Suppression of the observation of Stark ladders in optical measurements on superlattices by excitonic effects

We investigate experimentally and theoretically how excitonic effects influence the optical properties of semiconductor superlattices in the Stark-ladder regime. Excitonic effects are particularly important when the superlattice miniband width is comparable to the exciton binding energy. In order to observe a Stark ladder it is necessary that either the electron or hole wave function (or both) be at least partially delocalized. In an optical experiment the delocalization of the wave functions is affected by the electron-hole Coulomb interaction. Excitonic effects can therefore prevent the observation of the Stark ladder if the Coulomb interaction is strong enough to localize the wave functions completely. We have studied three GaAs/${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As superlattices, with calculated conduction-band miniband widths ΔE of 6, 11, and 23 meV. Experimentally, we observe a heavy-hole Stark-ladder fan diagram in the sample with the 23-meV miniband width, which indicates an electron wave-function delocalization over several superlattice periods. However, in the other two samples in which ΔE is comparable to the exciton binding energy, we do not observe a fan diagram, which indicates much stronger wave-function localization. Instead, we observe an anticrossing at a field strength of ∼5 kV ${\mathrm{cm}}^{\mathrm{-}1}$. In these conditions, the multiwell structure behaves more like many repeated pairs of coupled double wells rather than a superlattice. We interpret the observed anticrossings at ∼5 kV ${\mathrm{cm}}^{\mathrm{-}1}$ in the samples with the smaller miniband widths as an excitonic degeneracy similar to that observed previously at higher fields [A.M. Fox et al., Phys. Rev. B 44, 6231 (1991)]. We have been able to explain this behavior using both a variational exciton model based on three coupled quantum wells and a full Green’s-function solution for the excitons assuming a double-quantum-well structure.