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Neuromorphic computing offers parallel data processing and low energy consumption and can be useful to replace conventional von Neumann computing. Memristors are two-terminal devices with varying conductance that can be used as synaptic arrays in hardware-based neuromorphic devices. In this research, we extensively investigate the analog symmetric multi-level switching characteristics of zinc tin oxide (ZTO)-based memristor devices for neuromorphic systems. A ZTO semiconductor layer is introduced between a complementary metal-oxide-semiconductor (CMOS) compatible Ni top electrode and a highly doped poly-Si bottom electrode. A variety of bio-realistic synaptic features are demonstrated, including long-term potentiation (LTP), long-term depression (LTD), and spike timing-dependent plasticity (STDP). The Ni/ZTO/Si device in which the adjustment of the number of states in conductance is realized by applying different pulse schemes is highly suitable for hardware-based neuromorphic applications. We evaluate the pattern recognition accuracy by implementing a system-level neural network simulation with ZTO-based memristor synapses. The density of states (DOS) and charge density plots reveal that oxygen vacancies in ZTO assist in generating resistive switching in the Ni/ZTO/Si device. The proposed ZTO-based memristor composed of metal-insulator-semiconductor (MIS) structure is expected to contribute to future neuromorphic applications through further studies.