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Electrical nonlinearity of (Ni, Ta) doped SnO2 varistors
Materials Science and Engineering B99 (2003) 465 /469 www.elsevier.com/locate/mseb
Electrical nonlinearity of (Ni, Ta) doped SnO2 varistors Jin-Feng Wang *, Hong-Cun Chen, Wen-Xin Wang, Wen-Bin Su, Guo-Zhong Zang School of Physics and Microelectronics, National Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, PR China Received 14 June 2002; received in revised form 10 October 2002
Abstract The electrical nonlinearity of (Ni, Ta) doped SnO2 varistor system was investigated. The nonlinear coefficient a and the barrier height of this varistor system were calculated. It is found that the variations of electrical nonlinear coefficients with acceptor concentrations are in accordance with that of the barrier heights. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm 1 at 1 mA cm 2), but presents a relatively low densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses the highest breakdown electric field (469 V mm 1 at 1 mA cm 2) and the highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged acceptors substituting for Sn ions should not be located at the grain interfaces instead at SnO2 lattice sites of depletion layers. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Schottky barrier; Nolinear electrical properties; SnO2; Varistor
1. Introduction In recent years the new SnO2-based varistors attract one’s attention. Pianaro et al. succeeded in preparing SnO2-based varistor ceramics by doping Co2O3 and Nb2O5, they found that SnO2-based ceramics doped with 1.00 mol% CoO and 0.05 mol% Nb2O5 was a promising varistor material [1 /5]. Wang et al. found that (Bi, Nb) doped SnO2 and (Zn, Nb) doped SnO2 also possessed varistor nonlinearity [6,7]. Ni is a similar transition metal element to Co, and their ionic radiuses are quite similar (Ni2, 0.072 nm; Ni3, 0.062 nm; Co2, 0.074 nm; Co3, 0.063 nm). Ta and Nb belong to the same family, and their ionic radiuses are similar (Ta5, 0.073 nm; Nb5, 0.070 nm). Compared to Pianaro’s (Co, Nb) doped varistors, the (Ni, Ta) doped SnO2 should possess varistor properties. Based on this idea, the SnO2-based varistor system by doping Ni2O3 and Ta2O5 was prepared, and the effects
* Corresponding author. Tel.: /86-531-856-7851; fax: /86-531837-7031 E-mail address: [email protected] (J.-F. Wang).
of Ni dopant the electrical nonlinearity of the Ta-doped SnO2 varistor system were investigated. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged acceptors substituting for Sn ions should not be located at the grain boundaries instead at lattice sites.
2. Experimental procedure The oxides used in this study were analytical grade of SnO2 (99.5%), Ni2O3 (99%), Ta2O5 (99.95%). The molar composition was (99.95/x )% SnO2/x % Ni2O3/ 0.05% Ta2O5, with x /0.25, 0.5, 0.75, 1.0, and 2.0. Varistors were obtained by conventional ceramic processing. Powders were gained by ZrO2-ball milling process with alcohol for 12 h, then the dried powders with 5 wt.% PVA bond were pressed at 180 MPa into pellet shape (15 mm in diameter by 1.0 mm in thickness). Samples were put into Al2O3 crucible, fully surrounded with the powder of matching composition and sintered
0921-5107/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 4 7 5 - 0
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in air at 1375, 1420, and 1470 8C, separately, for 1 h and slowly cooled to room temperature. The ceramic phase was observed by X-ray diffraction (XRD). For microstructure characterization, the samples were analyzed by scanning electron microscopy (SEM). For electrical characterization of current density versus applied electrical field, an I /V graph (QT2) was used.
3. Results Fig. 1 shows the XRD patterns of pure SnO2 and SnO2 varistor doped with 2.0 mol% Ni2O3 and 0.05 mol% Ta2O5. The XRD pattern has no apparent second phases as ZnO-based varistors, but the matrix of SnO2 rutile phase. The SEM micrographs of the varistors doped with 0.5 mol% Ni2O3, 0.75 mol% Ni2O3, 1 mol% Ni2O3, 2 mol% Ni2O3 are shown in Fig. 2. It can be seen that the grains are tightly close each other and the grains grow larger with increasing Ni2O3 concentrations. The nonlinear characteristic in electrical properties of the SnO2 ×/Ni2O3 ×/Ta2O5 system sintered at 1420 8C is shown in Fig. 3. The relations of the barrier heights and the electrical nonlinear coefficients of the varistors sintered at 1420 8C with Ni2O3 concentrations are shown in Fig. 4. The electrical nonlinear coefficient a was obtained by a
log(I2 =I1 ) ; log(V2 =V1 )
Fig. 2. SEM microstruicture of (99.95/x )%SnO2 ×/x %Ni2O3 ×/ 0.05%Ta2O5 varistors sintered at 1420 8C, (a) x /0.5, (b) x/0.75, (c) x/1, (d) x/2.
(1)
where V1 and V2 are, respectively, the voltage at current I1 and I2. It is found from Fig. 4 that the barrier height and the coefficients of the varistors increases with the
Fig. 3. Electric field versus current for (99.95/x )%SnO2 ×/x % Ni2O3 ×/ 0.05% Ta2O5 sintered at 1420 8C: (a) x/0.25, (b) x/0.5, (c)x/ 0.75, (d) x/1.0, and (e) x /2.0.
amount of Ni2O3 up to 0.75 mol%, and that all reach a maximum for the 99.20% SnO2 ×/0.75% Ni2O3 ×/0.05% Ta2O5 composition, but that further increasing the concentration of Ni2O3 causes the barrier height and the nonlinear coefficients to decrease instead. Pianaro et al. [1] introduced a grain boundary defect model for (Co, Nb) doped SnO2 varistors analogous to the band comprising the Schottky barriers. For Schottky type of mechanism, the current density in ohmic region of a varistor is related to the electric field and temperature by Eq. (2) J AT 2 exp[(bE 1=2 fB )=kT] Fig. 1. XRD patterns of pure SnO2 and SnO2 varistor doped with 2.0 mol% Ni2O3 and 0.05 mol% Ta2O5.
2
3
(2)
where A , equal to 4remk /h , is Richardson’s constant, e is electron charge, m is electron mass, k is Boltzmann
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
467
4. Discussion The defects caused by acceptor and donor dopants in the SnO2 matrix should be responsible for the origin of the Schottky barriers at grain boundaries. But the detail of how acceptor and donor dopants penetrate into the SnO2 lattice is unclear. Since the deduction of substitution of acceptors and donors for Sn atoms is widely acceptable, how acceptor and donor atoms escaped from their oxides are not important for understanding varistor electrical nonlinear behavior. Therefore, we can consider that before substituting for Sn atoms the dopant oxides would be dissolved first: Fig. 4. Influence of Ni2O3 concentration on bB and a of the samples sintered at 1420 8C.
constant, h is Planck constant, fB is the interface barrier height, and b is a constant related to the relationship b8 1=(rv);
(3)
where r is the grain number per unit length and v is the barrier width. Making the current density in ohmic region and keeping the temperature of a tested varistor constant, from equations 1=2 J1 AT 2 exp[(bE1 fB )=kT]; J2 AT 2 exp[(bE21=2 fB )=kT];
(4) (5)
one can obtain fB and b . Table 1 shows the characteristic details of the (Ni, Ta) doped SnO2 varistors. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm1 at 1 mA cm 2), but presents a relatively lower densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses a highest breakdown electric field (469 V mm1 at 1 mA cm 2) and highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. The densities of (Ni, Ta) doped SnO2 varistors are somewhat low, the work for further improving the densities is under way.
1 Ni2 O3 0 2NiO O2 ; 2
(6)
1 NiO 0 Ni O2 ; 2
(7)
5 Ta2 O5 0 2Ta O2 : 2
(8)
At high firing temperature, oxygen vacancies and tin interstitials would be produced in SnO2 lattice: 1 SnO2 0 SnƒSn V::o Oxo O2 ; 2 x x x SnO2 0 VSn 2OO Snj ;
(9) (10)
where the inferior j denotes jamming. The ionic radius of Ni2 (0.072 nm) and Ni3 (0.062 nm) are similar to the ionic radius of Sn4 (0.071 nm). Ni coming into SnO2 lattice would occupy the tin vacancy according to: 1 NiVxSn 0 NiƒSn V::O O2 ; 2
(11)
1 2Ni2VxSn 0 2NiƒSn V::O O2 : 2
(12)
The atom in Eq. (11) presents two-valence, and the Ni atom in Eq. (12) presents three-valence. The oxygen vacancies not only speed up defects transporting, but also facilitate the shrinkage and densification of the varistor ceramics [8]. The reason that the grain grows
Table 1 Characteristics of SnO2 × Ni2O3 × Ta2O5 varistors Sintering temperature ( 8C)
Ni2O3 (mol%)
a
Density (g cm3)
Relative density (%)
E1mA (V mm1)
fB (eV) b 10 2 (eV V 1/2 mm 1/2)
1420 1420 1370 1420 1470 1420 1420
0.25 0.50 0.75 0.75 0.75 1.00 2.00
11.2 14.0 21.0 16.3 10.5 12.4 9.60
5.94 6.13 6.02 6.35 6.43 6.37 6.39
85.4 88.2 86.6 90.5 91.3 90.7 90.9
249 297 697 469 385 207 185
0.531 0.604 0.722 0.693 0.525 0.637 0.510
Theoretical density of SnO2 dt 6.95 g cm 3.
1.45 1.48 0.99 1.11 1.67 1.37 1.28
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
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larger with increasing Ni concentration, see Fig. 2, most probably originates from the emergence of oxygen vacancies. The addition of the donor dopants Ta2O5 in small amounts to the SnO2 lattice will leads to electron emergence according to: TaVxSn 0 Ta:Sn e?:
(13)
Snxj in interstitial sites cause the distortion of SnO2 lattice, which not only facilitate oxygen escaping from their lattice /
1 OxO 0 V::O 2e? O2 ; 2
(14)
but also make Snxj easily losing electrons to become positively charged ions Snxj Snxj Snxj Snxj
0 Sn:j e?; 0 Sn::j 2e?; 0 Sn::: j 3e?; 0 Sn:::: j 4e?:
(15) (16) (17) (18)
proposed by Gupta and Carlson [10] and the model for SnO2 based varistors by Bueno et al. [3], a modified defect barrier model for (Ni, Ta) doped varistors is introduced. In Fig. 5, the positively charged donors, Sn:j :::: :: : Sn::j ; Sn::: j ; Snj ; VO ; TaSn ; extending from both sides of a grain boundary are compensated by the negatively charged acceptors, NiƒSn ; Ni?Sn ; Oƒad ; O?ad : In the models proposed by Gupta and Carlson, as well as by Bueno et al., the negatively charged acceptors substituting for Sn locate at SnO2 grain interfaces. But, from Eqs. (11) and (12), one can see that the negatively charged acceptors substituting for Sn should locate at SnO2 lattice sites of depletion layers. This conclusion is also supported by the fact that a new phase precipitation in the grain boundary is not detected [1 /4]. It appears to us that the defect barrier model should be modified as shown in Fig. 5. Since a new phase precipitation in the grain boundary is not detected, the two barrier tops should touch each other. The depletion layers play an important role in the electric transport. This electric transport occurs by tunneling and is responsible for the nonlinear ohmic characteristic [7].
Oxygen in the above equations will be partly absorbed at SnO2 grain boundaries O2 0 2Oxad ;
(19)
where the inferior ad denotes adsorbed. Those absorbed oxygen easily capture electrons to become negatively charged ions Oxad e? 0 O?ad ; Oxad 2e? 0 Oƒad :
(20) (21)
The role of the absorbed oxygen in the formation of boundary barriers can be confirmed by conducting heat treatment for the varistors sintered at oxidizing and reducing atmospheres [5,9]. It is found from Fig. 4 and Table 1 that the solubility of the dopants has a maximum for the electrical nonlinearity of SnO2 based varistors. When the Ni2O3 exceeds 0.75 mol%, the extra Ni will not penetrate into SnO2 lattice instead of segregating at the boundary interfaces. The Ni segregating at boundaries will block defects transportation, which will impair the ceramics densification and the barrier formation. Why the solubility of the dopants has a maximum for the electrical nonlinearity of SnO2 based varistors is not sure, probably the capability of boundaries absorbing oxygen and the requirement of electricity neutrality would limit the dopants solubility. The essential concept of varistors is that the I /V behavior is controlled by electrostatic barrier existing at the grain boundaries. The defects introduced by dopant impurities make a SnO2 surface layer a depletion layer. All these localized defects originate a potential barrier associated with a double space charge distribution. By analogy with the model for ZnO based varistors
5. Conclusion (Ni, Ta) doped SnO2 ceramics possess a good electrical nonlinear behavior, but its density is somewhat low. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm1 at 1 mA cm 2), but presents a relatively poor densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses a highest breakdown electric field (469 V mm 1 at 1 mA cm 2) and highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged
Fig. 5. Schottky barriers model at grain boundary.
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
acceptors substituting for Sn ions should not stay at the grain interfaces instead at SnO2 lattice sites of depletion layers.
Acknowledgements Supported by the National Science Foundation of China under Grant No. 50072013.
References [1] S.A. Pianaro, P.R. Bueno, E. Longo, J.A. Varela, J. Mater. Sci. Lett. 14 (1995) 692 /694.
469
[2] S.A. Pianaro, P.R. Bueno, E. Longo, J.A. Varela, J. Mater. Sci. Lett. 16 (1997) 634 /638. [3] P.R. Bueno, S.A. Pianaro, E.C. Pereila, L.O.S. Bulhoes, E. Longo, J.A. Varela, J. Appl. Phys. 84 (1998) 3700 /3705. [4] A.C. Antunes, S.R.M. Antunes, S.A. Pianaro, M.R. Rocha, E. Longo, J.A. Varela, J. Mater. Sci. Lett 17 (1998) 577 /579. [5] E.R. Leite, A.M. Nascimento, P.R. Bueno, E. Longo, J.A. Varela, J. Mater. Sci. Mater. Electr. 10 (1999) 321 /327. [6] Y.J. Wang, J.F. Wang, C.P. Li, H.C. Chen, W.B. Su, W.L. Zhong, P.L. Zhang, L.Y. Zhao, Eur. Phys. J. AP. 11 (2000) 155 / 158. [7] Y.J. Wang, J.F. Wang, H.C. Chen, W.L. Zhong, P.L. Zhang, J. Phys. D: Appl. Phys. 33 (2000) 96 /99. [8] J.K. Varela, O.J. Whittemore, E. Longo, Ceram. Int. 16 (1990) 177 /181. [9] M.R.C. Santos, P.R. Bueno, E. Longo, J.A. Varela, J. Eur. Ceram. Soc. 21 (2001) 161 /165. [10] T.K. Gupta, W.G. Carlson, J. Mater. Sci. 20 (1985) 3487 /3500.
Electrical nonlinearity of (Ni, Ta) doped SnO2 varistors Jin-Feng Wang *, Hong-Cun Chen, Wen-Xin Wang, Wen-Bin Su, Guo-Zhong Zang School of Physics and Microelectronics, National Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, PR China Received 14 June 2002; received in revised form 10 October 2002
Abstract The electrical nonlinearity of (Ni, Ta) doped SnO2 varistor system was investigated. The nonlinear coefficient a and the barrier height of this varistor system were calculated. It is found that the variations of electrical nonlinear coefficients with acceptor concentrations are in accordance with that of the barrier heights. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm 1 at 1 mA cm 2), but presents a relatively low densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses the highest breakdown electric field (469 V mm 1 at 1 mA cm 2) and the highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged acceptors substituting for Sn ions should not be located at the grain interfaces instead at SnO2 lattice sites of depletion layers. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Schottky barrier; Nolinear electrical properties; SnO2; Varistor
1. Introduction In recent years the new SnO2-based varistors attract one’s attention. Pianaro et al. succeeded in preparing SnO2-based varistor ceramics by doping Co2O3 and Nb2O5, they found that SnO2-based ceramics doped with 1.00 mol% CoO and 0.05 mol% Nb2O5 was a promising varistor material [1 /5]. Wang et al. found that (Bi, Nb) doped SnO2 and (Zn, Nb) doped SnO2 also possessed varistor nonlinearity [6,7]. Ni is a similar transition metal element to Co, and their ionic radiuses are quite similar (Ni2, 0.072 nm; Ni3, 0.062 nm; Co2, 0.074 nm; Co3, 0.063 nm). Ta and Nb belong to the same family, and their ionic radiuses are similar (Ta5, 0.073 nm; Nb5, 0.070 nm). Compared to Pianaro’s (Co, Nb) doped varistors, the (Ni, Ta) doped SnO2 should possess varistor properties. Based on this idea, the SnO2-based varistor system by doping Ni2O3 and Ta2O5 was prepared, and the effects
* Corresponding author. Tel.: /86-531-856-7851; fax: /86-531837-7031 E-mail address: [email protected] (J.-F. Wang).
of Ni dopant the electrical nonlinearity of the Ta-doped SnO2 varistor system were investigated. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged acceptors substituting for Sn ions should not be located at the grain boundaries instead at lattice sites.
2. Experimental procedure The oxides used in this study were analytical grade of SnO2 (99.5%), Ni2O3 (99%), Ta2O5 (99.95%). The molar composition was (99.95/x )% SnO2/x % Ni2O3/ 0.05% Ta2O5, with x /0.25, 0.5, 0.75, 1.0, and 2.0. Varistors were obtained by conventional ceramic processing. Powders were gained by ZrO2-ball milling process with alcohol for 12 h, then the dried powders with 5 wt.% PVA bond were pressed at 180 MPa into pellet shape (15 mm in diameter by 1.0 mm in thickness). Samples were put into Al2O3 crucible, fully surrounded with the powder of matching composition and sintered
0921-5107/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 2 ) 0 0 4 7 5 - 0
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
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in air at 1375, 1420, and 1470 8C, separately, for 1 h and slowly cooled to room temperature. The ceramic phase was observed by X-ray diffraction (XRD). For microstructure characterization, the samples were analyzed by scanning electron microscopy (SEM). For electrical characterization of current density versus applied electrical field, an I /V graph (QT2) was used.
3. Results Fig. 1 shows the XRD patterns of pure SnO2 and SnO2 varistor doped with 2.0 mol% Ni2O3 and 0.05 mol% Ta2O5. The XRD pattern has no apparent second phases as ZnO-based varistors, but the matrix of SnO2 rutile phase. The SEM micrographs of the varistors doped with 0.5 mol% Ni2O3, 0.75 mol% Ni2O3, 1 mol% Ni2O3, 2 mol% Ni2O3 are shown in Fig. 2. It can be seen that the grains are tightly close each other and the grains grow larger with increasing Ni2O3 concentrations. The nonlinear characteristic in electrical properties of the SnO2 ×/Ni2O3 ×/Ta2O5 system sintered at 1420 8C is shown in Fig. 3. The relations of the barrier heights and the electrical nonlinear coefficients of the varistors sintered at 1420 8C with Ni2O3 concentrations are shown in Fig. 4. The electrical nonlinear coefficient a was obtained by a
log(I2 =I1 ) ; log(V2 =V1 )
Fig. 2. SEM microstruicture of (99.95/x )%SnO2 ×/x %Ni2O3 ×/ 0.05%Ta2O5 varistors sintered at 1420 8C, (a) x /0.5, (b) x/0.75, (c) x/1, (d) x/2.
(1)
where V1 and V2 are, respectively, the voltage at current I1 and I2. It is found from Fig. 4 that the barrier height and the coefficients of the varistors increases with the
Fig. 3. Electric field versus current for (99.95/x )%SnO2 ×/x % Ni2O3 ×/ 0.05% Ta2O5 sintered at 1420 8C: (a) x/0.25, (b) x/0.5, (c)x/ 0.75, (d) x/1.0, and (e) x /2.0.
amount of Ni2O3 up to 0.75 mol%, and that all reach a maximum for the 99.20% SnO2 ×/0.75% Ni2O3 ×/0.05% Ta2O5 composition, but that further increasing the concentration of Ni2O3 causes the barrier height and the nonlinear coefficients to decrease instead. Pianaro et al. [1] introduced a grain boundary defect model for (Co, Nb) doped SnO2 varistors analogous to the band comprising the Schottky barriers. For Schottky type of mechanism, the current density in ohmic region of a varistor is related to the electric field and temperature by Eq. (2) J AT 2 exp[(bE 1=2 fB )=kT] Fig. 1. XRD patterns of pure SnO2 and SnO2 varistor doped with 2.0 mol% Ni2O3 and 0.05 mol% Ta2O5.
2
3
(2)
where A , equal to 4remk /h , is Richardson’s constant, e is electron charge, m is electron mass, k is Boltzmann
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
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4. Discussion The defects caused by acceptor and donor dopants in the SnO2 matrix should be responsible for the origin of the Schottky barriers at grain boundaries. But the detail of how acceptor and donor dopants penetrate into the SnO2 lattice is unclear. Since the deduction of substitution of acceptors and donors for Sn atoms is widely acceptable, how acceptor and donor atoms escaped from their oxides are not important for understanding varistor electrical nonlinear behavior. Therefore, we can consider that before substituting for Sn atoms the dopant oxides would be dissolved first: Fig. 4. Influence of Ni2O3 concentration on bB and a of the samples sintered at 1420 8C.
constant, h is Planck constant, fB is the interface barrier height, and b is a constant related to the relationship b8 1=(rv);
(3)
where r is the grain number per unit length and v is the barrier width. Making the current density in ohmic region and keeping the temperature of a tested varistor constant, from equations 1=2 J1 AT 2 exp[(bE1 fB )=kT]; J2 AT 2 exp[(bE21=2 fB )=kT];
(4) (5)
one can obtain fB and b . Table 1 shows the characteristic details of the (Ni, Ta) doped SnO2 varistors. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm1 at 1 mA cm 2), but presents a relatively lower densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses a highest breakdown electric field (469 V mm1 at 1 mA cm 2) and highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. The densities of (Ni, Ta) doped SnO2 varistors are somewhat low, the work for further improving the densities is under way.
1 Ni2 O3 0 2NiO O2 ; 2
(6)
1 NiO 0 Ni O2 ; 2
(7)
5 Ta2 O5 0 2Ta O2 : 2
(8)
At high firing temperature, oxygen vacancies and tin interstitials would be produced in SnO2 lattice: 1 SnO2 0 SnƒSn V::o Oxo O2 ; 2 x x x SnO2 0 VSn 2OO Snj ;
(9) (10)
where the inferior j denotes jamming. The ionic radius of Ni2 (0.072 nm) and Ni3 (0.062 nm) are similar to the ionic radius of Sn4 (0.071 nm). Ni coming into SnO2 lattice would occupy the tin vacancy according to: 1 NiVxSn 0 NiƒSn V::O O2 ; 2
(11)
1 2Ni2VxSn 0 2NiƒSn V::O O2 : 2
(12)
The atom in Eq. (11) presents two-valence, and the Ni atom in Eq. (12) presents three-valence. The oxygen vacancies not only speed up defects transporting, but also facilitate the shrinkage and densification of the varistor ceramics [8]. The reason that the grain grows
Table 1 Characteristics of SnO2 × Ni2O3 × Ta2O5 varistors Sintering temperature ( 8C)
Ni2O3 (mol%)
a
Density (g cm3)
Relative density (%)
E1mA (V mm1)
fB (eV) b 10 2 (eV V 1/2 mm 1/2)
1420 1420 1370 1420 1470 1420 1420
0.25 0.50 0.75 0.75 0.75 1.00 2.00
11.2 14.0 21.0 16.3 10.5 12.4 9.60
5.94 6.13 6.02 6.35 6.43 6.37 6.39
85.4 88.2 86.6 90.5 91.3 90.7 90.9
249 297 697 469 385 207 185
0.531 0.604 0.722 0.693 0.525 0.637 0.510
Theoretical density of SnO2 dt 6.95 g cm 3.
1.45 1.48 0.99 1.11 1.67 1.37 1.28
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
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larger with increasing Ni concentration, see Fig. 2, most probably originates from the emergence of oxygen vacancies. The addition of the donor dopants Ta2O5 in small amounts to the SnO2 lattice will leads to electron emergence according to: TaVxSn 0 Ta:Sn e?:
(13)
Snxj in interstitial sites cause the distortion of SnO2 lattice, which not only facilitate oxygen escaping from their lattice /
1 OxO 0 V::O 2e? O2 ; 2
(14)
but also make Snxj easily losing electrons to become positively charged ions Snxj Snxj Snxj Snxj
0 Sn:j e?; 0 Sn::j 2e?; 0 Sn::: j 3e?; 0 Sn:::: j 4e?:
(15) (16) (17) (18)
proposed by Gupta and Carlson [10] and the model for SnO2 based varistors by Bueno et al. [3], a modified defect barrier model for (Ni, Ta) doped varistors is introduced. In Fig. 5, the positively charged donors, Sn:j :::: :: : Sn::j ; Sn::: j ; Snj ; VO ; TaSn ; extending from both sides of a grain boundary are compensated by the negatively charged acceptors, NiƒSn ; Ni?Sn ; Oƒad ; O?ad : In the models proposed by Gupta and Carlson, as well as by Bueno et al., the negatively charged acceptors substituting for Sn locate at SnO2 grain interfaces. But, from Eqs. (11) and (12), one can see that the negatively charged acceptors substituting for Sn should locate at SnO2 lattice sites of depletion layers. This conclusion is also supported by the fact that a new phase precipitation in the grain boundary is not detected [1 /4]. It appears to us that the defect barrier model should be modified as shown in Fig. 5. Since a new phase precipitation in the grain boundary is not detected, the two barrier tops should touch each other. The depletion layers play an important role in the electric transport. This electric transport occurs by tunneling and is responsible for the nonlinear ohmic characteristic [7].
Oxygen in the above equations will be partly absorbed at SnO2 grain boundaries O2 0 2Oxad ;
(19)
where the inferior ad denotes adsorbed. Those absorbed oxygen easily capture electrons to become negatively charged ions Oxad e? 0 O?ad ; Oxad 2e? 0 Oƒad :
(20) (21)
The role of the absorbed oxygen in the formation of boundary barriers can be confirmed by conducting heat treatment for the varistors sintered at oxidizing and reducing atmospheres [5,9]. It is found from Fig. 4 and Table 1 that the solubility of the dopants has a maximum for the electrical nonlinearity of SnO2 based varistors. When the Ni2O3 exceeds 0.75 mol%, the extra Ni will not penetrate into SnO2 lattice instead of segregating at the boundary interfaces. The Ni segregating at boundaries will block defects transportation, which will impair the ceramics densification and the barrier formation. Why the solubility of the dopants has a maximum for the electrical nonlinearity of SnO2 based varistors is not sure, probably the capability of boundaries absorbing oxygen and the requirement of electricity neutrality would limit the dopants solubility. The essential concept of varistors is that the I /V behavior is controlled by electrostatic barrier existing at the grain boundaries. The defects introduced by dopant impurities make a SnO2 surface layer a depletion layer. All these localized defects originate a potential barrier associated with a double space charge distribution. By analogy with the model for ZnO based varistors
5. Conclusion (Ni, Ta) doped SnO2 ceramics possess a good electrical nonlinear behavior, but its density is somewhat low. 0.75 mol% Ni2O3 doped sample sintered at 1370 8C exhibits a high nonlinear coefficient a of 21 and a high breakdown electric field (697 V mm1 at 1 mA cm 2), but presents a relatively poor densification. Among the samples sintered at 1420 8C, the sample doped with 0.75 mol% Ni2O3 and 0.05 mol% Ta2O5 possesses a highest breakdown electric field (469 V mm 1 at 1 mA cm 2) and highest electrical nonlinear coefficient a of 16.3, which is consistent to its highest defect barrier fB of 0.693 eV. An atom mode for the acceptors and donors to penetrate into SnO2 lattice was put forward. To illustrate the grain-boundary barrier formation of (Ni, Ta) doped SnO2 varistors, a modified defect barrier model was introduced, in which the negatively charged
Fig. 5. Schottky barriers model at grain boundary.
J.-F. Wang et al. / Materials Science and Engineering B99 (2003) 465 /469
acceptors substituting for Sn ions should not stay at the grain interfaces instead at SnO2 lattice sites of depletion layers.
Acknowledgements Supported by the National Science Foundation of China under Grant No. 50072013.
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