Abstract: The effect of HfO₂ functional layer thickness on the resistive switching performance of Cu/HfO₂/ITO devices was studied by DC magnetron sputtering method and adjusting the sputtering time. The crystal structure of the prepared HfO₂ thin film was tested by X-ray diffraction technique. The experimental results show that the intensity of the diffraction peak of the HfO₂ thin film increases with the increase of the thickness. The composition and valence state of 12 nm thick HfO₂ thin films were analyzed by X-ray photoelectron spectroscopy (XPS). The results show that the valence state of Hf in HfO₂ thin films is +4. By testing the I-V characteristics of Cu/HfO₂/ITO devices, the three Cu/HfO₂/ITO devices with different functional layer thicknesses all belong to bipolar transition and do not require initialization. The cycle tolerance test of Cu/HfO₂/ITO device shows that the device can still maintain good switching characteristics after 60 cycles. The stability of Cu/HfO₂/ITO device is analyzed. With the increase of thickness, the dispersion coefficient of RHRS and RLRS increases, and the stability of the device decreases. The Cu/HfO₂/ITO device with a functional layer thickness of about 12 nm has the best stability. The I-V curve of Cu/HfO₂/ITO device with a functional layer thickness of about 12 nm is fitted by double logarithm. The fitting results show that the device conforms to the ohmic conduction mechanism in the low resistance state (LRS) and the space charge limited current conduction mechanism in the high resistance state (HRS). By setting the SET limiting current of the Cu/HfO₂/ITO device with a functional layer thickness of about 12 nm, which shown that the device has the application potential of multi-valued storage. The results show that it is beneficial to improve the resistive change performance of Cu/HfO₂/ITO by adjusting the thickness of the functional layer HfO₂.