The purpose of this paper is to develop a direct method to measure e31 of PZT thin films regardless of the boundary conditions of the specimens. The experimental setup consists of a silicon beam with a PZT film excited by a tiny shaker. A charge amplifier detects the charge accumulated in the PZT film. A spectrum analyzer processes the charge amplifier’s output to obtain a frequency spectrum. In addition, three calibration points are defined along the PZT film as 1, 2, and 3. These points are evenly spaced with distance Δx. A laser Doppler vibrometer (LDV) measures the deflection w1, w2, and w3 of the calibration points 1, 2, and 3. According to Euler-Bernoulli beam theory, the normal strain is ε ≈ 0.5h(w1 – 2w2 + w3)/(Δx)2, where h is the thickness of the cantilever. Finally, the ratio of the charge to the strain ε gives e31. Note that this approach does not depend on the boundary conditions of the specimen. Therefore, the boundary conditions do not affect the accuracy of the measurements. To demonstrate the direct measurement method, we fabricate a silicon cantilever beam with a PZT film using sol-gel processes. The dimensions of the silicon canteliver and the PZT thin film are 30 mm × 7.5 mm × 0.4 mm and 4 mm × 4 mm × 1 μm, respectively. Using the resonance amplitude of the first bending mode at 520 Hz, we obtain e31 to be 0.24 C/m2.
Direct Measurements of Transverse Piezoelectric Coefficient e31 of PZT Thin Films
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Wu, C, Lee, C, Cao, GZ, & Shen, IY. "Direct Measurements of Transverse Piezoelectric Coefficient e31 of PZT Thin Films." Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition. Microelectromechanical Systems. Anaheim, California, USA. November 13–19, 2004. pp. 79-83. ASME. https://doi.org/10.1115/IMECE2004-59421
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