A semiconductor memory device includes a substrate, and a trench formed in the substrate. First and second floating gates, each associated with corresponding first and second memory cells, extend into the trench. Since the trench can be made relatively deep, the floating gates may be made relatively large while the lateral dimensions of the floating gates remains small. Moreover, the insulator thickness between the floating gate and a sidewall of the trench where a channel region is formed can be made relatively thick, even though the lateral extent of the memory cell is reduced. A programming gate extends into the trench between the first and second floating gates, and is shared, along with a source region, by the two memory cells.