Shape of piezoelectric hysteresis loop for non-ferroelastic switching
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C10.6.1
Shape of piezoelectric hysteresis loop for non-ferroelastic switching. A.K. Tagantsev, P. Muralt, and J.Fousek1 Ceramics Laboratory, Swiss Federal Institute of Technology, EPFL, 1015 Lausanne, Switzerland 1 Department of Electrical Engineering and Electromechanical Systems, Technical University of Liberec, CZ-46117 Liberec, Czech Republic ABSTRACT A simple theory for the shape of the piezoelectric hysteresis loops (piezoelectric coefficient d vs. applied electric field E) is developed for the case of non-ferroelelastic 1800 switching in ferroelectrics. The theory provides explanations for specific features of piezoelectric hysteresis loops, which have been observed in single crystals, thin films and in ceramics in particular. The piezoelectric coefficient may show a “hump”, i.e. when E decreases from the tip of the loop down to zero, d passes through a maximum, and a “nose”, i.e. a self-crossing of the loop close to its tips. The theory also explains the difference in the coercive fields seen in the polarization and piezoelectric loops.
INTRODUCTION Polarization hysteresis is a key property of ferroelectrics. It originates from the irreversible character of polarization switching. This irreversibility also manifests itself in the field dependences of other parameters like the dielectric constant or the piezoelectric coefficient. Hysteresis loops of these parameters are often more convenient for experimental observation than the polarization loop. For this reason the former are often used for monitoring the ferroelectric switching in the material. The piezoelectric d ij (E ) loop has become very popular especially for the characterization of ferroelectric thin films. Such loop is a small signal converse piezoelectric response as a function of a larger dc-field. To take this loop, the applied electric field E (t ) = E 0 (t ) + Eω cos ωt is composed of a slowly varying field E 0 (t ) with a triangular profile and a period >> 2π / ω , and a small sinusoidal signal whose amplitude Eω is much smaller than E 0 . One component of the field-induced deformation of the sample, u (t ) , is monitored. Then, the corresponding piezoelectric coefficient d is determined as d ( E 0 ) = u ω / Eω
where uω is the amplitude of the first harmonics of the field-induced deformation. The shape of the piezoelectric loops ( d vs. E0 ) is sometimes similar to that of typical polarization loops ( P vs. E0 ). However, often the shapes of polarization and piezoelectric loops are qualitatively different. The piezoelectric loop may have a “hump”, i.e. when E decreases from the tip of the loop down to zero, d passes through a maximum and a “nose”, i.e. a selfcrossing of the loop close to its tips. Examples of piezoelectric loops with a hump and a nose are shown in Fig.1. These features have been observed for single crystalline samples[2, 3], thin films
C10.6.2
60
40
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33
d (pm/V)
20
-20
"nose"
-40
"hump"
-60 -400 -300 -200 -100
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100
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Electric field (kV/cm)
Figure 1. Measured d 33 loop of a 300 nm thick PZT45
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