Tight-binding description of the band-edge states in GaAs/AlAs quantum wells and superlattices

We present a tight-binding investigation of the electron and hole band-edge states for GaAs/AlAs heterostructures. Quantum wells are studied near the critical width in which the system undergoes a direct- to indirect-gap transition. Results are compared for first- and second-nearest-neighbor models. For the first hole state both descriptions are in essential agreement. For the first electron state, however, important differences arise. Although the critical width is the same in both models, for the second-nearest-neighbor approach the indirect-gap regime is characterized by the wave function escaping from the well into the AlAs barriers, but keeping the same translational symmetry. In the first-nearest-neighbor case, the transition is characterized by a change in translational symmetry, and the wave function may or may not remain localized in the well. Type II superlattices are considered within the second-nearest-neighbor approach. For increasing thickness of the AlAs region, we show that the lowest electron state symmetry changes from $X_z$ to $X_{\mathrm{xy}},$ as observed experimentally.