Electric-Field-Induced Displacements in Pt/PZT/Pt/SiO 2 /Si System Investigated by Finite Element Method: Material-Const
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0902-T03-49.1
Electric-Field-Induced Displacements in Pt/PZT/Pt/SiO2 /Si System Investigated by Finite Element Method: Material-Constant Dependences Hirotake Okino1,4 , Masahiro Hayashi1 , Takashi Iijima2, Shintaro Yokoyama3, Hiroshi Funakubo3 , Nava Setter4 and Takashi Yamamoto1 1 Department of Communications Engineering, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, Japan 2 Research Institute of Instrumentation Frontier, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba 305-8568, Japan 3 Department of Innovative and Engineered Materials, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan 4 Ceramic Laboratory, Materials Institute, College of Engineering, Swiss Federal Institute of Technology – EPFL, 1015 Lausanne, Switzerland. ABSTRACT Electric-field-induced displacements of PZT film capacitor Pt/PZT/Pt/SiO2 /Si(100) were calculated by finite element method (FEM) with changing all piezoelectric and elastic constants of PZT so as to discuss how to evaluate intrinsic d 33 of piezoelectric thin films. Two kinds of conditions, namely, “ideal conditions” and “second-best conditions” are discussed. The ideal conditions indicate that the diameter of top electrode φTE is equal to or less than PZT film thickness t PZT and continuous PZT is etched to isolate the capacitor from the continuous piezoelectric film layer. Under the ideal conditions, d33 measured by atomic force microscopy (AFM) and double beam interferometry (DBI) were the same value that was equal to intrinsic d33 of PZT and was independent of other material constants. Under the second-best conditions, i.e. 20×t PZT < φTE for DBI and 20×tPZT < φTE < 0.5×(tsub : substrate thickness) for AFM, measured d33 depended on only d31 , s11 , s12 and s13 , and obeyed the Lefki’s equation qualitatively. However, quantitative differences between FEM analysis and the Lefki’s equation were not negligible. INTRODUCTION Nowadays, demands for measuring longitudinal and transverse piezoelectric constants of thin films have been growing up with interest in creating piezoelectric microelectromechanical systems (MEMSs). In fact, measuring material properties is important not only for materials research but also for designing devices using computer simulation. To evaluate longitudinal piezoelectric constants, double-beam interferometry (DBI)[1–4] and atomic force microscopy (AFM)[3, 5–8] have been employed by many researchers. Particularly, DBI has been the most precision technique to measure the electric-field-induced (EFI) displacements. On the other hand, AFM measured EFI displacements strongly depend on the ratio of top-electrode size to piezoelectric film thickness and the ratio of top-electrode size to substrate thickness.[8–10] However, AFM has also been widely utilized because AFM is easy to operate and has sufficient sensitivity. In our previous works,[9, 10] we investigated EFI displacements of PZT film capacitors in order to find out how to measure
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