Polar interface optical phonon modes and Fröhlich electron–phonon interaction Hamiltonians in wurtzite quantum well wires

Abstract

Within the framework of the dielectric continuum approximation and Loudon's uniaxial crystal model, the interface optical (IO) phonon modes and the corresponding Fröhlich electron–phonon interaction Hamiltonian in a wurtzite AlN/GaN/AlN quantum well wire (QWW) are derived and studied. Numerical calculations are mainly focused on the frequency dispersion of the IO phonons and electron–phonon interaction coupling function. Results reveal that, in general, there are four branches of IO phonon modes in the systems. The dispersions of the four branches of IO phonon modes are obvious only when the axial direction wave number kz or the azimuthal quantum number m is small. The degenerating behaviour of the IO phonon modes in wurtzite QWW has also been observed for small kz or m. When kz or m are relatively large, with the increasing of them, the frequencies of these IO phonon modes converge to the two definite limiting frequencies in wurtzite single planar heterostructure, and this feature has been explained reasonably from the mathematical and physical viewpoints. The calculations of the electron–phonon coupling function show that, though some branches of IO phonon modes exchange their localized positions with each other at a large m, there always exist two branches of IO phonon modes localized on each interface. The high-frequency IO phonon modes compared with the low-frequency ones play a more important role in the electron–phonon interaction. Detailed comparison of the dispersion behaviours of the IO phonons and electron–IO phonon couplings properties in wurtzite QWWs with those in zinc-blende QWWs has also been made.