Numerical modeling for piezo force microscopy measurements

G. Stan
National Institute of Standards and Technology,
United States

Keywords: piezo force microscopy, finite element analysis


Numerical modeling for piezo force microscopy measurements Gheorghe Stan National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899 Piezo Force Microscopy (PFM) is an Atomic Force Microscopy (AFM) technique in which the accuracy of the AFM detection is needed in the single digit picometer range. Traditionally, this detection was based on the common optical beam detection of an AFM that measures the slope of the deflected cantilever. However, in PFM, the slope detection might be affected by electrostatic contributions from the conductive body of the AFM probe. It has been shown [1] that this artifact can be mitigated by performing the detection at an “electrostatic blind spot” (EBS) along the cantilever. In addition to the slope detection of the cantilever, another AFM detection method that emerged recently is that based on an interferometric detection, which provides a direct measurement of the vertical deflection of the cantilever [2], right at the base of the tip. In this work, we used finite element analysis to model a conductive AFM probe in contact with a piezoelectric material and mimic the basic PFM response under different applied DC voltages. As expected, it was found that the vertical detection at the base of the tip directly measures the tip-sample deformation and, as such, provides a direct measurement for the inverse piezo coefficient. The same inverse piezo coefficient was extracted from the indirect measurement of the cantilever’s slope at the EBS of the cantilever. The two results were compared for various mechanical couplings of the tip-sample contact and tip conditions. The advantage of an integral representation of the PFM system as given by finite element analysis over disconnected analytical representations of the tip-sample contact and cantilever mechanics is that provides a direct connection between the piezoelectric parameters of the material probed and the measured response for both vertical and slope detections. [1]J. P. Killgore, L. Robins, and L. Collins, Nanoscale Adv. 4, 2036 (2022). [2]R. Proksch, R. Wagner, and J. Lefever, J. Appl. Phys. 135, 035104 (2024).