Cite this Article
Qiu Jian-Hua, Chen Zhi-Hui, Wang Xiu-Qin, Yuan Ning-Yi, Ding Jian-Ning. Dielectric and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 thin films. Chinese Physics B, 2016, 25(5): 057701  
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Dielectric and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 thin films
Qiu Jian-Hua1, 2, †, , Chen Zhi-Hui1, 2, Wang Xiu-Qin1, 2, Yuan Ning-Yi1, 2, Ding Jian-Ning1, 2
Jiangsu Province Cultivation Base for State Key Laboratory of Photovoltaic Science and Technology, Changzhou University, Changzhou 213164, China
Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering, Changzhou University, Changzhou 213164, China

 

† Corresponding author. E-mail: jhqiu@cczu.edu.cn

Project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Research Fund of Jiangsu Province Cultivation Base for State Key Laboratory of Photovoltaic Science and Technology, China, Major Projects of Natural Science Research in Jiangsu Province, China (Grant No. 15KJA43002), and Qing Lan Project of Education Department of Jiangsu Province, China.

Abstract
Abstract

A phenomenological Landau–Devonshire theory is developed to investigate the ferroelectric, dielectric, and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films. At room temperature, the tetragonal a1 phase, the orthorhombic a2c phase, the triclinic γ1 phase, and the triclinic γ2 phase are stable. The appearance of the negative polarization component P2 in the a2c phase and the γ1 phase is attributed to the nonlinear coupling terms in the thermodynamic potential. The γ phase of the Pb(Zr1−xTix)O3 thin films has better dielectric and piezoelectric properties than the a2c phase and the a1 phase. The largest dielectric and piezoelectric coefficients are obtained in the Pb(Zr0.5Ti0.5)O3 thin film. The piezoelectric coefficient of 110–150 pm/V is obtained in the (110) oriented Pb(Zr0.5Ti0.5)O3 thin film, and the Pb(Zr0.3Ti0.7)O3 thin film has the remnant polarization and relative dielectric constant of 50 μC/cm2 and 100, respectively, which are in agreement with the experimental measurements reported in the literature.

PACS: 77.22.Ej;77.22.–d;77.65.–j;
Keyword:polarization;dielectric property;piezoelectric property;
1. Introduction

The Pb(Zr1−xTix)O3 (PZT) thin films have attracted a great deal of attention for use in nonvolatile ferroelectric random access memories, sensors, and actuators because of their superior properties of large spontaneous polarization and piezoelectricity.[1–6] Some researches focused on the (001) oriented Pb(Zr1−xTix)O3 thin films grown on compressive cubic substrates with large remanent polarization,[7–9] such as SrTiO3. However, their dielectric and piezoelectric properties were not so prominent due to the residual strain in the Pb(Zr1−xTix)O3 thin films.[8] Actually, the dielectric and piezoelectric properties are strongly affected by the film orientation which is related to the substrates or the buffer layers,[10–12] and good dielectric and piezoelectric properties were observed in the (110) oriented films.[13–15]

Experimentally, the effect of the buffer layer on the film orientation and the piezoelectric properties was investigated. Epitaxial Pb(Zr0.52Ti0.48)O3 thin films with and without a CeO2 buffer layer were deposited on silicon substrates respectively using pulsed laser deposition.[14] The (110) oriented film was obtained on a YSZ/Si substrate, while the (001) oriented film was fabricated on a CeO2/YSZ/Si substrate. The longitudinal piezoelectric coefficient d33 of the (110) oriented film was larger than that of the (001) oriented film. On the other hand, the effect of the substrate on the film orientation and the dielectric properties in epitaxial Pb(Zr1−xTix)O3 thin films was investigated for different Ti concentrations.[15] The dielectric constant in the (110) oriented film was larger than that in the (001) oriented film, and the Pb(Zr0.5Ti0.5)O3 thin films had the better dielectric property.

Although the experimental results indicated that the (110) oriented Pb(Zr1−xTix)O3 thin films have better dielectric and piezoelectric properties than the (001) oriented films, there are no theoretical reports on the (110) oriented Pb(Zr1−xTix)O3 thin films. As we known, the Landau–Devonshire theory is an effective method to investigate the ferroelectric, dielectric, and piezoelectric properties of conventional ferroelectrics.[16–20] Therefore, (110) or (111) oriented films can be analyzed theoretically by the transformations of polarization, stress, and electric field in the frame of the Landau–Devonshire theory.[21,22]

Thus, the goal of this paper is to investigate the ferroelectric, dielectric, and piezoelectric properties of (110) oriented Pb(Zr1−xTix)O3 (x=0.4, 0.5, 0.6, and 0.7) thin films. The effects of composition and misfit strain on those properties are evaluated. New ferroelectric phases, which are rare in the (001) oriented films, result in the excellent dielectric and piezoelectric properties.

2. Model and method

We consider a (110) oriented Pb(Zr1−xTix)O3 thin film grown on a thick substrate. The elastic Gibbs function G of a cubic ferroelectric is given by the Landau–Devonshire theory[22,23]

where P̃i, ˜σi, and Ẽi are the polarization, stress, and electric field components defined in the crystallographic reference frame (X̃1, X̃2, X̃3) aligned with the cube axes of the material; α1, αi,j, and αi,j,k are the dielectric stiffness coefficients; sij are the elastic compliances at constant polarization; and Qij are the electrostrictive coefficients. These parameters of the Pb(Zr1−xTix)O3 thin film used for calculations come from Ref. [24]. In order to construct the thermodynamic potential in the film frame (X1, X2, X3), the polarization P̃i, stress σ̃i, and electric field Ẽi are transformed by using the frame transformation X̃i = Ai,jXj, where Ai,j is the frame transformation matrix. For a (110) oriented film, where the X3 axis is parallel to [011] and the X1 axis is parallel to [100], Ai,j is given by

Based on the previous work,[16] the thermodynamic potential of a single domain film is rewritten as

The mechanical boundary conditions are given by S1 = S2 = Sm, where Sm is the misfit strain along the in-plane direction, σ3 = σ4 = σ5 = 0, and S6 = 0. All the stress components in Eq. (3) can be eliminated by the mechanical boundary conditions and ∂G/∂σ1 = ∂G/∂σ2 = −Sm, ∂G/∂σ6 = 0. Therefore, the thermodynamic potential Gfilm is expanded as a function of polarization Pi, temperature T, misfit strain Sm, and electric field Ei

The polarization and its dependence on the misfit strain are given by the equilibrium condition ∂Gfilm/∂Pi = 0 (i = 1,2,3). For investigating the dielectric property of the Pb(Zr1−xTix)O3 thin film, we can derive an explicit expression for the reciprocal dielectric susceptibilities by differentiating the thermodynamic potential Gfilm, i.e., χij = ∂2Gfilm/∂Pi∂Pj. Consequently, the matrix (χ) of the reciprocal dielectric susceptibilities is obtained as

The matrix inversion then enables us to find the dielectric susceptibility η = χ−1 and dielectric constant ɛij = ɛ0 + ηij, here ɛ0 is the dielectric constant of free space. By substituting the equilibrium values Pi of the polarization components into the expression derived for χij via Eq. (4), the small-signal dielectric response ɛij is calculated. Generally speaking, the piezoelectric coefficient dln is calculated as dln = ∂Sn/∂El = bknηkl, where bkn = ∂Sn/∂Pk and ηkl is the dielectric susceptibility. The strain can be obtained by differentiating the elastic Gibbs function G, Sn = −∂G/∂σn.[25]

3. Results and discussion

For investigating the dielectric and piezoelectric properties of the (110) oriented Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films, the temperature–misfit strain phase diagrams are constructed firstly.[26] At room temperature, only the orthorhombic a2c phase (P1 = 0, P2 < 0, P3 > 0), the tetragonal a1 phase (P1 > 0, P2 = P3 = 0), the triclinic γ1 phase (P1 > 0, P2 < 0, P3 > 0), and the triclinic γ2 phase (P1 > 0, P2 > 0, P3 > 0) are stable. The effect of the misfit strain on the polarization at room temperature is presented in Fig. 1. The Pb(Zr1−xTix)O3 (x = 0.4, 0.5, and 0.6) thin films experience the first order phase transition from the orthorhombic a2c phase to the triclinic γ phase, and the Pb(Zr0.3Ti0.7)O3 thin film has the first order phase transition from the orthorhombic a2c phase to the tetragonal a1 phase. Even in the γ phase, the first order γ1–γ2 phase transition may take place in the Pb(Zr1−xTix)O3 (x = 0.4 and 0.5) thin films. Therefore, all the polarization components Pi are discontinuous. The polarization components P2 and P3 of the orthorhombic a2c phase are negative and positive, respectively. Moreover, the polarization component P3 increases and P2 decreases with increasing compressive misfit strain, because the Pb(Zr1−xTix)O3 thin films are grown along the [011] direction and the compressive misfit strain is beneficial to induce the polarization component P3. The appearance of the negative polarization component P2 in the a2c phase and the γ1 phase is attributed to the nonlinear coupling terms and in Eq. (4). Experimentally, the Pb(Zr0.35Ti0.65)O3,[11] Pb(Zr0.42Ti0.58)O3,[12] and Pb(Zr0.26Ti0.74)O3[15] thin films had the remanent polarizations Pr of 50 μC/cm2, 45 μC/cm2, and 48 μc/cm2, respectively, which are in agreement with the theoretical results.

Fig. 1. The effect of the misfit strain on the polarization components Pi in Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films at room temperature.

The misfit strain dependence of the spontaneous polarization Ps in the (110) oriented Pb(Zr1−xTix)O3 thin films is shown in Fig. 2. The spontaneous polarizations of the orthorhombic a2c phase and the triclinic γ phase have magnitudes of and respectively. With the increase of the compressive misfit strain, the spontaneous polarization Ps of the orthorhombic a2c phase increases for the Ti composition of x ≤ 0.6, while it decreases for the Ti composition of 0.7. This is because the spontaneous polarization Ps of the a2c phase mainly depends on the polarization component P3 and P2 for x ≤ 0.6 and x = 0.7, respectively. For the Pb(Zr0.6Ti0.4)O3 thin film, the spontaneous polarization Ps of the triclinic γ1 phase firstly increases and then decreases with the variation of the misfit strain from compressive strain to tensile strain. Moreover, the polarization Ps of the triclinic γ2 phase increases with further increase of the tensile misfit strain. The spontaneous polarization Ps in the Pb(Zr0.5Ti0.5)O3 thin film firstly decreases in the triclinic γ1 phase and then increases in the triclinic γ2 phase with increasing tensile misfit strain. The spontaneous polarizations Ps of the triclinic γ2 phase in the Pb(Zr0.4Ti0.6)O3 thin film and the tetragonal a1 phase in the Pb(Zr0.3Ti0.7)O3 thin film both increase as the tensile misfit strain increases. As is seen from the figure, the Pb(Zr0.3Ti0.7)O3 thin film has the largest spontaneous polarization due to its large Ti composition.

Fig. 2. The room temperature spontaneous polarizations Ps of Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films as a function of the misfit strain.

The dependence of the relative dielectric constant ɛii/ɛ0 on the misfit strain is plotted in Fig. 3. Because of the first order ferroelectric–ferroelectric phase transitions at room temperature, all the relative dielectric constants are discontinuous. In the a2c phase, the relative dielectric constants ɛ11/ɛ0 and ɛ33/ɛ0 decrease with increasing compressive misfit strain due to the increase of the polarization component P3, and the decrease of the polarization component P2 results in the increase of the relative dielectric constant ɛ22/ɛ0. In addition, the increase of the tensile misfit strain decreases the relative dielectric constants ɛii/ɛ0 of the a1 phase for the Pb(Zr0.3Ti0.7)O3 thin film because of the increase of the polarization component P1. The Pb(Zr0.5Ti0.5)O3 thin film has the best dielectric property with a relative dielectric constant ɛ33/ɛ0 of 4000 at the misfit strain of 3×10−3, which has potential applications in semiconductor memory devices. This is because the Ti composition of the Pb(Zr0.5Ti0.5)O3 thin film is near the morphotropic phase boundary (MPB) and the large dielectric property is obtained, which is in agreement with the experimental result. The Pb(Zr0.3Ti0.7)O3 thin film has the smallest dielectric constant due to its large spontaneous polarization, and the magnitude of 100 is in agreement with the experimental measurement.[15]

Fig. 3. The dependence of relative dielectric constants ɛii/ɛ0 on the misfit strain in Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films.

The dependence of the longitudinal piezoelectric coefficient d33 on the misfit strain for the Pb(Zr1−xTix)O3 thin films is shown in Fig. 4. The piezoelectric coefficient of the a2c phase deceases with the increase of the compressive misfit strain except for the Pb(Zr0.6Ti0.4)O3 thin film. Moreover, the piezoelectric coefficient of the a1 phase is zero because the Pb(Zr0.3Ti0.7)O3 thin film only has the in-plane polarization component P1. The new ferroelectric γ phase results in the excellent piezoelectric property, which is larger than that of the a2c phase and the a1 phase. The Pb(Zr0.5Ti0.5)O3 thin film has the largest piezoelectric coefficient due to the existence of the MPB. Nguyen et al. reported that the (110) oriented Pb(Zr0.52Ti0.48)O3 thin film grown on SrRuO3/YSZ/Si substrate has a longitudinal piezoelectric coefficient of 50–150 pm/V with the film thickness ranging from 100 nm to 2000 nm,[14,27] which is in good agreement with the theoretical result.

Fig. 4. The piezoelectric coefficients of the Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films.
4. Conclusion

The ferroelectric, dielectric, and piezoelectric properties of the (110) oriented Pb(Zr1−xTix)O3 (x = 0.4, 0.5, 0.6, and 0.7) thin films are investigated by the phenomenological Landau–Devonshire theory. The excellent dielectric and piezoelectric properties are obtained due to the new ferroelectric phases, such as the triclinic γ phase and the orthorhombic a2c phase, which cannot be obtained in the (001) oriented films. The appearance of the negative polarization component P2 in the a2c phase and the γ1 phase is attributed to the nonlinear coupling terms and The Pb(Zr0.5Ti0.5)O3 thin film with the Ti composition around the morphotropic phase boundary has the largest dielectric and piezoelectric coefficients. Moreover, the Pb(Zr0.3Ti0.7)O3 thin film has the remnant polarization and dielectric constant of 50 μC/cm2 and 100, respectively, which are in accordance with the experimental measurements.

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