  In this theoretical study, we focus on the high-frequency response of the
electrothermal NbO2-Mott threshold switch, a real-world electronic device,
which has been proved to be relevant in several applications and is classified
as a volatile memristor. Memristors of this kind, have been shown to exhibit
distinctive non-linear behaviors crucial for cutting-edge neuromorphic
circuits. In accordance with well-established models for these devices, their
resistances depend on their body temperatures, which evolve over time following
Newton's Law of Cooling. Here, we demonstrate that HP's NbO2-Mott memristor can
manifest up to three distinct steady-state oscillatory behaviors under a
suitable high-frequency periodic voltage input, showcasing increased
versatility despite its volatile nature. Additionally, when subjected to a
high-frequency periodic voltage signal, the device body temperature oscillates
with a negligible peak-to-peak amplitude. Since, the temperature remains almost
constant over an input cycle, the devices under study behave as linear
resistors during each input cycle. Based on these insights, this paper presents
analytical equations characterizing the response of the NbO2-Mott memristor to
high-frequency voltage inputs, demarcating regions in the state space where
distinct initial conditions lead to various asymptotic oscillatory behaviors.
Importantly, the mathematical methods introduced in this manuscript are
applicable to any volatile electrothermal resistive switch. Additionally, this
paper presents analytical equations that accurately reproduce the temperature
time-waveform of the studied device during both its transient and steady-state
phases when subjected to a zero-mean sinusoidal voltage input oscillating in
the high-frequency limit.
