A semiconductor-memory device that reduces leak off due to miniaturization of memory cells, and comprises as a single unit cell: a substrate 1 having a trench section 1a; a selector gate 3 that is located via an insulating film 2 on the substrate adjacent to the trench section 1a; a first well 1b that is formed on the surface of the substrate 1 below the selector gate 3; a floating gate 6 that is located via an insulating film 8a on the surface of the bottom section and sidewall section of the trench section 1a; a second well 1c that is formed on the surface of the bottom section of the trench section 1a below the floating gate 6; a first diffusion area 7a that is formed on the surface of the bottom section of the trench section 1a; and a control gate 11 located via an insulating film 8 on top of the floating gate 6; and where the area near the sidewall surface and bottom surface of the trench section 1a forms a channel in the selector gate 3; and the impurity density of the first well 1b is not more than the impurity density of the second well 1c.