The rapid development of nanoscience and nanotechnology in the last two decades was stimulated by the emergence of scanning probe microscopy techniques capable of accessing local material properties, including transport, mechanical, and electromechanical behaviors, on the nanoscale. Here, we analyze the general principles of electromechanical probing by piezoresponse force microscopy (PFM), a scanning probe technique applicable to a broad range of piezoelectric and ferroelectric materials. The relationship between vertical and lateral PFM signals and material properties is derived analytically for two cases: transversally isotropic piezoelectric materials in the limit of weak elastic anisotropy, and anisotropic piezoelectric materials in the limit of weak elastic and dielectric anisotropies. The integral representations for PFM response for fully anisotropic material are also obtained. The image formation mechanism for conventional (e.g., sphere and cone) and multipole tips corresponding to emerging shielded and strip-line-type probes is analyzed. Possible applications for orientation imaging on the nanoscale and molecular resolution imaging are discussed.
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