Spatial resolution, information limit, and contrast transfer in piezoresponse force microscopy.

Scanning probe-based ferroelectric domain imaging and patterning has attracted broad attention for use in the characterization of ferroelectric materials, ultrahigh density data storage, and nanofabrication. The viability of these applications is limited by the minimal domain size that can be fabricated and reliably detected by scanning probe microscopy. Here, the contrast transfer mechanism in piezoresponse force microscopy (PFM) of ferroelectric materials is analysed in detail. A consistent definition of resolution is developed both for the writing and the imaging processes, and the concept of an information limit in PFM is established. Experimental determination of the object transfer function and the subsequent reconstruction of an 'ideal image' is demonstrated. This contrast transfer theory provides a quantitative basis for image interpretation and allows for the comparison of different instruments in PFM. It is shown that experimentally observed domain sizes can be limited by the resolution of the scanning probe microscope to the order of tens of nanometres even though smaller domains, of the order of several nanometres, can be created.