Diamagnetic shift as a measure of the penetration of a quasi-two-dimensional exciton into quantum-well barriers

The diamagnetic shift of the exciton recombination in ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum wells goes through a minimum for a well thickness of 40 Å and increases for a thickness of 20 Å. We develop a theory of the exciton diamagnetic shift for intermediate and high fields (5–12 T) that takes into account the three-dimensional electron-hole Coulomb interaction. The theory shows a sensitivity of the diamagnetic shift to the quasi-two-dimensional exciton thickness and describes the experimentally found minimum in the diamagnetic shift. The exciton binding energy as a function of quantum-well thickness is also obtained. A correction term to the average distance of electrons and holes, which takes into account the underestimated theoretical penetration of electron and hole wave functions into the barrier, produces a close agreement with the experimental data.