Phenomenological modeling of memristive devices

Abstract

We present a computationally inexpensive yet accurate phenomenological model of memristive behavior in titanium dioxide devices by fitting experimental data. By design, the model predicts most accurately I-V relation at small non-disturbing electrical stresses, which is often the most critical range of operation for circuit modeling. While the choice of fitting functions is motivated by the switching and conduction mechanisms of particular titanium dioxide devices, the proposed modeling methodology is general enough to be applied to different types of memory devices which feature smooth non-abrupt resistance switching.

Modeling and simulation of large memristive networks

“…Although it seems that the real switching processes are more complex [10], the Pickett model fits well the measured characteristics of particular manufactured devices and can be seen as a prototype model describing the extreme nonlinearity of TiO 2 -based MIM memristor dynamics.…”

“…It is well known that the dynamic behavior of the internal state variables of existing memristive systems, described for example by Pickett's model, strongly depends on voltage or current. On the other hand, the S model is characterized by a very simple state Equation (10). In spite of this, the S model can be useful exactly for modeling large memristive networks: With increasing number of memristors in the circuit, the driving signal is divided among individual memristors such that the voltage swings on them, affecting the dynamics of the memristance variation, decreases.…”

“…Because the contemporary memristive devices work on various principles and utilize assorted materials, there is a wide variety of their models (a comprehensive survey is given in [10]). The bulk of the models of nonvolatile memristive systems are limited to one internal state variable, which appears in the differential equation of motion and simultaneously affects the memristance.…”

“…In the case of TiO 2 -based metal-insulatormetal (MIM) memristors, the class is represented by the physical-phenomenological Pickett model [21] and the simpler Bayat phenomenological model [10]. However, even these models are still not sufficiently accurate in the broad range of dynamic regimes.…”

“…However, even these models are still not sufficiently accurate in the broad range of dynamic regimes. Real memristive devices usually comprise several nonvolatile and volatile switching mechanisms [10], which require a higher order of the differential equation of motion. This class includes model [22] and more recent works [23][24][25] for TiO 2 , WO x , and TaO x memristors.…”