A quantum well structure is disclosed, which is comprised of a quantum well layer of a thickness substantially equal to the de Broglie wavelength of electrons and carrier confinement layers of an energy gap greater than that of the quantum well layer. A second material of a lattice constant different from that of a first material primarily for the quantum well layer is disposed in the quantum well layer to provide a phase shift in the period of the crystal lattice of the first material, thereby forming energy levels in the forbidden band of the quantum well layer. A semiconductor device which employs such a quantum well structure and is so constructed as to utilize its physical phenomenon which is caused by the energy levels in the forbidden band. In concrete terms, the present invention has its feature in allowing ease in the fabrication of an intermediate infrared or blue light emitting device, for instance.