**1. Introduction**

### **1.1. Varistors**

Varistor is an electrical device based on semiconductor materials used for protection against voltage spikes in the electric network, against overvoltage in electronic circuits of low voltage and electrical power systems [1,2].

Due to the high energy absorption, the ceramic varistors become many helpful in protecting electrical circuits, and their electrical properties are highly dependent on their microstructure. The development of devices ever more technological and brings the need for electrical protection due to the sensitivity equipment. The use of varistors as voltage protectors in electronic equipment is very simple: the varistor is directly connected in parallel to the power line of equipment, and in case of an increase in the electrical current on energy network, the varistor rapidly increases the conductivity, allowing the current flow toward the ground. For electrical appliances operating with few voltages, the varistors ceramics are called low-voltage varistors [1–3].

The first varistor ceramics were developed in 1930. They were constituted from compact silicon carbide (SiC) partially sintered and were designed by the System Bell Labs to replace selenium rectifiers that were used in the protection of telephone systems [4]. Over time, the processing of varistors has undergone successive improvements, and in 1968, Matsuoka [3] developed varistors based on zinc oxide with manganese and cobalt as a dopant to improve the electrical properties. One of the disadvantages of using ZnO-based varistors are the large amount of dopant added to ceramic matrix for its electric modification and consequently to its high chemical instability that leads to degradation of the varistor. Castro et al. [5] reported that the trapping of electrons, ion migration and oxygen adsorption are included as ZnO varistor degradation mechanisms. The exposure of ZnO varistors to high temperatures and oxidizing atmospheres leads to excess interstitial ions *DZn* <sup>⋅</sup> and *DZn* ⋅⋅ that migrate through the depletion layer and chemically interact with species that are in the grain boundary, causing decrease and enlargement of the potential barrier, and facilitate the electronic conduction, destroying its varistor property [5,6].

The SnO2-based varistors were introduced by Pianaro et al. [7] as an alternative to the ZnO varistors commercial, presenting nonlinear electrical characteristics similar to ZnO varistors. The SnO2-based system shows more advantages, for example, their simpler microstructure and no formation of secondary phases require a lower concentration of agents modifiers to promote the varistor characteristics and densification and higher chemical and thermal resistances. The use of M2+ ion as dopant improved significantly the densification of the varistor, the addition of M5+ ion promoted electrical conductivity, and the M3+ ion influenced on nonlinearity coefficient.

#### **1.2. Electrical properties**

The electrical properties of varistor ceramics are governed by potential barriers located in the grain boundaries. Potential barriers were formed by the addition of dopants elements to generate defects on crystal network, which segregate to the grain boundary region by diffusion during sintering. The presence of these barriers promotes the large-capacity power absorption and its flow when subjected to electrical overvoltage [4,8].

In denominated "smart ceramics," the ceramic varistor acts as variable resistors, with resistive behavior at low voltages and conductive behavior starting from a specific voltage value, known as the breakdown voltage (*V*R) or breakdown electric field (*E*R) [9,10].

These electrical responses featuring the varistor ceramics as main elements in the manufacture of devices for electrical protection equipment subjected to both low and medium voltages apply directly as of the electro-electronics components (telephony system, computers, medical devices, automotive electronics, industrial automation systems, alarms, transformers, etc.) and for the high voltages used as part of lightning protection devices installed in the terminals of the power substations [11].

The varistor characteristic associated to quality is the nonlinear coefficient (*α*). The higher their value, the greater the varistor efficiency. This coefficient can be obtained through empirical relationships current × voltage (Eq. 1) or current density versus electric field (Eq. 2) and expresses how much the material deviates from ohmic response when required, and it can be explained by a graphic representation (Figure 1) with distinct regions [12–15].

$$I = \mathbb{C}V^a \tag{1}$$

$$J = \mathbb{C}E^{\alpha} \tag{2}$$

where *C* is a constant related to the microstructure.

**1. Introduction**

26 Advanced Ceramic Processing

and electrical power systems [1,2].

atmospheres leads to excess interstitial ions *DZn*

Varistor is an electrical device based on semiconductor materials used for protection against voltage spikes in the electric network, against overvoltage in electronic circuits of low voltage

Due to the high energy absorption, the ceramic varistors become many helpful in protecting electrical circuits, and their electrical properties are highly dependent on their microstructure. The development of devices ever more technological and brings the need for electrical protection due to the sensitivity equipment. The use of varistors as voltage protectors in electronic equipment is very simple: the varistor is directly connected in parallel to the power line of equipment, and in case of an increase in the electrical current on energy network, the varistor rapidly increases the conductivity, allowing the current flow toward the ground. For electrical appliances operating with few voltages, the varistors ceramics are called low-voltage

The first varistor ceramics were developed in 1930. They were constituted from compact silicon carbide (SiC) partially sintered and were designed by the System Bell Labs to replace selenium rectifiers that were used in the protection of telephone systems [4]. Over time, the processing of varistors has undergone successive improvements, and in 1968, Matsuoka [3] developed varistors based on zinc oxide with manganese and cobalt as a dopant to improve the electrical properties. One of the disadvantages of using ZnO-based varistors are the large amount of dopant added to ceramic matrix for its electric modification and consequently to its high chemical instability that leads to degradation of the varistor. Castro et al. [5] reported that the trapping of electrons, ion migration and oxygen adsorption are included as ZnO varistor degradation mechanisms. The exposure of ZnO varistors to high temperatures and oxidizing

> <sup>⋅</sup> and *DZn* ⋅⋅

layer and chemically interact with species that are in the grain boundary, causing decrease and enlargement of the potential barrier, and facilitate the electronic conduction, destroying its

The SnO2-based varistors were introduced by Pianaro et al. [7] as an alternative to the ZnO varistors commercial, presenting nonlinear electrical characteristics similar to ZnO varistors. The SnO2-based system shows more advantages, for example, their simpler microstructure and no formation of secondary phases require a lower concentration of agents modifiers to promote the varistor characteristics and densification and higher chemical and thermal resistances. The use of M2+ ion as dopant improved significantly the densification of the varistor, the addition of M5+ ion promoted electrical conductivity, and the M3+ ion influenced

The electrical properties of varistor ceramics are governed by potential barriers located in the grain boundaries. Potential barriers were formed by the addition of dopants elements to

that migrate through the depletion

**1.1. Varistors**

varistors [1–3].

varistor property [5,6].

on nonlinearity coefficient.

**1.2. Electrical properties**

**Figure 1.** Electric field (*E*) versus current density (*J*) curves of a varistor [16].

The pre rupture region is also named as linear region and has an ohmic behavior when the material is under operation normal tension. The varistor acts as a resistor in this case with a small amount of current (known as leakage current) passing through the material due to the action of the potential barrier formed at grain boundary and preventing the electronic conduction between the grains. The conductivity in this region is of thermionic emission type, i.e., the electrical conduction is strongly dependent of temperature, thus being possible to retrieve information about the resistivity of the material [8,16,17].

The rupture region showed nonlinear behavior, i.e., non-ohmic behavior between the applied voltage and the current that the material is submitted. The conductivity of the material increases with a small variation in the applied voltage, indicating the varistor efficiency that starts to act as a conductor from a specific breakdown electric field (*E*R). Recombination of electron-hole pair at grain boundary interfaces, thermionic emission, and electron tunneling are suggested as electric conduction mechanisms of this region [8,16].

In the post rupture region, the ohmic behavior between the current and the applied voltage is observed once again and is characterized by high current density. The electric conduction in this region is controlled by the impedance of the grains [2,8].

The *V*R value provides the varistor voltage application, and it is a function of a grain size of sintered material. If the composition is fixed, the microstructure becomes strongly dependent on the processing conditions [12,15].

The varistor efficiency determined by the breakdown region can be evaluated by the *α* nonlinear coefficient of the curve in Figure 1, which is used in Eq. 6, derived from Eq. 3, which allows the calculation of the value of *α* by the field data electric (*E*) and current density (*J*) [18,19]:

$$\alpha = (\log\_2 - \log\_1) / (\log E\_2 - \log E\_1) \tag{3}$$

The electric field and the current density are obtained from the measurements of the electric current (I) generated when the sample is submitted to a potential difference (V), according to Eqs. 4 and 5 [18,19]:

$$E = \bigvee\_{\mathbf{d}} \tag{4}$$

$$\mathbf{J} = \bigvee\_{\mathbf{A}} \mathbf{A} \tag{5}$$

*d* is the thickness of the sample and *A* is the electrode area deposited on the film surface. For *α* calculation, the interval of 1 and 10 mA/cm2 of current density was used, i.e., *J*<sup>1</sup> = 1 and *J*2 = 10 [18,19]:

$$\alpha = \left(\log E\_2 - \log E\_1\right)^{-1} \tag{6}$$
