Collective excitations and their lineshapes for a modulation-doped GaAs/AlAs superlattice

The density-density correlation function has been calculated for a modulation-doped GaAs/AlAs superlattice. The superlattice is modelled to be an infinite periodic sequence of layers which consists of two dissimilar layers, one of GaAs and the other of AlAs, per unit cell. The conduction electrons are assumed to be confined to GaAs layers. Our calculation shows that although the electron gas is confined in the GaAs layers, the plasma oscillations can interact with the lattice vibrations of both GaAs and AlAs. The interaction between AlAs lattice vibrations and the plasmons significantly contributes to the light-scattering spectrum. It is therefore argued that the experimentally measured frequencies of the coupled plasmon-phonon modes and their lineshapes for a modulation-doped GaAs/AlAs superlattice cannot correctly be described by the previous theoretical calculations which have been performed for a layered electron gas embedded in a homogeneous dielectric background. For the special case of a homogeneous dielectric background, our results, however, agree with the previously reported calculations