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Quantitative Piezoresponse Force Microscopy: Calibrated Experiments, Analytical Theory and Finite Element Modeling

  • Lili Tian
  • Vasudeva Rao Aravind
  • Venkatraman Gopalan
Chapter

Abstract

We present quantitative experiments, analytical theory and finite element modeling­ (FEM) of vertical and lateral piezoresponse force microscopy (PFM) across a single antiparallel (180°) ferroelectric domain wall. There are three important aspects in making quantitative measurements. (1) Calibration and background subtraction of PFM displacements; (2) characterization of the tip shape and contact area; and (3) analytical theory and numerical simulations that incorporate all the relevant property tensors (dielectric, piezoelectric, and ferroelectric), tip shape, contact geometry, and the relevant physics of the feature being studied, such as the width of the wall. By calibrating the displacement of the tip, and using a reference sample, one can measure nanoscale piezoelectric coefficients, which are shown to be independent of tip size for a uniform sample. The shape of the contact area of a tip with the sample is characterized by field emission scanning electron microscopy (FE-SEM) to be disk-like. Only a true-contact with zero dielectric gap between the tip and the sample can explain the experimental PFM wall width versus tip radius measurements. Finally, in the limit of the tip disk-radius approaching zero, one can estimate the ferroelectric wall width from the vertical PFM profiles across the wall. The most complete analytical theory and finite element modeling to date are presented that can realistically simulate the PFM profile across a single wall. While vertical PFM signal agrees well with theory and simulations, the lateral PFM signal shows excellent qualitative agreement only. The experimental width of the lateral PFM signal across a wall is significantly wider than that predicted by FEM, suggesting elements of surface physics that are not captured in the current electromechanical theory of PFM.

Keywords

Finite Element Method Domain Wall Lithium Niobate Wall Width Piezoresponse Force Microscopy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors wish to gratefully acknowledge financial support from the National Science Foundation grant numbers DMR-0820404, 0602986, 0908718, and 0512165. Research was also sponsored in part by the Center for Nanophase Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Lili Tian
  • Vasudeva Rao Aravind
  • Venkatraman Gopalan
    • 1
  1. 1.Materials Science and EngineeringPennsylvania State UniversityUniversity ParkUSA

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