Top electrode size effect on hysteresis loops in piezoresponse force microscopy of Pb(Zr,Ti)O ₃-film on silicon structures

Abstract

Experimental and theoretical studies of hysteresis loops in piezoresponse force microscopy (PFM) directed on elucidating the influence of top electrode lateral sizes on loop peculiarities were performed for Pt/Pb(Zr,Ti)O₃/Pt/TiO_x/SiO₂/Si-substrate structures. The set of top Pt electrodes (50nm to 10μm of lateral size) was deposited on the Pb(Zr_xTi_1-x)O₃ film (x=0.54, thickness ≈1μm) by RF magnetron sputtering. Under approaching the top electrode lateral size to the film thickness, the transition-like behaviour of PFM response amplitude and coercive tip voltage was observed. The existence of the critical value of dimensionless electrode size parameter γd/h≈1 (γ is the dielectric anisotropy factor, d is the electrode size parameter, and h is the film thickness) was interpreted in the framework of the model based on Landau-Ginzburg-Devonshire theory combined with the decoupling approximation subject to the nonlinear electric field dependence of the ferroelectric polarization and dielectric permittivity.