Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well

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Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes aswell as the corresponding Frohlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-wellwire (Q WW) are derived and studied. Numerical calculations on GaAs/AlxGa1-xAs cylindrical QWW are performed.Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersionfrequencies ofIO or SO phonon modes sensitively depend on the Al mole fraction x in Alx Ga1-x As material and the wave-vector in z direction, kz. With the increasing of κz and quantum number m, the frequency of each IO mode approaches oneof the two frequency values of the single GaAs/Alx Ga1-xAs heterostructure, and the electrostatic potential distributionof the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the couplingbetween the electron-IO and -SO phonons becomes weaker.
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