Routes for increasing endurance and retention in ${\mathrm{HfO}}_2$-based resistive switching memories

We investigate metastable and thermodynamically stable phases that can be expected to occur in electroformed filaments in resistively switching hafnia, and discuss their relevance for the switching process. To this end, we conduct a study, based on density functional theory combined with an evolutionary algorithm determining the composition-dependent (meta)stable phases in ${\mathrm{HfO}}_x$, focusing on the region $0<x<2$. We find that oxygen vacancies in hafnia tend to form regular patterns, which leads to periodic metastable structures featuring one-dimensional open channels, thus favoring ionic conductivity in the host material, i.e., oxygen migration. The band gap of such structures is systematically lowered with increasing oxygen deficiency, resulting in metallic behavior when oxygen migrates out of the channels. Moreover, we find that the solubility of oxygen in metallic Hf is very high, up to one oxygen per six metallic atoms, the concentration corresponding to a thermodynamically stable and ordered metallic compound, ${\mathrm{Hf}}_6\mathrm{O}$. Therefore, thick enough metallic capping of Hf could play the role of an active electrode for hosting oxygen which migrates out of ${\mathrm{HfO}}_2$. In combination with reversible oxygen migration in predicted suboxide phases, this should lead to robust resistive memory cells with high endurance and long retention.

Figure 1

Composition diagram in the Hf-O system. Energies are given in eV per atom as a distance $\delta H$ from the convex hull to the metastable phase. Hexagonal Hf and molecular ${\mathrm{O}}_2$ form boundaries; hexagonal ${\mathrm{Hf}}_6\mathrm{O}$ and monoclinic ${\mathrm{HfO}}_2$ are thermodynamically stable compounds. The blue line indicates a boundary of phases with hexagonal structure, where oxygen atoms occupy vacant octahedral positions in a hexagonal close packed structure of metallic Hf. The red line indicates a boundary of suboxide phases with fluorite structure. The dotted red line defines region of fluorite structures with ordered one-dimensional chains of oxygen vacancies. The dashed green line indicates crossover between hexagonal and fluorite structures (see text for discussions). Diamonds are structures obtained in Ref. [31]. Lines are given as a guides for the eyes. Black dots are the relaxed phases of trial structures at the end of the evolutionary algorithm search. The lower scale shows the atomic ratio of oxygen to hafnium (i.e., the concentration of O, $x$, in the compounds ${\mathrm{HfO}}_x)$, whereas the upper one defines the atomic percent of oxygen in the compounds. In the plotted energy range no metastable structures were found for concentrations above $x\ge 2$.

Figure 2

Crystal structures of (a) $R\overline{3}\text{−}{\mathrm{Hf}}_6\mathrm{O}$ and (b) $P\overline{3}1c\text{−}{\mathrm{Hf}}_3\mathrm{O}$, showing the preferred occupation with oxygen in vacant octahedrally coordinated positions (depicted by the red octahedra) in hcp Hf host (yellow spheres).

Figure 3

Crystal structures of the monoclinic phases of (a) $Cm$-HfO and (b) $Cm\text{−}{\mathrm{Hf}}_4{\mathrm{O}}_5$, in the crossover region of the Hf-O composition diagram. Both structures share the same structural frame; however, $Cm\text{−}{\mathrm{Hf}}_4{\mathrm{O}}_5$ contains extra oxygen (shown by small blue spheres), which occupies the vacant positions present in $Cm$-HfO structure, forming one-dimensional chains. Hf atoms are depicted with yellow spheres. Oxygen atoms which are the constituents of the structural frame are shown as red spheres.

Figure 4

Crystal structures of (pseudo)tetragonal fluorite-like phases of (a) $Ibam\text{−}{\mathrm{Hf}}_2{\mathrm{O}}_3$ and (b) $I\overline{4}2m\text{−}{\mathrm{Hf}}_4{\mathrm{O}}_7$ in the suboxide region of hafnia. In metallic $Ibam\text{−}{\mathrm{Hf}}_2{\mathrm{O}}_3$ one-dimensional chains of oxygen vacancies are clearly seen. These chains are partially filled up by oxygen (shown by small blue spheres) in ${\mathrm{Hf}}_4{\mathrm{O}}_7$, resulting in an insulating state. The ordered $Ibam\text{−}{\mathrm{Hf}}_2{\mathrm{O}}_3$ phase is clearly split off from the rest of the structures of region $\left(iii\right)$ (see the solid red line in Fig. 1), indicating the natural preference of oxygen vacancies to form one-dimensional chains.

Figure 5

Calculated phonon spectrum of the low-energy $Ibam\text{−}{\mathrm{Hf}}_2{\mathrm{O}}_3$ structure with ordered vacancies revealing its dynamical stability.