Voltage mediated metal to insulator transition in VO$_{2}$ and V$_{2}$O$_{3}$ nanodevices*

We investigate the mechanism of the voltage mediated MIT in a series of vanadium oxides (VO$_{2}$ and V$_{2}$O$_{3})$ nano-scopic devices. All films presented \textasciitilde 4 orders of magnitude resistance change at the MIT. The devices consist of in-plane gold electrodes with 200 nm wide tip on top of lithographically defined vanadium oxide films. The gap size between electrodes was fixed at 140 nm. Unlike micron-scale devices, the current-voltage characteristics in nano-scale V$_{2}$O$_{3}$ cannot be accounted solely by an inhomogeneous joule-heating model, suggesting additional mechanisms may be playing a role in the switching behavior. However, in the case of nano-scopic VO$_{2}$ devices, it may be possible to explain the results with only inhomogeneous heating. We perform detailed electrical and thermal Finite Element Method (FEM) calculations on both the VO$_{2}$ and V$_{2}$O$_{3}$ devices. We couple the FEM analysis with a variety of theoretical models, which can shed light on the nanoscopic nature of the MIT in VO$_{2}$ and V$_{2}$O$_{3}$.