Effects of thermal strain on electric properties of lead zirconate titanate thin films upon LaNiO3 coated base metal plates

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Effects of thermal strain on electric properties of lead zirconate titanate thin films upon LaNiO3 coated base metal plates Hanting Dong∗, Maojun Chen, Hongjun Zhu, Ye Huang, Qi Ding, Jun Feng School of Mechanical Engineering, Zhejiang Industry Polytechnic College, No.151 Qutun Road, Shaoxing, 312000, People's Republic of China

A R T I C LE I N FO

A B S T R A C T

Keywords: PZT thin films Phenomenological model Dielectric Piezoelectric

Electric properties for ferroelectric lead zirconate titanate (PZT50/50, 45/55, 40/60, 30/70) thin films on base metal plates with different thermal expansion coefficient (TEC) were calculated by a phenomenological model. Results show that when the TEC of substrates increases, dielectric constant, tunability and piezoelectric coefficient d33 of all PZT thin films with tetragonal phase are decreased due to the larger compressive thermal strain. PZT50/50 thin films deposited on smaller TEC substrates can achieve higher dielectric constant, tunability and d33. The computed dielectric constant of PZT50/50 thin films is in accordance with the measured results from sol-gel experimental process, and the trend of dielectric constant of PZT films adjacent to morphotropic phase boundary (MPB) derived from some references also agrees with that from calculation. These results suggest that higher tunability and d33 of PZT films can be obtained by choosing smaller TEC substrates.

1. Introduction Lead zirconate titanate (PZT) solid solutions with excellent dielectric and piezoelectric properties have drawn much attention for many applications, for example, piezoelectric sensors, actuators, nonvolatile memories and so on [1–4]. Especially, PZT thin films fabricated upon base metal plates, such as Ni, Ti, Cu, Al and stainless steel (SS), exhibit potentiality in MEMS/flexible devices, attracting many researchers [5–7]. Base metal plates show the superiorities in low cost and avoiding bottom electrodes preparation [8,9]. Haribabu Palneedi et al. [6] investigated magnetoelectric properties of PZT thick films deposited upon Ni foils. Hongfang Li et al. [10] fabricated PZT films upon La0.5Sr0.5CoO3 buffered SS substrates, carrying out (100)-oriented thin films. Noticeably, because of lattice mismatch and/or thermal mismatch between films and metal plates, misfit strains have significant influence on lattice, dielectric, piezoelectric and ferroelectric features of PZT solid solutions [11–14]. Therefore, it is necessary to study the relationship between misfit strains and electrical properties distinctly. Compared to experimental methods, phenomenological theoretical calculations through Landau-Devonshire (L-D) thermodynamic model can reveal the above relationship more clearly. M. J. Haun et al. [12–14] systematically investigated the phase diagrams of PZT solid solutions. J. H. Qiu et al. [15] found that by adjusting misfit strains, PZT films with the components adjacent to morphotropic phase boundary (MPB) exhibited

∗

the highest dielectric and pyroelectric response. Jung-Kun Lee et al. [16] discussed the affects of ion-beam induced strain on ferroelectric characteristics for PZT films, observing that polarization and ferroelectric fatigue resistance would be increased by compressive stress. Thermal strain of films is resulting from the difference of thermal expansion coefficient (TEC) between films and substrates, and always significantly affects electric properties of films [8,17]. However, large lattice mismatch could be relaxed by introducing buffer layers, such as LaNiO3 (LNO) [4]. In this research, dielectric constant, tunability and piezoelectric coefficient of PZT50/50, PZT45/55, PZT40/60 and PZT30/70 films on different TEC base metal plates were calculated by a phenomenological model. Tetragonal phase PZT films on cubic substrates are chose for understanding the effects of thermal strain easily. The quantitative relationships between TEC of substrates and electric features are researched. PZT50/50 films on LNO coated SS, Ni, Ti plates were also prepared by sol-gel approach, and their dielectric properties can be compared to the computed results. Meanwhile, the trend of dielectric properties of PZT films near MPB from some references was introduced for contrast. 2. Phenomenological theoretical method L-D phenomenological model can be used to study misfit strain, lattice, dielectric and piezoelectric features of epitaxial PZT films [12–14]. In Cartesian coordinate system described as x1//[100], x2//

Corresponding author. E-mail address: [email protected] (H. Dong).

https://doi.org/10.1016/j.ceramint.2019.09.165 Received 7 August 2019; Received in revised form 14 September 2019; Accepted 17 September 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Please cite this article as: Hanting Dong, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.09.165

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[010] and x3//[001], consider an epitaxial film prepared upon the substrate with cubic lattice. As a function of applied field Ei, polariza∼ tion Pi and misfit strain um, thermodynamic potential G of a monodomain polycrystalline epitaxial film could be developed as [12–15].

Table 1 The coefficients of PZT50/50, PZT45/55, PZT40/60 and PZT30/70 thin films.

∼ ∗ ∗ 4 G = a1∗ (P12 + P22) + a3∗ P32 + a11 (P14 + P24 ) + a33 P3 ∗ ∗ 2 2 + a13 (P12 P32 + P22 P32) + a12 P1 P2 + a111 (P16 + P26

+ P36) + a112 [P14 (P22 + P32) + P34 (P12 + P22) + P24 (P12 + P32) ⎤ + a123 P12 P22 P32 + ⎥ ⎦ − (E1 P1 + E2 P2 + E3 P3).

2 um S11 + S12

(1)

Coefficient

PZT50/50

PZT45/55

PZT40/60

PZT30/70

Tc C a11 a12 S11 S12 S44 Q11 Q12 Q44

392.6 4.247E+05 4.764E+07 1.735E+08 1.05E-11 −3.70E-12 2.87E-11 0.0966 −0.0460 0.0819

405.5 3.456E+05 4.189E+07 2.484E+08 9.55E-12 −3.25E-12 2.50E-11 0.0889 −0.0378 0.0745

418.4 2.664E+05 3.614E+07 3.233E+08 8.60E-12 −2.80E-12 2.12E-11 0.0812 −0.0295 0.0671

440.2 1.881E+05 6.458E+06 5.109E+08 8.40E-12 −2.70E-12 1.75E-11 0.0789 −0.0248 0.0636

In Eq. (1), the renormalized coefficients are calculated via

a1∗ = a1 − um ∗ a11 = a11 + ∗ a33 = a11 + ∗ a12 = a12 − ∗ a13 = a12 +

Q11 + Q12 , S11 + S12

a3∗ = a1 − um S

2Q12

11 + S12

,

2 + Q 2 ) S − 2Q Q S (Q11 11 12 12 12 11 , 2 − S2 ) 2(S11 12 2 Q12

S11 + S12

,

2 + Q 2 ) S − 2Q Q S (Q11 11 12 11 12 12 2 − S2 S11 12

+

4 Q44

2S44

,

Q12 (Q11 + Q12) . S11 + S12

(2)

where a1, aij and aijk are the different degree dielectric stiffness coefficients. The temperature dependent dielectric stiffness a1 is expressed as a1=(T-TC)/2ε0C, where C is Curie-Weiss constant, TC is Curie-Weiss temperature and ε0 is the dielectric constant of free space [12–19]. In Eq. (2), Sij are the elastic compliances and Qij are the electrostrictive coefficients. Thermal misfit strain uT is given by Ref. [17].

Fig. 1. TEC of substrates dependent thermal misfit strain uT of PZT thin films.

TG

uT (TG ) =

∫ (αf − αs) dT , T

3. Calculated results and discussions

(3)

where αs is the TEC of substrate, and αf is the TEC of film. For c phase, dielectric constant along [001] as a function of E3 can be computed by ε33 (E3) ε0

=

Fig. 1 shows TEC of substrates dependent thermal misfit strain of PZT50/50, PZT45/55, PZT40/60 and PZT30/70 thin films. TEC values corresponding to some common kinds of base metal substrates are also intuitively exhibited in Fig. 1. When the TEC of substrates is smaller than that of PZT thin films, thermal misfit strain uT of PZT thin films with each components is gradually decreased with the increased TEC, and the corresponding strain is tensile; for commonly used substrates, such as Ti, Ni, Cu, SS, Al, their TEC is larger than that of PZT solid solution, thus, uT of PZT films is gradually increased with the increased TEC, and the strain is compressive. Therefore, compressive thermal strain in PZT is more concerned. For example, uT of PZT films respectively on Ti, Ni and SS plates is −0.029%, −0.180% and −0.330%, which belongs to compressive strain. When the TEC of substrates changes from 0 to 25 × 10−6/ °C, the phase of each PZT thin films is always c phase either uT is tensile or compressive by phenomenological theoretical calculation. This phenomenon can be attributed to the lowest free energy of c phase for thermodynamic equilibrium state at such conditions [12–15]. Therefore, the polarization along [100] and [010] is zero, that is P1]P2=0. Fig. 2 carries out TEC of substrates dependent polarization P3 (along [001]) in PZT thin films. P3 in PZT films with each components is gradually increased with the increased TEC of substrates. For PZT50/ 50, P3 of the films respectively upon Ti, Ni and SS is 27.1, 31.9 and 36.1 μC/cm2. This is because the lattice of PZT thin films will be stretched along [001] under in-plane compressive thermal stress, and thus P3 is increased. Moreover, P3 in the films rises with the reduced ratio value of Zr/Ti in PZT solid solutions, meaning PZT films with smaller ratio value of Zr/Ti have stronger c/a ratio. Fig. 3 exhibits TEC of substrates dependent dielectric constant ε33/ ε0 of PZT thin films. It is observed that dielectric constant of PZT films with each components is reduced when the TEC of substrates increases, indicating that PZT films prepared on smaller TEC plates can obtain

2 ∼ −1

∂ G = ⎛ε0 ∂P 2 ⎞ 3 ⎠ ⎝

1 ∗ (P 2 + P 2) + 6a ∗ P 2] . 2ε0 [a3∗ + a13 1 2 33 3

(4)

The corresponding tunability nr is usually described as

nr =

ε (E = 0) − ε (E ) . ε (E = 0)

(5)

The piezoelectric coefficient along [001] d33 is calculated by

d33 = 2ε0 η33 Q11 P3,

(6)

where ηij = Aij /Δ is the dielectric susceptibility coefficient, Aij and Δ are the cofactor and determinant for relative dielectric stiffness tensor [12–19]. The coefficients of PZT50/50, PZT45/55, PZT40/60 and PZT30/70 thin films are based on some available references [12–14] and are meanwhile presented in Table 1. The six-order terms of polarization in the expansion equation for free energy can be neglected in the calculation [17–19]. Besides, film thickness effect should be considered for the films with several hundreds nanometers thickness [14,17]. In our calculations, the film thickness is set as 600 nm. The range of TEC is from 0 to 25 × 10−6/ °C, which contains almost all TEC values of base metal substrates. The TEC of PZT thin films is ~7.26 × 10−6/ °C [17]. The annealing temperature of the films is 650 °C. The applied field for calculating tunability is set as 300 kV/cm. Thus, thermal misfit strain uT, polarization P3, dielectric constant, dielectric tunability and piezoelectric coefficient d33 as a function of TEC of substrates are calculated by the above phenomenological model. 2

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Fig. 2. TEC of substrates dependent polarization P3 of PZT thin films. Fig. 5. TEC of substrates dependent piezoelectric coefficient d33 of PZT thin films.

Fig. 3. TEC of substrates dependent dielectric constant ε33/ε0 of PZT thin films.

Fig. 4. TEC of substrates dependent tunability nr of PZT thin films. Fig. 6. XRD patterns of PZT50/50 thin films respectively on LNO coated SS, Ni and Ti plates (a) and their (110) peaks (b).

larger dielectric constant. For PZT50/50 thin films, dielectric constant of the films respectively upon Ti, Ni and SS is 534, 386 and 302. Also, for PZT with relatively larger ratio value of Zr/Ti, which are relatively near MPB, the dielectric constant would be higher, and the change of TEC of substrates dependent dielectric constant is more significant. For example, when the TEC of substrates changes from 0 to 25 × 10−6/ °C, dielectric constant of PZT50/50 is the highest and meanwhile its change is the largest, which is from 1557 to 228. On the contrary, the corresponding variety of dielectric constant for PZT30/70 is only from 269 to 163. Fig. 4 presents TEC of substrates dependent tunability of PZT thin films. The trend of tunability for PZT films is quite similar to that of dielectric constant as seen in Fig. 3. If PZT films are coated on the substrates with smaller TEC, larger tunability can be obtained. For PZT50/50 thin films, tunability of the films respectively upon Ti, Ni and SS is 39.7%, 31.0% and 25.3%. Besides, the change is also more

remarkable for PZT with relatively higher Zr/Ti ratio. TEC of substrates dependent piezoelectric coefficient d33 of PZT thin films is presented in Fig. 5. It is seen that, for each components of PZT films, piezoelectric coefficient d33 is reduced with the increase of the TEC of substrates. Higher dielectric constant, tunability and d33 can be attributed to smaller compressive thermal strain caused by smaller TEC of substrates, as shown in Fig. 1. This regularity is also in accordance with other ferroelectrics, such as barium strontium titanate (BST), BiFeO3, KNbO3 [20–24]. It is also found that PZT50/50 can achieve higher d33 when substrates with smaller TEC are used; while when the TEC of substrates (as Al) is very large, PZT30/70 have relatively higher d33.

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strain in Fig. 1. Dielectric constant of PZT50/50 thin films respectively on LNO coated SS, Ni and Ti plates is shown in Fig. 7. Dielectric constant of PZT50/50 is gradually decreased when the TEC of substrates increases. It reveals that the computed dielectric constant of PZT50/50 films is in accordance with the experimental results. This implies that greater thermal stress caused by larger TEC of substrates leads to lower dielectric response and the dielectric properties can be investigated via thermodynamic theoretical calculation. For more compare, dielectric constant of PZT films at MPB on LNO coated base metal substrates from references is also exhibited in Table 2. Due to the components adjacent to MPB, dielectric constant of such PZT from references is higher than that of PZT50/50. Although fabricating methods, film thickness, annealing temperature and even electrodes have obvious affects on dielectric response of PZT films, the trend of dielectric constant for PZT at MPB is quite similar to that of PZT50/50 films as shown in Fig. 7. Such results suggest that dielectric properties of ferroelectric films upon LNO coated metal plates can be predicted by phenomenological model.

Fig. 7. Dielectric constant of PZT50/50 thin films respectively on LNO coated SS, Ni and Ti plates. Table 2 Dielectric properties of PZT films near MPB on LNO coated base metal substrates from references. Substrates

Ti Ti Ni Ni SS

Zr/Ti ratio

Thickness/μm

52/48 53/47 52/48 52/48 52/48

8 0.25 0.9 0.6 4.5

Dielectric constant (@ 10 kHz)

Reference

~860 ~760 ~740 ~700 ~620

[25] [26] [27] [28] [29]

5. Conclusion Electrical properties of PZT50/50, PZT45/55, PZT40/60 and PZT30/70 thin films on base metal plates as the function of TEC of substrates were computed via the phenomenological model. It can be concluded that dielectric constant, tunability and d33 for all PZT films are decreased with the increased TEC of substrates. PZT50/50 thin films upon substrates with smaller TEC exhibit larger dielectric constant, tunability and d33. The calculated dielectric constant of PZT50/50 films agrees well with the sol-gel method derived tested data, and the trend of dielectric constant of PZT at MPB from references is also in accordance with that of computed results. Such results suggest that higher dielectric constant, tunability and d33 of ferroelectric films can be obtained by choosing smaller TEC substrates.

4. Experimental processes and results In order to verify the calculated results, PZT50/50 thin films respectively upon LNO coated Ti, Ni and SS substrates were fabricated via sol-gel approach. Tetrabutyl titanate [Ti(OC4H9)4], zirconium n-propoxide [Zr(OC3H7)4] and lead acetate [Pb(CH3COO)2] were prepared as crude materials, and 2-methoxy-ethanol and acetic acid were applied as solvents for preparing PZT50/50 precursor solution at 0.4 mol/L concentration. At 0.1 mol/L concentration, LNO precursor solution was obtained by nickel nitrate hexahydrate, Lanthanum nitrate hexahydrate, polyvinyl alcohol, H2O and acetic acid. The films were deposited on metal plates through spin-coated and annealing process. LNO precursor solution was firstly spin-coated upon cleaned substrates layer by layer to 150 nm, and then the films were crystallized at 700 °C. Repeated spin-coated process, PZT precursor solution with the thickness of 600 nm was coated on the crystallized LNO films. Finally, the annealing temperature for the films is 650 °C. The phase structure of the films was examined through X-ray diffraction (DLMAX-2200). For testing electrical properties, 0.4 mm diameter Au electrodes were sputtered on the film surface. Agilent 4294A Precision Impedance Analyzer was applied to check dielectric features. Fig. 6 presents XRD patterns of PZT50/50 films respectively upon LNO coated SS, Ni and Ti plates. Combining the calculated results, the phase structure of all films probably is the pseudo-cubic perovskite structure, although it seems to be the cubic structure. Besides the peaks of metal plates, no other phase structures can be observed from the XRD patterns, indicating that the films are crystallized well. The peaks of LNO films are not seen because of their weak peaks and relatively small thickness [8,9]. From Fig. 6(b), it can be found that (110) peak of PZT films is moved to lower angle with the increased TEC of substrates. When PZT thin films are under larger compressive thermal stress caused by bigger TEC of substrates, the lattice would be in-plane reduced and out-of-plane increased. Finally, the lattice volume is enlarged [12–14], bringing about the (110) peak moving to lower angle. Thus, (110) peak of PZT thin films on Ti plates exhibits highest diffraction angle. This qualitative analysis agrees well with the tendency of calculated thermal

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