Voltage modulated scanning force microscopy in contact mode or piezoresponse scanning force microscopy is now turning into an established technique for imaging ferroelectric domains in ferroelectric thin films. The quantities measured, however, are the amplitude and phase of a locally induced piezoelectric strain, and not the ferroelectric polarization itself. As all ferroelectrics possess piezoelectric properties, the domain structure visualized does correspond to that of the ferroelectric domains whose polarization is partly normal to the film surface, but the amplitude of the signal is actually not proportional to the magnitude of the normal component of the polarization. Likewise, the shear mode of scanning force microscopy allows the imaging of domains with a polarization component in the plane of the film. Methods to relate the amplitude of the piezoresponse signal to the magnitude of the ferroelectric polarization taking into account the anisotropic nature of the piezoelectric coefficients are described and discussed for the most common ferroelectric materials.
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Harnagea et al. (2002) studied this question.