The relevance of distributed loading and cantilever angle for Piezo-mode Force Microscopy measurements.

Bryan D. Huey

Piezo-mode Force Microscopy (PFM) is increasingly applied to characterize piezoelectric films. Generally this technique employs a standard atomic force microscope where forces are detected with the beam-bounce method, which is primarily sensitive to the angle of the lever instead of true displacement. These terms are proportional for loads or displacements applied purely to the AFM tip. For electrostatic cantilever-sample interactions, however, the resulting distributed loading modifies the angle along the lever, introducing previously unrecognized errors into the measured lever amplitude and phase. This effect is considered through simulations of PFM measurements for a variety of laboratory conditions. The PFM measured amplitude is found to vary significantly for reasonable ranges of surface charge, film dielectric constant, piezo-coefficients, and the lever position at which the detecting laser is aligned. Most significantly, the proportion of the measured amplitude resulting from piezoactuation, local tip-sample electrostatic interactions, and distributed lever-sample interactions are also derived. Making the often-imposed simplifying assumption that the measured amplitude is proportional to piezoactuation is shown to grossly overestimate the sample piezoresponse for increasing surface charge (decreased charge screening) and/or decreased film dielectric constant. Interferometry results providing the true lever displacement and simultaneous AFM measured deflections are presented to compare experiment and theory. Finally, these concepts are applied to interpret megahertz frequency PFM images and data.