A flash memory device includes a floating gate electrode formed within a substrate semiconductor layer having a doping of a first conductivity type, a pair of active regions formed within the substrate semiconductor layer, having a doping of a second conductivity type, and laterally spaced apart by the floating gate electrode, an erase gate electrode formed within the substrate semiconductor layer and laterally offset from the floating gate electrode, and a control gate electrode that overlies the floating gate electrode. The floating gate electrode may be formed in a first opening in the substrate semiconductor layer, and the erase gate electrode may be formed in a second opening in the substrate semiconductor layer. Multiple instances of the flash memory device may be arranged as a two-dimensional array of flash memory cells.