Metal–insulator–metal devices known as memristors offer voltage-regulated nanoscale conductivity and are of interest in the development of non-volatile random access memory. Typically, however, their tunable conductivity is the result of migrating ions within a stochastically formed filament, and as such their combined resistor–memory performance suffers. Here we show that amorphous silicon compositions, which are doped with oxygen or nitrogen and sandwiched between metal electrodes, can be used to create purely electronic memristors. The devices have coherent electron wave functions that extend to the full device thickness (more than 15 nm) and, despite the thinness and very high aspect ratio of the devices, electrons still follow an isotropic, three-dimensional pathway, thus providing uniform conductivity at the nanoscale. Such pathways in amorphous insulators are derived from overlapping gap states and regulated by trapped charge, which is stabilized by electron–lattice interaction. As a result, the nanometallic memristors also exhibit pressure-triggered insulator-to-metal transitions. Our silicon-based memristors, which could be readily integrated into silicon technology, are purely electronic and offer switching capabilities that are fast, uniform, durable, multi-state and low power.