Transfer matrix method for the Frohlich electron-interface optical phonon interaction in multilayer coaxial cylindrical quantum-well wires

摘要

Under dielectric continuum approximation, by adopting the transfer matrix method, interface optical (IO) phonon modes and the Frohlich electron-IO-phonon interaction Hamiltonian in a multilayer coaxial cylindrical quantum-well wire (QWW) were deduced and investigated. Numerical calculations on a four-layer GaAs/AlxGa1-xAs QWW have been performed. Results reveal that there are six branches of IO phonon modes. When the wave vector in z-direction k(z) and the azimuthal quantum number m are small, the dispersion frequencies of IO modes sensitively depend on k(z) and m. When k(z) and m are relatively large, with the increasing of k(z) and m, the frequency for each mode converges the limit frequency value of IO mode in single heterostructure, and the electrostatic potential distribution of each mode tends to be more and more localized at the interfaces, meanwhile, the coupling between the electron-IO-phonon becomes weaker and weaker. The calculation also shows that the phonon modes with higher frequencies have more significant contribution to the electron-phonon interaction. At last, it is found that k(z) and m have analogous effects on the frequencies and the electrostatic potentials of the IO phonons.