Chua's Constitutive Memristor Relations for Physical Phenomena at Metal–Oxide Interfaces

Abstract

Despite a considerable number of memristor models of different complexity proposed in the literature, there is an ongoing debate over what kind of memristor model should be universally adopted for exploration of the unique opportunities integrated memristor circuits may offer. Here, we follow Chua's approach, that models for $i-v$ characteristics are devoid of predictive power and that instead a memristor model should be expressed in terms of electric flux $\varphi$ and total charge $q$ only—independent of any specific driving input. Accordingly, Chua's constitutive memristor relations are constructed explicitly for Williams' famous TiO $_{2}$ device in terms of $q=q(\varphi)$ . It is shown that this kind of model describes correctly the prevalent physical phenomena at the metal–oxide interfaces and is able to predict without any further parameters or assumptions, the dependence of $V_{\rm set}$ and $V_{\rm reset}$ voltages on the particular input voltage wave form. The impact of thermal (memory) effects on device performance is explored in numerical simulations.