Piezomodulated-reflectivity study of minibands in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs superlattices

We report the observation of miniband formation in superlattices of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs, grown by molecular beam epitaxy, manifested in their piezomodulated-reflectivity spectra when studied as a function of well (${\mathit{l}}_{\mathit{w}}$) and barrier (${\mathit{l}}_{\mathit{b}}$) widths. The piezomodulated-reflectivity spectra reveal signatures of well separated optical transitions both at the Brillouin zone center and at the zone boundary extending to energies above the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As barrier. The clarity and sharpness of the spectral features allow an unambiguous identification of experimental transition energies with those calculated using the full eight-band k⋅p envelope-function approximation solved with the finite-element method. With ${\mathit{l}}_{\mathit{w}}$=25 Å [9 monolayers (ML)], ${\mathit{l}}_{\mathit{b}}$=20 Å (7 ML), and x=0.34, the lowest energy transition at the miniband zone center and at the corresponding zone boundary are separated by 158 meV. With ${\mathit{l}}_{\mathit{w}}$=74 Å (26 ML) and ${\mathit{l}}_{\mathit{b}}$=45 Å (16 ML), the spectra correspond to quantum states in a multiple quantum well. Features associated with monolayer fluctuations in layer thickness are also observed.