I. Introduction
Resistive random access memory (RRAM) devices are promising candidates to replace Flash memory, and their memory switching characteristics have been demonstrated in a variety of material systems [1]–[12]. RRAM devices can be integrated in a crossbar architecture, enabling the realization of large and dense memory arrays. The switching speeds of these devices are high (less than 10-ns switching time [11]), and they exhibit long retention times (over s at 100 °C [6]). Recent work also points to the potential of using RRAM devices for neuromorphic computing [2], [9], [13], and for efficiently realizing logic operations [1], [14]–[18]. All these applications require a comprehensive physics-based understanding and a physical model that captures the dynamics of the filament formation process, including its stability and switching times between resistance levels. The model should have the ability to simulate statistically relevant device parameters such as resistance values and switching times because of the stochastic nature of filament formation.