  In this work we report on the role of ion transport for the dynamic behavior
of a double barrier quantum mechanical
Al/Al$_2$O$_3$/Nb$_{\text{x}}$O$_{\text{y}}$/Au memristive device based on
numerical simulations in conjunction with experimental measurements. The device
consists of an ultra-thin Nb$_{\text{x}}$O$_{\text{y}}$ solid state electrolyte
between an Al$_2$O$_3$ tunnel barrier and a semiconductor metal interface at an
Au electrode. It is shown that the device provides a number of interesting
features for potential applications such as an intrinsic current compliance, a
relatively long retention time, and no need for an initialization step.
Therefore, it is particularly attractive for applications in highly dense
random access memories or neuromorphic mixed signal circuits. However, the
underlying physical mechanisms of the resistive switching are still not
completely understood yet. To investigate the interplay between the current
transport mechanisms and the inner atomistic device structure a lumped element
circuit model is consistently coupled with 3D kinetic Monte Carlo model for the
ion transport. The simulation results indicate that the drift of charged point
defects within the Nb$_{\text{x}}$O$_{\text{y}}$ is the key factor for the
resistive switching behavior. It is shown in detail that the diffusion of
oxygen modifies the local electronic interface states resulting in a change of
the interface properties of the double barrier device.
