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A self-consistent procedure for calculating the energy structure, wave functions, and charge distribution in spherically symmetric semiconductor quantum dots is presented that takes account of both bound and freeelectron states. The Schrödinger and Poisson equations are solved iteratively while using the Morse-type parametrized potential to keep the charge neutrality in each iterative step. Numerical calculations performed for a GaAs-Al 0.3 Ga 0.7 As based quantum dot indicate that under realistic doping conditions bound states account for most of the charge accumulated in the dot. However, the self-consistent potential very significantly modifies the free-state wave functions and hence the bound-free transition matrix elements.

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Two different approaches for the optimization of the quantum well profile are proposed and discussed. One is the multiparameter procedure, based on the inverse spectral theory ͑IST͒ and supersymmetric quantum mechanics ͑SUSYQM͒, which is an extension of the single-parameter procedure devised earlier for this purpose. Another approach combines the simulated annealing and variational calculus. The two approaches are compared on the example of optimizing the well profile to get maximal resonant second-order susceptibility at 10.6 m ͑116 meV͒. Within the multiparameter IST/SUSYQM procedures, we find that the two-parameter procedure delivers significantly better results than the single-parameter procedure, while introducing more parameters does not result in any further improvement. However, even better results ͑by about 20%͒ were obtained with the variational procedure, which, though more time consuming, is free from any unnecessary constraints and may thus lead to global optimization.

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