New interest in microscopic studies of ferroelectric materials with low piezoelectric coefficient, $d_{33}^\ast$, has emerged after the discovery of ferroelectric properties in HfO2 thin films, which are the main candidate for the next generation of nonvolatile ferroelectric memory. The study of the microscopic structure of ferroelectric HfO2 capacitors is crucial to get insights into the device behavior and performance. However, a small $d_{33}^\ast$ of ferroelectric HfO2 films leads to a low piezoresponse, especially in band excitation piezoresponse force microscopy (BE-PFM). In this work, we have implemented the BE-PFM technique with an increased scanning rate, thus improving this versatile tool for weak ferroelectrics. The acceleration of measurement was achieved by focusing excitation into a narrow frequency band and tuning the central frequency on-the-fly using an online real-time model estimation by fitting a complex BE response. The tracking of the contact resonance frequency was implemented using a pure mechanical cantilever response acquired in BE atomic force acoustic microscopy. To obtain optimal excitation parameters, we perform statistical analysis by minimizing estimator variance. The measurement precision of several PFM techniques was compared both by the simulation and experimentally using a Hf0.5Zr0.5O2-based ferroelectric capacitor.

Scanning probe microscopies (SPM) have opened the window into characterization of nanoscale functionalities of a broad panoply of materials and devices. This lecture series summarizes the principles, theoretical basis, techniques, and applications of piezoresponse force microscopy and electrochemical strain microscopies, the SPM techniques based on the electromechanical detection. The image formation mechanisms, spectroscopic and excitation modes, imaging in ambient, liquid, and vacuum environments and associated artifacts are discussed, as are application to broad ranges of materials systems from ferroelectrics to energy and information technology materials to biological systems. The lectures are available at YouTube: https://www.youtube.com/playlist?list=PLS6ZvEWHZ3OPifI9LVKnHX7tK38iTltOD.

Piezoresponse force microscopy (PFM) provides a novel opportunity to detect picometer-level displacements induced by an electric field applied through a conducting tip of an atomic force microscope (AFM). Recently, it was discovered that superb vertical sensitivity provided by PFM is high enough to monitor electric-field-induced ionic displacements in solids, the technique being referred to as electrochemical strain microscopy (ESM). ESM has been implemented only in multi-frequency detection modes such as dual AC resonance tracking (DART) and band excitation, where the response is recorded within a finite frequency range, typically around the first contact resonance. In this paper, we analyze and compare signal-to-noise ratios of the conventional single-frequency method with multi-frequency regimes of measuring surface displacements. Single-frequency detection ESM is demonstrated using a commercial AFM.