The present invention discloses a small-grain three-dimensional memory (3D-MSG). Each of its memory cells comprises a thin-film diode with critical dimension no larger than 40 nm. The thin-film diode comprises at least a small-grain material, whose grain size G is substantially smaller than the diode size D. The small-grain material is preferably a nano-crystalline material or an amorphous material. The critical dimension f of the small-grain diode is smaller than the critical dimension F of the single-crystalline transistor.