Nonlinear Dynamic Analysis Of Frictional Contact On Ferroelectric Materials Via Atomic Force Microscopy

Ferroelectric materials,possessing excellent piezoelectric,ferroelectric,dielectric,pyroelectric,and nonlinear optical properties,have broadly application prospects in many areas including information,biomedicine,energy,and laser technology,et al.As the rising microminiaturization and multi-function of the ferroelectric devices,it is urgent to develop some novel techniques on ferroelectric materials and the corresponding devices at the micrometer or even nanometer scale.Atomic force microscopy?AFM?having ultrahigh spatial resolution and sensitivity,can be widely utilized to nondestructively characterize ferroelectric domain structures,electromechanical properties,and electrocaloric effects,et al.in ferroelectric materials.Recently,AFM has been become one of the powerful tool to characterize the electromechanical performances in ferroelectric materials and devices.However,the roughness between the interfaces of scanning probe and ferroelectric material,makes the existence of frictional contact between them under contact mode AFM experiment.This frictional contact problem can be transformed to be the dynamic frictional contact via the dynamic multi-physical excitations,which leads to a great challenge on analyzing the electromechanical responses in ferroelectric materials.In this thesis,we study the static and dynamic frictional contact,and nonlinear dynamic of micro-cantilever using the developed the finite element analysis?FEA?methods during the AFM experiment.Wherein the electromechanical responses including displacements,potentials and resonances frequencies,are carried out to investigate their correlations among the friction coefficient,external mechanical and electrical loadings,geometry of the probe tip.The main works and conclusions are summarized as the follows.?1?Based on the contact mode AFM,the FEA method is applied to analyze the electromechanical responses in BaTiO₃ under different fiction coefficient,external loadings,and geometries of probe tips.The investigations demonstrate that the lateral friction force breaks the asymmetry of electro-elastic fields in BaTiO₃.And the non-asymmetry is much more obvious while the indentation depths barely change as increasing the friction coefficients.Under the identical mechanical loadings,the indentation depths and potential responses induced by the circular tip are larger than those induced by the punch tip.Furthermore,the asymmetry of electro-elastic fields are not likely to be broken under circular tip in AFM experiment.?2?We develop the FEA method based on the dynamic mechanical and electrical loadings,to simulate and analyze the point and scanning dynamic measurement in piezoresponse force microscopy?PFM?experiment.Our results show that the frictional contact between the probe and BaTiO₃ thin film has slight influences on the electro-elastic fields during the indentation.However,the lateral friction force easily breaks the asymmetry of electro-elastic fields as the AFM probe scanning over the BaTiO₃ thin film.?3?Based on the nonlinear dynamic theory of the micro-cantilever under the frictional contact,a spring oscillator is applied to approximate the complex interactions between the probe and BaTiO₃ material.Moreover,the FEA method is adopt to study the effects between the resonance vibration behaviors of the micro-cantilever and friction force under contact mode AFM experiment.Our results show that the bending mode resonant frequencies are not influenced by the friction coefficients,however,these friction coefficients have strong effects on the torsional modes resonant frequencies.And the influences of the elastic constants are obviously larger than dielectric and piezoelectric constants on resonance frequencies,which infers us that the dielectric and piezoelectric constants might be hard to resolve through the AFM measured resonance frequencies.Meanwhile,it suggests us that resolving the elastic constants and friction coefficients can be possible through AFM measured resonance frequencies.These studies provide the significant guidelines on quantitative analysis of the electromechanical responses in ferroelectric materials under static and dynamic multi-physical excitations.Meanwhile,the investigations on the nonlinear dynamic of the micro-cantilever suggest us to construct the direct relations between the AFM responses and intrinsic material properties as well as friction coefficients,which lays the foundations for resolving the materials properties and microstructures through measured electromechanical responses in ferroelectric materials under AFM experiment.