Consider a superlattice consisting of alternating layers of equal thickness of GaAs and AlAs. The potential is a square wave with the minima in GaAs for the F-valley, but for the X-valleys the minima are in AlAs (Figure 3.8). The lowest parts of the conduction band are the F minima in GaAs, so it seems obvious that this is where electrons would migrate. However, this does not take account of the zero-point energy in the quantum wells, which is strongly affected by the difference in mass. The lowest state in the X-valleys arises from the high longitudinal mass, mL ≈1.1 in AlAs (Section 5.8.1). Show that the lowest state for electrons moves from GaAs to AlAs as the period of the superlattice is reduced, and find the critical value. Use an infinitely deep well for a rough estimate, or a finite well for a more accurate result.
Are the holes affected in the same way? Is it possible to make a type II superlattice, where the electrons are confined in one material with the holes in the other?
