Possibilities and limitations of voltage-modulated scanning force microscopy: Resonances in contact mode

Voltage-modulated scanning force microscopy in contact mode (or piezoresponse scanning force microscopy) is now an established technique for imaging ferroelectric domains in ferroelectric thin films. The quantities measured are not the ferroelectric polarization but the amplitude and phase of a locally induced piezoelectric strain. Although piezoresponse images are providing interesting information about the ferroelectric domain configuration, a quantitative analysis is a very challenging task given the tensorial nature of piezoelectricity. Additionally, the overall piezoresponse signal comprises both the electromechanical and electrostatic contributions depending on the frequency of the small ac testing voltage. We establish that for soft cantilevers the piezoresponse signal is not only dependent on the elastic and piezoelectric properties of the material under investigation but mainly governed by the elastic properties of the cantilever. Indications for optimal measurement regimes are given.