Band Excitation Piezoresponse Force Microscopy Adapted for Weak Ferroelectrics: On-the-Fly Tuning of the Central Band Frequency.

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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.