Ellipsoidal valley donor binding energies in a quantum well

We describe a modification of the usual separable wave function approach to donor electrons confined in heterostructures which reflects the intersubband Coulomb coupling. The donor Coulomb potential is split into effective normal and in-plane components which are then used to solve for the corresponding wave functions. The procedure is carried out self consistently which can be shown to result in the best donor wave function that can be expressed in separable form. As an example the method is applied to calculate a few of the lower lying levels of a donor in a quantum well in a material with a single ellipsoidal valley conduction band.