Conventional computing architectures are poor suited to the unique workload demands of deep learning, which has led to a surge in interest in memory-centric computing. Herein, a trilayer (Hf0.8Si0.2O2/Al2O3/Hf0.5Si0.5O2)-based self-rectifying resistive memory cell (SRMC) that exhibits (i) large selectivity (ca. 104), (ii) two-bit operation, (iii) low read power (4 and 0.8 nW for low and high resistance states, respectively), (iv) read latency (<10 μs), (v) excellent non-volatility (data retention >104 s at 85 °C), and (vi) complementary metal-oxide-semiconductor compatibility (maximum supply voltage ≤5 V) is introduced, which outperforms previously reported SRMCs. These characteristics render the SRMC highly suitable for the main memory for memory-centric computing which can improve deep learning acceleration. Furthermore, the low programming power (ca. 18 nW), latency (100 μs), and endurance (>106) highlight the energy-efficiency and highly reliable random-access memory of our SRMC. The feasible operation of individual SRMCs in passive crossbar arrays of different sizes (30 × 30, 160 × 160, and 320 × 320) is attributed to the large asymmetry and nonlinearity in the current-voltage behavior of the proposed SRMC, verifying its potential for application in large-scale and high-density non-volatile memory for memory-centric computing.