Quantification of the electromechanical measurements by piezoresponse force microscopy

Piezoresponse force microscopy (PFM) is widely used for characterization and exploration of the nanoscale properties of ferroelectrics. However, quantification of the PFM signal is challenging due to the convolution of various extrinsic and intrinsic contributions. Although quantification of the PFM amplitude signal has received considerable attention, quantification of the PFM phase signal has not been addressed. A properly calibrated PFM phase signal can provide valuable information on the sign of the local piezoelectric coefficient-an important and nontrivial issue for emerging ferroelectrics. In this work, two complementary methodologies to calibrate the PFM phase signal are discussed. The first approach is based on using a standard reference sample with well-known independently measured piezoelectric coefficients, while the second approach exploits the electrostatic sample-cantilever interactions to determine the parasitic phase offset. Application of these methodologies to studies of the piezoelectric behavior in ferroelectric HfO2-based thin-film capacitors reveals intriguing variations in the sign of the longitudinal piezoelectric coefficient, d(33,eff). It is shown that the piezoelectric properties of the HfO2-based capacitors are inherently sensitive to their thickness, electrodes, as well as deposition methods, and can exhibit wide variations including a d(33,eff) sign change within a single device.