Structural and Electrical Properties of ZnO Varistor with Different Particle Size for Initial Oxides Materials

We report here structural, electrical and dielectric properties of ZnO varistors prepared with two different particle sizes for initial starting oxides materials (5 µm and 200 nm). It is found that the particle size of ZnO does not influence the hexagonal wurtzite structure of ZnO, while the lattice parameters, crystalline diameter, grain size and Zn-O bond length are affected. The nonlinear coefficient, breakdown field and barrier height are decreased from 18.6, 1580 V/cm and 1.153 eV for ZnO micro to 410 V/cm, 7.26 and 0.692 eV for ZnO nano.  While, residual voltage and electrical conductivity of upturn region are increased from 2.08 and 2.38x10-5 (Ω.cm)-1 to 4.55 and 3.03x10-5 (Ω.cm)-1. The electrical conductivity increases by increasing temperature for both varistors, and it is higher for ZnO nano than that of ZnO micro.  The character of electrical conductivity against temperature is divided into three different regions over the temperature intervals as follows; (300 K ≤ T ≤ 420 K), (420 K ≤ T ≤ 580 K) and (580 K ≤ T ≤ 620 K), respectively. The activation energy is increased in the first region from 0.141 eV for ZnO micro to 0.183 eV for ZnO nano and it is kept nearly constant in the other two regions. On the other hand, the average conductivity deduced through dielectric measurements is increased from 2.54x10-7 (Ω.cm)-1 for ZnO micro to 49x10-7 (Ω.cm)-1. Similar behavior is obtained for the conductivities of grains and grain boundaries. The dielectric constant decreases as the frequency increases for both varistors, and it is higher for ZnO nano than that of ZnO micro. These results are discussed in terms of free excited energy and strength of link between grains of these varistors.

microscope, D Electrical properties.
ZnO is an important material in various fields of applications such as varistors and gas sensors [1][2][3][4][5]. ZnO exhibits upturn region due to its electrostatic potential barrier formed at the grain boundaries [6][7][8][9][10]. The existence of the nonlinear region, in parallel with high current densities and breakdown fields, are the most significant properties of ZnO varistor. The upturn region is usually obtained at high current density beyond 10 3 A/cm 2 , and breakdown fields close to 5000 V/cm. This behavior represents the voltage drop in the grains, and restricts ZnO varistors applications [1]. The behavior of nonlinear region normally depends on density, chemical composition of the compound and also nanostructure development [11][12][13][14]. field of 20 V/cm, which is also required for special applications [17,18].

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The Electrical conductivity of ZnO varistor depends on the amount and nature of oxygen vacancies generated during its synthesized [19,20]. These oxygen vacancies are controlled by several parameters such as dopants and ZnO particle size [21][22][23][24]. It has been observed that these parameters are able to increase the current density in the upturn region of ZnO varistor and also shifted its onset value to lower fields, which is therefore necessary.
It is well known that electron traps, localized at the grain boundaries of ZnO, are adsorbed oxygen and capture the electrons coming from the donor states [25].
Therefore, Schottky barrier capacitance becomes dependent on the frequency signal. This is due to the finite time constants associated with the charging and discharging of the deep trap states in the depletion layer [26,27]. When low ac voltages ≈ 300 mV is applied across a varistor, a sinusoidal current will flow with the same angular frequency [28]. It has the great advantage over the dc techniques of being able to separate the electric response in different regions of ZnO ceramics, provided their electrical responses within the range of the instrumentation and the time constants [29,30]. This response is characterized by the complex impedance Z as a function of the frequency. The real and imaginary parts of complex impedance with respect to the applied voltages can be determined in the frequency range up to GHz.
Nanotechnology is of growing importance in many branches of research because of the interesting properties associated with depressing the material particle size [31][32][33]. These nanomaterials, due to their peculiar characteristics and size effects, often show novel physical properties compared to these of bulk materials. Today, nanoparticles of metal oxides have been the focuses of a number of research efforts due to the unusual properties that are expected upon entering this nanosize regime.
With this purse in mind, ZnO with two different particle sizes for starting materials (

Experimental details
Two ZnO samples with different particle size

Results and Discussions
As listed in Table 1, the bulk density of ZnO nano is higher than that of ZnO micro. The bulk densities are 82 % and 92 % of theoretical density 5.78 g/cm 3 for ZnO [34].
The crystal structure of the samples, shown in Figure 1, is hexagonal wurtzite, and no additional lines could be formed [35,36]. The lattice parameters listed in Table 1 are calculated in terms of The lattice parameters are increased from 3.20 Ǻ, 5145 Ǻ for ZnO micro to 3.22 Ǻ 5.17 Ǻ for ZnO nano, in agreement with the reported values elsewhere [37,38]. The wurtzite structure of ZnO is usually deviates from the ideal arrangement by changing U-parameter which describing the length of bond parallel to the c-axis. U parameter listed in Table 1 is given by [39].
The constant values of U-parameter (0.379) for two varistors specifies that the four tetrahedral distances stay almost constant through a distortion of tetrahedral angles due to long-range of polar interactions [40]. The surface morphology shown in Figure 2 indicates that the surface is rough and contains grains of crystallites which nearly having very varied shapes of different sizes. Furthermore, the crystallites are randomly distributed and irregularly disoriented, and there is no additional phases created at the boundaries of grains. In ZnO micro, the size and shape of grains are little bit different and there is a granular precipitation on the mother grains in the matrix structure. While, the grains appear with relatively small size and interfered with each other for ZnO Nano. The average grain size (D) is determined by the expression, , Where L is the random line length on the micrograph, M is the magnification of the micrograph, and N is the number of the grain boundaries intercepted by the lines [45]. The average grain sizes listed in Table 1    It is evident from I-V curves shown in Figure 3 that there are three different regions observed in both varistors. The first and third regions are nearly ohmic behavior, while the second region is nonlinear (upturn region). It is also noted that the nonlinear region is weaker for ZnO nano than that of ZnO micro, but it is not completely deformed.
While, the current is shifted to higher values for ZnO nano as compared to ZnO. The breakdown field EB is usually taken as the field applied when the current flowing through the varistor is 1 mA/cm 2 [44,45]. The values of EB listed in Table 1  The current -voltage relation of a varistor is given by the following equation [46,47]; Where J is the current density, E is the applied electric field, C is a proportionality constant corresponding to the resistance of ohmic resistor (nonlinear resistance), α is the nonlinear coefficient (α = logV/logI).  Table 1.

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The values of Kr are found to be 2.08 and 4.55 V/cm for ZnO micro and ZnO nano. This of course is in good agreement with the previous studies indicating that low residual voltage ratio provides high nonlinearity coefficient and breakdown field, while the high residual voltage ratio indicates low nonlinearity coefficient and breakdown field [49].
The electrical conductivity ς1 at room temperature is calculated in the first ohmic region by using the ohmic relation, J = ς1E [50]. It is clear form The electrical resistivity shown Figure 4 (a) is decreased by increasing temperature for both varsitors, but it is higher for ZnO micro than that of ZnO nano. From the values of resistivity, the electrical conductivities versus temperature could be obtained, and shown in Figure 4 (b).
However, the conductivity-temperature dependence is found to obey the well-known Arrhenius relation [54]; Where ς and ςo are the electrical conductivities at temperatures T and To (0K), and Ea is the activation energy. Within the temperature range selected for the conductivity measurements, it is possible to distinguish discrete regions corresponding to different activation energies. The character is divided into three regions over the temperature intervals as follows; (300 K ≤ T ≤ 420 K), (420 K ≤ T ≤ 580 K) and (580 K ≤ T ≤ 620 K), respectively.  The values of the activation energy Ea are calculated from the slope of each plot by using the above logarithmic relation and listed in Table 1.  [55,56].
In case of Cole-Cole model, the impedance representation is expressed by the following empirical relation [57,58]: Where is the impedance at infinite frequency, , where ω = 2πf and τo can be calculated from ωτo = 1 at the summit of the semicircle.
and (1 > γ > 0), and τ p is the relaxation time calculated from ωτp = 1 at the summit of the arc [59]. Figure 4 shows the real part of ac impedance versus imaginary part at different frequencies. It is clear that ZnO micro shows one semicircle, while one quarter of a circle is shown for ZnO nano. From these curves, the average grain and grain boundary conductivities are calculated and summarized in Table 1. As evidenced in Table 1, the conductivity of grains for ZnO nano is about 10 3 times more than the conductivity of the grain boundaries. Moreover, the conductivity of ZnO nano is always higher than that of ZnO micro. However, it has been found that the impedance spectra of calcined ZnO micro exhibited two arcs. The first arc at a low frequency is interpreted due to the grain boundary effect while the second arc at a high frequency region is attributed to the grain's effects [60,61]. While, a single arc is observed in all spectra of sintered ZnO micro [62,63] as we obtained.
The single arc means that the conduction processes through the grain and grain boundary has identical time constants, τ = (1/ω) = RC. This behavior indicates that the conduction in the grain and grain boundary occurs in the same process and could not be separated by the impedance spectroscopy [64,65]. The dielectric constant as a function of frequency (lnf) for the varistors is represented in Figure 5. It is apparent that the dielectric constant is decreases as the frequency increases for both varistors, but it is higher for ZnO nano as compared to ZnO micro, in agreement with the behavior of conductivity.

Conclusion
Structural and electrical properties of ZnO varistor with two different particle sizes for initial oxides materials are performed. We have shown that the particle