In many semiconductors such as GaAs, the conduction band has a conduction band minimum at zone center, and an indirect gap with higher energy at another minimum, at a critical point on the zone boundary. The zone-center minimum is typically called the Г-valley, while the other, indirect minima are called the X-valley and the L-valley.

Suppose that we make a superlattice with well material GaAs, which has a Г- valley 1.5 eV above the valence band maximum, and barrier material AlAs, which has a Г-valley 2.6 eV higher than the GaAs valence band maximum, but an [Xvalley] only 1.7 eV higher than the GaAs valence band maximum. If the GaAs quantum well width is small enough, the confined state of the Г-valley can be pushed higher than the AlAs X-valley, as shown in Figure 2.31. In this case, electrons will fall from the GaAs Г-valley into the X-valley of the barriers, so that the AlAs forms a quantum well for the electrons, with the GaAs layers acting as barriers. The valence quantum well for the electrons, with the GaAs layers acting as barriers. The valenceband holes will remain confined in the GaAs layers, however. This is called a Type II superlattice. A structure in which both the electrons and holes are in the same layer is called a Type Isuperlattice.

Assuming that there is negligible penetration of the wave function of the Г-valley electrons into the barriers, estimate the GaAs quantum well thickness at which the above structure will convert from a Type I to a Type II structure. The conduction electron effective mass is approximately 0.06m₀ for GaAs.