We apply a unique three-dimensional (3D) physics-based atomistic simulator to study silicon-rich (SiOx, x<2) resistive switching nonvolatile memory (RRAM) devices. We couple self-consistently a simulation of ion and electron transport to the 'atomistic' simulator GARAND and a selfheating model to explore the switching processes in these structures. The simulation model is more advanced than other available phenomenological models based on the resistor breaker network. The simulator is

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... with experimental data, and reconstructs accurately the formation and rupture of the conductive filament in the 3D space. We demonstrate how the simulator is useful for exploring the little-known physics of these promising devices, and show that switching is an intrinsic property of the SiOx layer. In general, the simulation framework is useful for providing efficient designs, in terms of performance, variability and reliability, for memory devices and circuits. The simulator validity is not limited to SiOx-based devices, and can be used to study other promising RRAM systems based, e.g., on transition metal oxides.