A semiconductor device includes a semiconductor island having at least one electrical dopant atom and encapsulated by dielectric materials including at least one dielectric material layer. At least two portions of the at least one dielectric material layer have a thickness less than 2 nm to enable quantum tunneling effects. A source-side conductive material portion and a drain-side conductive material portion abuts the two portions of the at least one dielectric material layer. A gate conductor is located on the at least one dielectric material layer between the source-side conductive material portion and the drain-side conductive material portion. The potential of the semiconductor island responds to the voltage at the gate conductor to enable or disable tunneling current through the two portions of the at least one dielectric material layer. Design structures for the semiconductor device are also provided.