Figure 4

Illustration of the role of defect dynamics for the two switching types and the formation of oxygen vacancies \({V}_{\mathrm{O}}^{2+}\) at the interface. (a) Filamentary switching is based on the formation, growth, and disruption of an oxygen vacancy filament in defect rich HfO_x. (b) Area-type switching in highly stoichiometric hafnium oxide, where the drift and diffusion of mobile vacancies change the potential landscape. (c) Density [\({V}_{\mathrm{O}}^{2+}\)] of double positively charged oxygen vacancies \({V}_{\mathrm{O}}^{2+}\) in the HfO₂ layer, calculated as a function of the applied voltage U and plotted together with the stoichiometric vacancy density \(\left[{V}_{\mathrm{O},\mathrm{s}}^{2+}\right]\) (maximum indicated by black, dashed line) in the HfO₂ layer, which is still consistent with the XPS measurements. The electric field-induced vacancy density \([{V}_{\mathrm{O},\mathrm{i}}^{2+}]\) is plotted for three different formation energies E_v.