Development of spatial nearest-neighbor analysis and Clustering/Gibbs statistical methodology for filament percolation in dielectric breakdown and forming process in ReRAM devices

In this work, we develop a spatial nearest-neighbor analysis methodology to investigate the spatial distribution (pattern) of filaments (or Breakdown (BD) spots) obtained by various physical experimental measurements, such as recently developed Photon Emission Microscopy (PEM) for ReRAM [1], Scanning Tunneling Microscopy (STM) [2], and IR-thermography [3]. For non-uniform spatial distributions of BD spots, a spatial clustering model is successfully used to explain the experimental data. For filament formation, found in ReRAM devices, a Gibbs process model using a Markov-Chain Monte-Carlo (MCMC) approach is developed to successfully account for the inhibitory and attractive interaction among filaments with a generalized Morse potential.