Piezoresponse force microscopy imaging of nanostructures created by conductive AFM lithography at oxide heterointerfac*

Nanoscale control of the metal-insulator transition in 3-unit cell (u.c.) LaAlO$_3$/SrTiO$_3$ heterostructures using conductive AFM (c-AFM) lithography allows the creation of conductive nanostructures \footnote{C. Cen, \textit{et al.} \textit{Nat. Mater}. \textbf{7}, 2136 (2008)}. Piezoelectric effects have recently been observed in planar LaAlO$_3$/SrTiO$_3$ heterostructures \footnote{C. W. Bark, \textit{et al.} \textit{Nano Letter}. 12(4), 1765 (2012)}, and the piezoresponse differs between the conducting and insulating states of 3-u.c. samples where c-AFM modulates the transition \footnote{M. Huang, \textit{et al.} arXiv: 1208.287 (2012)}. We have employed piezoresponse force microscopy (PFM) to detect and image the piezoresponse variations of nanostructures created by c-AFM lithography. PFM imaging allows visualization of the nanostructures, expanding capabilities for characterizing and studying individual devices.