To realize super high integration of single electronic transistor with such a structure, where electrons can be moved in up and down direction (vertically) of wafer, namely, stereoscopically.

A quantum well is formed by sandwiching a first well layer. consisting of an undoped Al0.2Ga0.8As drain layer 15 and an undoped Al0.2G0.8As source layer 17, etc., with a potential barrier layer containing an n-Al0.4Ga0.6 As electron supply layer 13 or 19. Then a non-doped GaAs island 16 as a second well layer, which generates a potential lower than the first well layer is inserted into the first well layer in the quantum well, and further a source electrode is formed in contact with a two-dimensional electron gas layer which is generated adjacent to a boundary of the first well layer. A drain electrode is formed in contact with a two-dimensional electron gas layer, which is generated adjacent to the other boundary thereof, and a gate electrode is formed to give a potential to the island layer 16 as the second well layer.