Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

358 Thin ﬁ lm growth

in Au or Sio

2

of the interconnect bridge versus the applied strain for

e

pre

= 20%, 40% and 60%. The interconnect bridge is made of polyimide

(h

1

= h

4

= 1.2 mm, E

1

= E

4

= 2.5 GPa, v

1

= v

4

= 0.34), Au (h

2

= 0.15 mm,

E

2

= 78 GPa, v

2

= 0.44) and SiO

2

(h

3

= 0.05 mm, E

3

= 70 GPa, v

3

= 0.17).

The lengths of interconnect bridges and device islands are L

bridge

= 460 mm

and L

island

= 236 mm, respectively. The elastic moduli and Poisson’s ratios

of the substrate and encapsution are E

substrate

= E

encapsulation

= 1.8 MPa and

v

substrate

= v

encapsulation

= 0.48. The bending strain decreases as the applied

strain increases because the amplitude of the interconnect bridge decreases.

However, as the applied strain increases, the membrane strain increases

rapidly due to the restriction of the encapsulation layer and dominates the

failure of the interconnect bridge.

The stretchability characterizes how much the non-coplanar mesh design

can accommodate further stretch. It is de ned as the critical applied strain

that leads to failure of the interconnect bridge. Because the bending strain

is negligible compared to the membrane strain as shown in Fig. 14.11, the

stretchability is obtained by equating the membrane strain in Eq. 14.26 to

the fracture strain e

f

of the material (e.g., 1%) as

()

=

1 –

1 +

applie

()

applie

()

dm

()

dm

()

ax

f

2

pr

e

prepr

()

e

()

e

l

e

Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

È

Î

Í

È

Í

È

Î

Í

Î

Í

Î

Í

Î

Í

Î

Í

Î

˘

˚

˙

˘

˙

˘

˚

˙

˚

˙

˚

˙

˚

˙

˚

˙

˚

–

+ (

1 +

)

pr

)

pr

)

ef

)

ef

)

prefpr

)

pr

)

ef

)

pr

)

ee

)

ee

)

pr

)

ee

)

pr

)

ef

ee

ef

)

ef

)

ee

)

ef

)

pr

)

ef

)

pr

)

ee

)

pr

)

ef

)

pr

)

[14.27]

0 20 40 60

Applied strain e

applied

(%)

20%

40%

e

pre

= 60%

Membrane strain

Bending strain

|Strain| (%)

1.0

0.5

0.0

14.11 The maximum bending strain and membrane strain in the

interconnect bridge versus the applied strain for the encapsulated

system. The prestrain is 20%, 40% and 60%. Reprinted with

ThinFilm-Zexian-14.indd 358 7/1/11 9:45:28 AM



359Controlled buckling of thin ﬁ lms on compliant substrates

where

l

p

=

(

)

s

(

s

(

ubs

(

ubs

(

tr

(

tr

(

at

(

at

(

ee

(

ee

(

ncap

su

latio

nb

)

nb

)

ri

dge

br

i

bribr

EE

( EE(

+ EE+

(

s

( EE(

s

(

ubs

( EE(

ubs

(

tr

( EE(

tr

(

at

( EE(

at

(

ee

EE

ee

(

ee

( EE(

ee

(

+

ee

+ EE+

ee

+

L

nb

L

nb

Eh

br

Eh

br

3

dge

ddged

br

idge

bridgebr

island

br

idge

bridgebr

f

L

LL

island

LL

island

+LL +

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

[14.28]

is a non-dimensional parameter that depends on the elastic moduli of

substrate and encapsulation layer, tensile stiffness of interconnect bridge,

and the lengths of device island and interconnect bridge. When there is no

substrate and encapsulation layer (i.e., l = 0), the stretchability is given by

e

pre

+ (1 + e

pre

)e

f

.

Figure 14.12 shows the stretchability (e

applied

)

max

versus non-dimensional

parameter l for the failure strain e

f

= 1% and prestrain e

pre

= 60%. The

geometric and material parameters of the bridges are same for Fig. 14.11

and can also be found in Section 14.3.1. The lengths of interconnect bridges

and device islands are L

bridge

= 460 mm and L

island

= 236 mm, respectively.

The elastic modulus and Poisson’s ratio of the substrate are E

substrate

= 1.8

MPa and n

substrate

= 0.48. The Poisson’s ratio of the encapsulation layer is

n

encapsulation

= 0.48. When there is no encapsulation layer, the interconnect

bridge can deform freely and the stretchability can reach the prestrain 60%.

When the encapsulation layer with E

encapsulation

= 1.8 MPa, which corresponds

Stretchability (%)

65

60

55

50

45

E

encapsulation

= 0.1 MPa

1.8 MPa

0.000 0.002 0.004 0.006 0.008 0.010

l

14.12 The stretchability of the encapsulated system versus the non-

dimensional parameter, which depends on the material properties

and geometry of interconnect bridges, the length of device islands,

and material properties of substrate and encapsulation layer. The

prestrain is 60%. The points marked on the curves represent the

materials properties and geometry used in Section 14.3.1. Reprinted

ThinFilm-Zexian-14.indd 359 7/1/11 9:45:28 AM



360 Thin ﬁlm growth

to l = 0.00857, is used, the stretchability is reduced to 48.8% from Eq.

14.27, which agrees well with the experimental value of 49% (Kim et al.,

2009). When a much more compliant encapsulation layer with E

encapsulation

= 0.1 MPa, which corresponds to l = 0.00452, is used, the stretchability

becomes 55.8% (closer to the prestrain 60%) from Eq. 14.27, which also

agrees well with the experimental measurement of 55% (Kim et al., 2009).

Therefore, in order to optimize the stretchability, a compliant encapsulation

layer, which helps to retain the stretchability, should be used.

The interconnect bridges described above are straight. To expand the

deformability even further, serpentine interconnect bridges may be used

(Kim et al., 2009). Figure 14.13 shows an SEM image of such a design after

executing the fabrication procedures of Fig. 14.4. Compared to the straight

interconnect bridges, the serpentine ones have two major advantages. First,

they are much longer than straight interconnect bridges, and therefore can

accommodate much larger prestrain. Second, once the applied strain reaches the

prestrain, straight interconnect bridges become at and lose their stretchability,

but serpentine interconnect bridges can be stretched much further because

large twist will be involved to accommodate larger deformation. Exploring

the non-coplanar mesh design with serpentine interconnect bridges represents

a fruitful topic for future work.

Acc.V Spot Magn Det WD Exp

5.00 kV 3.0 113x SE 32.9 18

500 µm

14.13 SEM image of an array of CMOS inverters with non-coplanar

mesh design that has serpentine interconnects. Reprinted with

Vacuum Society.

ThinFilm-Zexian-14.indd 360 7/1/11 9:45:28 AM



361Controlled buckling of thin ﬁlms on compliant substrates

14.4 Conclusions

One-dimensional non-coplanar mesh design: A nonlinear buckling model

is presented to study the mechanics of this type of lm/substrate system.

An analytical solution is obtained for the buckling geometry (wavelength

and amplitude) and the maximum strain in buckled thin lm. The solution

agrees very well with the experiments, and shows explicitly how buckling

can signicantly reduce the thin lm strain to achieve the system large

stretchability.

Two-dimensional non-coplanar mesh design: Mechanics models are

established for the cases of pre-encapsulation and post-encapsulation. The

maximum strains in the interconnect bridges are obtained analytically. A

simple, analytical expression for the stretchability of the encapsulated system

is obtained to help to design the encapsulated electronics via a single, non-

dimensional parameter.

14.5 References

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light-emitting devices using a phosphorescent sensitizer. Nature 403, 750–753.

Bowden N, Brittain S, Evans AG, Hutchinson JW, and Whitesides GM, 1998. Spontaneous

formation ordered structures in thin lms of metals supported on an elastomeric

polymer. Nature 393, 146–149.

Choi WM, Song J, Khang DY, Jiang H, Huang Y, and Rogers JA, 2007. Biaxially

stretchable “wavy” silicon nanomembranes. Nano Letters 7, 1655–1663.

Crawford GP, 2005. Flexible Flat Panel Display Technology. John Wiley & Sons, new

York.

Crone B, Dodabalapur A, Lin YY, Filas RW, Bao Z, LaDuca A, Sarpeshkar R, Katz

HE, and Li W, 2000. Large-scale complementary integrated circuits based on organic

transistors. Nature 403, 521–523.

Facchetti A, Yoon MH, and Marks TJ, 2005. Gate dielectrics for organic eld-effect

transistors: new opportunities for organic electronics. Advanced Materials 17,

1705–1725.

Garnier F, Hajlaoui R, Yassar A, and Srivastava P, 1994. All-polymer eld-effect transistor

realized by printing techniques. Science 265, 1684–1686.

Huang ZY, Hong W, and Suo Z, 2005. Nonlinear analyses of wrinkles in a lm bonded to

a compliant substrate. Journal of Mechanics and Physics of Solids 53, 2101–2118.

Jiang H, Sun Y, Rogers JA, and Huang Y, 2007. Mechanics of precisely controlled thin

lm buckling on elastomeric substrate. Applied Physics Letters 90, 133119.

Jiang H, Khang DY, Fei H, Kim H, Huang Y, Xiao J, and Rogers JA, 2008a. Finite width

effect of thin-lms buckling on compliant substrate: experimental and theoretical

studies. Journal of Mechanics and Physics of Solids 56, 2585–2598.

Jiang H, Song J, Huang Y, and Rogers JA, 2008b. ‘Mechanics of stretchable silicon

lms on elastomeric substrate’, in Unconventional Nanopatterning Techniques and

Applications (eds. Rogers JA and Lee HH), Wiley, Hoboken, NJ, pp. 483–514.

Jin HC, Abelson JR, Erhardt MK, and Nuzzo RG, 2004. Soft lithographic fabrication

of an image sensor array on a curved substrate. Journal of Vacuum Science and

Technology B 22, 2548–2551.

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362 Thin ﬁlm growth

Khang DY, Jiang HQ, Huang Y, and Rogers JA, 2006. A stretchable form of single-crystal

silicon for high-performance electronics on rubber substrate. Science 311, 208–212.

Kim DH, Ahn JH, Choi WM, Kim HS, Kim TH, Song J, Huang Y, Liu ZJ, Lu C, and

Rogers JA, 2008a. Stretchable and foldable silicon integrated circuits. Science 320,

507–511.

Kim DH, Choi WM, Ahn JH, Kim HS, Song J, Huang Y, Liu Z, Lu C, Koh CG, and

Rogers JA, 2008b. Complementary metal oxide silicon integrated circuits incorporating

monolithically integrated stretchable wavy interconnects. Applied Physics Letters 93,

044102.

Kim DH, Song J, Choi WM, Kim HS, Kim RH, Liu Z, Huang Y, Hwang KC, Zhang Y,

and Rogers JA, 2008c. Materials and non-coplanar mesh designs for integrated circuits

with linear elastic responses to extreme mechanical deformations. Proceedings of the

National Academy of Sciences of the United States of America 105, 18675–18680.

Kim DH, Liu Z, Kim YS, Wu J, Song J, Kim HS, Huang Y, Hwang KC, Zhang Y,

and Rogers JA, 2009. Optimized structural designs for stretchable silicon integrated

circuits. Small 5, 2841–2847.

Ko HC, Stoykovich MP, Song J, Malyarchuk V, Choi WM, Yu CJ, Geddes JB, Xiao

J, Wang S, Huang Y, and Rogers JA, 2008. A hemispherical electronic eye camera

based on compressible silicon optoelectronics. Nature 454, 748–753.

Koh CT, Liu ZJ, Khang DY, Song J, Lu C, Huang Y, Rogers JA, and Koh CG, 2007.

Edge effects in buckled thin lms on elastomeric substrates. Applied Physics Letters

91, 133113.

Lacour SP, Jones J, Wanger S, Li T, and Suo Z, 2005. Stretchable interconnects for

elastic electronic surfaces. Proceedings of the IEEE 93, 1459–1467.

Loo YL, Someya T, Baldwin KW, Bao Z, Ho P, Dodabalapur A, Katz H, and Rogers JA,

2002. Soft, conformable electrical contacts for organic semiconductors: high-resolution

plastic circuits by lamination. Proceedings of the National Academy of Sciences of

the United States of America 99, 10252–10256.

Lumelsky VJ, Shur MS, Wagner S, 2001. Sensitive skin. IEEE Sensors Journal 1,

41–51.

Nathan A, Park B, Sazonov A, Tao S, Chan I, Servati P, Karim K, Charania T,

Striakhilev D, Ma Q, and Murthy RVR, 2000. Amorphous silicon detector and thin

lm transistor technology for large-area imaging of X-rays. Microelectronics Journal

31, 883–891.

Sekitani T, Noguchi Y, Hata K, Fukushima T, Aida T, and Someya T, 2008. A rubberlike

stretchable active matrix using elastic conductors. Science 321, 1468–1472.

Shin G, Jung I, Malyarchuk V, Song J, Wang S, Ko HC, Huang Y, Ha JS, and Rogers

JA, 2010. Micromechanics and advanced designs for curved photodetector arrays in

hemispherical electronic eye cameras. Small 6, 851–856.

Someya T, Sekitani T, Iba S, Kato Y, Kawaguchi H, and Sakurai T, 2004. A large-area,

exible pressure sensor matrix with organic eld-effect transistors for articial skin

applications. Proceedings of the National Academy of Sciences of the United States

of America 101, 9966–9970.

Song J, Jiang H, Liu Z, Khang DY, Huang Y, Rogers JA, Lu C, and Koh CG, 2008a.

Buckling of a stiff thin lm on a compliant substrate in large deformation. International

Journal of Solids and Structures 45, 3107–3121.

Song J, Jiang H, Choi WM, Khang DY, Huang Y, and Rogers JA, 2008b. An analytical

study of two-dimensional buckling of thin lms on compliant substrates. Journal of

Applied Physics 103, 014303.

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363Controlled buckling of thin ﬁlms on compliant substrates

Song J, Jiang H, Huang Y, and Rogers JA, 2009a. Mechanics of stretchable inorganic

electronic materials. The Journal of Vacuum Science and Technology A 27, 1107–

1125.

Song J, Huang Y, Xiao J, Wang S, Hwang KC, Ko HC, Kim DH, Stoykovich MP, and

Rogers JA, 2009b. Mechanics of non-coplanar mesh design for stretchable electronic

circuits. Journal of Applied Physics 105, 123516.

Sosin S, Zoumpoulidis T, Bartek M, Wang L, Dekker R, Jansen KMB, and Ernst LJ, 2008.

Free-standing, parylene-sealed copper interconnect for stretchable silicon electronics.

Electronic Components and Technology Conference, 1339–1345.

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nano ribbons for stretchable electronics. Nature Nanotechnology 1, 201–207.

Wang S, Song J, Kim DH, Huang Y, and Rogers JA, 2008. Local versus global buckling

of thin lms on elastomeric substrates. Applied Physics Letters 93, 023126.

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encapsulated stretchable electronics, Acta Mechanica Solida Sinica (in press).

ThinFilm-Zexian-14.indd 363 7/1/11 9:45:28 AM



364

15

The electrocaloric effect (ECE) in

ferroelectric polymer films

S.-G. Lu and Q. M. ZhanG, The Pennsylvania State

university, uSa and Z. KuTnjaK, jozef Stefan Institute,

Slovenia

Abstract: The electrocaloric effect (ECE) is the entropy and temperature

change of a dielectric when subject to a change of electric eld. This

chapter will discuss briey thermodynamic considerations for materials that

exhibit large ECE and review previous results of the ECE in polar crystals,

ceramics, and thin lms. ECE results from direct measurement and deduced

from Maxwell’s relations will be presented along with the phenomenological

modeling for ferroelectric polymers, which have been recently discovered

to exhibit a large ECE. Finally the ECE of polar materials are modeled to

forecast their potential in future devices.

Key words: electrocaloric effect, ferroelectric polymer, electric

displacement–electric eld hysteresis loop, isothermal entropy change,

adiabatic temperature change.

15.1 Introduction

The electrocaloric effect (ECE) is the temperature change of a material when

subject to a change of electric elds (Lines and Glass, 1977; Jona and Shirane,

1993; Lang, 1976). The ECE effect is the inverse of the pyroelectric effect.

At constant stress (or strain) and constant electric eld, the pyroelectric

coefcient (dD/dT, D = electric displacement, T = temperature) is equal to

the electrocaloric coefcient (dS/dE, S = entropy, E = electric eld). This is

the Maxwell relation. In addition, secondary pyroelectric effects (newnham,

2005) caused by change of strain at constant stress may also contribute to

the electrocaloric effect.

The ECE may provide an effective means of realizing solid-state cooling

devices for a broad range of applications such as on-chip cooling and

temperature regulation for sensors or other electronic devices. Refrigeration

based on ECE has the potential of reaching high efciency relative to vapor-

compression cycle systems, and with no greenhouse gas emissions.

Solid-state electric-cooling devices based on the thermoelectric effect

(Peltier effect) have been used for many decades (Spanner, 1951; Nolas et

al., 2001). However, these systems require a large DC current which results

ThinFilm-Zexian-15.indd 364 7/1/11 9:45:56 AM



365The electrocaloric effect (ECE) in ferroelectric polymer ﬁ lms

in a large amount of waste heat through joule heating. For example, using

the typical coef cient of performance (COP) for these devices, e.g. 0.4 to

0.7, 2.4 to 3.5 W in the form of heat will be generated at the hot end of the

system to remove 1 W heat from the cold end. In contrast, no current conducts

through the polar materials used in ECE devices, e.g. ferroelectric polymers,

thereby eliminating this wasted heat during the refrigeration cycle.

a counterpart of ECE is the magnetocaloric effect (MCE), which has

been extensively studied for many years due to the  ndings of signi cant

MCE in several magnetic materials near room temperature (Gschneidner

jr. et al., 2005; V.K. Pecharsky et al., 2003). Both ECE and MCE devices

exploit the change of order parameter brought about by an external electric

or magnetic  eld. However, the dif culty of generating high magnetic  eld

for MCE devices to reach large MCE severely limits their wide application,

especially for miniaturized microelectronic devices. In contrast, high electric

 eld can easily be generated and manipulated, which makes it relatively easy

to con gure ECE cooling devices for a broad range of applications.

This chapter introduces the basic concept of ECE, the thermodynamic

considerations for materials with large ECE, and reviews previous

investigations of the ECE in polar crystals, ceramics, and thin  lms. A newly

discovered large ECE exhibited by ferroelectric polymers is presented in terms

of the direct measurements, and calculations based on Maxwell relations and

phenomenological theory. Finally the prospect of ECE devices using polar

materials will be discussed.

15.2 Thermodynamic considerations on materials

with large electrocaloric effect (ECE)

15.2.1 Maxwell relations

In general the Gibbs free energy G for a dielectric material could be expressed

as a function of temperature T, entropy S, stress X, strain x, electric  eld E

and electric displacement D in the form

G = U – TS – X

i

x

i

– E

i

D

i

[15.1]

where U is the internal energy of the system, the stress and  eld terms are

written using Einstein notation. The differential form of Eq. 15.1 could be

written as

dG = –SdT – x

i

dX

i

– D

i

dE

i

[15.2]

Entropy S, strain x

i

and electric displacement D

i

can be easily expressed

when the other two variables are assumed to be constant,

S

G

T

x

G

X

D

= –

∂

,

= –

∂

,

1

X,

D

i

1

i

X

i

X

T,

D

i

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

∂

X∂X

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

=

== =

–

∂

1

i

T,

X

G

E

i

E

i

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

[15.3]

ThinFilm-Zexian-15.indd 365 7/1/11 9:45:56 AM



366 Thin ﬁ lm growth

The Maxwell relation can be derived for (S, T) and (D, E) two pairs of

parameters (Lines and Glass, 1977),

∂

=

∂

i

T

, X

i

E,

X

S

E

i

E

i

D

T

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

∂

Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

[15.4]

or

∂

=

∂

=

S

E

T

E

T

c

D

T

Tp

c

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

[15.5]

where c

E

is the heat capacity, p

E

the pyroelectric coef cient. Eqs 15.4 and

15.5 indicate the mutually inverse relationships of ECE and the pyroelectric

coef cient. Hence, for the ECE materials with a constant stress X imparted,

the isothermal entropy change DS and adiabatic temperature change DT can

be expressed as (Lines and Glass, 1977):

D

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

Ú

S

D

T

E

= –

∂

= d

1

2

E

Ú

E

Ú

[15.6]

D

∂

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

Ú

T

D

T

E

= –

1

∂

d

1

2

E

T

c

E

Ú

E

Ú

r

[15.7]

Equations 15.4–15.7 indicate that in order to achieve large DS and DT, the

dielectric materials should posses a large pyroelectric coef cient over a

relatively broad electric  eld and temperature range. For ferroelectric materials,

a large pyroelectric effect exists near the ferroelectric (F)–paraelectric (P) phase

transition temperature and this large effect may be shifted to temperatures

above the transition temperature when an external electric  eld is applied. It

is also noted that a large DT may be achieved even if DS is small when the

c

E

of a dielectric material is small. however, as will be pointed out in the

following section, this is not desirable for practical refrigeration applications

where a large DS is required.

although a few studies on the ECE were conducted in which direct

measurement of DT was made (Sinyavsky et al., 1989; Xiao et al., 1998),

most experimental studies were based on the Maxwell relations where the

electric displacement D versus temperature T under different electric  elds

was characterized. DS and DT were deduced from Eqs 15.6 and 15.7 (see

below for details). For dielectric materials with low hysteresis loss and the

measurement is in an ideal situation, results obtained from the two methods

should be consistent.

In an ideal refrigeration cycle the working material (refrigerant) must

absorb entropy (or heat) from the cooling load while in thermal contact with

the load (isothermal entropy change DS). The material is then isolated from

ThinFilm-Zexian-15.indd 366 7/1/11 9:45:57 AM



367The electrocaloric effect (ECE) in ferroelectric polymer ﬁ lms

the load while the temperature is increased due to the application of external

 eld (adiabatic temperature change DT). The material is then in thermal

contact with the heat sink and entropy that was absorbed from the cooling

load is rejected to the heat sink. The working material is then isolated from

the heat sink and the temperature is reduced back as the  eld is reduced.

The temperature of the refrigerant will be the same as the temperature of

the cooling load when they are contacted. The whole process is repeated to

further reduce the temperature of the load. Therefore, both the isothermal

entropy change DS and the adiabatic temperature change DT are key parameters

for the ECE of a dielectric material for refrigeration (Wood and Potter,

1985).

15.2.2 Phenomenological theory of ECE

Phenomenological theory has been widely utilized to illustrate the macroscopic

phenomena that occur in the polar materials, e.g. ferroelectric or ferromagnetic

materials near their phase transition temperatures. In principle, the ECE is

one of the characteristics of ferroelectric materials that is associated with

the phase transition in terms of the order–disorder transition derived entropy

change. Therefore, phenomenological theory can be used to estimate the ECE

of ferroelectrics. The general form of the Gibbs free energy in terms of the

electric displacement can be expressed as (Lines and Glass, 1977):

GD

D

GD =GD

1

GD

1

GD

2

GD

2

GD

1

4

+

1

6

24

1

24

1

6

ax

GD

ax

GD

+

ax

+

4

ax

4

24

ax

24

+

24

+

ax

+

24

+

1

24

1

ax

1

24

1

z

D

z

D

24

D

24

ax

D

ax

24

ax

24

D

24

ax

24

[15.8]

where a = b(T – T

0

), and b, x and z are temperature-independent

phenomenological coef cients. Since (∂G/∂T)

D

= –DS, one can obtain

D

SD

SD = –SD

1

SD

1

SD

2

SD

2

SD

2

b

SD

b

SD

[15.9]

Then the adiabatic temperature change DT (= TDS/c

E

) can be obtained, i.e.

D

T

c

TD

= –

1

2

E

2

b

TD

b

TD

[15.10]

Based on Eqs 15.9 and 15.10, the entropy will be reduced when the material

changes to a polar state from a non-polar state when an external action,

e.g. temperature, electric  eld or stress, is applied. The entropy change and

temperature change are associated with the phenomenological coef cient b and

electric displacement D, namely, proportional to b and D

2

. Both parameters

will affect the ECE values of the materials. a material with large b and large

D will generate large ECE entropy change and temperature change near the

ferroelectric (F)–paraelectric (P) phase transition temperature.

ThinFilm-Zexian-15.indd 367 7/1/11 9:45:57 AM



Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

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