Imaging of Electrothermal Filament Formation in a Mott Insulator

Resistive switching—the current- and voltage-induced change of electrical resistance—is at the core of memristive devices, which play an essential role in the emerging field of neuromorphic computing. This study is about resistive switching in a Mott insulator, which undergoes a thermally driven metal-to-insulator transition. Two distinct switching mechanisms are reported for such a system: electric-field-driven resistive switching and electrothermal resistive switching. The latter results from an instability caused by Joule heating. Here, we present the visualization of the reversible resistive switching in a planar $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ thin-film device using high-resolution wide-field microscopy in combination with electric transport measurements. We investigate the interaction of the electrothermal instability with the strain-induced spontaneous phase separation in the $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ thin film at the Mott transition. The photomicrographs show the formation of a narrow metallic filament with a minimum width $\lesssim 500$ nm. Although the filament formation and the overall shape of the current-voltage characteristics (IVCs) are typical of an electrothermal breakdown, we also observe atypical effects such as oblique filaments, filament splitting, and hysteretic IVCs with sawtoothlike jumps at high currents in the low-resistance regime. We are able to reproduce the experimental results in a numerical model based on a two-dimensional resistor network. This model demonstrates that resistive switching in this case is indeed electrothermal and that the intrinsic heterogeneity is responsible for the atypical effects. This heterogeneity is strongly influenced by strain, thereby establishing a link between switching dynamics and structural properties.

Figure 1

(a) A schematic view of the planar $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ device under investigation. The two $\mathrm{Au}$ electrodes serve as combined current-voltage taps for two-probe electric transport measurements. The dotted green line indicates the area of interest (the field of view of the images is shown in (c)). (b) Resistively and optically detected MIT-IMT. The upper panel shows the electrical resistance $R(T)$ (measured with $I=5\mu \mathrm{A}$); the arrows indicate the sweep direction of the temperature $T$. Data points marked by letters correspond to images shown in (c). $T_b$ indicates the base temperature set for the measurements presented in Fig. 3. The inset shows $R(T)$, including the lowest temperature of the thermal cycle. The lower panel shows the reflectivity versus $T$ of the $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ film normalized to the reflectivity of the $\mathrm{Au}$ electrodes. The green curve represents the average over the area of interest, while the red curve represents the reflectivity of a single pixel at the location indicated by the red circles in (c). The vertical dashed lines indicate the local transition temperatures $T_{\mathrm{MIT}}$ and $T_{\mathrm{IMT}}$, determined for the single pixel. (c) A selection of photomicrographs acquired during one thermal cycle. The $\mathrm{Au}$ electrodes are indicated by the yellow areas.

Figure 2

The local transition temperatures of the $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ thin-film device: (a) $T_{\mathrm{MIT}}$ map; (b) $T_{\mathrm{IMT}}$ map. The large dark blue areas indicate $\mathrm{Au}$ electrodes.

Figure 3

The electrical breakdown in a planar $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ device at a base temperature $T_b=158$ K at the onset of the IMT. (a) Measured (blue) and simulated (red) IVCs. The letters label data points for which images are shown in (b). The arrows indicate the sweep directions. The thick gray arrows indicate resistive switching to a low- and high-resistance state, respectively. The inset shows an enlargement of the high-current section. (b) The left-hand column shows a selection of the photomicrographs acquired during the second current sweep. The middle and right-hand columns show a selection of the simulated spatial distribution of the current density $J$ and the local device temperature $T$, respectively. The dashed red lines for images B indicate an $\alpha \approx {17}^{\circ }$ inclination of the filament with respect to the $y$ direction.

Figure 4

The relations derived from the IVC and photomicrographs of the second current sweep in Fig. 3: (a) the conductance versus the current; (b) the current versus the power; (c) the estimated total filament width versus the current; (d) the resistivity of the metallic phase, estimated from the filament width, versus the current. The horizontal line indicates the resistivity of the metallic phase ${\rho }_{\mathrm{met}}$ used in the numerical simulations to obtain agreement with the experimentally measured resistance in the metallic phase.

Figure 5

The phase separation in $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ at the MIT-IMT: (a) $R(T)$ curves; (b) images acquired at the points, labeled A–T in (a), during cool-down and warm-up of the sample.

Figure 6

The domain configuration (left) and FFT (right) for selected temperatures of (a) $166\mathrm{K}$ and (b) $162\mathrm{K}$ in the cooling branch (MIT) and (c) $168\mathrm{K}$ and (d) $172\mathrm{K}$ in the heating branch (IMT). The dashed lines highlight the predominant directionality of the long axis of domains in the real-space images and in which the peaks occur. The angles are measured clockwise with respect to the vertical axis. The inner (outer) circles in the FFT correspond to a spatial frequency of $1/\mu \mathrm{m}$ ($2/\mu \mathrm{m}$).

Figure 7

The reproducibility of the domain configuration. (a),(b) Optical images, recorded at 168 K in the heating branch for two subsequent runs with a full thermal cycle in between. (c) The color-coded superposition of images from (a) and (b). Metallic domains that are present in both (a) and (b) appear dark. Metallic domains only present in (a) are green, while those only present in (b) are red. Insulating domains present in both micrographs are shown in yellow.

Figure 8

The resistor network of $m\times n$ primitive cells used to approximate the resistance of the sample. Each primitive cell (red squares) contains one node and four resistors (except for the columns $j=1$ and $j=n$, with only three resistors per primitive cell). A mesh current $I_{k,l}$ (blue) flows in each of the essential meshes of the resistor network. An additional mesh containing the current source is connected to the left-hand side of the resistor network.

Figure 9

On the definition of the currents $I_{i,j,1}$ to $I_{i,j,4}$ flowing through the resistors in the primitive cell $i,j$, which are calculated from the adjacent mesh currents.

Figure 10

The modeling of the temperature dependence of the $\mathrm{V}$${}_2$$\mathrm{O}$${}_3$ resistivity. For the cooling branch, ${\rho }_{\mathrm{MIT}}$ increases from ${\rho }_{\mathrm{met}}$ to ${\rho }_{\mathrm{ins}}$ for $T<T_{\mathrm{MIT}}$ (blue dashed line). In the heating branch ${\rho }_{\mathrm{IMT}}$ decreases to ${\rho }_{\mathrm{met}}$ for $T$ approaching $T_{\mathrm{IMT}}$ (green dashed line).

Figure 11

The temperature-dependent heat capacity $c_P$ (blue curve) and enthalpy $H$ (red curve). The latent heat $\mathrm{\Delta }H$ at the phase transition leads to a jump in enthalpy and a peak in heat capacity. The broken lines show the IMT at $T_{\mathrm{IMT}}$ and the solid lines the MIT at $T_{\mathrm{MIT}}$.

Figure 12

The flow chart for the simulation.