The ground-state energy of an exciton in a cylindrical quantum dot with finite potential barriers is calculated by the variation method within the envelope-function approximation. The computations are performed in the cases of infinite and finite band offsets. The limit of a strictly two-dimensional quantum disk is discussed. Our numerical results are particularized to the GaAs/Ga_1-x{Al}ₓ$As system with 0.10{≤}x{≤}0.30. In this case, the effect of the quantum confinement is the highest for dot dimensions near 50 {}.
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Goff et al. (1993) studied this question.
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