Three-Dimensional Non-Linear Complex Model of Dynamic Memristor Switching

A thermodynamical model of filament growing when a current pulse via memristor flows is introduced. The model is the boundary value problem, which includes nonstationary heat conduction equation with non-linear Joule heat source, Poisson equation, and Shockley-Read-Hall equations taking into account strong electron-phonon interactions in trap ionization and charge transport processes. The charge current, which defines the heating in the model, depends on the rate of the oxygen vacancy generation. The latter depends on the local temperature. The solution of the introduced problem allows one to describe the kinetics of the switch process and the final filament morphology.