Far-infrared spectroscopy of minibands and confined donors in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices

We present a far-infrared-absorption study of electrons in lightly doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices. A grating coupler enables us to observe transitions that require an electric-field polarization along the superlattice axis. We investigate weakly and strongly coupled superlattices, and demonstrate the difference between intersubband transitions and transitions between extended minibands. The line shape of the interminiband absorption deviates considerably from the predictions of a simple single-particle model. We discuss possible reasons in terms of fluctuations and localization. At low temperatures, the absorption spectra are dominated by donor transitions. The transition from the donor ground state to the pure 2${\mathit{p}}_{\mathit{z}}$ state, which is associated with the second subband, is observed. In a variational calculation, we compute the four-lowest donor states for a variety of superlattice parameters. Excellent agreement between experiment and theory is achieved.