Analyzing Nanoscale Electromechanical Coupling Of Ferroelectrics As Probed By PFM

Piezoelectrics and ferroelectrics possess excellent electromechanical properties, and have been widely used in microelectromechanical systems. In recent years, piezoresponse force microscopy (PFM) has been developed as a powerful tool to nondestructively characterize piezoelectrics and ferroelectrics at the nanoscale. However, the interpretation of PFM data remains to be difficult, especially in the aspect of quantitative analysis. Using decoupled and fully coupled methods, we carry out the quantitative analysis of PFM in this dissertation, including the electroelastic field, the piezoelectric coefficient, imaging of static ferroelectric domains, and the spatial resolution of PFM on ferroelectric nanostructures, based on decoupled and fully coupled method developed by us. It consists of the following major aspects:Firstly, we have developed the decoupled and fully coupled methods to quantitatively determine the electroelastic field between the conductive SPM tip and the specimen. On one hand, a numerical scheme is proposed to analyze the electroelastic field in ferroelectrics with arbitrary domain configurations. On the other hand, we have developed a rigorous analysis of PFM using the Hankel integral transform and the effective point charge model, which fully accounts for the electromechanical coupling of the transversely isotropic piezoelectric medium. With regard of the geometry of probes, different tip models are considered under fully coupled method. It is concluded that both the electric field and displacement underneath an SPM probe are highly localized. Comparing results between coupled and decoupled analysis, it is evident that the potential from the coupled method decays faster away from the probe, resulting in larger electric field near the probe tip, yet smaller displacement. Although the localized electric fields are distinct under different tip models, the corresponding displacements show similar variation.Secondly, two novel methods are proposed to accurately determine the actual piezoelectric coefficient d33at the nanoscale, under contact and non-contact modes of PFM experiments. Since the rotational symmetry of an electric field induced by PFM can be broken and tuned by using multiple tips, a double-tip PFM measurement method is proposed to quantitatively determine d33. Moreover, the correlation between effective piezoelectric coefficient and intrinsic materials properties as well as experimental parameters is established, which enables us to determinate the intrinsic piezoelectric coefficients through PFM measurement using inverse calculations. The results show that the piezoelectric coefficient can indeed be accurately determined by using double-tip method or inverse calculation method.Thirdly, we have developed a numerical integration method to simulate the PFM mapping on static ferroelectric domain structures, based on the decoupled method. Our results demonstrate that PFM mapping is not only influenced by polarization distribution on the sample surface but also three-dimensional polarization distribution inside the material. This suggests that all of the VPFM and LPFM signal are required for reconstruction of3D ferroelectric domain structures.Finally, a numerical approach has been developed to study the spatial resolution of PFM in resolving ferroelectric nanostructures, capable of analyzing complicated domain patterns with arbitrary three-dimensional heterogeneity. It is found that spatial resolution of PFM is not limited by probe tip radius, but by a nominal domain wall thickness resulted from the long-range electroelastic interactions between the tip and the probed samples. It is also shown that vertical PFM has better spatial resolution than lateral one, and probing ferroelectric nanostructures underneath of the sample surface is also possible. General agreements with experimental observations are also noted.We have quantitatively analyzed the electromechanical couplings in ferroelectrics at the nanoscale, using our developed decoupled and fully coupled method. It has laid the foundation for solving hetergeneous ferroelectrics and dynamic evolution of ferroelectric domain structures.