Confinement by massive walls

The transverse degree of freedom for an electron in a quantum well is studied in the limit that the effective mass in the barrier material becomes very large. Two remarkable features characterize this limit. The first is that the effective-mass eigenfunctions inside the well satisfy zero-slope boundary conditions. The second is that the energy eigenvalues decrease with increasing confinement, in contradistinction to the behavior when confinement is caused by an increasing offset. By comparing with exact model results we confirm that these predictions of effective-mass theory are qualitatively correct. As an application we consider the binding energy of a donor in a quantum dot.