Analyzing piezoresponse force microscopy for reconstruction of probed ferroelectric structures

Abstract

Piezoresponse force microscopy (PFM) has emerged as the tool of choice for characterizing piezoelectric and ferroelectric materials at nanoscale, yet the interpretation of PFM remains to be difficult and sometimes ambiguous. Built on earlier works, we developed a numerical integration scheme to analyze the expected PFM response in ferroelectrics with arbitrary domain configurations, with the ultimate goal to accurately reconstruct the underlying ferroelectric structure from PFM measurements. Using such technique, we demonstrated that the relationship between the effective and intrinsic piezoelectric coefficients is sensitive to a variety of factors that are intrinsic to the probed materials, and showed that the PFM mapping is not only influenced by polarization distribution on the sample surface but also three-dimensional polarization distribution inside the material. While relatively simple domain structures were used for demonstration, the approach is general, and can be applied to ferroelectrics with arbitrary polarization distributions.