A non-volatile solid state resistive device that includes a first electrode, a p-type poly-silicon second electrode, and a non-crystalline silicon nanostructure electrically connected between the electrodes. The nanostructure has a resistance that is adjustable in response to a voltage being applied to the nanostructure via the electrodes. The nanostructure can be formed as a nanopillar embedded in an insulating layer located between the electrodes. The first electrode can be a silver or other electrically conductive metal electrode. A third (metal) electrode can be connected to the p-type poly-silicon second electrode at a location adjacent the nanostructure to permit connection of the two metal electrodes to other circuitry. The resistive device can be used as a unit memory cell of a digital non-volatile memory device to store one or more bits of digital data by varying its resistance between two or more values.