**3. Charcterisitics of the ferroelectric materials**

An attractive and efficient material that has spontaneous polarization is a ferroelectric material. The presence of spontaneous polarization is highly temperature-dependent, and ferroelectric crystals generally have phase transitions where structural changes take place in the crystal [15]. The Curie temperature (Tc) is known as this transition temperature, at which the properties of the material change abruptly.

Thermodynamic properties show large anomalies, because the nature of the crystal structure close to the Curie temperature is totally changing. This is typically the case with the dielectric constant, which increases to a high value close to the Curie temperature, as indicated in **Figure 1**; it is also the transition point where the dielectric constant has the greatest sensitivity to the application of an electric field. This important characteristic can provide an attractive deployment of such materials for tunable electromagnetic components such as resonators, antennas, power dividers, hybrid couplers, and so on.

Several materials have shown a variable permittivity with the electric field, such as Strontium titanate (SrTiO3), Barium titanate (Ba, Sr. TiO3), (Pb, Sr)TiO3, (Pb, Ca)TiO3, Ba(Ti, Sn)O3, Ba(Ti, Zr)O3 and KTaO3 dopants [16–18].

However, strontium titanate (SrTiO3, STO) and barium strontium titanate (Bax Sr.(1-x) TiO3, BSTO), where x can vary from 0 to 1, are two of the most popular ferroelectric materials currently being studied for frequency-agile components and circuits. SrTiO3 is of special interest because of its crystalline compatibility with high-temperature superconductors (HTS) and its dominant properties at low temperatures.

Pure *STO* is not supposed to have Curie temperature above 0 Kelvin. Thin films and amorphous ceramic strucutres provide a low-temperature to achieve maimum dielectric constant. This implies that the Curie temperature is above 0 Kelvin,

**Figure 1.** *Curve of dielectric constant as a function of temperature [3].*

probably due to stresses or impurities in the films. For *BSTO*, as the value of *x* varies from 0 to 1, the Curie temperature varies from the value of *STO* to about 400 K, the Curie temperature of *BaTiO*3ð Þ *BTO* . This allows tailoring of the Curie temperature; generally, a value of *x* ¼ 0*:*5 is used to optimize for room temperature, and a value of around 0.1 is used when the material is to be used in conjunction with HTS films.

For microwave and wireless communication applications, there are several different forms of ferroelectric materials that are of extrme interest. Over many years, single crystal materials have been studied. Thin-film ferroelectric materials have recently been investigated; these films have been manufactured by laser ablation and are very small in thickness, typically less than 1 μm. The films are also mainly deposited on the LaAlO-3 substrate of lanthanum aluminate (it is an inorganic substrate and was chosen to design the proposed ZOR resonator circuit) and are usually combined with single layers such as HTS or a top-surface patterned normal conductor. Tri-layer (substrate-superstrate-HTS) films, forming an HTS/Ferroelectric/HTS structure, have also been produced, however. Films on a sapphire substrate were also produced with a CeO 2buffer layer of cerium oxide to compensate for the mismatch between lattice and thermal expansion [19]. More recently, the sol–gel technique [20] has been developed for producing Barium Strontium Titanate (BST). This method can generate material that is about 0.1 mm thick.

## **4. Thin film Sturucres dielectric properties**

The dielectric constant of bulk single-crystal STO is known to be independent of frequency up to 100–200 GHz [21–24]. The electric field and temperature dependence of the dielectric constant of single-crystal STO measured using a disk resonator at microwave frequencies [25] is shown in **Figure 2** *(The Matlab source code for calculating dielectric constant against the temperature and electric field is included in Appendix).* As can be seen, at a low temperature, the variation in the dielectric constant against an applied dc electric field is more sensitive.

**Figure 2.**

**Figure 3.**

**111**

*constant at different dc electric fields [25].*

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials*

*DOI: http://dx.doi.org/10.5772/intechopen.98475*

*(a) Electric field dependence of the STO dielectric constant (b) temperature dependence of the STO dielectric*

*Variation of the dielectric constant of a BST ceramic and thin film as a function of operating temperature [26].*

### **5. Properties of ferroelectric materials for microwave applications**

The dielectric constant for thin films is normally lower than the single crystal with the same composition, and the loss tangent can be one order higher. An example of the temperature dependence of the bulk and thin-film BST permittivity is shown in **Figure 3** of [26]. It should be noted that the permittivity is substantially lower than the bulk for the BST thin film and the sharp peak is not observed at the phase transition temperature. The effect of size or the presence of dead layers, misfit strain and thin film defects are considered to be the sources of the deviation of properties from the behavior of the bulk [27]. The theory of this deviation, however, is not well understood yet.

The most fundamental characteristics for microwave applications are the dielectric constant, tunability, and loss performance of ferroelectric materials. It is clear that for high-performance devices, high tunability and low dielectric loss are favorable. In response to the applied electric field, which is the basis of microwave applications, the dielectric constant ε of ferroelectrics varies. Tunability is a criterion for evaluating the dependence on permittivity in the electric field. The tunability of a ferroelectric material, defined as the ratio of the dielectric permittivity of the material at zero electric fields to its permittivity under electric field bias E, can be defined in two ways.

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials DOI: http://dx.doi.org/10.5772/intechopen.98475*

**Figure 2.**

probably due to stresses or impurities in the films. For *BSTO*, as the value of *x* varies from 0 to 1, the Curie temperature varies from the value of *STO* to about 400 K, the Curie temperature of *BaTiO*3ð Þ *BTO* . This allows tailoring of the Curie temperature; generally, a value of *x* ¼ 0*:*5 is used to optimize for room temperature, and a value of around 0.1 is used when the material is to be used in conjunction with HTS films. For microwave and wireless communication applications, there are several different forms of ferroelectric materials that are of extrme interest. Over many years, single crystal materials have been studied. Thin-film ferroelectric materials have recently been investigated; these films have been manufactured by laser ablation and are very small in thickness, typically less than 1 μm. The films are also mainly deposited on the LaAlO-3 substrate of lanthanum aluminate (it is an inorganic substrate and was chosen to design the proposed ZOR resonator circuit) and are usually combined with single layers such as HTS or a top-surface patterned normal conductor. Tri-layer (substrate-superstrate-HTS) films, forming an HTS/Ferroelectric/HTS structure, have also been produced, however. Films on a sapphire substrate were also produced with a CeO 2buffer layer of cerium oxide to compensate for the mismatch between lattice and thermal expansion [19]. More recently, the sol–gel technique [20] has been developed for producing Barium Strontium Titanate (BST). This method can generate material that is about 0.1 mm thick.

The dielectric constant of bulk single-crystal STO is known to be independent of frequency up to 100–200 GHz [21–24]. The electric field and temperature dependence of the dielectric constant of single-crystal STO measured using a disk resonator at microwave frequencies [25] is shown in **Figure 2** *(The Matlab source code for calculating dielectric constant against the temperature and electric field is included in Appendix).* As can be seen, at a low temperature, the variation in the dielectric

**4. Thin film Sturucres dielectric properties**

*Multifunctional Ferroelectric Materials*

however, is not well understood yet.

be defined in two ways.

**110**

constant against an applied dc electric field is more sensitive.

**5. Properties of ferroelectric materials for microwave applications**

The dielectric constant for thin films is normally lower than the single crystal with the same composition, and the loss tangent can be one order higher. An example of the temperature dependence of the bulk and thin-film BST permittivity is shown in **Figure 3** of [26]. It should be noted that the permittivity is substantially lower than the bulk for the BST thin film and the sharp peak is not observed at the phase transition temperature. The effect of size or the presence of dead layers, misfit strain and thin film defects are considered to be the sources of the deviation of properties from the behavior of the bulk [27]. The theory of this deviation,

The most fundamental characteristics for microwave applications are the dielectric constant, tunability, and loss performance of ferroelectric materials. It is clear that for high-performance devices, high tunability and low dielectric loss are favorable. In response to the applied electric field, which is the basis of microwave applications, the dielectric constant ε of ferroelectrics varies. Tunability is a criterion for evaluating the dependence on permittivity in the electric field. The tunability of a ferroelectric material, defined as the ratio of the dielectric permittivity of the material at zero electric fields to its permittivity under electric field bias E, can

*(a) Electric field dependence of the STO dielectric constant (b) temperature dependence of the STO dielectric constant at different dc electric fields [25].*

**Figure 3.** *Variation of the dielectric constant of a BST ceramic and thin film as a function of operating temperature [26].*

*Multifunctional Ferroelectric Materials*

$$m = \frac{\mathfrak{e}(\mathbf{0})}{\mathfrak{e}(E)}\tag{1}$$

and the relative tunability *nr* defined as the relative change of the permittivity between zero bias and an electric field *E* with respect to its permittivity at zero bias

$$n\_r = \frac{\varepsilon(\mathbf{0}) - \varepsilon(E)}{\varepsilon(\mathbf{0})} = \mathbf{1} - \frac{\mathbf{1}}{n} \tag{2}$$
