| Due to excellent dielectric, ferroelectric, and piezoelectric properties, ferroelectricthin films have been widely used in micro-electronics industry, such as memory, brake, andpressure sensor. Nowadays, as the requirement of the microminiaturization, intellectualizationand integration of electronic components, ferroelectric thin films have much more brighterfuture in term of their small size and good properties. It is known that the nonlinear behaviorof ferroelectric thin films is due to domain switching. However, the development of theaccurate domain switching model is still a challenging task. In addition, those films areworking in the complicated environment, and their performances are affected by thethermo-electro-mechanical coupling field. Thus, it is important and useful to develop a kindof suitable model to describe the nonlinear behavior of ferroelectric films under electric, stressand thermal multi-filed coupling loads.The spontaneous strains generated during the preparation of the ferroelectric filmswere introduced into the constitutive equations and the Gibbs free energy of a domain wasfigured out. According to the second thermodynamic law, a state with a higher Gibbs freeenergy tends to the state with a lower Gibbs free energy. The difference of the Gibbs freeenergy of two states results in the domain switching driving force. If the domain switchingdriving force reaches a certain threshold, the domain switching will occur. In a PZTferroelectrics, a domain can be switched by90°and180°, and they have different thresholds.Under applied fields, the macroscopic strain and electric displacement can be obtained byaveraging over all domains after the reorientation of possible domains.Based on the reduction in potential energy caused by the changes in spontaneous strainand spontaneous polarization, the spontaneous strain due to clamping effect and the remnantstrain induced by phase transition are taken into the piezoelectric equation, and we get animproved micro-mechanical model to simulate the electric displacement-electric field andstrain-electric field curves of lead zirconate titanate thin film under alternating electric andstatic stress fields. Not only the remanent polarization and coercive electric field but also thefield-induced strain is more close to the experimental results than those of the traditional Lumodel, and they are discussed by the interfacial mismatch, clamping effect, dipole switchingand reorientation of domains.Dielectric layer exists in the ferroelectric thin films, it is intrinsic and inevitable for the ferroelectric thin film/substrate system. It exists even in the perfect prepared ferroelectric thinfilm, and affects the nonlinear behaviors like the electric displacement-electric fieldhysteresis loops and strain-electric field butterfly shape curves. We considered the effect ofdielectric layer on the effective electric field and dielectric constant of the ferroelectric thinfilms and modeled the electric displacement-electric field hysteresis loops and strain-electricfield butterfly shape curves under electric and stress field. The simulation results areconsistent with the experimental data.To better describe the non-linear domain switching behavior under electric, stress andthermal multi-coupling loads, a constitutive model that can be used to predict the nonlinearbehavior of ferroelectric films is proposed. This model is based on the micro-mechanicalmodel in which the difference of potential energy is considered as the domain switchingdriving force. Remnant strain produced during the preparation process is taken into theconstitutive relation to describe the nonlinear behavior of ferroelectric films. The simulationresults are consistent with the experimental data and results of other models. |
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