Needle in a Haystack: Information Recovery in Low Signal-to-Noise Piezoresponse Force Microscopy Data.

Piezoresponse force microscopy (PFM) is a scanning probe microscopy (SPM)-based technique used to evaluate the nanoscale surface displacement developed in response to an applied electric voltage. PFM is routinely used to investigate the nanoscale functional response of ferroelectric materials: the piezoelectric response is dependent on the dielectric polarization and modification of the polarization state can result in measurable changes in the PFM signal. However, low signal-to-noise ratio (SNR) data is unavoidable, as both the response at domain walls, or at switching of the polarization, i.e., when polarization is extremely small or null, would result in limited or null piezoelectric strain. Given the importance of these features in understanding ferroelectric materials and their behavior, low SNR results can lead to unreliable information extraction, hampering the understanding of the material characteristics. Here, an information recovery framework is proposed, utilizing a Bayesian subspace-based matrix completion model, to improve the quality of extracted PFM parameters. The proposed framework enables efficient recovery and extraction of reliable information and provides valuable insights for characterization and experimentation practices. The recovery framework can also be applied to other functional SPM-based characterization techniques or any material characterization technique where low SNR data are expected within a series of correlated measurements.