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We investigate the effect of Cu concentration On-state resistance retention characteristics of W/Cu/Ti/HfO/Pt memory cell. The development of RRAM device for application depends on the understanding of the failure mechanism and the key parameters for device optimization. In this study, we develop analytical expression for cations (Cu+) diffusionmodel using Gaussian distribution for detailed analysis of data retention time at high temperature. It is found that the improvement of data retention time depends not only on the conductive filament (CF) size but also on Cu atoms concentration density in the CF. Based on the simulation result, better data retention time is observed for electron wave function associated with Cu+ overlap and an extended state formation. This can be verified by analytical calculation of Cu atom defects inside the filament, based on Cu+diffusionmodel. The importance of Cu diffusion for the device reliability and the corresponding local temperature of the filament were analyzed by COMSOL Multiphysics simulation.


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