Functionality of biological and inorganic systems ranging from nonvolatile computer memories and microelectromechanical systems to electromotor proteins and cellular membranes is ultimately based on the intricate coupling between electrical and mechanical phenomena. In the past decade, piezoresponse force microscopy (PFM) has been established as a powerful tool for nanoscale imaging, spectroscopy, and manipulation of ferroelectric and piezoelectric materials. Here, we give an overview of the fundamental image formation mechanism in PFM and summarize recent theoretical and technological advances. In particular, we show that the signal formation in PFM is complementary to that in the scanning tunneling microscopy (STM) and atomic force microscopy (AFM) techniques, and we discuss the implications. We also consider the prospect of extending PFM beyond ferroelectric characterization for quantitative probing of electromechanical behavior in molecular and biological systems and high-resolution probing of static and dynamic polarization switching processes in low-dimensional ferroelectric materials and heterostructures.

Piezoresponse force microscopy (PFM) and spectroscopy of domain structure and switching dynamics at small excitation voltages require resonance enhancement of the surface displacements. The contact stiffness depends strongly on local elastic properties and topography resulting in significant variations of the resonant frequency. Moreover, the resonant response is determined both by the Q factor and the electromechanical activity. Here we develop a resonance-enhanced PFM that allows mapping of the local electromechanical activity, contact stiffness, and loss factor, thus avoiding limitations inherent to conventional frequency tracking. We anticipate that this method will be instrumental in imaging weakly piezoelectric materials and probing inelastic phenomena in ferroelectrics.

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Shifts in the resonance frequencies of surface-coupled atomic force microscope (AFM) probes are used as the basis for the detection mechanisms in a number of scanning probe microscopy techniques including atomic force acoustic microscopy (AFAM), force modulation microscopy, and resonance enhanced piezoresponse force microscopy (PFM). Here, we analyze resonance characteristics for AFM cantilever coupled to surface in liquid environment, and derive approximate expressions for resonant frequencies as a function of vertical and lateral spring constant of the tip-surface junction. This analysis provides a simplified framework for the interpretation of AFAM and PFM data in ambient, liquid, and vacuum environments.