Title: Influence of thermal boundary conditions on the current-driven resistive transition in $\mathbf{VO_2}$ microbridges,
Abstract: We investigate the resistive switching behaviour of $\mathrm{VO_2}$
microbridges under current bias as a function of temperature and thermal
coupling with the heat bath. Upon increasing the electrical current bias, the
formation of the metallic phase can progress smoothly or through sharp jumps.
The magnitude and threshold current values of these sharp resistance drops show
random behaviour and are dramatically influenced by thermal dissipation
conditions. Our results also evidence how the propagation of the metallic phase
induced by electrical current in $\mathrm{VO_2}$, and thus the shape of the
resulting high-conductivity path, are not predictable. We discuss the origin of
the switching events through a simple electro-thermal model based on the domain
structure of $\mathrm{VO_2}$ films that can be useful to improve the stability
and controllability of future $\mathrm{VO_2}$-based devices.