Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications

Подождите немного. Документ загружается.

Handbook of dielectric, piezoelectric and ferroelectric materials750

bandwidth. Figure 24.24 shows the real part of the impedance frequency

spectrum of the pMUT as shown in Fig. 24.23. The measurement data was

fitted using the Lorentz function. The fitted parameters f

and ∆f were used

to estimate the Q value. The estimated Q value is about 110.

The equivalent circuit of the pMUT element can be modeled as shown in

Fig. 24.25. The static capacitance C

of the pMUT is around 200pF measured

with HP4284 LCR meter at 1kHz. Based on the measurement results of the

coupling coefficient k and the Q value, the dynamic equivalent circuit

parameters of the pMUT can be calculated as C

= 2.88pF, R

= 1926Ω and

= 0.1293H, according to the equations listed below.

1 –

⇒

24.3

(2 )

⇒

24.4

ππ

⇒

24.5

24.6.6 Size dependence of resonance frequency

The relationship between the resonance frequency of the diaphragm and its

size was investigated by employing the pMUT prepared with nanocomposite

PZT film. Three contiguous square diaphragms with respective side lengths

TKC701

OSC Level: 100mV

dc bias: 40 V

= 259.87 kHz

= 261.73 khz

= 1.42%

250 255 260 265 270

Frequency (kHz)

Impedance (Ω)

4000

3900

3800

3700

Phase (degree)

–85.5

–86.0

–86.5

–87.0

–87.5

–88.0

–88.5

24.23

Measurement results impedance frequency spectrum of a

pMUT element with a diaphragm size of 0.5 × 0.5 mm

of 7 µm-thick

PZT and 10µm-thick support layer.

WPNL2204

Piezoelectric thick films for MEMS application 751

of 2, 1.5 and 1mm were measured. Figure 24.26 shows the result. Their

fundamental resonance frequencies were 31.6, 57.8 and 124.5 kHz, respectively.

The sixth order harmonic modes of the two large diaphragms were also

detected. Figure 24.26(b) reveals that the resonance frequency of the diaphragm

is inversely proportional to the square of the side length, expressed as a,

provided that the diaphragms have the same multilayer structure and thickness.

This test confirms that the thick film diaphragms operate as clamped plates.

This result is significant because it reveals that the thickness of the PZT

layer is not the sole parameter that dictates the operating frequency (the

membrane resonance frequency), as it is the case in conventional ceramic

transducers. Instead, frequency is governed by the dimensions and the layering

materials of the diaphragm and can thus be controlled independent of the

PZT layer thickness, offering more design flexibility and control over the

frequency.

24.7 Summary

Thick piezoelectric film pMUTs with operating frequency of tens to hundreds

kilohertz have been developed by combining silicon micromachining and

/ ∆

= 260.89/2.37 = 110.1

Lorentz fit

′(Re)

250 255 260 265 270

Frequency (kHz)

Impedance Re (Ω)

300

250

200

150

100

24.24

Measured real part of the impedance frequency spectrum of

the pMUTs element with a diaphragm size of 0.5 × 0.5 mm

of 7 µm-

thick PZT layer and 10µm-thick silicon, fitted with Lorentz function

for calculation of the

value.

R1 C1 L1

24.25

Equivalent circuit of the resonant pMUT element.

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials752

the composite thick PZT film deposition technology. The success of the

fabrication of the pMUT is mainly due to the thick, crack-free and homogeneous

composite thick film. Preparing the slurry with submicrometer-sized PZT

powder is an effective way to improve the remanent polarizations, and thus

the piezoelectric coefficient of the composite film at the expense of the film

density. The leakage current density and breakdown field of the film, however,

are quite acceptable for MEMS device application in spite of relatively

higher porosity of the film in comparison with nanocomposite film. Using a

well-reacted TiO

layer instead of a pure metallic Ti layer as the adhesion

layer of the bottom electrode is an effective way to avoid the formation of

24.26

(a) Frequency dependence of deflection at central point of

square pMUT diaphragms driven by 3.5µm-thick nanocomposite PZT

film under 30V dc bias voltage. The backside Si was completed

etched off. (b) Relationship between measured resonance frequency

and the side length

of the diaphragm. A linear regression analysis

based on

is applied to the data points, where

is frequency,

and

equals 1/

. The linear regression coefficient

equals 0.9997.

2 × 2mm

1.5 × 1.5mm

1 × 1mm

57.75 kHz

(1,1)

31.6 kHz

(1,1)

124.5 kHz

(1,1)

113 kHz

(1,3)

202 kHz

(1,3)

0 40 80 120 160 200 240

Frequency (KHz)

(a)

Deflection amplitude (µm)

Linear regression

= 125.44666

= 0.999 71

Frequency (kHz)

140

120

100

0.0 0.2 0.4 0.6 0.8 1.0

(mm

–2

)

WPNL2204

Piezoelectric thick films for MEMS application 753

the blister. The resonance frequency of the square transmitter is inversely

proportional to the area of the membrane. At the resonance frequency the

oscillation amplitude at the center of the diaphragm can reach several

micrometers and the output sound pressure also reaches its maximum. The

generated SPL of up to 120dB indicates that the developed pMUT has quite

good ultrasound-radiating performance and the pMUT array has potential

applications in ultrasound beam forming and beam steering, either at low

ultrasonic frequency in air or high frequency in liquid medium or human

body.

24.8 Future perspective

Although the good materials properties and processing compatibility of the

composite PZT films have been demonstrated in this chapter, there is still the

potential to further improve the performance of the films. Regarding the

material’s properties, because the resultant films are composite and the added

powder occupies the majority of the volume fraction, the performances of

the films are dominated by the properties of the added powder. This feature

facilitates the property optimization of the composite films. For example,

according to the specific application, we can directly select the most suitable

commercial available piezoelectric ceramic (either a hard or soft composition)

as the added powder phase to prepare the slurry, which is a unique advantage

of the composite thick film technology. In comparison with the ordinary

modification methods by adding dopant or low melting point sintering aids

to the slurry, this advantage provides us with a very straightforward and

effective way to optimize the piezoelectric properties of the films. As to the

troublesome etching problem of the thick composite film, directly depositing

patterned thick film on silicon substrate can eliminate the need to etch the

film after deposition. Electrophoretic deposition is capable of coating complex

geometries. By combining composite slurry and electrophoretic deposition,

the PZT film will be deposited only on the patterned electrode and we expect

that the sintering temperature of the resultant film can be significantly reduced.

This will be an important extension of the composite thick film technology.

Regarding the application, the composite thick film is promising in sensors

and actuators field. We have demonstrated in this chapter that the thick film

pMUT are suited for applications at relatively low ultrasonic frequency.

However, there are still a number of challenges if the pMUT aims at high-

frequency (MHz) ultrasonic imaging.

24.9 References

1. Kurchania R and Milne S J, ‘Characterization of sol–gel Pb(Zr

0.53

0.47

films in

the thickness range 0.25–10µm’, J. Mater. Res., 1999 14(5) 1852–59.

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials754

2. Akedo J and Lebedev M, ‘Influnce of carrier gas conditions on electrical and optical

properties of Pb(Zr,Ti)O

thin films prepared by aerosol deposition method’, Jpn. J.

Appl. Phys., 2001 40(9B) 5528–32.

3. Yasuda Y, Akamatsu M, Tani M, Yoshida M, Kondo K and Iijima T, ‘Preparation of

lead zirconate titanate thick films by arc-discharged reactive ion-plating method’,

Jpn. J. Appl. Phys., 2001 40(9B) 5518–22.

4. Tsurumi T, Ozawa S, Abe G, Ohashi N, Wada S and Yamane M, ‘Preparation of

Pb(Zr

0.53

0.47

thick films by an interfacial polymerization method on silicon

substrates and their electrical and piezoelectric properties’, Jpn. J. Appl. Phys., 2000

39(9B) 5604–8.

5. Barrow D A, Petroff T E, Tandon R P and Sayer M, ‘Characterization of thick lead

zirconate titanate films fabricated using a new sol–gel based process’, J. Appl. Phys.,

1997 81(2) 876–81.

6. Sayer M, Lockwood G R, Olding T R, Pang G, Cohen L M, Ren W and Mukherjee

B K, ‘Macroscopic actuators using thick piezoelectric coatings’, Mat. Res. Soc.

Proc. 2001 655 cc13.6.1–11.

7. Zhu W, Wang Z, Zhao C, Tan O K and Hng H, ‘Low temperature sintering of

piezoelectric thick films derived from a novel sol–gel route’, Jpn. J. Appl. Phys.,

2002 41(11B) 6969–75.

8. Wang Z, Zhu W, Zhao C and Tan O K, ‘Dense PZT thick films derived from sol–gel

based nanocomposite process’, Mater. Sci. Eng., 2003 B99(1–3) 56–62.

9. Zhao C, Wang Z, Zhu W, Yao X and Liu W, ‘PZT thick films fabrication using a sol–

gel based 0-3 composite processing’, Int. J. Mod. Phys. B., 2002 16(1&2) 242–248.

10. Dorey R A, Stringfellow S B and Whatmore R W, ‘Effect of sintering aid and

repeated sol infiltrations on the dielectric and piezoelectric properties of a PZT

composite thick film’, J. Eur. Ceram. Soc., 2002 22(16) 2921–6.

11. Liu W, Zhu W and Tan O K, ‘Preparation of PZT thin films by a solid precursor sol–

gel routine’, in Hing P (Ed), Proceedings of the First International Conference on

Thermophysical Properties of Materials, Singapore, 1999, pp. 187–90.

12. Sporn D, Merklein S, Grond W, Seifert S, Wahl S and Berger A, ‘Sol-gel processing

of perovskite thin films’, Microelectronic Eng., 1995 29 161–8.

13. Chao C, Wang Z and Zhu W, ‘Scanning homodyne interferometer for characterization

of piezoelectric films and MEMS devices’, Rev. Sci. Instrum., 2005 76(6) 063906.

14. Chao C, Wang Z and Zhu W, ‘Measurement of piezoelectric displacement of PZT

using a modified double-beam interferometer’, Rev. Sci. Instrum., 2004 75(11) 4641–

15. Wang Z, Zhu W, Miao J, Chao C and Tan O K, ‘Measurement of longitudinal

piezoelectric coefficient of film with scanning-modulated interferometer’, Sens.

Actuators 2006 A128(2), 327–32.

16. Yao K and Tay F E H, ‘Measurement of longitudinal piezoelectric coefficient of thin

films by a laser-scanning vibrometer’, IEEE Trans Ultrason. Ferroelectr. Freq.

Control. 2003 50(2) 113–16.

17. Wang Z, Zhu W, Chao C, Zhao C and Chen X, ‘Characterization of composite

piezoelectric thick film for MEMS application’, Surf. Coat. Tech. 2005 198(1–3)

384–8.

18. Oralkan Ö, Ergun A S, Johnson J A, Karaman M, Demirci U, Kaviani K, Lee T H

and Khuri-Yakub B T, ‘Capacitive micromachined ultrasonic transducers: next-

generation arrays for acoustic imaging?’, IEEE Trans. Ultrason. Ferroelectr. Freq.

Control, 2002 49(11) 1596–610.

WPNL2204

Piezoelectric thick films for MEMS application 755

19. Akasheh F, Myers T, Fraser J D, Bose S and Bandyopadhyay A, ‘Development of

piezoelectric micromachined ultrasonic transducers’, Sens. Actuators, 2004 A111(2–

3). 275–287.

20. Bernstein J J, Finberg S L, Houston K, Niles L C, Chen H D, Cross L E, Li K K and

Udayakumar K, ‘Micromachined high frequency ferroelectric sonar transducers’,

IEEE Trans. Ultrason. Ferroelectr. Freq. Contr., 1997 44(5) 960–69.

21. Yamashita K, Katata H, Okuyama M, Miyoshi H, Kato G, Aoyagi S and Suzuki Y,

‘Arrayed ultrasonic microsensors with high directivity for in-air use using PZT thin

film on silicon diaphragms’, Sens. Actuators, 2002 A97–98 302–7.

22. Yamashita K, Chansomphou L, Murakami H and Okuyama M, ‘Ultrasonic micro

array sensors using piezoelectric thin films and resonant frequency tuning’, Sens.

Actuators, 2004 A114(2–3) 147–153.

23. Wang Z, Zhu W, Zhu H, Miao J, Chao C, Zhao C and Tan O K, ‘Fabrication and

characterization of piezoelectric micromachined ultrasonic transducers with thick

composite PZT films’, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 2005 52(12)

2289–297.

24. Wang Z, Zhu H, Zhu W, Miao J, Chao C and Tan O K, ‘Ultrasound radiating

performances of piezoelectric micromachined ultrasonic transmitter’, Appl. Phys.

Lett., 2005 86(3) art. no. 033508.

25. Wang Z, Zhu W, Miao J, Zhu H, Chao C and Tan O K, ‘Micromachined thick film

piezoelectric ultrasonic transducer array’, in Digest of Technical Paper, Transducers’05,

Seoul, Korea, June 5–9, 2005, 883–6.

26. Muralt P, Ledermann N, Baborowski J, Barzegar A, Gentil S, Belgacem B, Petitgrand

S, Bosseboeuf A and Setter N, ‘Piezoelectric micromachined ultrasonic transducers

based on PZT thin films’, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 2005

52(12) 2276–88.

WPNL2204

756

25.1 Introduction

Ferroelectricity and symmetry are intimately related. Indeed, the lack of a

centre of symmetry is a necessary condition for the existence of ferroelectricity,

the other condition being that the electric field needed to switch the polarization

be smaller than the breakdown field. It is therefore not surprising that subtle

changes in crystal symmetry can have enormous effects on the functional

properties of ferroelectric and piezoelectric materials. This justifies the large

research effort that is currently being invested in modifying crystal symmetries

(e.g. by using externally imposed strains) to tune and enhance the functional

properties of ferroelectric thin films.

In this chapter we give a short overview on the interplay between strain,

symmetry and functional properties of perovskite ferroelectrics. We have

limited ourselves to perovskites because their relative structural simplicity

and ease of fabrication make them the preferred model system in most academic

studies. Moreover, perovskites are also the basis for some of the most

industrially relevant ferroelectrics such as Pb(Zr,Ti)O

and (Ba,Sr)TiO

. We

warn the reader that, though we believe that all the works described in this

chapter are important, they are by no means exhaustive in this rapidly growing

and exciting field.

This chapter is organized as follows. In Sections 25.2 and 25.3 we review

some of the most important results to date on the physics of ferroelectric thin

films, including finite-size effects, domains, superlattices and strain relaxation.

In Section 25.4 we review the current views on the origin of the large

piezoelectric coefficients of low-symmetry perovskite-like systems, such as

morphotropic-boundary Pb(Zr,Ti)O

and lead-based relaxors. Section 25.5

will connect the previous, by summarizing the most important experimental

and theoretical results on symmetry-tuning through epitaxial strain in

ferroelectric thin films. This lowering of symmetry is a recurrent theme that

will also emerge in connection with recent results in multiferroics such as

BiFeO

The last two sections contain the authors’ view of what are likely to

Symmetry engineering and size effects in

ferroelectric thin films

B NOHEDA, University of Groningen, The Netherlands and

G C ATA L A N, University of Cambridge, UK

WPNL2204

Symmetry engineering and size effects in ferroelectric thin films 757

be the next ‘hot topics’ in ferroelectric thin film research, and a suggested

list of further reading.

25.2 Size effects

25.2.1 The ferroelectric size effect

The convergence between increasingly sophisticated experimental techniques

and larger computer capacity for ab-initio calculations, together with the

ever-present drive for device miniaturization, has in recent times spawned a

wealth of research looking at the science of ferroelectric thin and ultra-thin

films. Since the length scales at which ferroelectric films can be made and

measured are beginning to coincide with those that can be modelled, the

advancements in theory and experiment go hand-in-hand and feed off each

other [1]. One of the core areas of interest has been the physics of the

ferroelectric size effect, i.e. the change in symmetry and properties as the

thickness/size of a ferroelectric is reduced. Ferroelectricity is a collective

phenomenon which depends on the interaction between many unit cells, so

the first question that one may ask is: is there a thickness limit below which

a ferroelectric thin film stops being ferroelectric?

When decreasing the thickness of ferroelectric thin films, the surfaces

begin to dominate the behaviour. The structure of the epilayer of a film may

be different from that of the core due to the uncompensated atomic bonds at

the surface (surface tension), which can result in different polarization near

the surface [2–4], and/or in the appearance of surface symmetries different

from those at the core [4,5] (Fig. 25.1).

By far the most important surface effect is depolarization. The permanent

dipoles of a ferroelectric yield a charge density at the surfaces. This charge

creates an electric field that opposes the polarization and, eventually, should

lead to its cancellation. If the films have good metallic electrodes, or if they

have polarization in-plane, depolarization fields do not play a role, and

ferroelectricity may remain stable down to thickness of the order of a couple

of monolayers [6]. On the other hand, when the polarization is perpendicular

to the surface, and in the absence of screening charge, the depolarization

field does tend to cancel the ferroelectricity. Electrostatic considerations

(assuming a monodomain state) lead to estimates for the critical thickness of

a ferroelectric as high as tens or even hundreds of nanometres [7]. Probably

one of the most stunning results of the recent years has been the observation

of out-of-plane ferroelectricity in non-electroded films of lead titanate only

three unit cells thick [8] (Fig. 25.2), well below what was previously thought

to be the limit posed by the electrostatic calculations. So how is that possible?

The answer is that the depolarization field in real ferroelectric crystals is

not as big as assumed in the calculations. This is principally for two reasons:

domain formation and charge screening.

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials758

Domains

Ferroelectrics can reduce the depolarization field by creating domains of

opposite polarization, also known as 180° domains [9]: by alternating regions

of positive and negative charge at the surface, the net electrostatic energy is

reduced. This, however, is not a free trick, because the domains have an

energy cost (if it was free to have anti-parallel polarization, the material

would actually be anti-ferroelectric!). There is thus a balance between

depolarization energy (proportional to domain size) and domain wall energy

(proportional to the number of walls and hence inversely proportional to

domain size). The domain wall energy is also proportional to the wall size,

and hence to the film thickness d. For a pattern of regular, parallel-sided

domains of width w, the free energy F per unit surface of crystal due to both

contributions is

FUw

= + γ

25.1

where U is proportional to the volume energy density of the domains and γ

is the energy density per unit surface of the domain wall. Minimization of

this energy balance leads to the well-known expression

25.2

(a)

(b)

1/2-

25.1

Surface antiferrodistortive structure in PbTiO

(PTO). The surface

has a different symmetry and polarization than the bulk. Left: results

from

ab-initio

simulations (plan view (a) and cross-section (b)); [4]

right: experimental results (plan view) from grazing incidence

diffraction.[5] As the thickness of the PbTiO

decreases, the relative

importance of these surface states will increase. Reprinted figures

American Physical Society.

WPNL2204

Symmetry engineering and size effects in ferroelectric thin films 759

The proportionality w

= Ad was first proposed for ferromagnets by Landau

and Lifshitz [10], and later by Kittel [11] known as Kittel’s law sometimes,

but it is also valid for ferroelectrics [9], ferroelastics [12] and even non-

ferroic materials such as martensitic steels [13]: the only difference is the

value and the physical nature of U and γ in equation 25.2. It is important to

bear this in mind because most ferroelectrics are also ferroelastic, and thus

domains can be due to either depolarization or to strain minimization. This

is illustrated in Fig. 25.3, where we show stripe domains in single crystal

thin films of ferroelectric BaTiO

. These domains are 90° domains and

100 300 1000

Substrate

Temperature (K)

644

549

463

382

311

1234

Film thickness (unit cells)

25.2

Area scans in the HK0 scattering plane around the (303) Bragg

reflection of PbTiO

ultra-thin films with different thickness (1, 2 , 3

and 4 unit cells) at different temperatures, as measured by

synchrotron X-ray diffraction by Fong

et al.

[8] The measurements are

taken

in situ

during the growth by MOCVD and cool down of the

films. Modulations in the diffuse scattering for thickness of three unit

cells and above signal the presence of periodic polar domains, the

analysis of which indicates that the polarization in the stripes is

perpendicular to the substrate plane. Figure from ref.[9] Reprinted

with permission from AAA.

Intensity (counts per second)

WPNL2204