EDS results for marked points in Figure 2 (usage permitted by Elsevier).
Breakdown characteristics are of great importance for varistor ceramics, which largely depend on Schottky barriers at grain boundaries. In order to enhance breakdown performance for meeting the requirement of device miniaturization, different doping methods are introduced to not only restrict grain size from additional phase but also manipulate defect structure of Schottky barrier at grain boundaries from substitution. Distribution of barriers is another key point affecting breakdown characteristics in varistor ceramics. Dimensional effect, which is detected in not only ZnO ceramics but also CaCu3Ti4O12 ceramics, is practically and theoretically found to be closely correlated with uniformity of grains. As a result, breakdown characteristics of varistors are dominated by combination effect of single barrier performance and spatial barrier distribution. In this chapter, enhanced breakdown field in CaxSr1−xCu3Ti4O12 ceramics, in situ synthesized CaCu3Ti4O12-CuAl2O4 ceramics, and CaCu3Ti4O12-Y2/3Cu3Ti4O12 composite ceramics are investigated from the aspect of Schottky barriers at grain boundaries. In addition, dimensional effect is found in both ZnO and CaCu3Ti4O12 ceramics, which are investigated from grain size distribution through theoretical and experimental analysis.
- breakdown characteristics
- varistor ceramics
- Schottky barrier
- CaCu3Ti4O12 ceramics
- ZnO ceramics
Varistor ceramics exhibit excellent nonlinear current-voltage (
Besides methods of enhancing breakdown characteristics, a non-negligible phenomenon that electrical performance is not uniform in the bulk of the ceramics should be taken into consideration for design and practical application. The inhomogeneous electrical properties at the cross section have been widely reported. About 5–11% of cross-section region in varistor ceramics was found to exhibit lower breakdown voltage than the rest of the regions . This further results in current localization, which causes electrical puncture, thermal cracking, or even thermal runaway . In addition, dimensional effect, which exhibits as the thickness dependence of breakdown field, is found in not only ZnO ceramics but also CCTO ceramics [15, 16, 17]. It is found that breakdown field and nonlinear coefficient are significantly decreased below a critical thickness, which brings much trouble in designing. The spatial electrical nonuniformity was widely attributed to inhomogeneous grain size distribution and grain boundary characteristics. Electrical measurements using microcontact on single grain boundary suggested that 50% grain boundaries can be defined as “good,” 30% are “bad,” and the rest are ineffective . At the same time, reports from luminescence created by electrical breakdown also provide support for uneven grain boundaries . In this work, the structural origin of dimensional effect in varistor ceramics is investigated through experiment and simulation, which suggested that wide grain size distribution should be responsible. After careful processing of controlling grain sizes into narrower distribution, dimensional effect is diminished, which, to some extent, proves the responsibility of grain size distribution.
2. Enhancement of electrical breakdown field in varistor ceramics
2.1. Enhanced breakdown field in Ca1−
xSr xCu3Ti4O12 ceramics via tailoring donor density
2.1.1. Phase composition and surface morphology
X-ray diffraction (XRD) patterns of Ca1−
SEM images and corresponding grain size distribution are shown in Figure 2. Grain size of the samples is smaller than that in CCTO ceramics (>8 μm), while it changes little on the ratio of Sr/Ca (2.4–2.8 μm). Energy dispersive X-ray spectroscopy (EDS) is further measured at the marked regions in Figure 2 with the results listed in Table 1. No pure CaCu3Ti4O12 or SrCu3Ti4O12 is detected, indicating solid solution systems. Major discrepancy for those large grains (A1, B2, C2, D1) and small grains (A2, B3, C3, D2) is found to be Sr/Ca ratio. The higher Sr/Ca ratio in larger grains indicates Sr2+ might have benefit for grain growth in relatively low temperatures.
2.1.2. Enhanced breakdown field and complex impedance spectra
Figure 3 is current density-electric field (
2.1.3. Tailoring of donor density
Back-to-back Schottky barrier at grain boundary is crucial for the nonlinearity of varistors. Generally, the barrier height
For single grain boundary, the grain boundary capacitance of unit area
Dependence of (
Oxygen vacancy is considered as origin of electron formation due to weak cation▬O bonds. Space of
On the contrary, oxygen vacancy may be inhibited due to solid solution effect between SCTO and CCTO. Taking Sr2+ in CCTO as an example, besides SrCa, Sr exists as SrCu and Sri∙∙ as Cu2+ is easily loss in CCTO. Sr-Cu distortion is likely formed due to the same valence of Sr, Ca, and Cu ions. Increased
2.2. In situ synthesized CCTO-
xCuAl2O4 varistor ceramics
2.2.1. Preparation and characterization of in situ synthesized CCTO-
CCTO powders are prepared via traditional solid-state reaction method and suspended in Al(NO3)3 aqueous solution. Subsequently, the suspension was quantitatively titrated with NH4OH to make Al(OH)3 precipitate on the surface of CCTO particles. After drying, the powders are calcined at 950°C for 4 h to dehydrate Al(OH)3 into Al2O3. Finally, they were pressed into pellets and sintered in air at 1100°C for 4 h.
XRD patterns are presented in Figure 5(a). Only single phase of CCTO can be detected when
Surface morphology of the samples is characterized by SEM as shown in Figure 6. For CCTO ceramics, little secondary phase is found, and the average grain size is 19.1 μm as shown in Figure 6(a). As to samples with
2.2.2. Enhanced breakdown field in CCTO-
xCuAl2O4 ceramic samples
For comparison, CuAl2O4 is directly introduced into CCTO by solid-state reaction method following the same sintering condition. Dependence of
2.2.3. Complex impedance analysis for CCTO-xCuAl2O4 samples
Figure 8(a) is complex impedance spectra of CCTO-
2.3. CCTO-YCTO composite ceramics with enhanced nonlinearity
2.3.1. Phase composition and surface morphology
SEM pictures were taken, as shown in Figure 9. Large grains are formed in pure CCTO and YCTO ceramics with Cu-rich phase segregated in the intergranular region marked by red circles as shown in Figure 10(a) and (d). Discontinuous distribution of grain size is finally formed in CCTO samples. Stripy grains in pure YCTO ceramics suggest that sintering temperature is so high that grains could not hold the hexagonal shape. Meanwhile, two kinds of grains, with grain sizes of 4–6 μm and 1–2 μm, respectively, were found uniformly distributed in composite ceramics. Average grain size is reduced, which indicates that grain growth of CCTO and YCTO was suppressed by each other in the form of pinning effect.
2.3.2. Enhanced electrical nonlinearity
Complex impendence spectroscopy at room temperature is plotted in Figure 12.
Grain boundary resistance dominates the conduction process. So the hopping conduction is deduced, inhibiting improved grain boundary resistance and activation energy in composite ceramics. This inhibition may arise from increased number of grain boundaries or enhanced blocking effect of single barrier. There are three types of grain boundaries: CCTO/YCTO, CCTO/CCTO, and YCTO/YCTO.
3. Dimensional effect of varistor ceramics
3.1. Phenomenon of dimensional effect
Thickness dependence of
where the exponent
The summary of the parameters
3.2. Simulation of dimensional effect
Breakdown voltage of single grain boundary is acknowledged to be nearly constant (∼3 V), indicating other factors should be responsible for dimensional effect. To understand the structural origin of dimensional effect, a model based on the network of grains and grain boundaries is proposed. Grain sizes in varistor ceramics fit the normal distribution, in which the probability density
It is assumed that these
The amount of chains with grain sizes from to + Δfits:
Another assumption is that the current that went through one grain chain is independent on other chains. On this basis, the relationship between the voltage and the current in one grain chain can be expressed as:
Based on the model above,
In addition, if the average grain size is fixed, sample thickness
As for CCTO ceramics which also exhibits dimensional effect shown in Figure 13(b), SEM images and grain size distribution on longitudinal section morphologies are investigated, as shown in Figure 15. Grains are smaller near the surface, whereas they are larger and denser in the interior. Quantitative analysis shows that grain sizes are more uniform near the surface while the size distribution is wider in the interior. The average grain size increased from 20.23 μm near the surface to 23.94 μm in the interior, while the porosity decreased from 4.95% near the surface to 0.33% in the interior. Although the grains with size below 30 μm are dominant in number, they contribute less to the section area. It can be seen in Figure 15(b), (d), and (f) that although grains with size below 15 μm contribute to more than 50% of grains, the sum of their occupied area is less than 10%. Despite small increase of average grain size from the surface to interior part, the major grain size that contributed to section areas is significantly different. On the surface, amount of the grains between 20 and 40 μm is most, while grains between 40 and 60 μm dominate the section area. Especially, the grain size range extends to 50–90 μm in the interior. From this point, it can be deduced that nonuniform distribution of grain size indeed contributed to dimensional effect in varistor ceramics, which is in accordance with simulation discussed above.
3.3. Elimination of dimensional effect
In not only ZnO varistor ceramics but also CCTO ceramics, dimensional effect exists because of nonuniform grain size distribution, which restricts its practical application. Therefore, in order to diminish or to attenuate dimensional effect, it is important to make grain size distribution more uniform. Despite the traditional processed ZnO varistor ceramics (Tr), another amine processed (Am) samples are prepared. At first, ZnO is dissolved in NH4(OH) and NH4(HCO3) solution with other additives in solutions, which is consequently heated to 110°C. After careful monitoring and controlling the pH of this mixed solution to 8–9, the precipitations are separated from the solution by filtration and washed with diethylamine solution to remove all chloride ions. When the solution is dried, the remained powders are calcined at 500°C, and then traditional processes are followed.
SEM photos of traditional processed (Tr) and amine processed (Am) ZnO samples are shown in Figure 16(a) and (b), respectively. Lots of small grains are scattered between compactly aligned big grains in Tr samples, as shown in Figure 16(a). However, no such small grains are seen in Am samples. The grains in Am samples are more uniform than those in Tr samples. Lots of grains with size below 3 μm exist in Tr samples, while the grains are compact with almost no grains with size below 3 μm.
Thickness dependence of
Breakdown characteristics in varistor ceramics are investigated from grain boundary characteristics based on single barrier performance and barrier distribution. On one hand, different methods of doping including substitution and additional phase result in not only restriction on grain sizes but also manipulation of defects in Schottky barriers of varistor ceramics to enhance breakdown field to meet the requirement of device miniaturization. In addition, restriction on further decreased thickness of varistor ceramics is found as dimensional effect in not only ZnO ceramics but also CaCu3Ti4O12 ceramics. From theoretical analysis and experimental results, the dimensional effect is found closely related with the uniformity of grain sizes, which influence the distribution of grain boundaries quite well. Consequently, the breakdown characteristics in varistor ceramics are understood from the aspect of single barrier performance and spatial distribution of barriers.
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