# How fast can vanadium dioxide neuron-mimicking devices oscillate? Physical mechanisms limiting the frequency of vanadium dioxide oscillators

## Abstract

The frequency of vanadium dioxide ($VO_2$) oscillators is a fundamental figure of merit for the realization of neuromorphic circuits called oscillatory neural networks (ONNs) since the high frequency of oscillators ensures low-power consuming, real-time computing ONNs. In this study, we perform electrothermal 3D technology computer-aided design (TCAD) simulations of a $VO_2$ relaxation oscillator. We find that there exists an upper limit to its operating frequency, where such a limit is not predicted from a purely circuital model of the $VO_2$ oscillator. We investigate the intrinsic physical mechanisms that give rise to this upper limit. Our TCAD simulations show that it arises a dependence on the frequency of the points of the curve current versus voltage across the $VO_2$ device corresponding to the insulator-to-metal transition (IMT) and metal-to-insulator transition (MIT) during oscillation, below some threshold values of $C_{\mathrm{ext}}$. This implies that the condition for the self-oscillatory regime may be satisfied by a given load-line in the low-frequency range but no longer at higher frequencies, with consequent suppression of oscillations. We note that this variation of the IMT/MIT points below some threshold values of $C_{\mathrm{ext}}$ is due to a combination of different factors: intermediate resistive states achievable by $VO_2$ channel and the interplay between frequency and heat transfer rate. Although the upper limit on the frequency that we extract is linked to the specific VO2 device we simulate, our findings apply qualitatively to any $VO_2$ oscillator. Overall, our study elucidates the link between electrical and thermal behavior in $VO_2$ devices that sets a constraint on the upper values of the operating frequency of any $VO_2$ oscillator.