Extended Data Fig. 7: Eliminating artefacts from scanning probe microscopy.

a, Topography and PFM phase contrast images for ten-cycle HZO which did not (left) and did (right) undergo annealing after ALD deposition. The terraced topography in the non-annealed film indicates that the weak phase contrast is falsely caused by field-induced topographic changes. This is consistent with charge injection or ion migration, which plague amorphous HfO₂ films²⁵. Phase-annealed films do not display such field-induced topographic distortions yet demonstrate much clearer phase contrast, indicating the origin of PFM phase contrast in crystalline HZO films is different than that of amorphous HZO films. In the images shown, ±7 V were applied in a ‘box-in-box’ poling sequence. b, Time-dependent PFM phase contrast images on a ten-cycle HZO film across a 24-h period. In the images shown, ±7 V was applied in the indicated checkerboard poling pattern. c, Collapse of the PFM loop from V_ac-series. Schematic capacitor structure probed by PFM (top) and piezoresponse as a function of V_ac in the ‘OFF’ (V_dc = 0) state (bottom), demonstrating the collapse of the PFM loop as V_ac approaches the coercive voltage. This provides further confirmation of the ferroelectric origin of the PFM signal as opposed to tip bias-induced mechanisms⁴⁶. The non-ideal shape of the piezoresponse loops, particularly at higher voltages, is probably caused by non-ferroelectric contributions from the additional dielectric SiO₂ layer through which most of the voltage is dropped (Methods). d, IDS switching-spectroscopy measurements on ten-cycle (1 nm) HZO, demonstrating hysteresis for the PFM tip on-surface (top) versus no hysteresis for the tip off-surface (bottom). The on-surface loops indicate 180° phase hysteresis and butterfly-shaped d₃₃, indicative of ferroelectric behaviour. IDS PFM measurements (Methods) remove the long-range electrostatics and cantilever resonance artefacts that plague typical voltage-modulated PFM switching spectroscopy²⁶. This ferroelectric origin of the hysteresis is further supported by non-hysteretic off-surface loops²⁶, which probe electrostatic contributions.