Gibbs spatial process for characterization of filament interaction in ReRAM devices via photon emission microscopy

In this work, we investigate spatial statistical properties of filament patterns in resistive random-access memory (ReRAM) devices measured from a newly developed near-infrared photon emission microscopy (PEM) [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Stellari et al., in Proceedings of the 47th International Symposium for Testing and Failure Analysis Conference (ISTFA) (ASM International, 2021), pp. 115-121]. Unlike previous reports on uncorrelated filaments [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Wu et al., Appl. Phys. Lett. 99, 093502 (2011)], we report a strong clustering and non-Poisson pattern of filaments constructed from individual devices. A Poisson-mixture model incorporating the clustering (attractive) effect is introduced with an excellent agreement with the PEM data for global and nearest-neighbor spatial statistics. On the other hand, a two-filament pattern is also detected within the ReRAM devices. We found that both attractive and repulsive interactions among the filaments are required in a Gibbs process to explain the filament spatial distribution. We implemented a birth-death algorithm using a Markov-chain Monte Carlo approach and achieve good agreement with the PEM data using a generalized Morse potential.