Phase-field model of filament formation and growth in percolating memristive systems of nanoparticles

Based on the phase-field theory, a two-dimensional model describing the formation and growth of filaments in a system of conducting particles immersed in a dielectric matrix with active electrodes has been developed. We simulate and analyze the dynamics of redistribution of active substance, which undergoes reversible intercalation through the particle surface and forms conductive phase within the matrix. This phase corresponds to the filaments connecting particles either to each other or to the electrodes. It has been demonstrated that the system exhibits hysteresis in current–voltage curves observed under conditions of sawtooth-like variation of the electrical current. In the proposed model, the primary mechanism for the formation and growth of filaments is the non-uniform distribution of conductivity throughout the system, resulting in the formation of a highly non-uniform electric field. This non-uniform electric field may lead to the movement of fragments of the conductive phase, corresponding to the extraction of filaments from the particles or active electrodes. Experimental investigations of percolation network of silver nanoparticles in a HfOx dielectric matrix are presented. The results reveal that even when a percolation ensemble of silver nanoparticles is coated with hafnium oxide, memristive effects remain preserved. Additionally, the practical use of the phase-field model is demonstrated, as it qualitatively reproduces the memristive dynamics observed in percolation ensembles of nanoparticles. This model takes into account the concurrent evolution of phases and the redistribution of electric voltages within the sample. The findings can have important implications for understanding and manipulating memristive behavior in nanoparticle-based systems with potential applications in neuromorphic computations.