A semiconductor memory comprises a capacitor with a data storage portion, and an insulated-gate field-effect transistor. The capacitor is formed by a plate which is made up of the side walls and base of a groove formed in a semiconductor substrate, and by a capacitor electrode formed on the side walls and the base, over an insulation film, and which is connected electrically to the source or drain of the insulated-gate field-effect transistor. Various embodiments are provided for reducing size and preventing leakage between other memory cells, including forming stacked capacitors, forming the transistor over the capacitor, using a silicon-over-insulator arrangement for the transistor, forming a common capacitor plate and providing high impurity layers within the substrate.