Optimal migration route of Cu in HfO2

The movement of Cu in a HfO2-based resistive random access memory （RRAM） device is investigated in depth by first-principle calculations. Thermodynamics analysis shows that the dominant motion of Cu tends to be along the [001] orientation with a faster speed. The migration barriers along different routes are compared and reveal that the [001] orientation is the optimal migration route of Cu in HfO2, which is more favorable for Cu transportation. Furthermore, the preferable HfOz growth orientation along [100], corresponding to Cu migration along [001], is also observed. Therefore, it is proposed that the HfO2 material should grow along [100] and the operating voltage should be applied along [001], which will contribute to the improvement of the response speed and the reduction of power consumption of RRAM.