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In this work, we demonstrate the enhanced synaptic behaviors in trilayer dielectrics (HfO₂/Si₃N₄/SiO₂) on highly doped n-type silicon substrate. First, the three dielectric layers were subjected to material and chemical analyses and thoroughly investigated via transmission electron microscopy and X-ray photoelectron spectroscopy. The resistive switching and synaptic behaviors were improved by inserting a Si₃N₄ layer between the HfO₂ and SiO₂ layers. The electric field within SiO₂ was mitigated, thus reducing the current overshoot in the trilayer device. The reset current was considerably reduced in the trilayer device compared to the bilayer device without a Si₃N₄ layer. Moreover, the nonlinear characteristics in the low-resistance state are helpful for implementing high-density memory. The higher array size in the trilayer device was verified by cross-point array simulation. Finally, the multiple conductance adjustment was demonstrated in the trilayer device by controlling the gradual set and reset switching behavior.