Fig. 4

Controlled manipulation of oxygen vacancies. a Simulated surface deformation profiles under a spherical (upper panel) and flat-ended (lower panel) tip for a static contact force of 4 µN. b Simulated in-plane distribution of the z-component, \(E_z^{{\rm{dep}}}\) (upper panel) and x-component, \(E_x^{{\rm{dep}}}\) (lower panel) of the depolarisation field induced by the flat-ended tip. The ripples in \(E_x^{{\rm{dep}}}\) are numerical artefacts. c, d The normalised vacancy concentration (NVC) maps after mechanical scans were performed using a sharp c and blunt tip d with a contact force of 9.5 µN within the grey coloured boxes. Horizontal arrows mark the corresponding fast scan direction. Before mechanical sans, the \(V_{\rm{o}}^{ \cdot \cdot }\)-enrichment were performed by poling the pristine surface with a tip bias of −5 V. e, f NVC profiles along lines M1, M2, M3 and M4 in c(e) and in d(f). M1 and M4 are placed 0.5 µm away from the borders between the \(V_{\rm{o}}^{ \cdot \cdot }\)-enriched and pristine regions. The vertical arrow marks the maximum net increase (\(\Delta _{{\rm{max}}}^{{\rm{inc}}}\)) or decrease (\(\Delta _{{\rm{max}}}^{{\rm{dec}}}\)) in NVC. Horizontal black lines in e, f mark the background, which is used to estimate the net change in the NVC. The NVC profiles are averaged over a 0.5-µm-wide averaging window. Note that the boundaries between the \(V_{\rm{o}}^{ \cdot \cdot }\)-enriched and pristine regions in d are more diffused compared to those in c. This is caused by the use of the blunt tip during the KPFM imaging. The scale bar in c, d represents 1 µm