Piezoelectric and pyroelectric properties of (001) oriented KNbO3 film

Accepted Manuscript Piezoelectric and pyroelectric properties of (001) oriented KNbO3 film J.H. Qiu, T.X. Zhao, Z.H. Chen, X.Q. Wang, N.Y. Yuan, J.N. Ding PII:

S0038-1098(18)30309-0

DOI:

10.1016/j.ssc.2018.09.002

Reference:

SSC 13494

To appear in:

Solid State Communications

Received Date: 26 May 2018 Revised Date:

23 August 2018

Accepted Date: 4 September 2018

Please cite this article as: J.H. Qiu, T.X. Zhao, Z.H. Chen, X.Q. Wang, N.Y. Yuan, J.N. Ding, Piezoelectric and pyroelectric properties of (001) oriented KNbO3 film, Solid State Communications (2018), doi: 10.1016/j.ssc.2018.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Piezoelectric and pyroelectric properties of (001) oriented KNbO3

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film J.H. Qiu,a,b,∗ T.X. Zhao,a Z.H. Chen,a X.Q. Wang,a N.Y. Yuan,a and J.N. Dinga,b a

School of Mathematics and Physics,

Jiangsu Province Cultivation base for State Key

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Laboratory of Photovoltaic Science and Technology,

Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering,

School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

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b

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Changzhou University, Changzhou 213164, Jiangsu, China

∗

Corresponding author at: School of Mathematics and Physics, Changzhou University, Changzhou 213164, Jiangsu, China. E-mail: [email protected].

Typeset by REVTEX

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Abstract A phenomenological Landau-Devonshire theory is used to investigate the “misfit strain-

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temperature“ phase diagram and physical properties of (001) oriented KNbO3 film. Three ferroelectric phases, such as c phase, aa phase, and γ phase, occur in the phase diagram. In-plane compressive misfit strain is beneficial to form c phase and tensile strain makes aa phase stable. Physical properties of KNbO3 film largely depend on misfit strain and electric field. At room

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temperature, γ phase of KNbO3 film with the tensile misfit strain has larger piezoelectric and pyroelectric coefficients than that of c phase with the compressive strain. Large piezoelectric and

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pyroelectric coefficients are 180 pm/V and 8.5×10−4 C/m2 K respectively at the electric field of 100 KV/cm and misfit strain of 6.7×10−3 , which are comparable with the experimental results of Pb(Zrx Ti1−x )O3 film. Therefore, choosing the appropriate substrates can be used to improve the physical properties of KNbO3 film. In addition, the applied electric field decreases the dielectric, piezoelectric and pyroelectric properties of (001) oriented KNbO3 film.

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Keywords: A. Ferroelectric film; D. Piezoelectric property; D. Pyroelectric property.

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PACS numbers: 77.80.-e; 77.65.-j; 77.70.+a

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1.Introduction Potassium niobate (KNbO3 ) has been intensively investigated due to its large electro-

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optical coefficients, nonlinear optical coefficients and electromechanical coupling factors for various electro-optical and nonlinear optical devices.[1−4] As temperature decreases, KNbO3 single crystal undergoes a series of first order phase transitions, i.e. from cubic phase to tetragonal phase at 435 ◦ C, tetragonal to orthorhombic phase at 225 ◦ C, and orthorhom-

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bic to rhombohedral phase at -50 ◦ C.[5] Until now, main efforts in studies of KNbO3 were concentrated on the phase transition and optical properties.[6−9] However, few researches on

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dielectric, piezoelectric and pyroelectric properties were involved because of the low dielectric and piezoelectric coefficients of KNbO3 single crystal.[10−12]

A good choice to improve the piezoelectric property is domain engineering which is an important technique for obtaining enhanced piezoelectric property in ferroelectrics.[13−15] The piezoelectric property of KNbO3 crystal with the engineered domain configurations showed much higher values than those of the single domain crystal. Moreover, the piezoelectric

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property increased with decreasing the domain sizes of the engineered domain configuration. On the other hand, strain engineering is another effective way to enlarge the piezoelectric property of KNbO3 film. The longitudinal piezoelectric coefficient of 125 pm/V at 21 KV/cm was observed in KNbO3 film grown on the pt-si substrate, which is much larger than that

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of single crystal.[16] Therefore, KNbO3 film has been considered as a candidate for lead-free piezoelectric material due to the good piezoelectric property. However, there has no studies

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on the effect of misfit strain on the piezoelectric property which originates from the lattice mismatch between the film and substrate. In this paper, the phenomenological Landau-Devonshire theory is applied to construct the “misfit strain-temperature“ phase diagram of (001) oriented KNbO3 film. The phase transition properties are analysed theoretically. Moreover, the effects of misfit strain and electric field on the ferroelectric, dielectric, piezoelectric, and pyroelectric properties are investigated. Theoretical results indicate these properties largely depend on the misfit strain

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and electric field. Consequently, strain engineering can be used to improve the piezoelectric and pyroelectric properties which may provide useful guidance for further experimental

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researches. 2.Theory

In the phenomenological Landau-Devonshire theory, the spontaneous polarization P=(P1 , P2 , P3 ) and stress σi (i=1-6) are chosen as the order parameters. The thermodynamic

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potential of single crystal is expanded as a polynomial of the polarization components Pi (i=1, 2, 3) and stress σi (i=1-6). Here, the thermodynamic potential is constructed into an

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eighth-order polynominal function of polarization components.[5,11]

G = α1 (P12 + P22 + P32 ) + α11 (P14 + P24 + P34 ) + α12 (P12 P22 + P12 P32 + P22 P32 ) +α111 (P16 + P26 + P36 ) + α112 [P14 (P22 + P32 ) + P24 (P12 + P32 ) + P34 (P12 + P22 )] +α123 P12 P22 P32 + α1111 (P18 + P28 + P38 )

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+α1112 [P16 (P22 + P32 ) + P26 (P12 + P32 ) + P36 (P12 + P22 )] + α1122 (P14 P24 + P14 P34 + P24 P34 ) 1 +α1123 (P14 P22 P32 + P24 P12 P32 + P34 P12 P22 ) − s11 (σ12 + σ22 + σ32 ) 2 1 −s12 (σ1 σ2 + σ1 σ3 + σ2 σ3 ) − s44 (σ42 + σ52 + σ62 ) − Q11 (σ1 P12 + σ2 P22 + σ3 P32 ) 2 2 2 2 −Q12 [σ1 (P2 + P3 ) + σ2 (P1 + P32 ) + σ3 (P12 + P22 )] − Q44 (P2 P3 σ4 + P1 P3 σ5 + P1 P2 σ6 ), (1)

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−E1 P1 − E2 P2 − E3 P3 ,

where α1 , αi,j , αi,j,k and αi,j,k,l are dielectric stiffness coefficients, sij is elastic compliance at

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constant polarization, Qij is electrostrictive coefficient, and Ei is the applied electric field. The temperature dependence of ferroelectricity is mainly governed by the dielectric stiffness coefficient α1 , and the other dielectric stiffness coefficients may be taken as temperatureindependent parameters. These parameters used for calculations in Eq. (1) are shown in Table I.[5,11]

The thermodynamic potential of a (001) oriented film is given by the following Legendre

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transformation of G.[17] (2)

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Gf ilm = G + u1 σ1 + u2 σ2 + u6 σ6 .

The mechanical boundary conditions are given by u1 =u2 =um , where um is the misfit strain along the in-plane direction, σ3 = σ4 = σ5 = 0 and u6 = 0. All the stress components in equations (1) and (2) can be eliminated by the mechanical boundary conditions, ∂G/∂σ1 =

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∂G/∂σ2 =-um and ∂G/∂σ6 =0. Therefore, the thermodynamic potential Gf ilm of a (001) oriented film becomes a function of polarization Pi , misfit strain um , and electric field Ei .

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˜ = α1∗ (P12 + P22 ) + α3∗ P 2 + α∗ (P 4 + P 4 ) + α∗ P 4 + α∗ P 2 P 2 + α∗ (P 2 + P 2 )P 2 G 3 11 1 2 33 3 12 1 2 13 1 2 3 +α111 (P16 + P26 + P36 ) + α112 [P14 (P22 + P32 ) + P24 (P12 + P32 ) + P34 (P12 + P22 )] +α123 P12 P22 P32 + α1111 (P18 + P28 + P38 )

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+α1112 [P16 (P22 + P32 ) + P26 (P12 + P32 ) + P36 (P12 + P22 )] + α1122 (P14 P24 + P14 P34 + P24 P34 ) u2m 4 2 2 4 2 2 4 2 2 , (3) +α1123 (P1 P2 P3 + P2 P1 P3 + P3 P1 P2 ) − E1 P1 − E2 P2 − E3 P3 + s11 + s12 where

Q11 + Q12 um , s11 + s12

(4)

α3∗ = α1 −

2Q12 um , s11 + s12

(5)

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α1∗ = α1 −

1 [(Q211 + Q212 )s11 − 2Q11 Q12 s12 ] , 2 s211 − s212

(6)

∗ α33 = α11 +

Q212 , s11 + s12

(7)

∗ α12 = α12 −

[(Q211 + Q212 )s12 − 2Q11 Q12 s11 ] Q244 + , s211 + s212 2s44

(8)

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∗ α11 = α11 +

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∗ α13 = α12 +

Q12 (Q11 + Q12 ) . s11 + s12

(9)

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∗ Here αi∗ and αij are the renormalized dielectric stiffness coefficients. The temperature and

misfit strain dependence of ferroelectricity are mainly governed by the renormalized coefficient αi∗ , and the other coefficients are taken as temperature and misfit strain independent parameters.

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The polarization components Pi as a function of misfit strain, temperature, and electric field are given by the equilibrium conditions ∂Gf ilm /∂Pi =0 (i=1,2,3).[18,19] The relative dielectric constants εij can be calculated from the reciprocal dielectric susceptibilities

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χij = ∂ 2 Gf ilm /∂Pi ∂Pj , which are obtained by differentiating the thermodynamic potential Gf ilm . The matrix inversion then enables us to find the dielectric susceptibility η = χ−1 and to calculate the relative dielectric constant εij = 1 + ηij /ε0 . By substituting the polarization components Pi into the expression of χij , the relative dielectric constants εij are calculated as a function of misfit strain, temperature and electric field. Generally speaking, the piezo-

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electric coefficient dln is calculated as dln =∂un /∂El =bkn ηkl , where bkn =∂un /∂Pk and ηkl is the dielectric susceptibility.[20] The strain un = −∂G/∂σn can be obtained by differentiating the thermodynamic potential G.

In the presence of an applied electric field E3 =E normal to the film substrate interface

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([001] direction), the pyroelectric coefficient p is given as the sum of the variations of the out-of-plane polarization P3 and the dielectric constant ε33 with the temperature.[21]

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p=

∂P3 ∂ε33 (E) +E . ∂T ∂T

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3.Results and Discussion The “misfit strain-temperature“ phase diagram of KNbO3 film is constructed in figure 1. The ferroelectric polarization states are determined by performing the minimization of Gf ilm with respect to the polarization components Pi . The following phases are found in phase diagram: (i) para phase, where P1 =P2 =P3 =0; (ii) c phase, where P1 =P2 =0, P3 6= 0; (iii) aa phase, where P1 =P2 6= 0, P3 =0; (iV) γ phase, where P1 =P2 6= 0, P3 6= 0. In-plane 6

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compressive misfit strain is beneficial to form c phase and tensile strain makes aa phase stable, which is similar to the theoretical phase diagrams of PbTiO3 and Pb(Zrx Ti1−x )O3 films.[17,20]

strain from compressive to tensile misfit strain.

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At room temperature, c phase, γ phase, and aa phase are stable with the variation of misfit

The polarization components at room temperature are shown in figure 2. The applied electric field induces the out-of-plane polarization component P3 in aa phase and therefore

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transforms aa phase to γ phase within the range of strain we studied, because the electric field makes the centers of positive and negative charge shift along the [001] direction.

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Consequently, the applied electric field changes the phase symmetry of aa phase and moves the critical misfit strain to higher strain which corresponds to the phase transition between γ phase and aa phase. The polarization components P1 =P2 increase and polarization P3 decreases with decreasing the compressive misfit strain and increasing the tensile strain. Moreover, the polarization components are continuous because of the second order phase transition between γ phase and c phase (or aa phase). Experimentally, Lee et al. reported

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(001) KNbO3 film has a high remanent polarization of 42 µC/cm2 with the in-plane misfit strains of ε1 = ε2 = −1.25%,[22] which is in agreement with the theoretical result (39.6 µC/cm2 ). The electric field has little effect on polarization components P1 =P2 , but can 5×10−3 .

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increase the polarization component P3 largely especially near the critical misfit strain of

Misfit strain dependence of dielectric properties for KNbO3 film is presented at room

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temperature in figure 3. The in-plane dielectric constants ε11 and ε22 are equal because of the in-plane misfit strains (u1 =u2 ). Under the electric field of 0 KV/cm, the dielectric constants ε33 and ε11 (ε22 ) diverge at the phase boundaries between γ phase and aa phase and between c phase and γ phase respectively, which correspond to the typical second order phase transition characteristics. Because dielectric constant ε33 largely depends on the polarization component P3 and dielectric constants ε11 and ε22 mainly depend on polarizations P1 and P2 . The polarization components P3 and P1 (or P2 ) are equal to zero at the γ-aa and c-γ 7

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phase boundaries respectively, which lead to the divergence of dielectric constants. Dielectric constants ε11 =ε22 are not affected by electric field which has little impact on the polarization

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components P1 and P2 . However, the applied electric field decreases the dielectric constant ε33 in γ phase and leads to a maximum of dielectric constant ε33 . It can be explained that the applied electric field increases the polarization component P3 and thus results in the decrease of dielectric constant ε33 . The KNbO3 film has the large out-of-plane dielectric

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constant ε33 and in-plane dielectric constants ε11 and ε22 for tensile and compressive misfit strain, respectively.

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The longitudinal piezoelectric coefficient d33 with the effects of misfit strain and electric field is shown in figure 4. At room temperature, c phase with compressive misfit strain has the small piezoelectric coefficient and large piezoelectric coefficient is obtained in γ phase under the tensile strain, especially near the critical misfit strain of 5×10−3 . At E=0 KV/cm, the piezoelectric coefficient is equal to zero in aa phase because of the absence of polarization component P3 . Moreover, the piezoelectric coefficient increases with the decrease of

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compressive misfit strain and the increase of tensile strain. The applied electric field decreases the piezoelectric coefficient of γ phase which is in agreement with the experimental result of Pb(Zrx Ti1−x )O3 film.[23] Piezoelectric coefficient increases firstly and then decreases gradually with the decrease of compressive misfit strain and the increase of tensile strain,

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and a maximum occurs near the critical misfit strain. A large piezoelectric coefficient of 180 pm/V is obtained at the tensile misfit strain of 6.7×10−3 and the electric field of 100

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KV/cm, which is in agreement with the experimental result of 125 pm/V in KNbO3 film and is also comparable with the observation of Pb(Zrx Ti1−x )O3 film.[16,24] Therefore, misfit strain originated from the lattice mismatch between the film and substrate can be used to improve the piezoelectric property largely. The effects of misfit strain and electric field on the pyroelectric coefficient p are presented at room temperature in figure 5. The pyroelectric coefficient in c phase is relatively small and the electric field has little influence on it. However, the electric field largely decreases

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the pyroelectric coefficient in γ phase, which is in accordance with other theoretical result.[25] Most importantly, large pyroelectric coefficient is obtained in γ phase and a maximum lo-

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cates near the critical misfit strain of 5×10−3 which corresponds to the maxima of dielectric constant ε33 and piezoelectric coefficient d33 . Therefore, the pyroelectric coefficient largely depends on the misfit strain. The pyroelectric coefficient p is 8.5×10−4 C/m2 K at E=100 KV/cm and um =6.7×10−3 which is comparable with the result of Pb(Zrx Ti1−x )O3 film.[26−28]

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Consequently, control of the misfit strain is an effective method to improve the pyroelectric property which may open more opportunities for practical applications. In view of this, two

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kinds of substrates are suggested as the candidates for (001) oriented KNbO3 film. (001) MgAl2 O4 single crystal, Pb(Zr0.52 Ti0.48 )O3 layer buffered MgO or SrTiO3 substrates have the lattice constants of a=8.085 ˚ A and a≈4.06 ˚ A which can generate an in-plane misfit strain of ∼7×10−3 in KNbO3 film with the cubic lattice parameter of 4.016 ˚ A or 4.03 ˚ A, respectively.[29−32] The misfit strain of ∼7×10−3 is near the strain which corresponds to the maxima of piezoelectric and pyroelectric properties and may result in the large piezoelectric

4.Conclusion

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and pyroelectric properties in (001) oriented KNbO3 film based on the theoretical results.

In summary, the “misfit strain-temperature“ phase diagram is constructed by using the eighth-order phenomenological Landau-Devonshire theory. Three ferroelectric phases are sta-

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ble at room temperature. The ferroelectric, dielectric, piezoelectric, and pyroelectric properties are investigated with the effects of misfit strain and electric field. These properties

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strongly depend on the misfit strain and electric field. The γ phase of KNbO3 film grown on tensile misfit strain has the larger piezoelectric and pyroelectric coefficients than that of c phase which has the compressive strain. Strain engineering is an effective way to improve the piezoelectric and pyroelectric properties by choosing the appropriate substrates. Two kinds of substrates are suggested as the candidates. On the other hand, the applied electric field decreases the dielectric, piezoelectric, and pyroelectric properties. This work can provide useful guidance for further experimental researches.

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Acknowledgments This project is supported by the National Natural Science Foundation of China (Grant

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No. 51702024), Priority Academic Program Development of Jiangsu Higher Education Institutions, Research Fund of Jiangsu Province Cultivation Base for State Key Laboratory of Photovoltaic Science and Technology, Major Projects of Natural Science Research in Jiangsu Province 15KJA43002 and 16KJD430006, and China Postdoctoral Science Foun-

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dation 2017M611719.

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TABLE I: Parameters used for calculation of thermodynamic potential for (001) oriented KNbO3

Coefficient

This work

4.273×105 ×(T-377) C−2 m2 N

α1

-6.36×108

C−4 m6 N

α12

9.66×108

C−4 m6 N

α111

2.81×109

α112

-1.99×109

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α11

C−6 m10 N

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C−6 m10 N

6.03×109

C−6 m10 N

1.74×1010

C−8 m14 N

5.99×109

C−8 m14 N

2.50×1010

C−8 m14 N

-1.17×1010

C−8 m14 N

Q11

0.12

m4 C2

Q12

-0.053

m4 C2

Q44

0.052

m4 C2

s11

4.6×10−12

m2 N

s12

-1.1×10−12

m2 N

s44

11.1×10−12

m2 N

α123 α1111 α1112 α1122

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α1123

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Unit

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film.

Figure Captions

Fig. 1: The “misfit strain-temperature“ phase diagram of (001) oriented KNbO3 film. All the phase transitions are of the second order. Fig. 2: The effects of misfit strain and electric field on the polarization components Pi (i=1-3) in (001) oriented KNbO3 film. The electric field is applied along [001] direction. 13

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Fig. 3: The misfit strain dependence of dielectric constants εii (i=1-3) with the effect of electric field in (001) oriented KNbO3 film. The electric field is applied along [001] direction.

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Fig. 4: The longitudinal piezoelectric coefficient d33 of (001) oriented KNbO3 film with the effects of misfit strain and electric field. The electric field is applied along [001] direction. Fig. 5: The pyroelectric coefficient p of (001) oriented KNbO3 film as a function of misfit

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strain. The electric field is applied along [001] direction.

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1400

1000

para

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800 600 400

aa

c

200 0 -200 -15

-10

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0

Temperature--T ( C)

1200

-5

0

5

Misfit strain--u

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m

15

10

-3

(10 )

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Fig. 2 0

E=0 KV/cm

E=50 KV/cm

E=100 KV/cm

0.4

P

E=200 KV/cm

3

0.3 P = P

2

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1

0.2

0.1

aa( )

C

0.0 -15

-10

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i

2

Polarization--P (C/m )

T=25

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0.5

-5

0

5

Misfit strain--u

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m

16

10

-3

(10 )

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Fig. 3

T=25

E=50 KV/cm E=100 KV/cm E=200 KV/cm

2000 =

33

22

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11

1000

C

0 -15

-10

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Dielectric constant--

ii

E=0 KV/cm

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3000

-5

0

5

Misfit strain--u

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m

17

aa( )

10

-3

(10 )

15

T=25

0

C

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500

E=0 KV/cm

400

E=50 KV/cm E=100 KV/cm E=200 KV/cm

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300

200

100

C

0 -15

-10

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Piezoelectric coefficient--d

33

(pm/V)

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-5

0

5

Misfit strain--u

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m

18

10

-3

(10 )

15

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0 -2

-4

T=25

-4

0

C

E=50 KV/cm

-6

E=100 KV/cm

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E=200 KV/cm

-8 -10 -12

C

aa(

-14 -15

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Pyroelectric coefficient--p (10

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2

C/m K)

Fig. 5

-10

-5

0

5

Misfit strain--u

AC C

EP

TE D

m

19

10

-3

(10 )

15

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 1

1400

0

Temperature--T ( C)

1200 1000

para

800 600 400

aa

c

200 0 -200 -15

-10

-5

0

5

Misfit strain--u

m

10 -3

(10 )

15

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Piezoelectric coefficient--d

33

(pm/V)

Fig. 4 500 T=25

0

C

E=0 KV/cm

400

E=50 KV/cm E=100 KV/cm E=200 KV/cm

300

200

100

aa( )

C

0 -15

-10

-5

0

5

Misfit strain--u

m

10 -3

(10 )

15

ACCEPTED MANUSCRIPT

Highlights

1. Piezoelectric and pyroelectric properties of (001) oriented KNbO3 film largely depend on misfit strain and electric field.

RI PT

2. Large piezoelectric and pyroelectric coefficients are obtained in γphase with the tensile misfit strain.

3. The applied electric field decreases the dielectric, piezoelectric and pyroelectric

AC C

EP

TE D

M AN U

SC

coefficients.