Non-linear dynamics and simulation of VO$_{\mathrm{2}}$ oscillators for micro-electronics applications

Vanadium dioxide (VO$_{\mathrm{2}})$ is a promising electronic material for emerging technologies. VO$_{\mathrm{2}}$ undergoes a reversible phase transformation accompanied by several orders of magnitude change in resistivity and hysteresis. Such attributes are ideal for designing novel devices with tunable and reconfigurable characteristics. In this work we investigated two-terminal devices based on VO$_{\mathrm{2}}$ thin films. The fabricated devices exhibited large amplitude electrical relaxation oscillation under voltage actuation conditions. We developed a circuit equivalent model for the VO$_{\mathrm{2}}$ based system and excellent agreement between experiment and simulation was verified. We have also analyzed the non-linear dynamics in such systems by deriving the dynamical differential equations for the oscillator circuit. A phase portrait analysis for the VO$_{\mathrm{2}}$ relaxation oscillator is presented.