History Erase Effect in a Non-Volatile Memristor

This work presents a detailed study of the nonlinear dynamics of a tantalum oxide memristor recently fabricated at Hewlett Packard Labs. Our investigations uncover direct current, quasi-static, and alternating current behavior of the nanodevice. A thorough study of the dynamics emerging in the nanoscale element under various input/initial condition combinations reveals a fundamental property of the tantalum oxide device, which was unnoticed so far. The initial condition has no effect on the steady-state operation of the memristor under non-zero input. This property, known as fading memory in system theory, implies the uniqueness of asymptotic behavior of the memristor. The progressive input-induced memory erase phenomenon is solely determined by the switching dynamics of the nanodevice, mathematically described by the state evolution function, which governs the rate of evolution of the memristor state. A constant-sign DC input will activate on or off switching dynamics only. Consequently, due to the limited on/off memductance ratio, the memristor will asymptotically attain a fully-conducting or highly-resistive state, irrespective of the initial condition. Most interestingly, under AC periodic excitations, it is the pronounced asymmetry in the state dependence of on and off switching processes which is at the basis of the reported history erase effect. It is important to point out that this novel fading memory phenomenon does not compromise the nonvolatile behavior of the nanostructure. In fact, despite the device may be stimulated so as to forget its past history, it still has a continuum of analog nonvolatile memory states.

I. Introduction

The literature about the memristor [1], theoretically postulated in 1971 [2], has been growing exponentially with time since 2008 [3]. Most of current research is devoted to the fabrication of devices with improved performance in view of their most appealing engineering applications, namely non-volatile memory design, neuromorphic system development, and novel dynamic circuit conception [4]. Some papers on two-terminal elements exhibiting fingerprints of memristive behavior report insightful analyses of device dynamics, carried out in the lab and/or through proper post-processing on numerical solutions of mathematical models. However, in many cases, details on experimental or simulation settings are omitted or partially described, and investigations are mainly focused on a limited set of device properties under optimization. From a circuit theoretic point of view these aspects do not allow a proper assessment of the nonlinear behavior of the device, motivating us to carry out the work presented in this paper, in which the mathematical model of a device manufactured at Hewlett Packard Labs [5] and based upon one of the most promising materials for memristor technology, namely tantalum oxide, is thoroughly investigated to uncover the underlying nonlinear dynamics. Excitation of the memristor through various distinct input sources and, for each case, record of the system response for a number of initial conditions, swept uniformly across the entire existence domain of the memristor state, allows us to draw a detailed picture of the nonlinear behavior of the nanodevice. Very importantly, the results of the theoretical analysis are confirmed through experiments conducted on a sample device.