Interface and surface optical phonons in a free-standing GaAs/AlxGa1-xAs cylindrical quantum-well wire

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fröhlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) were derived and studied. Numerical calculations on GaAs/AlxGa1-xAs cylindrical QWWs have been performed. Results reveal that, in the case of taking the “two-mode” behavior of the AlxGa1-xAs material into account, there have four branches of IO phonon modes and two branches of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction x in AlxGa1-xAs material and the wave-vector in z direction kz. With the increasing of kz and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs/AlxGa1-xAs heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO or -SO phonon becomes weaker.