TiO$_2$-based Memristors and ReRAM: Materials, Mechanisms and Models (a Review)

The memristor is the fundamental non-linear circuit element, with uses in computing and computer memory. ReRAM (Resistive Random Access Memory) is a resistive switching memory proposed as a non-volatile memory. In this review we shall summarise the state of the art for these closely-related fields, concentrating on titanium dioxide, the well-utilised and archetypal material for both. We shall cover material properties, switching mechanisms and models to demonstrate what ReRAM and memristor scientists can learn from each other and examine the outlook for these technologies.