An in-depth physical study of conductive filaments (CFs) density in Ni/HfO2/Si-n+ unipolar resistive random access memories (RRAMs) has been performed. To do so, the authors have employed both experimental measurements and simulations by means of a 3D kinetic Monte Carlo (kMC) tool. The kMC simulator accounts for redox reactions and ion migration considering the three dimensional (3D) temperature and electric potential distributions within the device dielectric at each simulation time step. The formation and destruction of conductive filaments are described; in particular, the CF density is calculated making use of a new methodology proposed here. The CF ohmic resistance can be linked to the CF density. Finally, the 2D and 3D percolation paths within the conductive filaments are analyzed to characterize the low resistance state of the RRAM under study.

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