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In the paper we adopt the analytical Landau-Ginzburg-Devonshire theory to describe the ferroelectric domain structure formation using Scanning Probe Microscopy. We calculate the effective local piezoresponse of the domain structure within the decoupling approximation using the conventional relation between piezoelectric tensor components and the spontaneous polarization vector. The depth profile of the polarization distribution was derived from the nonlinear Landau-Ginzburg-Devonshire equation. We demonstrate that depending on the material parameters such as the intrinsic domain wall width and probe apex geometry, the shape of the nucleating nanodomains induced by the probe can be either oblate or prolate. The derived analytical expressions for the polarization redistribution caused by the biased probe are valid for both first and second order ferroelectrics.

Domain structure formation by using Scanning Probe Microscopy: equilibrium polarization distribution and effective piezoelectric response calculations