The ground-state energy and binding energy of an exciton, confined in a quantum disk, are calculated as a function of an external magnetic field. The confinement potential is a hard wall of finite height. The diamagnetic shift is investigated for magnetic fields up to 40 T. Our results are applied to ${\mathrm{In}}_y{\mathrm{Al}}_{1-y}{\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ self-assembled quantum dots, and good agreement with experiments is obtained if we assume that the light hole is involved in the exciton formation. Furthermore, we investigated the influence of the dot size on the diamagnetic shift by changing the disk radius. The exciton excited states are found as a function of the magnetic field. The relative angular momentum is not a good quantum number and its value changes with the magnetic field strength.

• Received 25 February 2000

DOI:https://doi.org/10.1103/PhysRevB.63.205311