We report on resistive switching of memristive electrochemical metallization devices using 3D kinetic Monte Carlo simulations describing the transport of ions through a solid state electrolyte of an Ag/TiO$_{text{x}}$/Pt thin layer system. The ion transport model is consistently coupled with solvers for the electric field and thermal diffusion. We show that the model is able to describe not only the formation of conducting filaments but also its dissolution. Furthermore, we calculate realistic current-voltage characteristics and resistive switching kinetics. Finally, we discuss in detail the influence of both the electric field and the local heat on the switching processes of the device.
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