Semiconducting Ceramics: Varistor Applications

2.1 Electrical Conductivity in Ceramics

Ceramic materials displays both electrical insulating and electrical conducting properties. Many of the important properties of cermaics have been developed because of their electrical insulating characteristics, ceramics possess good electrical conductivity and some ceramic materials have characteristics of superconductors. Below shows a table of conductivities of cermaics.

Table 1. Conductivities of some cermaics 

A basic summary of the electron band gap between metals, semiconductors and insulators is shown in figure 1. Semiconductors fall into a group that its band gap is usually between 0.02 to 2.5 eV. When the band gap energy is towards the lower part of the energy range a significant amount of electrons are in the conduction band.

Figure 1. Electron energy band in solids 

Understanding the basic principles of semiconductors we can now relate the band gap energies to how electrons and holes may be generated in ceramic materials. There are a few situations that can occur for semiconductors :

• Intrinsic properties - electrons moving across the band gap
• Extrinsic properties - dopants or impurties are add
• Nonstoichiometric properties - creating defects to obtain necessary properties

2.2 Semiconducting Ceramics: Intrinsic properties

When an electron is excited and moves from the valence band to the conduction band, a hole is created in the valence band. We know certain characteristics of the valence and conduction bands and we can determine the intrinsic conductivity of the material.

Where, n is the number of electrons in the conduction band

(1)
\begin{align} n=N_cexp[-{\ E_g \over {\ 2kT}}] \end{align}

Where, p is the number of holes in the valence band

(2)
\begin{align} p=N_vexp[-{\ E_g \over {\ 2kT}}] \end{align}

Density of states for the conduction and valence band are given, respectively

(3)
\begin{align} N_c=2 {\left[2\pi m_{e}^* kT \over {h}^2 \right]}^{3\over2} \end{align}

and

(4)
\begin{align} N_v=2 {\left[2\pi m_{h}^* kT \over {h}^2 \right]}^{3\over2} \end{align}

where, $m_{e}^*$ and $m_{h}^*$ are the masses of the electrons and holes. Taking into consideration that $m_{e}^*$ = $m_{h}^*$ we can denote that the mass of the electrons in the valence band is the same as the mass of the electrons in the conduction band. This is denoted as

(5)
\begin{equation} n_i = p_i \end{equation}

Then

(6)
\begin{align} n_i = (N_cN_v)^{1\over2} exp[-{\ E_g \over {\ 2kT}}] \end{align}

Thus the intrinsic conductivity is given by 

(7)
\begin{align} \sigma_i = qn_i(\mu_e + \mu_h) \end{align}

Due to the large $E_g$ that semiconductors have their intrinsic conductivity is usually low. Intrinsic characteristics in semiconductors are used in transmission electron microscopes (TEM) and scanning electron microscopes (SEM) .

2.3 Semiconducting Ceramics: Extrinsic properties

Unlike intrinsic semiconductors, extrinsic semiconductors have impurties. These impurties are either introduced intentionally or accidentally. Figure shows the effect that dopants have on the band gap in a material. If the energy level that is associated with dopant is closer to the conduction band, that dopant is consider an electron donor. Likewise, if the energy level for the dopant is closer to the valence band, than that dopant is an electron acceptor.

Figure 2. Effect of band gap due to dopants 

There are different characterizations for the way dopants effect the band gap. These are n-type and p-type semiconductors. If the dopant is an electron donor then the material is referred to as an n-type semiconductor, and if the dopant accepts electrons then the material is a p-type semiconductor. For further reading on n-type and p-type dopants in semiconductor click here. Please note a basic understanding of p-type and n-type semiconductors are needed for varistors.

2.4 Applications: Varistors

Varistors are used for protection against large voltage pulse, this can be compared to surge protectors. When a large volatge surge enters into a electrical circuit, a varistor will act as a switch and direct the large voltage to ground. To understand what materials are exceptable for this application we must first look at the I-V relationship. Figure 3 shows the I-V characteristic of ZnO and SiC, we can see that there is a broader range for ZnO in the breakdown zone compared to the dotted line of SiC. This breakdown zone is the threshold that the voltage needs to reach inorder for the varistor to switch to ground. So it takes a larger amount of voltage in a ZnO material to reach the upturn region compared to a SiC material. This zone is referred to as an $\alpha$ parameter.

Figure 3. I-V characteristic for ZnO and SiC 

To form this system, ceramic powders are mixed together and then fired. Metallization occurs during the process to create an electrical connection . During the curing process a multi-crystalline structure is formed and this can be seen in figure 4.

Figure 4. Multi-crystalline structure of a varistor 

At low voltages the varistor acts in a linear relationship causing voltage to flow into the electrical circuit but if the voltage increases above the threshold value then the varistor will direct the voltage to ground. A material that has a larger breakdown area in the I-V curve will work better than a material that has a smaller region. In the case of SiC, one can see that the breakdown area is rather small compared to ZnO, so this means that a smaller surge will direct the voltage to ground. Now for some electrical circuits this material would not be suitable because there is only a small variation between operating voltage and threshold voltage, meaning that if the voltage were to vary only slightly then the electrical circuit will go to ground. So for this example we will be investigating ZnO as an acceptable material for varistor applications. This concept can be compared to a diode but the main difference between a varistor and a diode is that a varistor can be used within an ac and dc circuits.

Metal oxide varistors (MOV), such as ZnO are nonlinear (at high voltage), voltage dependent devices. Shown below, in figure 5, there is a sharp breakdown characteristic that provides excellent tranisent surpression performance . When a large voltage is applied across the varistor the impedence changes by many orders of magnitude. The varistor changes from an open circuit, flowing voltage into the electrical circuit, to a highly conductive level, where the system goes to ground. This highly conductive level reduces the voltage to a safe operating level .

Figure 5. Varistor I-V curve 

2.4.1 ZnO Varistor

ZnO is an acceptable material for varistor applications not only because of its large breakdown area but its microstructure. The ZnO grains are about 15-20 $\mu m$ in size and when doped with a bismuth intergranular film (IGF) it creates seperations within the ZnO microstructure of between 1 nm and 1 $\mu m$. Below is a micrograph of the ZnO varistor.

Figure 6. Microstructure of ZnO doped bismuth IGF 

The migration of bismuth to the grain boundaries (GB) results in the creation of acceptor levels. The actual understanding of how these sites are produced is still being investigated but some believe that due to the Zn vacancies it might be possible that the Bismuth is stablizing the acceptor defects. These GBs create P-N junction semiconductor characteristics at the integranluar sites. The GBs are responsible for blocking conduction at low voltages and are the source for the nonlinear characteristics at high voltages . The electrical characteristics of an MOV are related to the bulk of the device. Each intergranular boundary functions as a P-N junction. Since the nonlinear electrical behavior occurs at the intergranular boundaries of the ZnO grains, the varistor can be considered a "multi-junction" device composed of many series and parallel connections of grain boundaries. Grain size and distribution play a major role in electrical characteristics .

In figure 7 the above picture shows the two different fermi levels between the $E_f$(grain) and $E_f$(GB). The below picture shows the system at equilibrium where the two fermi levels align causing depletion zones in the conduction and valence bands. The IGFs create GB which form depletion zones causing a certain barrier height ($e \phi$) which can be seen in figure 5.

Figure 7. Band diagram of ZnO doped Bi grain boundaries (a) the top band diagram shows the different fermi levels and acceptor levels between ZnO and Bi (b) equilibrium, the two fermi levels align and create a depletion layer .

In order for conduction to occur, electrons must overcome that barrier height ($e \phi$). When a potential is applied to the system the $e \phi$ barrier is reduced. Allowing for different barrier heights to be achieved and thus different potentials to turn the system to zero. Conduction occurs when electrons crosses the barrier height by thermal activation or by tunneling. This system is reversible and if the voltage drops below the breakdown threshold then the varistors will return to its normal operating condictions.

2.5 References

 Carter, C. "Ceramic Materials." Springer Science + Business Media, LLC. 2007

 Hummel, E. "Electronic Properties of Materials." Springer Science + Business Media, LLC. 2001

 Omar, M. "Elementary Solid State Physics." Pearson Eduction, Inc. 1999

 Maximum Intregated Products, Dallas Semiconductor. April 29 2009. <http://korea.maxim-ic.com>.

 Materials Research. April 30 2009. <http://www.scielo.br>.

 ITEM Publications. April 24 2009. <http://www.interferencetechnology.com/>.