Binding energies of hydrogenic impurities in finite-quantum-well structures with effective-mass mismatch: Simple and accurate variational treatments

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Abstract
Simple two- and three-dimensional (2D and 3D) effective-mass approximations are applied to the calculation of the energy levels due to hydrogenic impurities in finite-quantum-well structures. For two materials with identical effective masses the 2D and 3D treatments both give results of accuracy comparable to that of more sophisticated numerical calculations. In the case of effective-mass mismatch, however, only the 2D treatment can satisfy the correct boundary conditions, which leads to the introduction of an equivalent parallel effective mass. The method is shown to be accurate and can be extended to the determination of all levels derived from different subbands.