Quantitative measurements of shear displacement using atomic force microscopy

We report a method to quantitatively measure local shear deformation with high sensitivity using atomic force microscopy. The key point is to simultaneously detect both torsional and buckling motions of atomic force microscopy (AFM) cantilevers induced by the lateral piezoelectric response of the sample. This requires the quantitative calibration of torsional and buckling response of AFM. This method is validated by measuring the angular dependence of the in-plane piezoelectric response of a piece of piezoelectric α-quartz. The accurate determination of the amplitude and orientation of the in-plane piezoelectric response, without rotation, would greatly enhance the efficiency of lateral piezoelectric force microscopy.