A plasma-based ferroelectric undoped HfOx capacitor is fabricated using plasma-enhanced atomic layer deposition (PE-ALD), and the multilevel characteristics of synaptic behavior are investigated. A gradual ferroelectric phase transition in the material is confirmed by grazing incidence X-ray diffraction (GI-XRD) for different O-2 plasma periods. The metal-ferroelectric-metal (MFM) capacitor presents excellent remnant polarization (P-r) up to 13 mu C/cm(2) and a switching endurance of more than 10(8) cycles. Superior small potentiation/depression nonlinearity (alpha(p)/alpha(d) = -0.08 /-1.66 for voltage modulation stimulation) for synaptic training and almost symmetry training curve ( vertical bar alpha(p) - alpha(d)vertical bar) are obtained. High stability under multilevel operation with five consecutive cycles of alternating potentiation and depression is exhibited without significant polarization variation for each training step (pulse).