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The work investigated the shape and orientation of oxygen vacancy clusters in HfO-base resistive random access memory (ReRAM) by using the first-principle method based on the density functional theory. Firstly, the formation energy of different local Vo clusters was calculated in four established orientation systems. Then, the optimized orientation and charger conductor shape were identified by comparing the isosurface plots of partial charge density, formation energy, and the highest isosurface value of oxygen vacancy. The calculated results revealed that the [010] orientation was the optimal migration path of Vo, and the shape of system D4 was the best charge conductor in HfO, which effectively influenced the SET voltage, formation voltage and the ON/OFF ratio of the device. Afterwards, the PDOS of Hf near Vo and total density of states of the system D4_010 were obtained, revealing the composition of charge conductor was oxygen vacancy instead of metal Hf. Furthermore, the migration barriers of the Vo hopping between neighboring unit cells were calculated along four different orientations. The motion was proved along [010] orientation. The optimal circulation path for Vo migration in the HfO super-cell was obtained.


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