The nature and direction of the hysteresis in memristive devices is critical to device operation and performance and the ability to realise their potential in neuromorphic applications. TiO2 is a prototypical memristive device material and is known to show hysteresis loops with both clockwise switching and counter-clockwise switching and in many instances evidence of negative differential resistance (NDR) behaviour. Here we study the electrical response of a device composed of a single nanowire channel Au-Ti/TiO2/Ti-Au both in air and under vacuum and simulate the I-V characteristics in each case using the Schottky barrier and an ohmic-like transport memristive model which capture nonlinear diffusion and migration of ions within the wire. The dynamics of this complex charge conduction phenomenon is obtained by fitting the nonlinear ion-drift equations with the experimental data. Our experimental results support a nonlinear drift of oxygen vacancies acting as shallow donors under vacuum conditions. Simulations show that dopant diffusion under bias creates a depletion region along the channel which results in NDR behaviour, but it is overcome at higher applied bias due to oxygen vacancy generation at the anode. The model allows the motion of the charged dopants to be visualised during device operation in air and under vacuum and predicts the elimination of the NDR under low bias operation, in agreement with experiments.
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