With the exploration of ferroelectric materials, researchers have a strong desire to explore the next generation of non‐volatile ferroelectric memory with silicon‐based epitaxy, high‐density storage, and algebraic operations. Herein, a silicon‐based memristor with an epitaxial vertically aligned nanostructures BaTiO3–CeO2 film based on La0.67Sr0.33MnO3/SrTiO3/Si substrate is reported. The ferroelectric polarization reversal is optimized through the continuous exploring of growth temperature, and the epitaxial structure is obtained, thus it improves the resistance characteristic, the multi‐value storage function of five states is achieved, and the robust endurance characteristic can reach 109 cycles. In the synapse plasticity modulated by pulse voltage process, the function of the spiking‐time‐dependent plasticity and paired‐pulse facilitation is simulated successfully. More importantly, the algebraic operations of addition, subtraction, multiplication, and division are realized by using fast speed pulse of the width ≈50 ns. Subsequently, a convolutional neural network is constructed for identifying the CIFAR‐10 dataset, to simulate the performance of the device; the online and offline learning recognition rate reach 90.03% and 92.55%, respectively. Overall, this study paves the way for memristors with silicon‐based epitaxial ferroelectric films to realize multi‐value storage, algebraic operations, and neural computing chip applications.

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In this work, a memristor device with Pd/HfO2:Gd/La0.67Sr0.33MnO3/SrTiO3/Si was prepared, and its synaptic behavior was investigated. The memristor shows excellent performance in I–V loops and ferroelectric properties. Through polarization, the conductance modulation of the memristor is achieved by the reversal of the ferroelectric domain. In addition, we simulate biological synapses and synaptic plasticities such as spike-timing-dependent plasticity, paired-pulse facilitation, and an excitatory postsynaptic current. These results lay the foundation for the development of synaptic functions in Hf-based ferroelectric thin films and will promote the development of synaptic applications for neuromorphic computing chips.