Oxygen-modulated quantum conductance for ultrathin ${\mathrm{HfO}}_2$-based memristive switching devices

Memristive switching devices, candidates for resistive random access memory technology, have been shown to switch off through a progression of states with quantized conductance and subsequent noninteger conductance (in terms of conductance quantum $G_0)$. We have performed calculations based on density functional theory to model the switching process for a $\mathrm{Pt}\text{−}{\mathrm{HfO}}_2$-Pt structure, involving the movement of one or two oxygen atoms. Oxygen atoms moving within a conductive oxygen vacancy filament act as tunneling barriers, and partition the filament into weakly coupled quantum wells. We show that the low-bias conductance decreases exponentially when one oxygen atom moves away from interface. Our results demonstrate the high sensitivity of the device conductance to the position of oxygen atoms.

Figure 1

(a) Optimized atomic structure of model 1 in device set I (see text). Green, yellow, and pink colors represent Pt, Hf, and O atoms, respectively, with the blocking oxygen highlighted in red. The numbers in both (a) and (b) represent oxide atomic layers in the ${\mathrm{HfO}}_2$; (b) cartoon of the modeled reset process in which a single oxygen atom moves from the top Pt electrode to block the ${\mathrm{V}}_{\mathrm{o}}$ filament in the oxide film; (c) evolution of the device conductance in units of $G_0$ for both sets I and II as an oxygen atom blocks the ${\mathrm{V}}_{\mathrm{o}}$ filament at different atomic layers. The dashed line (set II*) uses a smaller energy range to estimate the conductance (see text); (d) electron transmission $\left(T\right)$ in units of $G_0$ as a function of energy for selected models in set II. The locations of the conduction-band minimum (CBM) and the valence-band maximum (VBM) of stoichiometric ${\mathrm{HfO}}_2$ are indicated at the top of the panel. It is clear that transmission around the device Fermi level (set to zero energy) is dominated by the ${\mathrm{V}}_{\mathrm{o}}$ filament.

Figure 2

Local density of states (LDOS) of the ${\mathrm{HfO}}_2$ film sandwiched between Pt electrodes (selected models in set II). The horizontal axis represents the $z$ axis with the numbers 1, 3, 5,...,8, denoting the location of the corresponding oxide atomic layer. The vertical solid line shows the position of the blocking oxygen atom. The color maps denote the LDOS in arbitrary units. The Fermi level is set at zero energy and indicated by dotted horizontal lines.

Figure 3

Averaged PDOS of QWs (see text) for selected models.“Left” (“right”) denote the averaged PDOS to the left (right) of the blocking atom. The Fermi level is set at zero energy.

Figure 4

(a) Transmission in units of $G_0$ as a function of energy for representative models in the case of two blocking oxygen atoms. (b) to (d) Corresponding LDOS of the two-blocking-atom models in arbitrary unit. For all plots, device Fermi level is aligned to zero energy.

Figure 5

Electronic properties of device set I. (Top) $T$ in units of $G_0$ as a function of energy for selected models. (Middle) LDOS of oxide in arbitrary units. (Bottom) Averaged PDOS of QWs as a function of energy. For all plots, the device Fermi level is aligned to zero energy.

Figure 6

Total energy $\left(E_{\mathrm{tot}}\right)$ variation when one oxygen atom blocks ${\mathrm{V}}_{\mathrm{o}}$ filament at different locations for both device sets. $E_{\mathrm{tot}}$ for models 1 and 1′ have been aligned to zero energy.