Calculating Macroscopic Resistance using Microscopic Reflectance in VO₂ thin films

Vanadium Dioxide (VO₂) exhibits multiscale pattern formation while it undergoes a temperature-driven Metal-Insulator (MI) phase transition. We use optical microscopy techniques to image the entire surface of a two-terminal etched VO₂ microbridge, simultaneously measuring the macroscopic resistance of the device. Patches of metal and insulator form while undergoing the MI phase transition and display hysteresis.  We employ a random field Ising model to predict sub-pixel spatial structure below optical resolution, mapping the reflectivity of each pixel to the Ising pseudomagnetization, in order to predict the effective microscopic resistance of each pixel.  We use the (exact) bond propagation algorithm to reduce the 2D resistor grid into a single equivalent resistance.  These studies pave the way toward a deeper understanding of resistance avalanches, memory effects, and spiking behavior in VO₂.