**4. Electrical properties of the PZT thick films as a function of the number of infiltrations**

We have already seen that in PZT thick films the structural and microstructural properties are highly dependent on the number of infiltrations, but what about the dielectric, ferroelectric and piezoelectric properties? It is well-known that in bulk materials the dielectric, ferroelectric and piezoelectric properties are highly dependent on grain size, porosity, phase formation, stoichiometric, crystallographic orientation, amongst others. However, in PZT thick films this dependence may be notably different because the electrical properties are also affected by substrate clamping, surface powder agglomeration and the mixture of phases coming from the precursors PZT powder and PZT sol-gel solution, etc.

Piezoelectric Thick Films: Preparation and Characterization 363

tan

02468

Fig. 7. Dielectric behavior of the PZT thick films, prepared based on a low molecular weight

0 20 40 60 80 100

Powder Volumen Fraction (%)

Fig. 8. Dielectric constant of PZT composite predicted by 0-3 composite and cube models. Inset plot shows the dielectric constant values calculated taking into account a 30% to 0% variable porosity in parallel with the PZT composite (0.66/0.33 powder/solution ratio).

70 75 80 85 90 95 100

with porosity

precursor solution, as a function of the number of infiltrations (Pérez et al., 2007).

 Cube model 0-3 Connectivity

Number of infiltrations

0.00

0.02

0.04

0.06

Dielectric loss

0.08

0.10

0.12

1200

(Copyright Elsevier)

0

500

1000

1500

Dielectric constant

2000

2500

3000

3500

1400

1600

1800

Dielectric constant

2000

2200

2400

#### **4.1 Dielectric behavior of the PZT thick films as a function of the number of infiltrations**

Figure 7 shows the dielectric constant and dielectric losses behavior reported by Pérez and co-workers for infiltrated PZT thick films (Pérez et al., 2007). It is observable that the dielectric constant increases as the number of infiltrations increase, while the dielectric loss remains around 0.05. This dielectric constant behavior is consistent with the decrease in porosity as the film is infiltrated, reaching its maximum around 2320. This value is far from the 3420 reported on the TRS600 PZT powder (Kholkin et al., 2001, TRS, 1998). However, it should be taken into account that a phase mixture is presented in the PZT thick film, being the dielectric constant of the PZT layer obtained from the sol-gel solution ~1900 (Pérez et al., 2004), and, furthermore, that there is some closed porosity .

The increases in the dielectric constant as the number of infiltrations increase could be easily explained based on connectivity models (Barrow et al., 1997; Kholkin et al., 2001). These models describe the connectivity degree between the PZT powders particles inside the PZT films matrix formed after the deposition process.

#### **4.1.1 Dielectric constant models for connected composite material**

Based on the deposition process of the PZT infiltrated thick films reported by Pérez and coworkers, which includes intermediate infiltrations, the dielectric constant might be modeled as a 0-3 composite material, where the sol gel matrix is fully connected in three directions and the ceramic particles (powder) are not connected in any direction. Assuming that the particles are uniformly dispersed in the sol gel matrix, then the resulting dielectric constant can be given by (Moulson & Herbert, 2004):

$$\mathfrak{c}\_{m} = \mathfrak{e}\_{2} \left[ 1 + \frac{3 \ast V\_{1}(\mathfrak{e}\_{1} - \mathfrak{e}\_{2})}{\mathfrak{e}\_{1} + 2 \ast \mathfrak{e}\_{2} - V\_{1}(\mathfrak{e}\_{1} - \mathfrak{e}\_{2})} \right] \tag{7}$$

where 1 is the dielectric constant of the PZT powder, 2 is the dielectric constant of the sol gel matrix, and V1 is the volume fraction of the ceramic powder.

Practically, this equation is only valid for low powder volume fraction values V1<0.1 (Barrow et al., 1997), because at higher concentrations, the dispersed phase starts to form continuous structures throughout the bulk that have nonzero connectivity. However, due to the intermediate infiltration process carried out in the preparation of the PZT thick films the 0-3 connectivity is practically maintained. Thus, this model can be applied for relatively higher powder volume fraction values.

Although the 0-3 connectivity model is not faraway from reality, a more likely scenario is that proposed by Pauer (Barrow et al., 1997; Pauer, 1973], where the material exists in a combination of series and parallel phases (cube model). In this case the effective dielectric constant can be calculated by:

$$\varepsilon\_m = \frac{\varepsilon\_1 \varepsilon\_2}{(\varepsilon\_2 - \varepsilon\_1)V\_1^{-\frac{1/3}{3}} + \varepsilon\_1 V\_1^{-\frac{2/3}{3}}} + \varepsilon\_2 (1 - V\_1^{\frac{2/3}{3}}) \tag{8}$$

Assuming that in a highly infiltrated PZT films the powder/solution volume fraction is 0.66/0.33, the dielectric value calculated by both models is ~2580, a little higher than the one obtained in the experimental results (see Figure 8). Note both models did not take into consideration the porosity of the films. For that reason, we could expect lower effective dielectric values than 2580.

Figure 7 shows the dielectric constant and dielectric losses behavior reported by Pérez and co-workers for infiltrated PZT thick films (Pérez et al., 2007). It is observable that the dielectric constant increases as the number of infiltrations increase, while the dielectric loss remains around 0.05. This dielectric constant behavior is consistent with the decrease in porosity as the film is infiltrated, reaching its maximum around 2320. This value is far from the 3420 reported on the TRS600 PZT powder (Kholkin et al., 2001, TRS, 1998). However, it should be taken into account that a phase mixture is presented in the PZT thick film, being the dielectric constant of the PZT layer obtained from the sol-gel solution ~1900 (Pérez et al.,

The increases in the dielectric constant as the number of infiltrations increase could be easily explained based on connectivity models (Barrow et al., 1997; Kholkin et al., 2001). These models describe the connectivity degree between the PZT powders particles inside the PZT

Based on the deposition process of the PZT infiltrated thick films reported by Pérez and coworkers, which includes intermediate infiltrations, the dielectric constant might be modeled as a 0-3 composite material, where the sol gel matrix is fully connected in three directions and the ceramic particles (powder) are not connected in any direction. Assuming that the particles are uniformly dispersed in the sol gel matrix, then the resulting dielectric constant

<sup>1</sup> <sup>3</sup> 2

 

 *<sup>m</sup> V*

 

 <sup>2</sup> 11 2 1 2 11 2

*V*

( )

 

( )

(7)

 

where 1 is the dielectric constant of the PZT powder, 2 is the dielectric constant of the sol

Practically, this equation is only valid for low powder volume fraction values V1<0.1 (Barrow et al., 1997), because at higher concentrations, the dispersed phase starts to form continuous structures throughout the bulk that have nonzero connectivity. However, due to the intermediate infiltration process carried out in the preparation of the PZT thick films the 0-3 connectivity is practically maintained. Thus, this model can be applied for relatively

Although the 0-3 connectivity model is not faraway from reality, a more likely scenario is that proposed by Pauer (Barrow et al., 1997; Pauer, 1973], where the material exists in a combination of series and parallel phases (cube model). In this case the effective dielectric

> 

Assuming that in a highly infiltrated PZT films the powder/solution volume fraction is 0.66/0.33, the dielectric value calculated by both models is ~2580, a little higher than the one obtained in the experimental results (see Figure 8). Note both models did not take into consideration the porosity of the films. For that reason, we could expect lower effective

<sup>3</sup> 2 1

2 <sup>3</sup> 1

( ) (8)

2

 

 *m V V V*

1 2

1 <sup>3</sup> 1 1

( )

2 11

**4.1 Dielectric behavior of the PZT thick films as a function of the number of** 

2004), and, furthermore, that there is some closed porosity .

**4.1.1 Dielectric constant models for connected composite material** 

 

gel matrix, and V1 is the volume fraction of the ceramic powder.

films matrix formed after the deposition process.

can be given by (Moulson & Herbert, 2004):

higher powder volume fraction values.

constant can be calculated by:

dielectric values than 2580.

**infiltrations** 

Fig. 7. Dielectric behavior of the PZT thick films, prepared based on a low molecular weight precursor solution, as a function of the number of infiltrations (Pérez et al., 2007). (Copyright Elsevier)

Fig. 8. Dielectric constant of PZT composite predicted by 0-3 composite and cube models. Inset plot shows the dielectric constant values calculated taking into account a 30% to 0% variable porosity in parallel with the PZT composite (0.66/0.33 powder/solution ratio).

Piezoelectric Thick Films: Preparation and Characterization 365

increase. It is comprehensible that as the channel of the pore and the pore size itself are reduced; the infiltration becomes more and more difficult, resulting in a blocking of the infiltration process. The saturation in dielectric constant and remnant polarization also indicates that infiltration and pore size reduction is almost stopped for higher number of

Figure 10 illustrates the piezoelectric coefficient as a function of the number of infiltration and the piezoelectric loop of the PZT thick film prepared with 8 top infiltrations. The trend in the piezoelectric coefficient is similar to those reported for the polarization, showing a piezoelectric coefficient (*d33*) of ~65 pm/V in the films with 8 top infiltrations. It is notable that the piezoelectric coefficients observed in the 8 times infiltrated PZT thick film is of the same order of magnitude as those reported for a 1m PZT coating films prepared using a modified solution (Pérez et al., 2004). On the other hand, in the non-infiltrated film the piezoelectric coefficient is not reported due to the high surface roughness, which does not

02468

8 infiltrations

*d33* (pm/V)

Number of infiltrations

Fig. 10. *d33* piezoelectric thick film behavior as a function of the number of infiltrations. Inset plot show the piezoelectric loop of the PZT thick films prepared using 8 top infiltrations.

Dorey *et. al.,* reported the same piezoelectric coefficient (~65 pm/V) for PZT thick film infiltrated with a high molecular weight solution (Dorey et al., 2002). The *d33* coefficients obtained by Dorey and Pérez suggests that the piezoelectric response of the infiltrated PZT thick films is highly conditioned by the piezoelectric response of the PZT phase formed from


Applied Voltage (V)


**4.3 Piezoelectric behavior of the PZT thick films as a function of the number of** 

infiltrations.

**infiltrations** 

allow the piezoelectric measurement of this film.

0

the sol-gel solution (Dorey et al., 2002; Pérez et al., 2007).

10

20

30

*d33* (pm/V)

40

50

60

70

In the hypothetic scenario that 8% of the films is free space or porosity filled by air and also that they are connected in parallel with the composite material (powder/solution), the dielectric constant values match with the experimental results (see inset plot Figure 8). At the extremes, one observes deviations from the experimental values due to the irremovable porosity at higher dielectric volume fraction and the actuation of a serial porosity component at a "lower" composite volume fraction. The irremovable porosity is enclosed in the powder agglomeration, which hinder its elimination while the serial porosity contribution appears when the composite films are not infiltrated. It is clear that in noninfiltrated PZT thick films the porosity contributes to both serial and parallel capacitances of the system, degrading the dielectric constant of these films.

#### **4.2 Ferroelectric behavior of the PZT thick films as a function of the number of infiltrations**

Figure 9 shows the hysteresis loop of PZT thick films prepared using different number of infiltrations. It is visible that the remnant polarization values increases with the increase of the number of infiltrations. A large remnant polarization in the orders of *Pr*=35 C/cm2 and a small coercive field *Ec*=59 kV/cm are obtained in PZT thick film prepared with 8 top infiltrations, as shown in the inset of Figure 9. The remnant polarization value is similar to the one reported for 1m coating PZT films prepared using a modified solution (Pérez et al., 2004). However, the coercive field is lower suggesting that it is easier to switch the polarization in infiltrated PZT thick films. In this study, the polarization trend results for a decrease of the porosity and improvement of the films surface as the number of infiltration

Fig. 9. Remnant polarization of the PZT thick films as a function of the number of top infiltration. Inset plot show the hysteresis loop of the films with 0 and 8 infiltrations (Pérez et al., 2007).

In the hypothetic scenario that 8% of the films is free space or porosity filled by air and also that they are connected in parallel with the composite material (powder/solution), the dielectric constant values match with the experimental results (see inset plot Figure 8). At the extremes, one observes deviations from the experimental values due to the irremovable porosity at higher dielectric volume fraction and the actuation of a serial porosity component at a "lower" composite volume fraction. The irremovable porosity is enclosed in the powder agglomeration, which hinder its elimination while the serial porosity contribution appears when the composite films are not infiltrated. It is clear that in noninfiltrated PZT thick films the porosity contributes to both serial and parallel capacitances of

**4.2 Ferroelectric behavior of the PZT thick films as a function of the number of** 

Figure 9 shows the hysteresis loop of PZT thick films prepared using different number of infiltrations. It is visible that the remnant polarization values increases with the increase of the number of infiltrations. A large remnant polarization in the orders of *Pr*=35 C/cm2 and a small coercive field *Ec*=59 kV/cm are obtained in PZT thick film prepared with 8 top infiltrations, as shown in the inset of Figure 9. The remnant polarization value is similar to the one reported for 1m coating PZT films prepared using a modified solution (Pérez et al., 2004). However, the coercive field is lower suggesting that it is easier to switch the polarization in infiltrated PZT thick films. In this study, the polarization trend results for a decrease of the porosity and improvement of the films surface as the number of infiltration

02468

Fig. 9. Remnant polarization of the PZT thick films as a function of the number of top infiltration. Inset plot show the hysteresis loop of the films with 0 and 8 infiltrations (Pérez

 0 Infiltrations 8 Infiltrations

*P* (C/cm2 )

Number of infiltrations


*E* (kV/cm)


the system, degrading the dielectric constant of these films.

**infiltrations** 

10

15

20

Remnant Polarization (

et al., 2007).

C/cm2

)

25

30

35

40

increase. It is comprehensible that as the channel of the pore and the pore size itself are reduced; the infiltration becomes more and more difficult, resulting in a blocking of the infiltration process. The saturation in dielectric constant and remnant polarization also indicates that infiltration and pore size reduction is almost stopped for higher number of infiltrations.

#### **4.3 Piezoelectric behavior of the PZT thick films as a function of the number of infiltrations**

Figure 10 illustrates the piezoelectric coefficient as a function of the number of infiltration and the piezoelectric loop of the PZT thick film prepared with 8 top infiltrations. The trend in the piezoelectric coefficient is similar to those reported for the polarization, showing a piezoelectric coefficient (*d33*) of ~65 pm/V in the films with 8 top infiltrations. It is notable that the piezoelectric coefficients observed in the 8 times infiltrated PZT thick film is of the same order of magnitude as those reported for a 1m PZT coating films prepared using a modified solution (Pérez et al., 2004). On the other hand, in the non-infiltrated film the piezoelectric coefficient is not reported due to the high surface roughness, which does not allow the piezoelectric measurement of this film.

Fig. 10. *d33* piezoelectric thick film behavior as a function of the number of infiltrations. Inset plot show the piezoelectric loop of the PZT thick films prepared using 8 top infiltrations.

Dorey *et. al.,* reported the same piezoelectric coefficient (~65 pm/V) for PZT thick film infiltrated with a high molecular weight solution (Dorey et al., 2002). The *d33* coefficients obtained by Dorey and Pérez suggests that the piezoelectric response of the infiltrated PZT thick films is highly conditioned by the piezoelectric response of the PZT phase formed from the sol-gel solution (Dorey et al., 2002; Pérez et al., 2007).

Piezoelectric Thick Films: Preparation and Characterization 367

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### **5. Conclusion**

In this work an exhaustive review on the preparation of PZT thick films have been carried out, taking specific focus in the effect of the infiltration in the preparation of high-quality films. Solution powder agglomeration, films densification, phase formation temperature, among others, have been analyzed. Moreover, the infiltration process is discussed based on Darcy´s law, while the improvement of structural and microstructural properties has been analyzed as a function of the infiltration process. The dielectric properties are characterized as function of the number of infiltrations and the results compared with those obtained by the 0-3 composite connectivity and the cube models. Finally, ferroelectric and piezoelectric properties are also discussed, as function of the number of infiltrations.

### **6. References**


Finally, it should be noted that although the piezoelectric coefficient of highly infiltrated PZT thick film does not reach the piezoelectric coefficient of the PZT ceramics, it is good enough for micromechanical applications. Note it is much higher than for non-ferroelectric piezoelectrics clamping by rigid substrate (ZnO, AlN) (Trolier-McKinstry & Muralt, 1973) and in the same order as that of PZT thin film deposited onto a platinized substrate (Pérez et

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al., 2004).

**5. Conclusion** 

**6. References** 


**15** 

Cheng-Yao Lo

*National Tsing Hua University Taiwan (Republic of China)* 

**Possibilities for Flexible MEMS:** 

**Take Display Systems as Examples** 

After the development of cathode ray tube (CRT) in the 19th century and the commercialization of television (TV) in the 1930s display devices are always one of the dream products in daily life. The revolutionary innovation from black-and-white to color display, from small size to large area, from curved surface to flat panel, and from spaceconsuming tube to short tube, all proved that the demands and distribution of display

Along the popularization of personal computer, the demand of CRT put the display technology and its industry to a highly growth field for the past few decades until the late 20th century. On the other hand, with the leaping progress of research and development on liquid crystal, liquid crystal display (LCD) also attracted customers' attention and overwhelmingly replaced CRT and suppressed CRT industry because of its light weight and thin body. Even though LCD's starting price was high, most of customers were still switching their display device from CRT since the bulky CRTs cost more when talking about office or house rent. Similarly to CRT, researchers also spent time developing thinner, lighter, wider viewing angle, shorter response time, and larger size LCDs. As a result, LCD became a main stream not only for computer displays, but also for recreation displays such as TV. In the same time, plasma display panel (PDP), and organic light emitting diode (OLED) also found their application fields as a flat panel display device to replace the role of CRT. Unfortunately, PDP's high resolution and fast response time come with low life time and high power dissipation. The original advantage of large size display was also gradually replaced by the up-to-date LCD produced from the 6th-8th generation glass substrate. Thus PDP market is now suppressed by LCD and PDP manufacturers are also reducing their production. Although OLED was proved to be display-capable, recently commercialized OLED's blue color degradation still limits its application on information display. Since the demand for larger display size, wider viewing angle, and smaller body size are still growing, projection display such as back projection TVs and overhead projectors are built in parallel. Back projection TV, owing to its bulky size and low resolution, had limited applications and disappeared from market rapidly; overhead projectors, even though still find their way in the early 21th century, it was neither portable nor long lasting. Thus, how to realize a light weight, small size, and large display area comes to one end – flexible display. When display device becomes flexible, it must be light weight and portable. It must

device was growing and played a critical role on civilization and industrialization.

**1. Introduction** 

Substrates and Their Electric and Piezoelectric Properties, *Japanese Journal of Applied Physics*, Vol.39, No.9B. pp. 5604–5608

