Nonlinear dynamics and stability analysis of locally-active Mott memristors using a physics-based compact model

TL;DR

The paper develops and analyzes a physics-based compact model for locally-active Mott memristors based on VO$_2$, connecting device physics to nonlinear dynamics through small-signal linearization and Chua's local activity theory. It maps edge-of-chaos regions in current-voltage and frequency spaces, derives a complex-domain small-signal and an equivalent circuit with negative-capacitance behavior, and demonstrates both local (1D) and global (2D) dynamical phenomena, including saddle-node and Hopf-like bifurcations, Canard-like transitions, and limit-cycle oscillations. The study extends to a 2D relaxation oscillator formed by a Mott memristor in a Pearson–Anson configuration, using nullcline, Jacobian, and tr-det analyses to reveal Hopf bifurcations and phase-space structures, with numerical phase portraits corroborating analytical predictions. Experimental VO$_2$ relaxation-oscillator data show strong agreement with SPICE simulations based on the compact model, supporting the model's relevance for designing neuromorphic circuits with high dynamical richness and bandwidth potential, particularly as device geometry scales down to smaller channel radii.

Abstract

Locally-active memristors are a class of emerging nonlinear dynamic circuit elements that hold promise for scalable yet biomimetic neuromorphic circuits. Starting from a physics-based compact model, we performed small-signal linearization analyses and applied Chua's local activity theory to a one-dimensional locally-active vanadium dioxide Mott memristor based on an insulator-to-metal phase transition. This approach allows a connection between the dynamical behaviors of a Mott memristor and its physical device parameters as well as a complete mapping of the locally passive and edge of chaos domains in the frequency and current operating parameter space, which could guide materials and device development for neuromorphic circuit applications. We also examined the applicability of local analyses on a second-order relaxation oscillator circuit that consists of a voltage-biased vanadium dioxide memristor coupled to a parallel reactive capacitor element and a series resistor. We show that global nonlinear techniques, including nullclines and phase portraits, provide insights on instabilities and persistent oscillations near non-hyperbolic fixed points, such as a supercritical Hopf-like bifurcation from an unstable spiral to a stable limit cycle, with each of the three circuit parameters acting as a bifurcation parameter. The abruptive growth in the limit cycle resembles the Canard explosion phenomenon in systems exhibiting relaxation oscillations. Finally, we show that experimental limit cycle oscillations in a vanadium dioxide nano-device relaxation oscillator match well with SPICE simulations built upon the compact model.

Figures (36)

• Figure 1: Experimental quasi-DC I–V curves for (a) a TaO$_y$-Ta$_2$O$_5$ bilayer passive memristor, and (b) a VO$_2$ locally-active memristor, fabricated and characterized by HRL Laboratories, LLC. Resistance switching events are indicated by dashed arrows. Insets of (a): layer structure and optical image of the 5$\times$5 $\upmu$m$^2$ TaO$_y$-Ta$_2$O$_5$ ($y<2$) crossbar device. Insets of (b): layer structure and scanning electron micrograph of the 50$\times$50 nm$^2$ VO$_2$ nano-crossbar device (scale bar: 500 nm). Memristor crossbars are tested in a four-terminal Kelvin connection (see Yi19 for details). The external voltage is swept at $\sim$1 V/s rate in the sequence of 0 $\rightarrow$ +$V_\text{p}$$\rightarrow$ 0 $\rightarrow$ –$V_\text{n}$$\rightarrow$ 0 (repeated 10 times). $V_\text{p}(V_\text{n})=2.5(2)$ V in (a) and $V_\text{p,n}=1.45$ V in (b). The metal electrodes contribute a series resistance of 600--800 $\Omega$.
• Figure 2: Schematics of the biphasic thermal model for a Mott memristor that undergoes an insulator-to-metal transition, illustrating a cylindrical conduction channel with a metallic-phase core surrounded by an insulating-phase shell. The model assumes that the metallic core is clamped to the transition temperature $T_\text{c}$, and the outer edge of the conduction channel is clamped to the ambient temperature $T_0$. The black solid line shows a calculated radial temperature profile. The top and bottom electrodes are not shown for clarity.
• Figure 3: Analytically calculated power-off plots $f_x(x,0)$ vs. $x$ for three different-sized VO$_2$ Mott memristors (as labeled) in the small $x$ region ($0<x<0.3$). Inset shows the same power-off plots for a much wider range of $0<x<1$.
• Figure 4: Analytically calculated dynamic route map of $f_x(x,i_0)$ at constant input current levels for the midsize VO$_2$ Mott memristor, plotted with (a) a narrow range of $i_0$ from 0 to 10 $\upmu$A, and (b) a wide range of $i_0$ from 0 to 3 mA. The open circle in (a) and (b) highlights a fixed point $Q$ where the $f_x(x,i_0)$ locus intersects the $x$-axis. Arrowheads show the direction of move for a solution $x(t)$ starting from an initial state located close to $Q$.
• Figure 5: (a) Dynamic route map of $f_x(x,v_0)$ at constant input voltages in the range of 0 to 1.2 V, calculated for the midsize VO$_2$ Mott memristor. (b) is a zoomed portion of (a) to show that at $v_0>0.0973$ V, the DR locus intersects the $x$-axis at two distinctive locations. At $v_0=0.0973$ V, the DR locus becomes tangent to the $x$-axis with only one intersection point. At $v_0<0.0973$ V, the DR locus stays in the fourth quadrant and does not intersect the $x$-axis.