The Numerical Study Of Frequency And Size Dependent Electro-mechanical Behaviors Of Ferroelectric Nano Films

Ferroelectric thin films are widely used in micro-electro-mechanical system,high-speed memories and semiconductor industry.Their unique electro-mechanical properties receive great interests in the new functional materials and micro-electrical devices applications.For example,the fast response of ferroelectric thin films,which is denoted by domain switching,is very crucial for the application of ferroelectric random access memories.In addition,many nanoscale ferroelectric devices require operations at very high loading frequencies,which will greatly affect the properties of ferroelectric thin films,even lead to the failure of devices.On the other hand,with the advancement of nano-fabrication technology and the increasing trend of the miniaturization and integration of micro-electrical devices,the ferroelectric thin films are required to be smaller in size.Such small size could bring in a lot of new problems on the property of nano films,such as the significant influence of surface and interface layers.Therefore,in order to guarantee the functional and stable performance of micro-electrical devices,it is essential to perform a systematic investigation on the effects of the electric-field frequency and the size change on the electro-mechanical properties of ferroelectric nano films.In this paper,the phase field approach based on the continuum thermodynamics framework is presented to investigate the frequency and size dependent electro-mechanical behaviors of ferroelectric single-crystalline nano films and columnar-grained nano films,respectively.The main contents are summarized as follows:(1)A two dimensional(2D)model of Ba Ti O₃ single-crystalline film epitaxially grown on a substrate is developed.The time dependent Ginzburg-Landau kinetic equation is used to evaluate the evolution of polarization vectors.Based on the model,the effects of epitaxial strain on the ferroelectric properties of single-crystalline films were studied.According to the relavent experiments,we considered the cases with either compressive or tensile strain,ranging from-3.2%to 1%.Based on the obtained hysteresis and butterfly loops,the results showed that the compressive epitaxial strain can generally enhance the remnant polarization and the coercive field,as opposed to the effect of the tensile one.We then examined the domain structure in the films under different epitaxial strains.The increase of compressive epitaxial strain can lead more polarizations aligned to the out-of-film-plane direction,and vortex structures start to appear in the film.The polarization experiences an instant 180°switch as the electric filed changes.While under the tensile epitaxial strain,more polarizations tend to align in the in-plane direction,forming a horizontal 180°domain structure.A 90°polarization switch takes place in this case.(2)We further investigated the effect of the high-strength electric-field frequency and film thickness on the electro-mechanical behaviors of Ba Ti O₃ single-crystalline film,respectively.The frequency varies from 0.1 to 100 k Hz,and the frequency response of thin films is calculated under two epitaxial-strain values,i.e.,-0.1%and-1.74%,respectively.It was found that,at low frequencies(0.1-20 k Hz),the coercive field increases sharply and the remnant polarization increases slightly with the rise of the applied frequency.Once the frequency gets higher than 20 k Hz,the coercive field increases slightly and the remnant polarization drastically reduces with the increasing frequency.In the meanwhile,the hysteresis loop exhibits an elliptic shape and the sharp tails of the butterfly loop are diminishing.We noticed that the frequency dependency is more sensitive to the epitaxial strain within the low-frequency range.Based on the obtained microstructural evolution process,we found that the 180°polarization reversal is more likely to occur under low-frequency field,while the polarization cannot be fully reversed in high-frequency hysteresis,leading to an unsaturated polarization state in the film.In the study the influence of thickness,the results showed that,as the film thickness reduces from 100 to 5 nm,the remnant polarization and the coercive field both increase.Meanwhile,the dielectric constant and the piezoelectric constant both tend to decrease as the film thickness decreases.These film-thickness dependent properties are attributed to the domain patterns which are dependent on the film thickness.It is found that multi-domains are more likely to appear in thicker films,which is easier to reverse as opposed to the mono-domain structure found in thinner films,leading to the size effects in the simulation.(3)The columnar-grained ferroelectric thin film exhibits remarkable properties due to its unique microstructures.We then turn to study the effects of frequency and size on the ferroelectric properties of Ba Ti O₃ thin films with columnar-grained microstructure.We devised a 2D thin film model with four vertically aligned columnar grains and low-permittivity grain boundaries,taking into accounts of the effects of the epitaxial strain,the defects and the low-permittivity surface layer.The simulation results showed that the frequency dependent behaviors in columnar-grained films are very similar to the ones in single-crystalline films.This is due to the fact that the frequency dependence of ferroelectric hysteresis is a result of direct competition between the speed of polarization evolution and the speed of external loading.However,the size effects in columnar-grained films are quite different with the ones in single-crystalline films,which is mainly attributed to the presence of grain boundaries with different properties from the constitute grains in columnar-grained films.The size dependence in columnar-grained films refers to two aspects,the grain-size effect and film-thickness dependence,in which the grain boundary plays different level of significance.For the study of grain-size effects,the dilution effect due to the low permittivity and paraelectric property of the grain boundary plays a major role.As the grain size decreases from 200 to 20 nm,the volume fraction of the grain boundary increases,resulting in a continuous decrease of the coercive field,remnant polarization,dielectric constant and piezoelectric constant.The underlying domain dynamics discloses that vortex structures appear at small grain size due to the strong depolarization field induced by the dead layer at grain boundaries.We further investigated the influence of film thickness,which is associated with the domain pattern and microstructure evolution induced by the interaction between the grains and grain boundaries.As the film thickness increases from 80 to 380 nm with a common grain size of 60 nm,the coercive field,remnant polarization and piezoelectric constant gradually increase while the dielectric constant decreases.The increase of film thickness leads a large number of electric polarization aligned to the polar axis,thus the remnant polarization is higher in thicker films.The increased height of grain boundaries brings more defects and results in an increased occurrence of multi-domains.It was observed that there exists two types of polarization reorientation in columnar-grained thin films.A direct 0-to-180°polar reorientation dominates the polarization switching in thinner films,whereas a gradual 0-to-90°-to-180°polar reorientation takes places in a lot more regions in films of higher thickness.The research work in this paper connects the microstructure of ferroelectric nano films to its electro-mechanical behaviors.This work provides the theoretical basis for the realization of enhanced performance of ferroelectric films with strain engineering or optimal size,and for the further application in high-frequency field.