Blow-up overheating instability in vanadium dioxide thin films

Abstract

We study an insulator-metal transition (IMT) in vanadium dioxide films. We argue that the main features of the voltage-induced IMT in these systems can be understood within a theory of the blow-up overheating instability. In the blow-up regime, the IMT occurs locally even in uniform films: a narrow ``hot'' metallic channel along the current direction arises in the insulating ``cool'' environment. We derive an instability criterion and analytical formulas for a characteristic instability time and the hot-channel width. We apply our results to the experiments on the epitaxial films available in the literature and our measurements performed on the specially prepared ${\mathrm{VO}}_{2}$ granular films. The main features of the voltage-induced IMT are the same for all considered samples and can be described in the framework of the proposed theory. Interestingly, the mathematical description of the voltage-induced IMT in the vanadium oxide is similar to that proposed for the superconductor-normal state transition in high-${T}_{c}$ tapes. However, the hot channel in high ${T}_{c}$ is directed across the current flow, while in the case of the IMT it is directed along the current.