RTCR material with the same composition as that of sample B-3.
resistivity of the materials, and this may also be the case for the data obtained in the present experiment. The rate of the resistivity change when the ambient gas was turned from O2 to CO, and vice versa, was measured at several temperatures. The results are shown in Fig. 6. From this figure the height of grain boundary potential barrier is found to be lowered very quickly at temperatures above 250°C in the CO atmosphere, and it is also found that the lowered potential barrier heights can be raised again very quickly by exposing the sample to O2 gas at those temperatures. This clearly indicate that twodimensional acceptor states formed by the adsorption of oxygen, the existence of which was postulated by Heywang, generate potential barriers at the grain
250.C
300
2-
2 103/T (K-l)
Fig. 4. Arrhenius plots of the resistivities present porous barium titanate ceramics. Curie point.
3
obtained for the Arrows indicate
0
I
2
3 t
4
5
6
7
(min)
Fig. 6. Response characteristics of the resrstivity for the FTCR material used in the experiment of the ambient gas dependence when the atmosphere was turned from 0, to CO, and vice versa, at several temperatures.
Barrier height in barium titanate ceramics
boundaries. From this experiment the assumption, proposed by Daniels et al., that three-dimensional acceptor states form potential barrier layers at the grain boundaries may be discarded in the present samples because the concentration of barium vacancies do not seem to change so quickly as seen in this figure at such low temperatures as those used in the present experiments. 4. CONCLUSION
In the present study, the resistivity-temperature characteristics of barium titanates in the FTCR region have been definitely confirmed to follow eqn (1) proposed by Heywang, and it has also been confirmed that the nature of acceptor states forming potential barriers at the grain boundaries is not barium vacancies concentrated in the region near the grain boundaries, but oxygen species adsorbed near the grain boundary interfaces. It is concluded that the mechanism of the PTCR effect can be described completely, at least from a phenomenological point of view, on the basis of the Heywang model. Acknowledgement-The
financial support of the Ministry of
Education, Science and Culture of Japan in the form of a Grant-in-Aid knowledged.
for Special Research, No. 57116001, is ac-
REFERENCES
1. 0. Saburi, J. Phys. Sot. Jpn. 14, 1159 (1959). 2. W. Heywang, Solid-St. Electron. 3, 51 (1961).
935
3. W.T. Peria, W. R. Bratshun and R. D. Fenity, J. Am, Ceram. Sot. 44, 249 (1961). 4. G. Goodman, J. Am. Ceram. Sot. 46, 48 (1963). 5. W. Heywang, J. Am. &ram. SW. 47, 484 .( 1964). 6. G. H. Jonker. Solid-St. Electron. 7. 895 (1964). 7. J. B. MacChesney and J. F. Potter, j. Am: Ceram. Sot. 48, 81 (1965). 8. G. T. Mallick, Jr. and P. R. Emtage, J. Appl. Phys. 39, 3088 (1968). 9. H. Schmelz, Phys. Status Solidi 35, 219 (1969). 10. B. M. Kulwicki and A. J. Purdes. Ferroelectrics 1. 253
(1970). 11. S. A. Long and R. N. Blumenthal, J. Am. Ceram. Sot. 54, 515 (1971). 12. M. Kahn, Am. Ceram. Sot. Bull. 50, 676 (1971). 13. P. Gerthscn and B. Hoffman, Solid-St. Electron. 16, 617 (1973). 14.
A. M. J. H. Seuter, Philips Res. Repts. Suppl. No. 3, (1974).
H. Ihrig, Phys. Status Solidi (a), 17, 437 (1978). 16. J. Daniels, K. H. Hardtle and R. Wemicke, Philips
15.
Tech. Rev. 38, 73 (1978/74). 17. P. W. Haaiiman. R.W. Dam and H. A. Klasens. West German Pa;. 924350, June 23, 1955. 18. C. A. Miller, J. Ph_vs. D. 4, 690 (1971). 19. M. Kuwabara, J. Am. Ceram. Sot. 64, 639 (1981). 20. M. Kuwabara, Jpn. J. Appl. Phys. 20, (1981) Suppl.
20-4, pp. 131-34. 21. B. Jaffe, W. R. Cook Jr. and H. Jaffe, Piezoelectric Ceramics, pp. 91-102. Academic Press, London (1971). 22. M. Kuwabara and H. Inoue, Proc. Int. Meeting on Chem. Sensors, Fukuoka, pp. 182-86, 19-22 September (1983). 23. T. Matsuoka, Y. Matsuo, H. Sasaki and S. Hayakawa, J. Am. Cerum. Sot. 55, 108 (1972). 24. H. Nemoto and I. Oda, J. Am. Ceram. Sot. 63, 398 (1980).