The Importance of Distributed Loading and Cantilever Angle in Piezo-Force Microscopy

Piezo-force microscopy (PFM) is a variation of atomic force microscopy that is widely applied to investigate piezoelectric thin films at the nanometer scale. Curiously, PFM experiments are found to be remarkably sensitive to the position along the cantilever at which deflection is detected, complicating attempts to use this technique to quantify surface actuation and thereby measure the converse piezoelectric coefficient. A straightforward analytical theory is proposed that accounts for this observation by combining standard PFM analyses with subtleties of the typical AFM detection mechanism as well as the concept of distributed loading. Corresponding simulations of PFM measurements indicate that these experimental artifacts can even lead to an apparent inversion of the detected domain orientation. To better understand the importance of these effects, simulations are used to qualitatively map the theoretical PFM response for a wide range of typical experimental parameters, as well as the relative difference between these measurements and true piezoactuation.