Orientation dependence of the electrocaloric effect of ferroelectric bilayer thin films

Solid State Communications 149 (2009) 1549–1552

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Orientation dependence of the electrocaloric effect of ferroelectric bilayer thin films J.H. Qiu a,∗ , Q. Jiang b a

Department of Electronics Science and Engineering, Jiangsu Polytechnic University, Changzhou 213164, China

b

Department of Physics, Suzhou University, Suzhou 215006, China

article

info

Article history: Received 8 May 2009 Accepted 31 May 2009 by T. Kimura Available online 6 June 2009 PACS: 77.22.Ej 77.70.+a 77.80.-e Keywords: A. Ferroelectric bilayer thin film D. Electrocaloric effect D. Adiabatic temperature change

abstract An analytical thermodynamic theory is applied to investigate the electrocaloric effect of ferroelectric BaTiO3 /SrTiO3 bilayer thin films with different orientations at room temperature. Theoretical analysis indicates that the strong electrostatic coupling between the layers results in the suppression of ferroelectricity at a critical relative thickness which occurs approximately at 50%, 23%, and 12% of SrTiO3 fraction in the (001), (110), and (111) bilayer thin films, respectively. The ferroelectric bilayer thin films are respected to have the largest electrocaloric effect at this critical relative thickness. Moreover, the electrocaloric effect strongly depends on the orientation and the (110) oriented bilayer thin films have the largest electrocaloric effect. Consequently, control of the orientation and the relative thickness of SrTiO3 layer can be used to adjust the electrocaloric effect of ferroelectric bilayer thin films, which may provide the potential for practical application in refrigeration devices. © 2009 Published by Elsevier Ltd

1. Introduction When an electric field is applied to a dielectric material, it will induce a change in the material’s polarization. The consequent changes in the entropy and temperature of the material under adiabatic conditions are referred to as the electrocaloric (EC) effect [1–3]. In fact, as the inverse electrothermal conversion of the pyroelectric effect, the EC effect has attracted increasing interest in refrigeration devices and in thermodielectric power converters since the 1960s [4–9]. Due to the small EC effect reported in experiment [10–12], the EC materials have not been exploited commercially as the EC effect was insufficient for practical applications. However, intense interest in the EC effect has recently been renewed, especially since the giant EC effects in Pb(Zr0.95 Ti0.05 )O3 thin film [3] and ferroelectric P(VDF–TrFE) copolymer [13] have been reported. For instance, a giant EC effect of 12 K in 25 V was reported in 350 nm Pb(Zr0.95 Ti0.05 )O3 thin film near its ferroelectric Curie temperature of 226 ◦ C [3]. Neese et al. revealed that the ferroelectric P(VDF–TrFE) 55/45 mol% copolymer film exhibits an adiabatic temperature change 1T of more than 12 ◦ C under an electric field of 209 MV/m and temperature around 80 ◦ C [13].

∗

Corresponding author. Tel.: +86 519 86330294. E-mail address: [email protected] (J.H. Qiu).

0038-1098/$ – see front matter © 2009 Published by Elsevier Ltd doi:10.1016/j.ssc.2009.05.049

But until now, all the experimental and theoretical researches of the EC effect including Pb(Zr0.95 Ti0.05 )O3 ferroelectric thin film [3], (1 − x)PbMg1/3 Nb2/3 O3 –xPbTiO3 relaxor ferroelectric [2,14,15], and BaTiO3 thin film [16,17] only referred to a single layer thin film. Indeed, artificially fabricated ferroelectric bilayer or multilayer thin films show many striking phenomena and properties, such as substantial variations in phase transition characteristics [18,19], an enhancement in remnant polarization [20–22], a large dielectric response [23–25], tunability [26,27], and huge effective pyroelectric response [28]. Recently, Kim et al. reported 94% tunability from 100 nm thick BaTiO3 /SrTiO3 (BT/ST) superlattice with a stacking periodicity of 2 unit cells at a potential of 5 V [29]. This is by far larger than the highest reported tunability of 74% observed in Bax Sr1−x TiO3 thin films [30]. Zhong et al. investigated a pseudomorphic (001) BT/ST heteroepitaxial bilayer on (001) ST and a stress-free BT/ST bilayer [31,32]. Theoretical results demonstrated that these structures are capable of tunability greater than 90% and a gigantic dielectric response due to electrostatic and electromechamical coupling between layers. On the other hand, the dielectric and ferroelectric properties of the ferroelectric bilayer or multilayer thin films are strongly affected by the thin films’ orientation [33]. Therefore, control of the orientation of constituent layers is an effective method for the design of the bilayered or multilayered structure to modulate and tailor the ferroelectric properties of the material over a wide range. However, there are no systematic investigations of the effect of orientation on the EC effect except that the EC and pyroelectric

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properties of 0.75 PbMg1/3 Nb2/3 O3 –0.25 PbTiO3 single crystals with different orientations were studied by Sebald et al. [15]. The EC effect of h111i oriented single crystal is much larger than that of h110i and h001i single crystals and is about the same as ceramics. It is thus expected that the EC effect of ferroelectric bilayer or multilayer thin films with different orientations could be interesting and useful. In this letter, we investigate the effect of orientation on the electrocaloric effect of ferroelectric BaTiO3 /SrTiO3 bilayer thin films by using a thermodynamic theory. Our study points out that complete polarization suppressions occur at 50%, 23%, and 12% of SrTiO3 fraction in the (001), (110), and (111) bilayer thin films respectively at which BaTiO3 /SrTiO3 bilayer thin films have the largest electrocaloric effect. In addition, the orientation of bilayer thin films strongly affects the electrocaloric effect. Thus, by controlling the orientation and volume fraction of SrTiO3 layer in BaTiO3 /SrTiO3 bilayer thin films, we can obtain good properties of the electrocaloric effect which could open more opportunities for practical application in cooling systems.

For a (111) oriented bilayer thin film epitaxially grown on a thick (111) single crystal substrate [33],

2. Theory We consider a bilayer thin film of two ferroelectric layers between electrodes on a thick substrate [32,33]. The free energy density of the bilayer thin film is given by [31–34] F = (1 − α)(F1 − EP1 ) + α(F2 − EP2 ) + FEL FEL =

1 2ε0

α(1 − α)(P1 − P2 )2

Fi = F0,i + a∗i Pi2 + b∗i Pi4 + ci∗ Pi6

(2)

(3)

where F0,i is the free energy density of layer i at the high temperature paraelectric state. The coefficients a∗i , b∗i , and ci∗ are renormalized coefficients. For a (001) oriented bilayer thin film epitaxially grown on a thick (001) single crystal substrate, the renormalized coefficients a∗i , b∗i , and ci∗ can be written as [35] a∗i = α1,i − xi

ci = α111,i . ∗

2Q12,i S11,i + S12,i 2 Q12 ,i

S11,i + S12,i

a∗i = α1,i − xi b∗i =

(1)

where α is the relative thickness of layer 2, Fi (i = 1, 2) is the free energy density of layer i, Pi is the polarization of layer i normal to the interlayer interface, E is an applied electric field parallel with the polarization, FEL is the electrostatic coupling energy. We focus primarily on (001), (110), and (111) oriented BT/ST bilayer thin films epitaxially grown on (001), (110), and (111) single crystal ST substrates, respectively [33]. Due to the same orientation of ST thin film and ST substrate, the pseudocubic misfit strain of ST thin film x2 is equal to zero. The in-plane misfit strain of BT thin film x1 = −2.28% is the same at these three orientations [32]. Based on the thermodynamic theory [35], the in-plane compressive misfit strain is responsible for enhancing the stability of out-of-plane polarization. Thus, only the out-of-plane polarization is considered in our thermodynamic theory. The free energy density of layer i can be presented as follows [33]:

b∗i = α11,i +

Fig. 1. Average polarization hP i as a function of volume fraction of SrTiO3 layer for BaTiO3 /SrTiO3 bilayer thin films.

,

ci∗ =

1 3

2(2Q11,i + 4Q12,i − Q44,i ) 4S11,i + 8S12,i + S44,i

(α11,i + α12,i ) −

1 27

,

1 (2Q11,i + 4Q12,i − Q44,i )2 4S11,i + 8S12,i + S44,i

6

(3α111,i + 6α112,i + α123,i ).

, (5)

The coefficients α1,i , α11,i , α12,i , α111,i , α112,i , and α123,i are dielectric stiffness coefficients of layer i at constant stress. S11,i , S12,i , and S44,i are the elastic compliances of layer i at constant polarization. Q11,i , Q12,i , and Q44,i are the electrostrictive coefficients of layer i. The parameters used for thermodynamic calculations result from Refs. [33,35]. The value of out-of-plane polarization and its dependence on electric field are expressed by the equilibrium conditions ∂ F /∂ P1 = ∂ F /∂ P2 = 0. For the constant electric field and stress, the entropy S of a bilayer thin film is defined by [16,17]

∂F S=− ∂T 



.

(6)

E

In the presence of a uniform applied electric field E normal to the film substrate interface, the electrocaloric coefficient p is [17]

 p=

∂S ∂E



.

(7)

T

Reversible adiabatic temperature change 1T of a bilayer thin film with an applied electric field E is given by [17]

1T = −T

Z

Eb Ea

1 CE (T , E )



∂hP (E )i ∂T



dE ,

(8)

E

where CE (T , E ) is the heat capacity per unit volume at constant electric field, hP (E )i = (1 − α)P1 + α P2 is the average polarization, and 1E = Eb − Ea is the difference in the applied electric field. 3. Results and discussion

, (4)

For a (110) oriented bilayer thin film epitaxially grown on a thick (110) single crystal substrate [33], see Box I.

The effects of orientation and electric field on the average polarization of BT/ST bilayer thin films at room temperature (RT) are presented in Fig. 1. As a result of the strong electrostatic coupling between the BT/ST bilayer thin films, the spontaneous average polarization decreases with the increase of volume

J.H. Qiu, Q. Jiang / Solid State Communications 149 (2009) 1549–1552

a∗i = α1,i − xi b∗i = ci∗ =

1 4 1 4

1551

(2Q11,i + 4Q12,i − Q44,i )(S11,i − S12,i ) + Q12,i S44,i , 2 2 2S11 ,i − 4S12,i + S11,i (2S12,i + S44,i )

(2α11,i + α12,i ) +

2 1 (2Q11,i − Q44,i )[(2Q11,i − Q44,i )S11,i + 4Q12,i (S11,i − 2S12,i )] + 4Q12,i (3S11,i − 2S12,i + S44,i )

8

2 2 2S11 ,i − 4S12,i + S11,i (2S12,i + S44,i )

,

(α111,i + α112,i ). Box I.

Fig. 2. Orientation dependence of electrocaloric coefficient p for BaTiO3 /SrTiO3 bilayer thin films with the effect of applied electric field.

Fig. 3. Effect of orientation on the adiabatic temperature change 1T for BaTiO3 /SrTiO3 bilayer thin films.

fraction of the ST layer and completely vanishes at a critical relative thickness of α = 50%, 23%, and 12% for (001), (110), and (111) orientations, respectively. Moreover, the phase transitions between the ferroelectric phase and the paraelectric phase are of the second-order. The applied electric field undoubtedly results in an enhancement of average polarization and induces the paraelectric phase to a ferroelectric phase. For a given volume fraction of the ST layer, the average polarization of (001) oriented BT/ST bilayer thin films is larger than that of (110) and (111) orientations which is agreement with the results of PbTiO3 /SrTiO3 bilayer [33] and Pb(Zr0.8 Ti0.2 )O3 /Pb(Zr0.2 Ti0.8 )O3 multilayer thin films [36]. The orientation dependence of the electrocaloric coefficient p for BT/ST bilayer thin films with the effect of electric field is depicted in Fig. 2. For the given orientation and electric field, the electrocaloric coefficient p increases first and then it decreases with further increase of the volume fraction of the ST layer. The electrocaloric coefficient p exhibits a maximum at the critical relative thickness of the ST layer, e.g. p = 1.37 × 10−3 C/m2 K, p = 1.8 × 10−3 C/m2 K, and p = 1.83 × 10−3 C/m2 K for (001), (110), and (111) oriented BT/ST bilayer thin films at E = 50 kV/cm. It is attributed to the assumption of the Maxwell ∂hP i ∂hP i relation p = ( ∂∂ ES )T = ( ∂ T )E . The value of ( ∂ T )E obtained from Fig. 1 is not a monotonous function of the volume fraction of the ST layer and a maximum exists at the critical relative thickness of the ST layer. The applied electric field decreases the electrocaloric coefficient p and reduces its dependence on the volume fraction of the ST layer, however, the critical relative thickness of the ST layer corresponding to the maximum of electrocaloric coefficient p remains the same due to the second-order phase transition between ferroelectric phase and the paraelectric phase. This is in accordance with the general conclusions of the electrocaloric effect [37]. Furthermore, there exists a critical electric field E ∗ ' 50 kV/cm. At E ≤ E ∗ , the maximal electrocaloric coefficient p is achieved for (111) oriented BT/ST bilayer thin films. The (110)

oriented BT/ST bilayer thin films have the largest electrocaloric coefficient at E > E ∗ . It may ascribed to the competition between the orientation and the applied electric field. In spite of the value of the applied electric field, the (001) oriented BT/ST bilayer thin films have the smallest electrocaloric coefficient. Additionally, the electrocaloric coefficient p of the BT/ST bilayer thin films is larger than that of pure BT thin films (α = 0) and ST thin films (α = 1) which is in agreement with the conclusions of the PT/ST bilayer thin films [33]. Fig. 3 shows the orientation dependence of adiabatic temperature change 1T at RT for BT/ST bilayer thin films. As shown in Eq. (8), the adiabatic temperature change 1T depends on both the initial electric field Ea and the field change 1E = Eb − Ea . In order to analyze the adiabatic temperature change at high electric fields, we perform the integration for 1E = 100 kV/cm and 300 kV/cm with the initial electric field Ea = 50 kV/cm. The absolute value of specific heat CE (T , E ) used for thermodynamic calculations in Eq. (8) is considered to be a linear relation of (1 − α)CBT + α CST for simplicity, where the specific heat CBT = 3.05 × 106 J/m3 K is approximately the value of single crystal BT and CST = 2.78 × 106 J/m3 K is the value of a single crystal ST. In fact, the specific heat of the BT/ST bilayer thin films is smaller than that of a single crystal [16]. As a result, it results in a larger adiabatic temperature change 1T based on the Eq. (8). With the increase of the volume fraction of the ST layer, the adiabatic temperature change 1T is not a monotonous function and exhibits a maximum at the critical relative thickness of 50%, 23%, and 12% for (001), (110), and (111) oriented BT/ST bilayer thin films respectively, which are in accordance with the results of the electrocaloric coefficient p and is the explanation for the electrocaloric coefficient being responsible for this. It is clear that the adiabatic temperature change 1T of (110) oriented BT/ST bilayer thin films is largest and that of (001) oriented is smallest in these three orientations because of the applied high electric field E > 50 kV/cm. On the other hand, it is expected that an increase in the field change 1E can lead to a linear increase

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in the magnitude of the adiabatic temperature change 1T due to the EC effect [3,13,16,17]. We should like to note that the EC effect depends on the orientation, the volume fraction of the ST layer, and the applied electric field. Therefore, the giant EC effect can be obtained by controlling the orientation and volume fraction of the ST layer for the BT/ST bilayer thin films as well as the applied electric field, e.g. 1T = 1.4 ◦ C and 3.33 ◦ C for (110) oriented BT/ST bilayer thin films with the field change of 1E = 100 kV/cm and 300 kV/cm respectively. Most importantly, it may provide the potential for practical application in refrigeration devices. 4. Conclusion In summary, a analytical thermodynamic theory is employed to investigate the effect of orientation on the electrocaloric effect of ferroelectric BaTiO3 /SrTiO3 bilayer thin films. The electrocaloric effect strongly depends on the orientation and exhibits a maximum at the critical relative thickness of SrTiO3 layer of 50%, 23%, and 12% for (001), (110), and (111) oriented BaTiO3 /SrTiO3 bilayer thin films, respectively. Moreover, the (110) oriented BaTiO3 /SrTiO3 bilayer thin films have the largest electrocaloric effect in these three orientations. Consequently, by choosing a suitable orientation and volume fraction of SrTiO3 layer, the electrocaloric effect can be controlled. It may open more opportunities for practical application in cooling systems. Acknowledgments This project is supported by the Jiangsu Polytechnic University Foundation under Grant No. JS200803 and National Natural Science Foundation of China under Grant No. 50832002. References [1] F. Jona, G. Shirane, Ferroelectric Crystals, McMillan, NY, 1962. [2] A.S. Mischenko, Q. Zhang, J.F. Scott, R.W. Whatmore, N.D. Mathur, Appl. Phys. Lett. 89 (2006) 242912. [3] A.S. Mischenko, Q. Zhang, J.F. Scott, R.W. Whatmore, N.D. Mathur, Science 311 (2006) 1270. [4] J.D. Childress, J. Appl. Phys. 33 (1962) 1793.

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