Effects of band nonparabolicity and central-cell corrections on the spectrum of Si donors in GaAs quantum wells

Data on donor magneto-optical 1s→2${\mathit{p}}_{+1\mathrm{}}$ transitions in four center-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells ranging in width from 10 to 52 nm is presented and analyzed for magnetic fields between 0 and 6 T. It is found that both band nonparabolicity and central-cell corrections must be considered in the narrower wells in order to obtain satisfactory agreement with experiment. A theory of band nonparabolicity is introduced which includes important terms arising from the donor Coulomb potential, terms previously ignored in the analysis of quantum-well donor spectra. In the narrower wells relatively large central-cell corrections are calculated for Si donors from bulk data. A central-cell correction of ∼0.75 ${\mathrm{cm}}^{\mathrm{-}1}$ is estimated for bulk Si donors at zero magnetic field from analysis of published data on Si-doped GaAs epitaxial films.