Influence of GeO2 on the microstructure and electrical properties of TiO2–Nb2O5–Ho2O3 –SiO2 varistors

Journal Pre-proof Influence of GeO2 on the microstructure and electrical properties of TiO2–Nb2O5– Ho2O3 –SiO2 varistors Fengchao Peng, Dachuan Zhu, Qun Yan, Yadong Li PII:

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https://doi.org/10.1016/j.matchemphys.2020.122638

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MAC 122638

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Materials Chemistry and Physics

Received Date: 16 October 2019 Revised Date:

6 January 2020

Accepted Date: 7 January 2020

Please cite this article as: F. Peng, D. Zhu, Q. Yan, Y. Li, Influence of GeO2 on the microstructure and electrical properties of TiO2–Nb2O5–Ho2O3 –SiO2 varistors, Materials Chemistry and Physics (2020), doi: https://doi.org/10.1016/j.matchemphys.2020.122638. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Influence of GeO2 on the microstructure and electrical properties of TiO2-Nb2O5 -Ho2O3 -SiO2 varistors Fengchao Penga, Dachuan Zhua,*, Qun Yana, Yadong Lib a

College of Material Science and Engineering, Sichuan University,

Chengdu Sichuan, 610065, China b

Shanxi Aerospace Qinghua Equipment Co., Ltd, Changzhi Shanxi,

046000, China a

Fengchao Peng; E-mail: [email protected]

* Corresponding author; E-mail: [email protected] (D. C. Zhu) a

Qun Yan; E-mail: [email protected]

b

Yadong Li; E-mail: [email protected]

Postal address: College of Material Science and Engineering, Sichuan University, Chengdu, Sichuan, P.R. China.

Abstract: TiO2 varistor ceramics co-doped with GeO2, Ho2O3, Nb2O5 and SiO2 were prepared by a conventional solid-state method. Meanwhile, the effects of GeO2 on the microstructure, varistor properties and dielectric properties were investigated in details. The SEM-EDS results revealed that the addition of GeO2 could induce more Nb5+ and Ho3+ ions to dissolve into TiO2 matrix and make Ho3+ ions well-distributed. Moreover, the incorporation of GeO2 significantly improved the dielectric properties. All samples showed a good temperature (-150～200

) and

frequency（100 Hz～100 kHz） stability of dielectric properties and the

sample with 0.9 mol% GeO2 obtained a giant dielectric constant about 2.68×105. Besides, the doping of GeO2 was found to be capable of reducing the breakdown voltage and increasing the nonlinear coefficient as well. Particularly, the 0.3 mol% GeO2-doped sample possessed a low breakdown voltage of 2.7 V/mm and the one doped with 0.6 mol% GeO2 showed the maximum nonlinear coefficient value of 6.7. Keywords: TiO2 varistor ceramic; Dielectric properties; Varistor properties; Grain-boundary barrier model 1 Introduction Varistors with nonlinear electrical property have drawn considerable attentions owing to their applications in overvoltage protection, high-energy surge absorption and high-voltage stabilization1-2. During the past decades, several categories of varistors have been intensively studied, such as ZnO-based3, SnO2-based4, TiO2-based5 varistors and so on. Among them, ZnO-based varistor ceramics have been extensively applied due to their excellent electrical properties of high breakdown voltage and high nonlinear coefficient. However, with the development of electronic devices towards miniaturization, it is necessary for varistors to integrate the low breakdown voltage with multi-function including dielectric properties6-7. Apparently, ZnO-based varistors cannot meet this demand. In this situation, TiO2-based varistors, possessing a relatively low

breakdown voltage and a high dielectric constant, have attracted much interest8-9. In order to obtain excellent varistor properties or a colossal dielectric constant, TiO2-based varistors have been broadly researched since they were found in Bell Labs in 1982. Nowadays, most studies concentrate on TiO2 ceramics doped with metallic oxides, such as Nb2O5, Ta2O5, MnO2, Cr2O3, Bi2O3 and rare earth oxides. Neto et al. studied the effect of Nb on the TiO2-Cr2O3 system10, and the result showed that the breakdown voltage increased from 4.41 V/mm to 9.71 V/mm and nonlinear coefficient varied from 4.6 to 15.3 with the increase of Nb2O5. Gong et al. investigated the effect of MnO2 on the nonlinear electrical properties of TiO2 varistors11 and found that 0.3 mol% MnO2 endowed the TiO2 varistor sample with a homogeneous microstructure and excellent electrical properties, with the breakdown voltage of 4.95 V/mm, the nonlinear coefficient of 5.07 and the dielectric constant of 11.09×104. Delbrücke et al.12 found that the single dopant SrO had a significant influence on microstructure and electrical properties. Experimental results revealed that a small amount of SrO is beneficial to improve nonlinear coefficient, whereas excessive SrO is deleterious to the electric properties due to the formation of SrTiO3 layer at the grain boundary. Li and Wang13 reported that (99.75%TiO2 -0.60%Y2O3 -0.10% Nb2O5) TiO2 varistor system exhibited a very high and narrow grain boundary barrier, which

induced a low breakdown voltage of 8.8 V/mm, a high nonlinear coefficient of 7.0 and an ultrahigh dielectric constant of 7.6×104. Gong and Chu14 obtained the maximum dielectric constant value of 1.64×105 and excellent varistor properties in the 0.3 mol% Pr6O11-doped TiO2 ceramics. Similar results were obtained by doping other rare earth oxides in these literatures15-16. Recently, Kang et al17. found that co-doping (Ge-GeO2) was helpful to decrease breakdown voltage while heighten nonlinear coefficient. Particularly, the samples doped with 0.4 mol% Ge and 1.2 mol% GeO2 showed the optimal electrical properties, with the highest nonlinear coefficient of 12.1 and a low breakdown voltage of 20.8 V/mm. However, the dielectric properties were not reported in their works. In fact, TiO2 varistor ceramics have been universally thought as potential dielectric materials. To qualify for promising applications concerning dielectric materials, TiO2 ceramics need to possess a high dielectric constant at room temperature or a specific frequency, and simultaneously maintain a good frequency and temperature stability, as suggested by Li and Amaral’s group18-19. Currently, the stability of dielectric properties is rarely mentioned in the studies about TiO2 varistor ceramics. In this work, we investigated the effects of GeO2 on the microstructure and electrical properties of TiO2 ceramics on the basis of our previous work20. Especially, the stability of dielectric property at different

frequency and temperature was investigated. Moreover, a defect model was established to illustrate the formation of barriers on the TiO2 grain boundary. 2 Experimental procedure TiO2 ceramics in this work were prepared by a conventional solid-state reaction method and the designed composition of samples was shown in Table 1. The raw chemical materials including rutile TiO2 (99.0%,), Nb2O5 (99.99%), SiO2 (99.0%) and Ho2O3 (99.9%) were purchased from Chengdu Chron Chemicals Co., Ltd. China, while GeO2 (99.999%) was obtained from Sinopharm Chemical Reagent. China. Firstly, all powders were weighted according to the designed fraction and then mixed in planetary mill by agate ball for 10 h, using anhydrous ethanol as medium. Next the mixed slurry was dried in an oven at 60

for 24 h. The dried

mixtures were combined with moderate 5 wt% polyvinyl alcohol (PVA) as the binder and then were pressed into disks of 15mm in diameter and 2 mm in thickness under a pressure of 120 MPa. All green pellets were sintered in air for 2 h at 1400 , and then cooled naturally to room temperature. In purpose of measuring electrical properties, both sides of the pellets were coated with silver and then sintered at 600

for 30

minutes to form electrodes. The schematic synthetic route of TiO2-based varistor ceramics was shown in Fig.1. Apparent density was measured by Archimedes method using

a solid densimeter (ET-320, Etnaln, Beijing, China). The crystal phase of TiO2 ceramic samples was identified by an X-ray diffraction (XRD) machine (DX-2000) with Cu Kα radiation at a scanning speed of 0.04°s-1 within 2θ range of 20-80°. The surface microstructure of TiO2 ceramic samples was observed by scanning electron microscopy (SEM, JSM-7500F; Jeol, Japan) after samples were polished and thermally etched at 1300

for 20 minutes. Energy-dispersive X-ray spectroscopy

(EDS) was performed to analyze the elements contents and distributions. The breakdown voltage, nonlinear coefficient and J-E characteristic curves were measured by a varistor DC parameter instrument (CJ1001). The dielectric constant and dielectric loss of TiO2 ceramic samples were recorded on an LCR meter (TH2816A) at 1 kHz. Meanwhile, correlations of dielectric properties with temperature were assessed over the temperature range of -150 – 200

at a heating rate of 1

·min-1 with a

frequency of 1 kHz. Variations of the dielectric properties with frequencies were examined by an impedance analyzer (Agilent 4294A) over a range of 100 Hz–100 kHz. Table1. Designed composition of TiO2-based varistor ceramics. Sample S1 S2 S3 S4 S5

Raw materials (mol%) TiO2

Nb2O5

SiO2

Ho2O3

GeO2

99.05 98.75 98.45 98.15 97.85

0.2 0.2 0.2 0.2 0.2

0.3 0.3 0.3 0.3 0.3

0.45 0.45 0.45 0.45 0.45

0 0.3 0.6 0.9 1.2

Fig. 1. Schematic illustration of synthetic route of TiO2-based varistor ceramics. 3 Results and Discussion 3.1 Phase Composition and Microstructure Analysis The XRD patterns of TiO2 varistor ceramic samples doped with different amount of GeO2 are demonstrated in Fig 2. Fig. 2(a) shows that all samples possess a TiO2 rutile phase and a minor phase of Ho2TiO5, which is demonstrated as a second phase in our previous work20. Fig. 2(b) illustrates the enlarged spectra of Fig. 2(a) near 2θ = 27.5°. After the GeO2 is doped in, the peaks shift to low-angle direction. Moreover, with the increase of GeO2 content, the shift becomes noticeable. The results indicate that doping GeO2 can change the crystal structure of TiO2 varistor ceramics. It is noteworthy that the radius of Ge4+ (0.053 nm) is close to that of Ti4+ (0.061 nm), so Ge4+ ions can easily dissolve into TiO2 lattice and cause a slight increment of the atomic plane spacing17.

According to Bragg equation11, if the atomic plane spacing widens, the diffraction angle would diminish, i.e., 2θ starts to shift to lower angle. λ=2dsinθ

(1)

where λ is X-ray wavelength, d is the atomic plane spacing, and θ is the angle of incident wave and crystal plane.

Fig. 2. XRD patterns of TiO2 samples doped with different amount of GeO2. Fig. 3 reveals the surface microstructure of samples doped with 0, 0.3, 0.6, 0.9 and 1.2 mol% GeO2. With the content of GeO2 increasing, all the samples display a dense microstructure and relative density of each sample is 97.4%, 97.9%, 97.5%, 97.6%, 96.9% respectively. Fig. 4 shows the statistics of grain size of the TiO2 ceramics. It is noted that the grain size of samples slightly increases after doped with GeO2 and reaches a

maximum of 8.74 µm at 0.9 mol% GeO2. The growth of grain can be ascribed to the low melting point of GeO2 (1086 are sintered at 1400

). When the samples

, GeO2 particles will melt to liquid phase and

accelerate the diffusion of ions and vacancies, promoting the grain growth. Similarly, F. Amaral’s work indicates that the addition of GeO2 is an effective way to accelerate grain size enlargement of CCTO ceramics21. In addition, the standard deviation of grain size can be obtained from Fig. 4, which turns out to be 0.129 µm for the GeO2-free sample and 0.110, 0.104, 0.115, 0.123 µm for the 0.3, 0.6, 0.9, 1.2 mol% GeO2-doped samples respectively. From the decrease of the standard deviation, it can be deduced that doping GeO2 is favorable to the uniformity of grain size.

Fig. 3. The surface microstructure of TiO2 varistor ceramics doped with different concentration of GeO2.

Fig. 4. The statistics of grain sizes in the TiO2 varistor ceramics doped with different concentration of GeO2. In order to clearly understand the effect of GeO2 on the grain and grain boundary of TiO2 ceramics, the EDS spot analysis of samples doped with 0 mol% and 0.9 mol% GeO2 was conducted respectively. Fig. 5 shows the element contents inside the grains and at the grain boundary, wherein one can observe that the addition of GeO2 has an evident effect on the distribution of Nb and Ho. The contents of Nb and Ho inside the grains of GeO2-doped TiO2 ceramics are higher than those of the undoped sample. At the grain boundaries, however, GeO2-free sample tends to have more Nb and Ho. It is deduced that the incorporation of Ge4+ ions into TiO2 matrix can generate a certain extent of lattice distortions, thereby enabling more Nb5+ and Ho3+ ions to dissolve into the grains. In addition,

the dissolution of Ho will change the amount of the oxygen vacancies, resulting in the growth of grains15, which is consistent with the microstructural observation from Fig. 3. The elemental mapping graphs of Ho doped in TiO2 ceramics are shown in Fig. 6. It can be seen that the distribution of Ho in TiO2 ceramic with 0.9 mol% GeO2 is more even in comparison with that of the undoped samples. Notably, the segregation of Ho at TiO2 grain boundaries is alleviated after doping GeO2, which may change the distribution and content of the second phases.

Fig. 5. The element contents in the grains and at the grain boundaries of samples with 0 mol% and 0.9 mol% GeO2.

Fig. 6. Elemental mapping of TiO2 ceramics doped 0 mol% and 0.9 mol% GeO2. 3.2 Current-Voltage characteristic curves analysis Fig. 7(a) shows the current density(J)- electrical voltage (E) relations of TiO2 varistor ceramics with different content of GeO2. The curves in Fig. 7(a) can be divided into two important parts. One is low-current linear region, in which the sample possesses ultra-high resistivity. The other is high-current nonlinear region, where current sharply increases with a small increment of applied electric voltage. Basically, the flatter the J-E curve in the high-current region presents, the better varistor properties are. It is observed that the curves of samples doped with GeO2 in high-current region are flatter compared with those of the undoped ones, indicating that doping of GeO2 is beneficial to the enhancement of the varistor properties. The nonlinear current-voltage characteristic curve can be explained by

the theory of double Schottky potential barriers, which points out that the resistivity in low-current region is dominated by potential grain boundary barrier when the applied voltage is at a low level. But when the applied voltage surpasses a certain value, the resistivity of TiO2 varistor will dramatically decline because of the tunneling effect. Therefore, according to the theory, the relationship of J and E in low current region is given by Eq. (2)22. In order to calculate the value of Φ , β, we transform the Eq. (2) to Eq. (3) by mathematical method. J= A*T2exp ( lnJ =

/

)

E1/2 +lnA*T2﹣

(2) (3)

where A* is the Richardson constant, K is Boltzmann constant, and T is the absolute temperature, Φ is the interface barrier height, β is related to the barrier width ω by the relationship Eq. (4)23: β= [(

)] 1/2

)(

(4)



where dn is the number of grains per unit length, e is the electron charge (1.602×10-19C), and

is

the vacuum dielectric constant (8.85×10-14 F/cm),

is the intrinsic dielectric constant of TiO2 (114)24. The lnJ-E1/2

curves are plotted in Fig. 7(b). The value of Φ can be obtained from the intersection of the extrapolated line of the plot with lnJ axis, and the value of β can be acquired from the slope of the curve. Further, the value of the barrier width ω is calculated by Eq. (4). In addition, the donor density ND and the density of interface states NS at the grain boundary are

estimated by the following equations25: ω2=

(5)

NS=ND ω

(6)

Some characteristics of TiO2 ceramics samples with different concentration of GeO2 are given in Table 2.

Fig. 7(a) J-E characteristic curves and (b) lnJ-E1/2 curves of TiO2 samples doped with different amount of GeO2.

Table 2. Electrical characteristics of TiO2 samples doped with different GeO2(mol%)

d(µm)

Φb(V)

Ns (1016m-3)

ND (1025m-3)

ω(10-9m)

0

8.28

0.455

17.67

0.62

28.41

0.3

8.36

0.466

63.74

7.90

8.07

0.6

8.47

0.471

66.88

8.61

7.77

0.9

8.74

0.469

66.76

8.60

7.76

1.2

8.49

0.462

58.61

6.74

8.69

amount of GeO2.

3.3 Effect of GeO2 on the dielectric properties Fig. 8 shows the dielectric constant (εr) and dielectric loss (tanσ) of TiO2 ceramic samples measured at the frequency of 1 kHz and at room temperature. As shown in Fig. 8, the dielectric loss of samples continuously rises, reaching a maximum value at 0.9 mol% GeO2, and then drops with higher GeO2 content. Meanwhile, the dielectric constant of samples can be also enhanced by doping GeO2. Remarkably, 0.6 mol% GeO2-doped sample possesses the highest εr of about 2.68×105, which is superior to the previous results26-28. In this study, the giant dielectric constant of samples doped with GeO2 can be explained by the following mechanisms. Firstly, the distribution of the second phase (Ho2TiO5) at the grain boundary plays a crucial role in relative permittivity29. The results of elemental mapping and EDS spot analysis suggest an even distribution and a reduction in the content of the second phase after doping GeO2, which can lead to a thinner insulating layer. Secondly, the grain growth is also responsible for the colossal dielectric constant, and their relationship is expressed by the following Eq. (7)30: εr=εbdg/tB

(7)

where εb is the intrinsic dielectric constant of TiO2, dg is the mean grain size and tB is the average width of grain boundary. According to Eq (7), εr is proportional to dg/tB. Thus, the giant εr of sample doped with GeO2 may

be attributed to its relative high dg/tB.

Fig. 8 The dielectric constant (εr) and dielectric loss (tanσ) of TiO2 ceramic samples measured at 1 kHz. Fig. 9 shows the temperature dependence of dielectric properties of TiO2 ceramics samples doped with different amount of GeO2, measured at a frequency of 1kHz and within the temperature range of -150～200

. It

can be clearly observed in Fig.9 that dielectric constant of TiO2 ceramics is enhanced after the incorporation of GeO2, maintaining a giant value (104～105) over a wide temperature range of -150～200 temperature of about 0

except for the

, where electrons hopping between Ti3+ and Ti4+

ions gives rise to a relative dielectric relaxation31. In general, the samples exhibit a good temperature stability of dielectric constant when

temperature changes from -150

to 200

. However, the dielectric loss

is changeable over the temperature range, showing a poor temperature stability.

Fig. 9. Temperature dependence of dielectric constant and dielectric loss of TiO2 ceramics, measured at 1 kHz over the temperature range of -150～200

.

Fig. 10 exhibits the frequency dependence of dielectric property of TiO2 ceramics samples, measured in a frequency range of 100 Hz-100 kHz at room temperature. As shown in Fig.10, the correlations of relative permittivity and dielectric loss of all TiO2 ceramic samples with frequency is not strong. It is noted that the εr values of all samples decline slowly while the loss tanσ values increase gradually, which is indicative of a good frequency stability. Furthermore, compared with the undoped

samples, the doping of GeO2 endows the TiO2 ceramics with a higher dielectric constant and dielectric loss, and 0.6 mol% GeO2 is proved to have the optimum effect.

Fig. 10. Frequency (10 Hz-100 kHz) dependence of dielectric constant and dielectric loss of TiO2 ceramics, measured at room temperature. 3.4 Varistor properties analysis Fig. 11 shows the varistor properties of TiO2 ceramics doped with different amount of GeO2. One can clearly see that doping GeO2 can dramatically reduce the breakdown voltage (E1mA) of TiO2 ceramics. Particularly, the sample doped with 0.3 mol% GeO2 obtains the lowest E1mA of approximately 2.7 V/mm, which is better than the previous reported results32-34. The decrease of breakdown voltage can be explained by the following reasons. Firstly, the radius of Ge4+ is similar to that of

Ti4+, which makes it easy for GeO2 to dissolve into the TiO2 lattice and thus decrease the resistivity of grains33. Furthermore, GeO2 promotes more Ho3+ ions to merge into TiO2 grains, thus the content of second phase Ho2TiO5 at grain boundary will decrease, resulting in a reduction of grain boundary impedance35. Both of the two factors contribute to the lessening of breakdown voltage. Secondly, breakdown voltage E1mA is related to the average grain size dg and can be expressed by the equation14 : E1mA = L/dg Vgb

(8)

where L is the sample thickness and Vgb is the voltage barrier of per grain boundary. As listed in Table 2, the grain size slightly increases after sample doped with GeO2, thereby diminishing E1mA, according to Eq. (8).

Fig. 11. The breakdown voltage (E1mA) and nonlinear coefficient (α) of TiO2 ceramics with different amount of GeO2. As depicted in Fig. 11, the doping of GeO2 is also of benefit to the increase of nonlinear coefficient α and the 0.6 mol% GeO2-doped sample possesses a maximum value of 6.7. However, the nonlinear properties start to deteriorate when the dopant exceeds 0.6 mol%. It is widely acknowledged that the nonlinear coefficient is associated with grain boundary36-37. To understand the effects of GeO2 on the nonlinear electrical properties, a barrier model for TiO2 varistor ceramics is established, which is similar to the grain-boundary barrier model proposed in ZnO-based38 and SnO2-based4 varistor ceramics, as shown in Fig. 12. On the one hand, the positive charged defects introduced by Nb2O5 are distributed at both sides of grain and form a depletion layer; on the other hand, the negative charged defects generated by Ho2O3 deposit at the grain boundary interface to compensate for the positive charged ones. The charged defects above are generated through the solid dissolution, as illustrated in the following defect equations: !"#

,

Nb2O5$%&2'()! +2*+4"× " + "# (g) #

!"#

,

× 2TiO2 $%&2 !- ! +.#) / +3"" + "# (g) #

!"#

#) Ho2O3$%&20/- ! +3"× " +./

(9) (10) (11)

The radius of Nb5+ is close to that of Ti4+, hence Nb5+ ions are able to easily dissolve into TiO2 lattice. According to the Eq. (9), the substitution of Nb5+ for Ti4+ can introduce free electrons, which are beneficial to the formation of barrier and would be captured by nearby Ti4+ to from Ti3+ acceptor

39

. Meanwhile, the substitution can also introduce positive

charged defects Nb5 Ti . Additionally, the dissolution of Ho2O3 can generate negative charged defects 67-89 and oxygen vacancies :7#)

. The

dissolution process about Eq. (9), (10) and (11) is shown in Fig. 13. The radius of Ho3+ (0.0901nm) is much larger than that of Ti4+ (0.061nm), so most of Ho3+ ions are prone to segregate at the grain boundary and only small traces of Ho3+ ions can dissolve into TiO2 lattice.

Fig. 12. The barrier model for TiO2 ceramic.

Fig.13.

The effects of Ho and Nb on the crystal structure of TiO2

ceramics system. As mentioned before, the addition of GeO2 can cause a certain extent of lattice distortion, which induces more Nb2O5 and Ho2O3 to dissolve into TiO2 matrix and then generate more oxygen in the grains. According to the reactions (12), (13) and (14), the oxygen emigrates to the grain boundary through high temperature chemical absorption, and then captures electrons to form negatively charged defects <- and <-- .

= (g) → =?

=? +e → =

=- +e→

=--

(12) (13) (14)

Consequently, the density of interface states NS will increase, resulting in the improvement of barrier height @A , which accords with Table 2. It is known from the Eq. (15): B

α= DE F/# C

(15)

where γ is a constant, E is the strength of external applied electric field.

According to Eq. (15), the improvement of barrier height will enhance the nonlinear coefficient α. When the concentration of GeO2 exceeds 0.6 mol%, however, a great deal of Ge4+ ions dissolving into TiO2 matrix will generate severe lattice distortion, which hinders the transportation of vacancies and electrons. Oxygen vacancies :7#) in the grains will combine electrons and oxygen under this situation. The reaction is shown in Eq. (16) ,



× .#) / +2*+ "# (g) → "" #

(16)

This reaction is harmful to the formation of depletion layer and thus decreases the barrier height @A , causing the decline of nonlinear coefficient. Therefore, the nonlinear coefficient firstly increases to 6.7 and then descends with the dopant of GeO2 increasing. 4. Conclusion In this study, the addition of GeO2 facilitates the growth of grain size and induces more Nb5+ and Ho3+ ions to dissolve into TiO2 matrix. In addition, doping GeO2 is an effective method to improve dielectric constant. All the samples show a good temperature stability and frequency stability of dielectric constant, although the temperature stability of dielectric loss is poor. In addition, the addition of GeO2 can enhance varistor properties. The breakdown voltage firstly decreases and then maintains a relatively stable value of 2.7 V/mm. With the increase of doped GeO2 from 0 mol% to 1.2 mol%, the nonlinear coefficient rises to

a maximum value of 6.7 when sample is doped with 0.6 mol% GeO2 and then decreases. It is expected that the low breakdown voltage value and giant dielectric constant enable the system of TiO2 ceramics to be used in the practical applications.

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Highlights: The breakdown voltage and dielectric constant are improved after doping GeO2. Samples show a good temperature and frequency stability of εr and loss tanσ. The effect of GeO2 on microstructure and electrical properties is explored. Some electrical characteristics are calculated by J-E characteristics curves. A grain-boundary barrier model for TiO2 varistor ceramic is established.

Declaration of interest statement ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

All authors have declare that: (i) no support, financial or otherwise, has been received from any organization that may have an interest in the submitted work ; and (ii) there are no other relationships or activities that could appear to have influenced the submitted work.