Magnetic g factor of electrons in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

The magnitude and sign of the effective magnetic splitting factor ${\mathit{g}}^{\mathrm{*}}$ for conduction electrons in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells have been determined as a function of well width down to 5 nm. The experimental method is based on combined measurements of the decay time of photoluminescence and of the suppression of its circular polarization under polarized optical pumping in a magnetic field perpendicular to the growth axis (Hanle effect). Measurements as a function of hole sheet density in the wells reveal a transition from excitonic behavior with very small apparent g value for low density, to larger absolute values characteristic of free electrons at higher densities. For 20-nm wells ${\mathit{g}}^{\mathrm{*}}$ for electrons is close to the bulk value (-0.44), and increases for narrower wells passing through zero for well width close to 5.5 nm. A theoretical analysis based on three-band k⋅p theory, including allowance for conduction-band nonparabolicity and for wave-function penetration into the barriers, gives a reasonable representation of the data, leading to the conclusion that ${\mathit{g}}^{\mathrm{*}}$ in quantum wells has a value close to that of electrons in the bulk at the confinement energy above the band minimum.