Modelling hysteresis in vanadium dioxide oscillators

Introduction: Vanadium dioxide (VO2) is a correlated electron material that exhibits abrupt insulator-to-metal (IMT) and metal-to-insulator (MIT) phase transitions under the application of a critical electric field (transitions may also be triggered by other stimuli, such as strain and thermal excitation) [1]. These phase transitions correspond to a large and abrupt change in electrical conductivity. Recently, it has been shown that connecting a VO2 device with a resistor and a capacitor, of proper resistance and capacitance values, it is possible to fabricate very compact relaxation nano-oscillators [2]. The simple fabrication flow, the easy scalability with the possibility to achieve high packaging density, make VO2 nano-oscillators promising candidates to integrate a large array of coupled oscillators for bio-inspired neurocomputing [2, 3]. However, electrical measurements reveal that the switching-like behaviour of a two-terminal VO2 comes at the expense of a hysteresis with the IMT and the MIT transition being driven by two different critical electric field values. In this Letter, we provide, for the first time, a circuit-level model of the hysteresis mechanism which is a key to predicting and controlling the dynamics of relaxation oscillators built on VO2 devices. We show how the proposed model, after being tuned with experimental data, allows us to predict the parameter values for which relaxation oscillation occurs.