Microscopic interface phonon modes in structures of GaAs quantum dots embedded in AlAs shells

1 By means of a microscopic valence force field model, a series of novel microscopic interface phonon modes are identified in shell quantum dots (SQDs) composed of a GaAs quantum dot of nanoscale embedded in an AlAs shell of a few atomic layers in thickness. In SQDs with such thin shells, the basic principle of the continuum dielectric model and the macroscopic dielectric function are not valid any more. The frequencies of these microscopic interface modes lie inside the gap between the bulk GaAs band and the bulk AlAs band, contrary to the macroscopic interface phonon modes. The average vibrational energies and amplitudes of each atomic shell show peaks at the interface between GaAs and AlAs. These peaks decay fast as their penetrating depths from the interface increase. Interesting results have been reported on the surface and interface modes of phonons and polaritons in layered or spherical structures by means of macroscopic continuum model. By using the Rosenzweig model, G. Armand et al. [1] have found that there are surface phonon modes in the gap of the bulk phonon modes and below the lowest bulk band. Maradudin et al.[2] have predicted that there are surface phonon waves propagating in the gap between the bulk phonon bands and below the lowest bulk phonon band in structures that a semi-infinite GaAs/AlAs superlattice is in contact with a thin film of GaAs or AlAs. The amplitudes of some surface modes show strong decaying or variation as their penetrating depths from the surface increase. At about the same time, Quinn et al. predicted that there are surface plasmon modes without suffering Landau damping surviving below , above or between the bands of bulk plasmon frequencies in both type-I and type-II semi-infinite semiconductor superlattices[3, 4]. Interface and surface modes in shell quantum dots (SQDs) composed of a spherical core of one material (core material) embedded in a matrix of another materiel (shell material) have been studied by many authors [5, 6, 7, 8]. However, most of the theoretical treatments on shell QDs are performed in the framework of mechanical continuum model [2], continuum dielectric model[4, 7], or continuum model coupling both the mechanical vibrational amplitudes and the electrostatic potential [5]. Their regions of validity is limited to modes whose effective wavelength is large compared to the interatomic spacing. In the case of surface plasmons the continuum dielectric approach is limited to dots whose size is …