Resistive switching in a metal-free silicon-based material offers a compelling alternative to existing metal oxide-based resistive RAM (ReRAM) devices, both in terms of ease of fabrication and of enhanced device performance. We report a study of resistive switching in devices consisting of non-stoichiometric silicon-rich silicon dioxide thin films. Our devices exhibit multi-level switching and analogue modulation of resistance as well as standard two-level switching. We demonstrate different operational modes that make it possible to dynamically adjust device properties, in particular two highly desirable properties: nonlinearity and self-rectification. This can potentially enable high levels of device integration in passive crossbar arrays without causing the problem of leakage currents in common line semi-selected devices. Aspects of conduction and switching mechanisms are discussed, and scanning tunnelling microscopy (STM) measurements provide a more detailed insight into both the location and the dimensions of the conductive filaments.