Evaluation of Intrinsic Shear Piezoelectric Coefficient

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Evaluation of Intrinsic Shear Piezoelectric Coefficient d15 of c-Axis Oriented Pb(Zr,Ti)O3 Films Isaku Kanno, Kenji Akama, Kiyotaka Wasa, and Hidetoshi Kotera Micro Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan Received July 23, 2009; accepted August 18, 2009; published online xxxx yy, zz Piezoelectric shear strain was measured for c-axis oriented epitaxial Pb(Zr,Ti)O3 (PZT) thin films. The PZT films, with a composition near the morphotropic phase boundary (MPB), were epitaxially grown on (001) MgO substrates and then microfabricated into a rectangular shape by wet etching of the films. Lateral electrodes were deposited on both sides of the PZT films, to apply an external electric field perpendicular to the polarization. A sinusoidal input voltage of 100 kHz was applied between the lateral electrodes, and in-plane shear vibration was measured by a laser Doppler vibrometer. In-plane displacement due to shear mode piezoelectric vibration was clearly observed and increased proportionally with the voltage. Finite element method (FEM) analysis was conducted to determine the horizontal electric field in the PZT film, and the piezoelectric coefficient d15 was calculated to be 440 10 12 m/V. The d15 of the PZT film represents the intrinsic shear piezoelectric effect, which is slightly smaller than that of bulk PZT, due to the absence of extrinsic effects such as longitudinal and transverse piezoelectric strain or domain rotation. # 2009 The Japan Society of Applied Physics DOI: 10.1143/APEX.2.xxxxxx

iezoelectric thin films have attracted attention for applications in micro-electro-mechanical systems (MEMS) as high-sensitivity microsensors, resonators, or low-voltage microactuators.1–4) For microactuator applications, Pb(Zr,Ti)O3 (PZT) thin films are commonly used in a variety of MEMS devices and can be prepared on Si substrates because of their compatibility with well-established Si microfabrication technologies. Most piezoelectric MEMS devices have cantilever or membrane structures with facing electrodes along the thickness. For thin-film actuators, the transverse piezoelectric effect is commonly used rather than the longitudinal or shear mode piezoelectric effect because of the large anisotropic aspect ratio between the planar dimension and thickness. Therefore, measurement of the transverse piezoelectric properties is important for the design of piezoelectric MEMS devices.5–8) Also, the longitudinal piezoelectric properties are often evaluated using scanning probe microscopy (SPM).9,10) The change in thickness of thin films is easy to measure and is typically not used to develop MEMS applications, but to evaluate fundamental piezoelectric characteristics such as domain motion of epitaxial films. In contrast, it is well-known that the piezoelectric coefficient is usually large in the order of d15 > d33 > d31 . For bulk PZT ceramics with a composition at the morphotropic phase boundary (MPB), the piezoelectric coefficient d15 was reported as 494 1012 m/V, which is larger than the other piezoelectric coefficients, d33 (223 1012 m/V) and d31 (93:5 1012 m/V).11) A large value of the piezoelectric strain coefficient is useful for generating large deformation by low voltage in actuators; as a result of which, shear piezoelectric actuators using PZT bulk ceramics have already been utilized in practical products.12) The shear piezoelectric properties of thin films, however, have not been reported. The reason for this being the polarization direction always follows the external electric field along the thickness and a method of measuring the shear piezoelectric strain of thin films has not been established yet.13) To evaluate the shear piezoelectric coefficient of thin films, we prepare electrodes parallel to the polar direction and measure the generated shear displacement by an external electric field perpendicular to the polarization. Furthermore, the deformation from long-

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itudinal and transverse piezoelectric strain would usually be superimposed on conventional polycrystalline films due to off-axis polarizations.13) We eliminate their effects for the precise measurement of intrinsic shear piezoelectric effects. In this study, we measured the intrinsic shear piezoelectric strain of PZT thin films. To eliminate the piezoelectric strains of the longitudinal and transverse modes, we evaluated epitaxial PZT thin films with c-axis orientation. We applied a horizontal electric field in the direction perpendicular to the c axis of the films and measured the inplane displacement due to the shear piezoelectric strain. From the shear displacement, we calculated the intrinsic shear piezoelectric coefficient d15 of PZT thin film for the first time. A 3.5-m-thick PZT thin film with a Zr/Ti composition of around 52/48 was deposited on (001) MgO substrates by rf-magnetron sputtering. The details of the deposition conditions were provided in previous reports.7,8) In order to observe domain structure of the PZT film, we conducted both of out of plane and in-plane X-ray diffraction (XRD) measurements and results were shown in Figs. 1(a) and 1(b), respectively. In the out of plane XRD pattern, strong diffractions from the c axis of PZT were observed without the other crystal phases. On the other hand, the clear peaks from the a axis were confirmed by the in-plane XRD measurements along with the [100] direction as shown in Fig. 1(b). These results indicate that the PZT film was epitaxially grown with highly c-axis orientation and the piezoelectric effect of the a domain in the PZT film was negligible. Since the PZT films were deposited directly on MgO without bottom electrodes, we did not conduct a conventional poling treatment on the as-grown films by applying an external electric field along the thickness. However, generation of self-polarization has been reported in sputtered Pb-based ferroelectric thin films, especially in c-axis oriented epitaxial films.7,8,14,15) To observe the polarization state, the surface potential of the PZT films was observed by Kelvin force microscopy (KFM);16) topographic and potential images are provided in Figs. 1(c) and 1(d), respectively. Although some contrast was observed in the KFM image [Fig. 1(d)] corresponding to the topographic feature [Fig. 1(c)], the surface of the PZT films showed only

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Fig. 1. XRD patterns and KFM images of the PZT films on (001) MgO; (a) and (b) are out of plane and in-plane XRD patterns. The diffraction peaks of (00l) and (h00) PZT are observed in out of plane and in-plane XRD patterns, respectively, indicating epitaxial growth of the PZT films. (c) and (d) are topographic and surface potential images of the surface of the PZT films, representing the PZT films are self-polarized from the bottom to the surface.

positive potential and no area with negative potential was detected. From the results of XRD and KFM measurements, we could conclude that the polarization was aligned in the same direction from the bottom to the surface in the absence of 90 and 180 domains. In this configuration, we can observe the intrinsic shear piezoelectric effect only by preparing lateral electrodes on the side of self-polarized PZT films with perfect c-axis orientation. The PZT films were mirofabricated by wet etching with a HF and HNO3 solution, and a rectangular specimen was prepared on the MgO substrate as shown in Fig. 2. Since the wet etching of the PZT films usually accompanies side etching, we used the photo-mask with relatively large line width of 50 m. The length of the PZT sample was 2 mm and aligned to [010]. After depositing a Cr electrode over the PZT specimen, the top of the specimen was grained out to prepare for the lateral electrodes; the resulting thickness of the PZT film was 3.1 m. We observed the shape of the specimen by scanning electron microscopy (SEM) and found that its cross-section was a trapezoidal in shape, with a top and bottom width of 32 and 42 m, respectively, due to side etching in the wet etching process [Fig. 2(b)]. Although the lateral electrodes were not prepared parallel to each other, it hardly affected the generation of the uniform horizontal electric field due to relatively wide electrode spacing, as mentioned later.

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Fig. 2. Schematic illustration of the specimen; (a) overview and (b) cross-section of the specimen, respectively. The cross-section of the PZT is trapezoidal in shape, and the lateral electrodes were deposited on both sides of it. He–Ne laser beams were irradiated on the center of the specimen, and in-plane displacement along [100] was measured.

In-plane displacement was observed by a laser Doppler vibrometer (Neoark MLD-230D-200), in which two He–Ne laser beams (633 nm), with inclined angles, are focused on the center of the specimen. The laser beams were aligned to measure the piezoelectric shear vibration along the width of the specimen. To enhance the resolution of the displacement measurements, a bipolar sinusoidal voltage at a high frequency (100 kHz) was applied between the lateral electrodes. When the voltage was applied along the width of the specimen, in-plane vibration with the same frequency was clearly observed due to shear piezoelectric strain. Figure 3 shows the in-plane displacement as a function of the peak-to-peak voltage (Vpp ) of the sinusoidal signals. The

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Voltage [V] Fig. 3. In-plane displacement along [100] as a function of applied voltage. The displacement increases proportionally with voltage due to the intrinsic shear piezoelectric strain.

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Fig. 4. FEM calculations of (a) electric field and (b) deformation of the specimen at an application voltage of 150 Vpp . The uniform horizontal electric field of 4:4 106 V/m was generated at the center of the specimen by the application of 150 Vpp between lateral electrodes, and shear piezoelectric coefficient d15 is calculated to be 440 10 12 m/V.

displacement increased proportionally with the voltage, and a maximum displacement of 6.0 nm was obtained at 150 Vpp . After the measurements, we confirmed that the PZT films maintained c-axis orientation by XRD measurements. Note that as the PZT thin film was oriented along the c axis, the generated vibration was caused only by shear piezoelectric strain without longitudinal or transverse piezoelectric effects. The shear mode piezoelectric strain is expressed by =t ¼ d15 E1 ;

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where , t, d15 , and E1 are displacement, thickness, shear piezoelectric coefficient, and electric field along [100], respectively. Since the cross-section of the specimen is trapezoidal, we conducted finite element method (FEM) analysis for a precise evaluation of the electric field along [100] and the shear piezoelectric coefficient of the PZT film. First, we calculated the electric field E1 using a twodimensional model of the cross-section of the specimen. The calculation determined that the application of 150 Vpp yielded uniform horizontal electric field E1 ¼ 4:4 106 V/m at the center of the specimen, as shown in Fig. 4(a). From eq. (1), the shear piezoelectric coefficient d15 was calculated to be 440 1012 m/V. An FEM calculation of the piezoelectric strain was also conducted using the material properties of bulk PZT,11) and the resulting d15 was substituted for the value obtained above. The calculated two-dimensional deformation is provided in Fig. 4(b). Although vertical deformation near the electrodes is observed due to the distorted electric field at the edge of the specimen, the lateral displacement of the FEM simulation is consistent with that of the experiment, implying the validity of the obtained d15 value. The piezoelectric coefficient d15 of the epitaxial PZT thin films, 440 1012 m/V, is slightly lower than that of bulk ceramics. In a previous study, we measured the transverse piezoelectricity both of epitaxial PZT thin films on (001) Pt/ MgO and polycrystalline PZT on (111) Pt/Ti/Si substrates,

and demonstrated that the polycrystalline PZT films showed larger piezoelectricity than the epitaxial films due to the extrinsic effects of domain rotation.8) The shear piezoelectric coefficient d15 of the c-axis oriented epitaxial films is also caused by intrinsic shear deformation without the other piezoelectric strains or domain rotation. This is consistent with the excellent linearity of the displacement shown in Fig. 4. This study made it clear that PZT thin films also have shear piezoelectric properties compatible with those of bulk PZT ceramics, and the results should lead to new functional microdevices using the shear piezoelectric effect. In summary, we successfully evaluated the intrinsic shear piezoelectric coefficient d15 of c-axis oriented epitaxial PZT films for the first time. The PZT films were grown on (001) MgO substrates and fabricated into a rectangular shape with lateral electrodes. A sinusoidal input voltage of 100 kHz was applied between the lateral electrodes, and the in-plane vibration was measured using a laser Doppler vibrometer. In-plane vibration was clearly observed, and the displacement increased proportionally with the voltage. The horizontal electric field was calculated by FEM, and the shear piezoelectric coefficient d15 was calculated to be 440 1012 m/V. Since the PZT was a self-polarized c-axis oriented film, the generated strain is caused by the intrinsic shear piezoelectric effect without the other piezoelectric effects. Acknowledgments The authors thank Mr. Y. Kobayashi and Mr. O. Takano, Neoark Corp. for their help in the measurement of shear piezoelectric vibration using a laser Doppler vibrometer. This study was supported by the Kyoto City Collaboration of Regional Entities for the Advancement of Technological Excellence of Japan Science and Technology Agency.

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