Quantitative Analysis Of The Nanoscale Piezoelectric Deformation Of Ferroelectric Domains

Ferroelectric materials have superior physical properties and a broad prospect of application due to the unique microscopic domain structures, which have attracted a lot of attentions. Piezoresponse force microscropic(PFM), as an important tool for characterizing the ferroelectrics at nanoscale, is widely used for the investigation of ferroelctric domains. However, the inhomogeneous domains, the highly localized electric field induced by SPM tip, and the long range electroelastic interactions between the SPM tip and probed sample make the quantitative analysis of the deformation tested by PFM difficult, which seriously hinders the study of the electromechanical coupling of ferroelectrics at the nanoscale and slows down the development of the electronic devices underpinned by the nanoscale electromechanical coupling. In this thesis, we quantitatively analyze the effects of ferroelectric domains, inculding domain size, domain wall and its thinckness, on the nanoscale piezoelectric deformation. It consists of the following major aspects:Firstly, we have established the theory model for the analysis of nanoscale piezoelectric deformation in ferroelectrics with complex domain patterns. The tip-induced electric filed has been determined using the method of image charge. Considering the polarization directions of the complex domain structures and the inhomogeneous distributions of the piezoelectric tensor, the nanoscale piezoelectric deformation of ferroelectrics has been derived from the solutions of elastic constitutive equations via Green function method. The thoery model can provide the theoretical foundations for the analysis of the effects of domain size and domain wall on the nanoscale pizeoresponse.Secondly, we have analysized the nanoscale piezoresponse around the domain walls, and revealed the mechanisms of its abnormal nanoscale piezoelectric deformation. The analysis results show that the out-of-plane uncharged domains have abnormal in-plane piezoresponse at domain walls, while the in-plane charged domain have abnormal out-of-plane piozeresponse at domain walls. The broken antisymmetry of the long range electroelastic constraint induces the in-plane piezoresponse in the out-of-plane uncharged domains, while the discontinuity of the in-plane piezoelectric displacement induces the the out-of-plane piezoresponse in the in-plane charged domains.Thirdly, we have analysized the effects of domain wall thickness on the nanoscale piezoelectric deformation of the ferroelectric domains, and suggested that the enhancement of electromechanical coupling at nanoscale can be realized by increasing the domain wall thickness. We treated the domain wall as a piezoelectric medium, whose piezoelectric coefficients are depended on the domain wall thickness and piezoelectric coefficients of adjacent domains. It is found that increasing the domain thickness can enhance the lateral piezoresponse force microscopy response of uncharged 90° domains and vertical piezoresponse force microscopy response of charged 90° domains, suggesting a new method that increasing the domain wall thickness enhances the electromechanical coupling in ferroelectrics at nanoscale.Fourthly, we have analysized the effects of the domain size, the tilted domain wall and the domain wall thickness on the nanoscale piezoelectric deformation of the periodic ferroelectric domains. Through the analysis of ferroelectric domains with the periodic polarization variation, we observed that the tilted domain wall breaks the symmetry of the nanoscale piezoresponse, but it does not change the periodic variation of the nanoscale piezoresponse. It is also found that the ferroelectrics should have the suitable domain size for simultaneously keeping the good eletrochemical properties and small fluctuation.Based on the above analysis, we have quantitatively analyzed the nanoscale piezoresponse of ferroelectric domains. Those works provide good theoretical foundations and guidance for the application and development of PFM, and also suggest some new methods for the preparation of ferroelectrics with excellent nanoscale piezoelectric properties.