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Electric-Field-Induced Displacements in Pt/PZT/Pt/SiO2/Si System Investigated by Finite Element Method: Material-Constant Dependences

  • Hirotake Okino (a1), Masahiro Hayashi (a2), Takashi Iijima (a3), Shintaro Yokoyama (a4), Hiroshi Funakubo (a5), Nava Setter (a6) and Takashi Yamamoto (a7)...

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, d 33 measured by atomic force microscopy (AFM) and double beam interferometry (DBI) were the same value that was equal to intrinsic d 33 of PZT and was independent of other material constants. Under the second-best conditions, i.e. 20×t PZT < φTE for DBI and 20×t PZT < φTE < 0.5×(t sub: substrate thickness) for AFM, measured d 33 depended on only d 31, s 11, s 12 and s 13, and obeyed the Lefki's equation qualitatively. However, quantitative differences between FEM analysis and the Lefki's equation were not negligible.

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