Dynamics of voltage-driven oscillating insulator-metal transitions

Recent experiments demonstrated emerging alternating insulator and metal phases in Mott insulators actuated by a direct bias voltage, leading to oscillating voltage outputs with characteristic frequencies. Here, we develop a physics-based nonequilibrium model to describe the dynamics of oscillating insulator-metal phase transitions and experimentally validate it using a ${\text{VO}}_{\text{2}}$ device as a prototype. The oscillation frequency is shown to scale monotonically with the bias voltage and series resistance and terminate abruptly at lower and upper device-dependent limits, which are dictated by the nonequilibrium carrier dynamics. We derive an approximate analytical expression for the dependence of the frequency on the device operating parameters, which yields a fundamental limit to the frequency and may be utilized to provide guidance to potential applications of insulator-metal transition materials as building blocks of brain-inspired non-von Neumann computers.

Figure 1

(a) Schematics of the ${\mathrm{VO}}_2$ oscillator. $V_a$ is the bias direct voltage, $R_s$ is the series resistor, $V_s$ denotes the voltage drop across the series resistor, and $C$ represents the parasitic capacitance explicitly or it could be an external capacitor. (b) Oscillation patterns of $V_s/V_a$, the ${\mathrm{VO}}_2$ resistance $R$, the order parameters, and the temperature $T$ at $V_a=7.8\mathrm{V}$ and $R_s=4.7\mathrm{k}\mathrm{\Omega }$. The light-blue and the light-red shaded regions indicate the processes of the MIT and the IMT, respectively. The numbered red crosses correspond to the phases in Fig. 2.

Figure 2

(a) Phases at a sequence of moments represented by the order parameters superimposed on the intrinsic bulk free energy density landscape for $V_a=7.8\mathrm{V}$ and $R_s=4.7\mathrm{k}\mathrm{\Omega }$. The red crosses in (a) correspond to those in Fig. 1. The temperature at each moment is shown. The M1 and R minima are marked in $1\text{APTARACIRCLED}$ and $4\text{APTARACIRCLED}$, respectively. (b) $I\text{−}V$ characteristics of ${\text{VO}}_{\text{2}}$ at $V_a=7.8\mathrm{V}$ and $R_s=4.7\mathrm{k}\mathrm{\Omega }$. The $x$ coordinate is the voltage drop across the ${\text{VO}}_{\text{2}}$ channel. $I_1$ and $I_2$ are the current through ${\text{VO}}_{\text{2}}$ (including the capacitor current) and the current through the resistor (excluding the capacitor current), respectively.

Figure 3

(a) Experimentally measured (markers) and simulated (lines) frequency scaling with the bias voltage $V_a$ at $R_s=4.7$ and $10\mathrm{k}\mathrm{\Omega }$. The scaling calculated with different $\tau$ and $C$ is shown. I: $R_s=4.7\mathrm{k}\mathrm{\Omega }$, $\tau =7\mu \mathrm{s}$, $C=250\mathrm{pF}$; II: $R_s=10\mathrm{k}\mathrm{\Omega }$, $\tau =7\mu \mathrm{s}$, $C=250\mathrm{pF}$; III: $R_s=4.7\mathrm{k}\mathrm{\Omega }$, $\tau =11\mu \mathrm{s}$, $C=550\mathrm{pF}$; IV: $R_s=10\mathrm{k}\mathrm{\Omega }$, $\tau =11\mu \mathrm{s}$, $C=550\mathrm{pF}$; V: $R_s=4.7\mathrm{k}\mathrm{\Omega }$, $\tau =14\mu \mathrm{s}$, $C=700\mathrm{pF}$; VI: $R_s=10\mathrm{k}\mathrm{\Omega }$, $\tau =14\mu \mathrm{s}$, $C=700\mathrm{pF}$. (b) Experimentally measured (markers) and analytical (lines) frequency scaling with $R_s$ at different $V_a$. (c) Numerically simulated (solid lines) and analytical (dotted lines) frequency scaling with $V_a$ at various $R_s$. The colored numbers indicate the corresponding $R_s$ values in units of $\text{k}\mathrm{\Omega }$. The light yellow and light blue shades mark the regions of oscillation and no oscillation, respectively. (d) Numerically simulated (solid lines) boundaries of the range of oscillation superimposed on the frequency map over the bias voltage and series resistance obtained by the analytical formulas.

Figure 4

Comparison of the experimentally measured frequency scaling (crosses) and the analytical frequency formulas derived from this model (solid lines) and the quasisteady model (dashed lines). The upper panel is for the scaling with $V_a$ at $R_s=4.7\mathrm{k}\mathrm{\Omega }$ and the lower panel is for the scaling with $R_s$ at $V_a=15\mathrm{V}$.