### Quantum well Super-lattice dispersion

In the following example we demonstrate how the eigenvalue dispersion of a super-lattice ($GaAs$\) can be calculated.

The lattice is built from $GaAs$ wells, which have $3 nm$ width, and the $Al_{0.3}Ga_{0.7}As$ barriers with $5 nm$ of width. We need to apply periodic boundary conditions to the structure in the Global Parameters window. Also in order to calculate the eigenvalue dispersion of the structure we have to add an envelope function calculator with $k$ space dispersion (values in the x direction).

The ground state electron wave-function, and the first excited one is plotted in Figure 1. It shows that the electron penetrates in the AlGaAs barrier.

The electron eigenvalue dispersion is plotted in Figure 2.

It shows that the dispersion of the ground state WF is very flat, while the excited states are very like to a free moving electron dispersion.

The hole dispersion in the $k.p$ 6 band formulation is plotted in Figure 3.(without spin degeneracy), which shows that just the first two WFs seem to be bound.