Magneto-optical studies of GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As multi-quantum-well structures grown by molecular-beam epitaxy

We have measured the diamagnetic shifts of both the heavy-hole and the light-hole excitons as a function of the well size and the magnetic field (up to 36 kG) in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As multi-quantum-well (MQW) structures using high-resolution optical spectroscopy at liquid-helium temperatures. The applied magnetic field is parallel to the plane of the MQW structures which were grown by molecular-beam epitaxy. We find that in this range of the magnetic field, the diamagnetic shift varies quadratically with the applied field. At a given value of the magnetic field, the diamagnetic shifts of both exciton systems vary almost linearly with the well size. We have also determined, for the first time, the variation of the effective g values of the heavy and light holes as a function of the well size assuming that the electron g value is independent of the well width. A comparison of our measured values of the diamagnetic shifts with those of another group and with the results of a recent calculation is discussed.