## Abstract

Rutile**-**TiO_{2} ceramics are very promising electronic ceramic materials which can be applied in varistors because of their good electrical properties. In this work, Dy_{2}O_{3} was used to improve the electrical properties of a TiO_{2} varistor doped with 0.60 mol.% Nb_{2}O_{5} and 0.30 mol.% SiO_{2}. Results showed that the TiO_{2} varistor doped with 0.30 mol.% Dy_{2}O_{3} possessed optimal electrical properties with good nonlinear coefficient (\( \alpha = 5.7 \)), very low breakdown voltage (\( E_{\text{B}} = 1.34\;{\text{V}}\,{\text{mm}}^{ - 1} \)) and colossal dielectric constant (\( \varepsilon_{\text{r}} = 8.01 \times 10^{5} \)). The microstructural analysis showed that after the incorporation of Dy_{2}O_{3} into the TiO_{2} varistor, the grains tended to be more semiconducting due to the defect carriers derived from the substitution of Dy^{3+} for Ti^{4+}. Meanwhile, the moderate dopant of Dy_{2}O_{3} also increased the grain size and narrow grain boundary. Consequently, the breakdown voltage decreased, while the nonlinear coefficient and dielectric constant improved.

## Introduction

Titanium dioxide ceramic is a kind of electronic ceramic that can attain good nonlinear electrical properties and dielectric constant by special methods, which makes it of great interest for a broad application concerning varistors and capacitors. In the past, the ZnO varistor was most widely used owing to its excellent nonlinear characteristics.1 However, the ZnO varistor cannot be applied in low-voltage electronic circuits because of its high breakdown voltage.2 In recent years, with the miniaturization and integration of electronic circuits, it is necessary to develop multifunctional varistors with low breakdown voltage.3,4,5 As one of the typical electronic ceramics with multifunction, the TiO_{2} varistor has attracted extensive attention due to its low breakdown voltage and good dielectric properties. However, the application of the TiO_{2} varistor is limited by its low nonlinear coefficient and relatively high breakdown voltage for electronic circuits.

In theory, the breakdown voltage and nonlinear coefficient of the TiO_{2} varistor mainly depend on the potential barrier and the grain size of TiO_{2} ceramics.1,6,7 In order to improve the nonlinear electrical properties of TiO_{2} ceramics, most researchers concentrated on donor doping (Nb^{5+},Ta^{5+}) and acceptor doping (Ho^{3+},Cr^{3+}).8,9 In addition, the influences of sintering temperature and heat treatment atmosphere on the electrical properties of the TiO_{2} ceramic were also studied.10,11,12 In 1995, Yan and Wu found that doping 0.25 at.% Nb^{5+} was beneficial to the varistor properties of (Ba-Bi-Nb)-doped TiO_{2}.13 Meanwhile, Luo et al. reported that Ta_{2}O_{5} could effectively improve the properties of (Ca, Si, Ta)-doped TiO_{2} varistor.14 These two reports confirmed that donor doping could effectively enhance the varistor properties of TiO_{2} ceramics, but the high breakdown voltage still limited its application. Sousa et al. investigated the effect of Ta_{2}O_{5} as well as Cr_{2}O_{3} on the varistor properties of TiO_{2} 9 and Kang et al. reported the (Ge, GeO_{2}, Ta_{2}O_{5}, BaCO_{3}) co-doped TiO_{2} varistor with an α value up to 12.1 and a low breakdown voltage of 20.8 V/mm.15 Although both donor doping and acceptor doping were shown helpful to the electrical properties of the TiO_{2} varistor, the difficulties of coordinating the breakdown voltage and nonlinear coefficient, i.e., how to further reduce the breakdown voltage and enhance the nonlinear coefficient simultaneously, has become a challenge for researchers. In addition, heat treatment atmospheres also had a favorable effect on TiO_{2} varistor properties. For instance, Zhao et al. implied that after the TiO_{2} varistor was heat-treated in oxygen atmosphere, the acceptor state density as well as the height and width of the potential barriers increased, the conductivity decreased and the breakdown voltage rose significantly as a consequence of oxygen accumulation at grain boundaries.10

Previous studies on TiO_{2} ceramics mainly focused on the improvement of nonlinear properties. However, recently, researchers found that the doping of In^{3+} + Nb^{5+} (1:1) into TiO_{2} ceramics (INTO) produced colossal dielectric properties, making the TiO_{2} ceramics a potential capacitor.16 Subsequently, Thongbai et al. reported the effects of sintering conditions and doping concentrations on Sc^{3+} + Nb^{5+} (1:1) co-doped TiO_{2} ceramics and found that Sc^{3+} captured free electrons at internal insulating layers while Nb^{5+} produced free electrons. The work revealed that the interfacial polarization at insulating layers and large activation energy contributed to colossal dielectric properties of ScNTO ceramics.17 Lately, there has been much research about Eu^{3+} + Nb^{5+},18 La^{3+} + Ta^{5+},19 Er^{3+} + Ta^{5+},20 Bi^{3+} + Eu^{3+} + Nb^{5+},21 B^{3+} + Eu^{3+} + Nb^{5+}22 co-doped rutile TiO_{2} ceramics with high dielectric constant and low dielectric loss. Admittedly, the dielectric properties of TiO_{2} ceramics have been greatly improved in a short time.23,24,25,26 However, with the integration and multifunction of electronic circuits, multifunctional TiO_{2} ceramics are drawing increasing intention. To the best of our knowledge, there are few works reporting both the nonlinear characteristic and dielectric properties of TiO_{2} varistors.

It has been confirmed that SiO_{2} controls the grain size of the varistor while acceptor doping improves the varistor properties of TiO_{2} ceramic.6,27 Herein, this work reported that (0.30Dy_{2}O_{3}-0.60Nb_{2}O_{5}-0.30SiO_{2}-98.80TiO_{2}) (mol.%) co-doped TiO_{2} ceramic systems with low breakdown voltage, high nonlinear coefficient and colossal dielectric constant were procured via optimizing sintering temperature and doping concentrations of Dy_{2}O_{3}. The dependence of electrical properties on microstructure was thoroughly investigated and a defect model was proposed to illustrate the effects of Dy_{2}O_{3} on the properties of the TiO_{2} varistor.

## Experimental Details

TiO_{2} ceramic samples (99.10-*x*)TiO_{2}-*x*Dy_{2}O_{3}-0.60Nb_{2}O_{5}-0.30SiO_{2} (mol.%, *x *= 0, 0.15, 0.30, 0.45, 0.60) were prepared by the conventional solid state sintering method. The raw materials TiO_{2} (99.9%), SiO_{2} (99.9%), Dy_{2}O_{3} (99.99%) and Nb_{2}O_{5} (99.99%) were purchased from Chengdu Chron Chemicals Co., Ltd., China. A total of 0.18 mol chemicals were weighed in stoichiometric proportions and milled in a planetary ball mill for 12 h using 100 mL ethanol as the medium. After drying at 70°C for 18 h, the homogeneous powder mixture was blended with a small amount of PVA (polyvinyl alcohol) solution (PVA/H_{2}O = 8 wt.%). Afterwards, the mixed powder was pressed at 120 MPa into pellets of 15 mm in diameter and 2 mm in thickness. Next, all the pellets were sintered at a designed temperature (1350°C, 1400°C, 1450°C) for 2 h and cooled to room temperature in furnace. To characterize the varistor and dielectric properties of the sintered tablets, both the surfaces were polished and then deposited with silver electrodes, followed by heat treatment at 600°C for 1 h. The varistor properties, including nonlinear coefficient (α) and breakdown voltage (*E*_{1mA}), were measured by a varistor DC parameter instrument (CJ1001). The dielectric constant, dielectric loss at 1 kHz and the dielectric properties measurements dependent on temperature were conducted over the range of − 150–200°C at a heating rate of 1°C min^{−1} by an LCR meter (TH2816A). The dielectric properties of samples in the frequency range of 100 Hz–100 kHz were measured by an impedance analyzer (Agilent 4294A) at room temperature. The true density of TiO_{2} ceramics was estimated by a density meter (ET-320) based on the Archimedes method and the relative density was calculated by the true density and theoretical density accordingly. The crystal structure of TiO_{2} ceramic samples was determined by an x-ray diffractometer (XRD) (DX-2000) with Cu Kα radiation at a scanning speed of 0.04° s^{−1} in the 20°–80° 2*θ* range. After polishing and thermally etching, the surface of TiO_{2} ceramic samples was observed by scanning electron microscopy (SEM, JSP 7500, Japan). The average grain size is calculated by the intercept method proposed by Mendelson9:

where *L* is the length of a random line on the SEM image, *M* is the magnification of the SEM image and *N* is the number of grain boundaries that the line crosses.

Energy-dispersive x-ray spectroscopy (EDS) was used to analyze the elemental composition and distribution. The valence state of elements in TiO_{2} samples was tested by x-ray photoelectron spectroscopy (XPS, Kratos AXIS Ultra DLD, Japan).

## Results and Discussion

### Nonlinear Characteristics

Table I presents the electrical performances of TiO_{2} ceramics doped with Dy_{2}O_{3} at different sintering temperatures. When the sintering temperature increases, the nonlinear coefficient and dielectric constant increase, while breakdown voltage and dielectric loss decrease. Altogether, it is observed that the samples possess the best varistor properties after sintering at 1450°C. This phenomenon may be explained by the following equations:

where \( E_{\text{B}} \) is the breakdown voltage, \( N \) is the number of grains per unit length, \( V_{\text{gb}} \) is the voltage barrier at the grain boundary.

According to the above equations, the titanium ion defects can be generated by the dopant of Nb_{2}O_{5} and the breakdown voltage is determined by the grain size. Increasing the sintering temperature can improve the solubility of Nb_{2}O_{5}, so the ion segregation at the grain boundary is moderated. In this case, more Nb^{5+} ions replace Ti^{4+} ions and the resulting ion defects promote the degree of semiconducting of the grains. In addition, the grains grow as the sintering temperature rises, leading to the enhancement of grain boundary barriers and a decrease of grain boundaries per unit thickness.8,12 As a consequence, α increases while \( E_{\text{B}} \) decreases. Throughout this work, we, therefore, picked 1450°C as the sintering temperature for all the Dy_{2}O_{3}-doped samples.

After sintering at 1450°C, the breakdown voltage and nonlinear coefficient of different samples are depicted in Fig. 1a, and the other parameters of samples with different *x* values are listed in Table II. \( \varPhi_{\text{B}} \) is calculated by the following equations:

where *A** is the Richardson constant, *K* is the Bolzmann constant, *T* is the absolute temperature, \( \varPhi_{\text{B}} \) is the interface barrier height, and *β* refers to the relationship illustrated in Eq. 6:

where *d* is the number of grains per unit length, *e* is the electron charge (1.602 × 10^{−19} C), \( \varepsilon_{0} \) is the vacuum dielectric constant (8.85 × 10^{−14} F/cm), and \( \varepsilon_{\text{r}} \) is the dielectric constant of TiO_{2} ceramic. Table II and Fig. 1a show that the doping of Dy_{2}O_{3} obviously affect the properties and microstructure of Nb_{2}O_{5}-SiO_{2}-TiO_{2} ceramics. Compared to the sample without Dy_{2}O_{3}, all those doped with Dy_{2}O_{3} possess lower breakdown voltage and higher relative density. The doped Dy_{2}O_{3} also greatly enhances the dielectric constant without increasing the dielectric loss significantly. In addition, an appropriate doping content of Dy_{2}O_{3} can improve the nonlinear coefficient of TiO_{2} ceramics. When the TiO_{2} varistor is doped with 0.30 mol.% Dy_{2}O_{3}, the breakdown voltage decreases to 1.34 V mm^{−1}, *α* ascends to 5.7, and the dielectric properties (\( \varepsilon_{\text{r}} \) = 8.01 × 10^{5}, \( \tan \delta \) = 0.362) and relative density are optimal (98.22%). However, when doped with excessive Dy_{2}O_{3} (*x *> 0.30), the electrical properties of Nb_{2}O_{5}-SiO_{2}-TiO_{2} ceramics deteriorate. Figure 1b shows that the doping content of Dy_{2}O_{3} also exerts an evident influence on the *J*–*E* characteristics. The curves can be divided into two regions: one is a low-current linear region (*J* < 0.03 mA cm^{−2}), the other is a nonlinear region.13 The contrast of curves of the Dy_{2}O_{3}-doped samples and the undoped one shows that Dy_{2}O_{3} can efficiently reduce the breakdown voltage of TiO_{2} ceramics. In sum, the doping of Dy_{2}O_{3} remarkably ameliorates the α and \( E_{\text{B}} \) of TiO_{2} ceramics, while modifying the concentration of Dy_{2}O_{3} only makes a noticeable contribution to the former. Consequently, Nb_{2}O_{5}-SiO_{2}-TiO_{2} ceramics doped with 0.30 mol.% Dy_{2}O_{3} demonstrates the optimum varistor properties.

The classical defect reaction equation can be used to understand how Dy_{2}O_{3} influences the electrical properties of Nb_{2}O_{5}-SiO_{2}-TiO_{2} ceramics. To start with, the radius of Dy^{3+} (0.091 nm) is much larger than that of Ti^{4+} (0.061 nm), which causes severe lattice distortion and leads to the poor solubility of Dy^{3+} in TiO_{2} lattice, thus most of the Dy^{3+} ions segregate at the grain boundary.8,28 Furthermore, the dissolution of Dy_{2}O_{3} into TiO_{2} lattice also induces oxygen vacancies for charge transfer when Dy^{3+} substitutes for Ti^{4+}, as shown in Eq. 7 below.

When a moderate content of Dy_{2}O_{3} is doped in the TiO_{2} varistor, on the one hand, some of the dopant dissolves in the TiO_{2} lattice to generate oxygen vacancies, and on the other hand, the remaining Dy^{3+} ions segregate at the grain boundary to form the secondary phase. Consequently, the electrical properties are improved. Nonetheless, if the dopant of Dy_{2}O_{3} is excessive, more quantities of the secondary phase will be generated by consuming a large number of Dy^{3+} ions at grain boundary, which decreases the acceptor interface state density at the depletion layer. The final outcome is a decrease in the height of the grain boundary barrier, which can be explained by Eq. 829:

where *N*_{S} is the acceptor interface state density, \( \varepsilon_{\text{r}} \) is the dielectric constant, \( \varepsilon_{0} \) is the dielectric constant of vacuum and *N*_{D} is the donor content in the depletion layer. According to Eq. 8, the height of the grain boundary barrier \( \varPhi_{\text{B}} \) is proportional to the acceptor interface state density.

### Dielectric Properties

Figure 2 shows the dielectric properties of Nb_{2}O_{5}-Dy_{2}O_{3}-SiO_{2} co-doped TiO_{2} ceramics at room temperature in the frequency range of 10^{2}–10^{5} Hz. It can be seen from Fig. 2 that the dielectric constant and dielectric loss are nearly steady in the frequency range of 10^{2}–10^{3} Hz. However, with the increase of frequency (\( > 10^{3} \) Hz), the dielectric constant decreases while the dielectric loss increases obviously. In addition, when 0.30 mol.% Dy_{2}O_{3} is added into the TiO_{2} varistor, the best comprehensive dielectric properties can be obtained at the frequency of 100 Hz, where the dielectric constant is higher than 10^{6} and the dielectric loss is lower than 0.3. Furthermore, in the frequency range of 10^{2}–10^{5} Hz, the dielectric constant (> 1 × 10^{5}) of the TiO_{2} samples is much better than the previously reported results.19,21,22,30,31 However, the dielectric loss is still higher than other reports, which makes it necessary to further reduce its dielectric loss for capacitor applications.

Figure 3 shows the dielectric properties of Nb_{2}O_{5}-Dy_{2}O_{3}-SiO_{2} co-doped TiO_{2} ceramics at different temperatures measured at 100, 1k, 10k and 100k Hz respectively. It can be seen that the dielectric constant and dielectric loss remain relatively stable over − 150–200°C temperature range at different frequencies, except for an expanded dielectric relaxation around 0°C, which may be caused by electron hopping between Ti^{4+} and Ti^{3+}.32 In summary, it can be concluded from Figs. 2 and 3 and Table I that 0.30 mol.% Dy_{2}O_{3}-doped TiO_{2} ceramic possesses the best dielectric properties, with the highest dielectric constant, lower dielectric loss, relatively higher frequency stability.

### XRD Analysis

The XRD patterns of TiO_{2} ceramics doped with different contents of Dy_{2}O_{3} are exhibited in Fig. 4. Figure 4a demonstrates that only one major phase corresponds to rutile TiO_{2} (PDF#87-0710) in all the samples. Meanwhile, as the concentration of Dy_{2}O_{3} increases, the secondary phase Dy_{2}Ti_{2}O_{7} (PDF#17-0453) appears. Figure 4b is the enlarged partial spectra of Fig. 4a around \( 2\theta = 27.5^{^\circ } \). It can be seen that after Dy_{2}O_{3} is doped in, the peaks around \( 27.5^{^\circ } \) shift to a larger angle and their full width at half maximum (FWHM) widens, while increasing the content of Dy_{2}O_{3} dopant makes little difference to the shifting. Basically, the dissolution of Dy^{3+} in the TiO_{2} lattice results in severe lattice distortion, thereby decreasing the interplanar spacing value. According to the Bragg formula (9), the angle \( \theta \) shifts to the large-angle direction if the interplanar spacing value \( d \) decreases.15

where *λ* is the wavelength of the x-ray, \( d \) is the interplanar distance, \( \theta \) is the angle between the incident wave and the crystal plane. Since the solid solubility of Dy^{3+} in the TiO_{2} lattice is low, the undissolved Dy^{3+} ions diffuses to the grain boundary, which is beneficial to the increase of the width of depletion layers and the enhancement of grain boundary potential barrier; therefore, the nonlinear coefficient increases based on the following formula5:

where \( \gamma \) is a constant, *E* is the external electric field, \( \varPhi_{\text{B}} \) is the potential barrier height. Additionally, the segregation of Dy^{3+} ions along the grain boundary also produces a secondary phase Dy_{2}Ti_{2}O_{7}.

### SEM Analysis

Figure 5 illustrates the SEM images and grain size of different TiO_{2} ceramic samples. The microstructures show that after Dy_{2}O_{3} is doped in, the grain size increases, the grain boundary is narrowed and the secondary phase is evenly distributed at the grain boundary initially. Furthermore, as more Dy_{2}O_{3} is doped, more secondary phase particles are observed. Noticeably, the grain size reaches a maximum of 18.56 *μ*m at *x *= 0.30 and tends to diminish with the continuous addition of Dy_{2}O_{3}. This phenomenon can be explained as follows: when moderate Dy_{2}O_{3} is added, oxygen vacancies are generated due to the substitution of Dy^{3+} ions for Ti^{4+} ions, which change the oxygen pressure in rutile TiO_{2.}33 Therefore, the dopant of Dy_{2}O_{3} promotes the growth of grains.8,33 According to Eq. 3, the breakdown voltage (*E*_{B}) decreases greatly. In addition, the moderate secondary phase can also enhance the dielectric properties due to their high resistance.34 However, the deposition of excessive secondary phase (*x *> 0.30) at the grain boundary can limit the grain growth. Accordingly, *E*_{B} increases as a result of the decreasing of grain size. Moreover, by consuming a large number of Dy^{3+} and Nb^{5+} ions, the formation of an inordinate secondary phase reduces the acceptor interface state density at the depletion layer, thus causing the nonlinear coefficient to drop according to Eq. 8.

### EDS Analysis

To further analyze the elemental distribution and explore the effect of Dy_{2}O_{3} on the microstructure, the EDS analysis of TiO_{2} ceramics doped with different contents of Dy_{2}O_{3} is conducted. Figure 6 shows the point scanning spectra of EDS for samples *x *= 0 and *x *= 0.30, respectively, and the corresponding elemental composition is listed in Tables III and IV. Figure 6a and b shows that a small amount Si exists in the grain of both samples. Meanwhile, Fig. 6b and c depicts the difference in elemental composition between the grain and the gain boundary of the 0.30 mol.% Dy_{2}O_{3}-doped sample. Particularly, there exists a very small amount of Dy (~ 0.04%) in the grain, whereas the grain boundary is enriched with a large amount of Dy, Si, Nb in the form of the secondary phase. A reasonable explanation for the phenomenon is that since both radii of Si^{4+} (0.040 nm) and Dy^{3+} (0.091 nm) ions differ markedly from the radius of Ti^{4+} (0.061 nm) ions, the solubility of Si^{4+} and Dy^{3+} in TiO_{2} lattice is low, resulting in the segregation of a large amount of Si^{4+} and Dy^{3+} at the grain boundary. Altogether, EDS analysis and the aforementioned XRD detection leads to the conclusion that the stable secondary phase at the grain boundary is Dy_{2}Ti_{2}O_{7}.

Figure 7 shows the elemental mapping of TiO_{2} ceramics doped with 0 mol.%, 0.30 mol.% as well as 0.60 mol.% Dy_{2}O_{3} , respectively. It can be seen from Fig. 7a that for the undoped TiO_{2} varistor, all elements except for Si are evenly distributed in the grain and at the grain boundary, which is consistent with the EDS point analysis. When Dy_{2}O_{3} is added to the TiO_{2} varistor, however, the elements Nb, Dy, Si and O are enriched at the grain boundary and the enrichment becomes more obvious with the doping content increasing to 0.60 mol.%. The observation suggests that the doping of Dy_{2}O_{3} notably changes the elemental distribution of Si and Nb. Normally, the segregated elements are involved in the formation of depletion layers. Nevertheless, there is a secondary phase once the accumulated Nb^{5+} and Si^{4+} exceed the saturation value.6,28

Figure 8 depicts the line scanning spectra of EDS for Dy_{2}O_{3}-free and 0.30 mol% Dy_{2}O_{3}-doped TiO_{2} samples, respectively. As presented in Fig. 8a, the elemental content of Nb and Ti displays no conspicuous variation within the scanning distance, while the content of Si and O fluctuates apparently between the interior and boundary of grain. However, remarkable fluctuations emerge in all the EDS spectra for 0.30 mol% Dy_{2}O_{3}-doped sample at the grain boundary as illustrated in Fig. 8b. These findings are consistent with the results of elemental mapping analysis. Moreover, the grain boundary width can be estimated according to the abrupt variation in the EDS spectra, which turns out to be about 600 nm for the Dy_{2}O_{3}-free sample and approximately 400 nm for the 0.30 mol.% Dy_{2}O_{3}-doped sample, separately. Therefore, the doping of Dy_{2}O_{3} can also narrow the grain boundary, thereby increasing the density of TiO_{2} ceramics. In other words, the moderate dopant of Dy_{2}O_{3} promotes grain growth, narrows the grain boundary and increases the density of TiO_{2} ceramics, leading to the decrease of grain boundaries per unit thickness. According to Eq. 2, the breakdown voltage decreases.

### XPS Analysis

To investigate the corresponding chemical valance states of the TiO_{2} ceramic sample doped with 0.30 mol.% Dy_{2}O_{3}, XPS analysis is conducted and the results are shown in Fig. 9. It was reported that the dopant of electron-donors such as Nb^{5+} or Ta^{5+} generate free electrons in rutile-TiO_{2} ceramics.17 According to Eqs. 2 and 11, Ti^{3+} ions is produced by Ti^{4+} ions capturing free electrons.

Figure 9a shows that two obvious peaks correspond to Ti 2p_{1/2} and Ti 2p_{3/2} of BE (binding energy) at 463.5 eV and 457.8 eV, which confirms the presence of Ti^{4+} ions.35 Furthermore, the other two weak peaks of BE at 458.2 eV and 457.5 eV are attributed to Ti^{3+}.36 Figure 9b shows the O 1 s peaks for the TiO_{2} sample. It can be seen that three peaks of BE exist at 530.8 eV, 529.5 eV and 529.0 eV. A major peak at 529.0 eV is related to the Ti-O bonds, and the other two peaks at 529.5 eV and 530.8 eV correspond to the existence of other cation-oxygen bonds (i.e., Nb-O, Dy-O and Si-O) and oxygen vacancies or surface hydroxyl, which verifies that some of the dopants (Nb, Dy, Si) enter the lattices and bond with oxygen.16,36 According to Eq. 7, the dopant of acceptor ions like Dy^{3+} can cause the formation of oxygen vacancies. The defects such as oxygen vacancies and free electrons can increase the conductivity of grains, thus improving the varistor properties of TiO_{2} ceramics. Meanwhile, Fig. 9c shows two peaks in the BE spectrum of Nb at 209.1 eV as well as 206.3 eV, and the splitting of the spin–orbit is approximately 2.8 eV, which is consistent with the previous report, confirming the existence of Nb^{5+} ions.16 Figure 9d and e present only a single peak at 152.1 eV and 101.4 eV, respectively, verifying the presence of Dy^{3+} and Si^{4+}.

### Discussion

The dopant of Dy_{2}O_{3} has a great influence on the microstructure and varistor properties of the Nb-Si co-doped TiO_{2} ceramics. The model is shown in Fig. 10, where it can been seen that some Ti^{4+} ions in the lattice are replaced by Dy^{3+} ions after the addition of Dy_{2}O_{3}, which causes severe lattice distortion and some defect carriers such as oxygen vacancies are generated, thus making the grain more semiconducting.37,38 Therefore, the electrical properties are improved. At the same time, the remaining dopant (Dy_{2}O_{3}) segregates at grain boundary. A moderate content of Dy^{3+} segregating at the grain boundary improves depletion layer width and increases grain boundary barrier height. As a result, the nonlinear coefficient increases. Moreover, the moderate amount dopant of Dy_{2}O_{3} also gives rise to the growth of grains. Notably, the secondary phase caused by trivalent ions is helpful to the decrease of dielectric loss.39 According to Eqs. 3 and 10 and the following Eq. 12, the breakdown voltage decreases, the nonlinear coefficient further increases and the dielectric constant ascends.

where \( \varepsilon_{\text{r}} \) is the dielectric constant, \( \varepsilon_{\text{B}} \) is TiO_{2} intrinsic dielectric constant, \( D \) is the average grain size, \( t_{\text{B}} \) is the mean width of the grain boundary.

However, excessive dopant of Dy_{2}O_{3} will generate superfluous secondary phase, which inhibit grain growth and degrade the electrical properties. According to the previous report, the IBLC (internal barrier layer capacitance) effect is strengthened as the grain size diminishes.40 Therefore, a colossal dielectric constant can also be achieved in the TiO_{2} samples containing a mass of secondary phases.40

## Conclusion

By optimizing the sintering temperature and the doping content of Dy_{2}O_{3}, good comprehensive varistor properties were obtained in Nb-Dy-Si co-doped TiO_{2} ceramic systems. The doping of Dy_{2}O_{3} improves the varistor properties of TiO_{2} ceramics. When the doping content of Dy_{2}O_{3} was 0.30 mol.%, the TiO_{2} ceramic system presented the best varistor properties, with a very low breakdown voltage (1.34 V/mm), good nonlinear coefficient (5.7) and colossal dielectric constant (8.01 × 10^{5}) measured at 1 k Hz. Reassuringly, compared to the previous works,41,42 the TiO_{2} ceramic system in this work has a higher dielectric constant, although the challenge of further reducing its dielectric loss still remains. Table V shows the comparison of electrical properties of different TiO_{2} varistor samples. In conclusion, the comprehensive varistor properties of the TiO_{2} ceramic system (99.80TiO_{2}-0.60Nb_{2}O_{5}-0.30Dy_{2}O_{3}-0.30SiO_{2}, mol.%) are better than the previous works, which makes it a potential candidate for low voltage varistors.8,12,14

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## Acknowledgments

The authors appreciate Wang Hui from the Analytical & Testing Center of Sichuan University for her help with SEM and EDS characterization.

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Liao, X., Peng, F., Pu, Y. *et al.* Effects of Dy_{2}O_{3} on the Electrical Properties of a (Nb_{2}O_{5}-Dy_{2}O_{3}-SiO_{2}) Co-doped TiO_{2} Varistor.
*J. Electron. Mater.* **50, **1963–1979 (2021). https://doi.org/10.1007/s11664-020-08727-1

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DOI: https://doi.org/10.1007/s11664-020-08727-1

### Keywords

- Varistor
- Dy
_{2}O_{3} - rutile-TiO
_{2} - electrical properties
- microstructure