Local dielectric constant at the pzt surface

Both Sac and Sdc may be deduced from force measurements as denoted by Equation (12.1) and (12.3). In pfs we measure the overall force acting on the tip when pulling the tip back from the surface. Thus such a dc force may be written as  

In Equation (12.7), a specifies the geometry while e(U) now denotes the local dielectric constant probed with the tip. 

Experimentally, both the pfm and pfs measurements are performed at one and the same surface spot, and an absolute matching of the two curves is intended using a polynomial fitting. Such an approach is reasonable since it is both Pz and a which contribute to the ac and DC force terms via Equation (12.4) and (12.5). Our experiment [24] then allows the following results to be deduced  

) pfm probes the piezoelectric properties even for tip-sample voltages up to 10 V. 

) Only for larger fields exceeding 10 V in reversed polarization direction will mobile surface charges contribute to the overall signal SAC in pfm (deposited upon switching). In contact experiments, however, such mobile charges are directly eliminated via the conductive tip. 

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