Fig. 4

a Bandgap of HfO₂ with defect states depending on the charge state of V_o. b Reconstructed 3D C-AFM images of V_o evolution and migration in HfO_x-based RS device. c Atomic structure of monoclinic HfO₂ with GB at the center (dashed line). The 4-Å-wide shadow region near the GB is a favorable region for V_o aggregation. d Current scan map using C-AFM of polycrystalline HfO₂. e Topography (blue) and current (red) data along the green solid line in d. Schematic of conduction mechanism in HfO₂ f before and g after breakdown. h Schematic and HRTEM of a complete CF resulting from V_o aggregation in an LRS device with a typical polymorphous HfO_x region, namely h-Hf₆O and m-HfO₂ regions a reproduced with permission from [76]. b reproduced with permission from [80]. c reproduced with permission from [83]. d, e reproduced with permission from [184]. h reproduced with permission from [79]