a piezoelectric crystal is caused mainly due to 90° switching of domains that are in a metastable state [17]. Higher applied stresses impose greater mechanical constraint on domains that could undergo 90° switching thereby lowering the number of domains that cause hysteresis at ~200 MPa when the remnant polarization is identical on both sides of hysteresis loop. Symmetrical butterfly loops would imply equal number of domains able to remain polarized in each direction and depend on the film thickness, residual stresses and the fabrication conditions. 0 100 200 300 400 500 600 700 -10 -5 0 5 10 Voltage (V) Stress (MPa) Figure 5. Electric field induced stress hysteresis loops for a PZT stack. 4. CONCLUSIONS In this paper, the mechanical and piezoelectric behavior of PZT films was investigated. The stress vs. strain curve of the PZT composite was nonlinear due to domain switching at strains larger than 0.35%. The initial modulus of PZT at up to 0.3% strain was extracted from the stress vs. strain curves of SiO2, SiO2-TiPt, SiO2-TiPt-PZT, and SiO2-TiPt-PZT-Pt freestanding films, by using simple lamination theory, as 84±2 GPa with the failure strength averaging 510±35 MPa, after accounting for the residual stress in the PZT layer The same PZT stack films were employed to measure the piezoelectric coefficient d31 and to quantify their hysteretic response as a function of applied pre-stress. A multilayer beam bending model was used to calculate an estimate for the d31 coefficient as 176±27 pm/V. The alternating electric field induced stress hysteresis “butterfly” loops that were asymmetric at smaller applied stresses, became symmetric at applied stresses beyond 300 Mpa which corresponded to the stress at which the PZT films showed elastic softening. Due to a change in the number of domains that switched with applied stress, the intersection of the hysteresis loops shifted from the negative to positive electric field at about 200 MPa of applied pre-stress. This non-linear electromechanical behavior has a significant effect on the performance of MEMS devices when operated at hundreds of MPa applied stresses due to the inaccurate estimate of stress and strain associated with the application of a combination of a voltage bias and a mechanical stress. 265
RkJQdWJsaXNoZXIy MTMzNzEzMQ==