| Summary: | 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 VO _2 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.
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