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The major hindrance for high-density application of two-terminal resistive random-access memory (RRAM) array design is unintentional sneak path leakage through adjacent cells. Herein, we propose a bilayer structure of Ta₂O₅/Al₂O₃-based bipolar type RRAM by evaluating the intrinsic nonlinear characteristics without integration with an additional transistor and selector device. We conducted X-ray photoelectron spectroscopy (XPS) analysis with different etching times to verify Ta₂O₅/Al₂O₃ layers deposited on the TiN bottom electrode. The optimized nonlinear properties with current suppression are obtained by varying Al₂O₃ thickness. The maximum nonlinearity (~71) is achieved in a Ta₂O₅/Al₂O₃ (3 nm) sample. Furthermore, we estimated the comparative read margin based on the I-V characteristics with different thicknesses of Al₂O₃ film for the crossbar array applications. We expect that this study about the effect of the Al₂O₃ tunnel barrier thickness on Ta₂O₅-based memristors could provide a guideline for developing a selector-less RRAM application.