Modified cantilevers to probe unambiguously out-of-plane piezoresponse

Abstract

We demonstrate and investigate the coupling of contributions from both in-plane (IP) polarization and out-of-plane (OP) components in ${\mathrm{BiFeO}}_{3}$ (BFO) thin-film polarization probed by piezoresponse force microscopy (PFM). Such coupling leads to image artifacts which prevent the correct determination of OP polarization vector directions and the corresponding piezoelectric coefficient ${d}_{33}$. Using material strength theory with a one-dimensional modeling of the cantilever oscillation amplitude under electrostatic and elastic forces as a function of the tip length, we have evidenced the impact of IP piezoresponse to the OP signal for tip length longer than 4 \ensuremath{\mu}m. The IP polarization vector induces a significant longitudinal bending of the cantilever, due to the small spring constant of long tips, which provokes a normal deviation superimposed to the OP piezoresponse. These artifacts can be reduced by increasing the longitudinal spring constant of the cantilever by shortening the tip length. Standard cantilevers with 15-\ensuremath{\mu}m-long tips were modified to reach the desired tip length, using focused ion-beam techniques and tested using PFM on the same BFO thin film. Tip length shortening has strongly reduced IP artifacts as expected, while the impact of nonlocal electrostatic forces, becoming predominant for tips shorter than 1 \ensuremath{\mu}m, has led to a non-negligible deflection offset. For shorter tips, a strong electric field from a cantilever beam can induce polarization switching as observed for a 0.5-\ensuremath{\mu}m-long tip. Tip length ranging from 1 to 4 \ensuremath{\mu}m allowed minimizing both artifacts to probe unambiguously OP piezoresponse and quantify the ${d}_{33}$ piezoelectric coefficient.