  Piezoresponse force microscopy (PFM) has been extensively utilized as a
versatile and an indispensable tool to understand and analyze nanoscale ferro-
/piezoelectric properties by detecting the local electromechanical response on
a sample surface. However, it has been discovered that the electromechanical
response not only originates from piezoelectricity but also from other factors
such as the electrostatic effect. In this study, we explore the dependence of
off-field PFM hysteresis loops on the surface-potential-induced electrostatic
effect in a prototypical ferroelectric thin film by applying an external
voltage to the bottom electrode during measurement. We simplify the situation
by equating the surface potential to the direct current voltage waveform
variations and predicting the contribution of the surface-potential-induced
electrostatic effect to the PFM hysteresis loops. The experimental results
approximately match our prediction-the coercive voltage linearly decreases with
the surface potential, whereas the saturated amplitude and piezoresponse remain
nearly constant owing to the relatively large piezoelectric coefficient of the
ferroelectric thin film.
