We report an improvement in minimizing the dispersion of resistive switching (RS) parameters such as ON/OFF state resistances and switching voltages of Cu/ZnO/Pt structures in which ZnO films have been deposited at elevated temperature with N doping. This deposition process can enlarge the ZnO grain size and lessen grain boundaries while maintaining a high initial resistance since ZnO naturally shows n-type conductivity and N is a p-type dopant but with a low solubility. Cu filaments with a diameter of 15 nm are found to form at the ZnO grain boundaries. Therefore, fewer grain boundaries could depress the randomicity of the formation/rupture of Cu filaments and result in more stable RS performances. Such memory devices show a fast programming speed of 10 ns.