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Influence of the Shape of the PFM Tip on the Distribution of the Electrostatic Field

We study the dependence of the electric field induced by the tip of a piezoresponse force microscope over a ferroelectric sample on its shape. It is assumed that the probe needle is thin, i.e. its largest diameter is much smaller than the length. The microscope tip is considered as a surface of revolution. The accuracy of the proposed approach depends on the ratio of the dielectric constants of the dielectric and ferroelectric (air and sample).