Complex Negative Differential Resistance Characteristics In NbO_x And Its Voltage-controlled Coupled Oscillator

Oscillatory phenomena are very common in nature,and modern neuroscience research shows that human brain calculations are performed through oscillations.In recent years,artificial neural networks based on memristors have received extensive attention in brain-like research.With the development of semiconductor preparation technology,nanoscale,low power consumption and highly integrated oscillators can already be realized,laying a hardware foundation for imitating human brain computing.Volatile memristor,also called as threshold switch,exhibits an S-type negative differential resistance(S-NDR)phenomenon on the current-voltage curve and can be used to fabricate nano-oscillators.Studying the origin of NDR is of great significance for exploring the potential applications of volatile memristors,and studying the dynamic behavior of coupled oscillators is helpful for the use of oscillating neural networks to achieve neuromorphic computing.We study the physical origin of multiple complex NDR phenomena in niobium oxide.First,considering the fact that there is a conductive filament in the device,a core memristor-shell resistance model is constructed.When the shell resistance is a linear resistance,the influence of the critical resistance R_C and the maximum absolute NDR value R_NDR on the hysteresis region is discussed;when the shell resistance is a nonlinear resistance,the basic S-NDR curve and Snap-back(SB)type NDR curve are reproduced.Then based on the assumption of multifilament and infinite shell resistance,a dual-core memristor model was constructed to achieve a complex multi-NDR coexistence curve,including dual S-NDR,dual SB-NDR,and combined S-NDR and SB-NDR.These simulation results show that the current distribution in the space is not uniform when current is flowing through the device.Finally,the device with double S-NDR phenomenon is put into the oscillation circuit,and the oscillation appears,disappears,then reappears and finally re-disappears as the source voltage V_S increases with the fixed load resistance R_L.Two oscillation regions are plotted on the V_S-R_L diagram,which is qualitatively consistent with the double-window oscillation behavior observed in the experiments.We also study the rich dynamic behavior of niobium oxide oscillators and coupled oscillators.For a single oscillator,its oscillation frequency has a strong correlation with the effective capacitance C,source voltage V_S and load resistance R_L.For the coupled oscillator,only the case of capacitive coupling is considered,and the complex dynamic behavior including in-phase coupling and anti-phase coupling is studied.Based on the measured voltages V_D1 and V_D2 on the two devices,the different phase traces are plotted on the V_D1-V_D2 phase planes.The evolution of the phase diagram of the source voltage-coupling capacitance(V_S-C_C)is shown when the load resistance is mismatched.Four regions can be identified in all phase diagrams,including butterfly coupling region,linear coupling region,transition region and non-coupling region.As the load resistance mismatch increases from 1.0%to 3.9%,the linear coupling region gradually disappears,while the butterfly coupling region gradually expands.When the load resistance mismatch is greater than 9.5%,the butterfly coupling region gradually decreases,while the non-coupling region increases significantly.Both the in-phase coupling and anti-phase coupling phenomena,have been initially confirmed in the experiment,which provides a basis for the realization of associative computing by the coupled oscillator network.