TRANSFER MATRIX METHOD FOR THE FRÖHLICH ELECTRON–INTERFACE OPTICAL PHONON INTERACTION IN MULTILAYER COAXIAL CYLINDRICAL QUANTUM-WELL WIRES

Abstract

Under dielectric continuum approximation, by adopting the transfer matrix method, interface optical (IO) phonon modes and the Fröhlich 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 / Al x Ga 1-x As QWW have been performed. Results reveal that there are six branches of IO phonon modes. When the wave vector in z-direction kz and the azimuthal quantum number m are small, the dispersion frequencies of IO modes sensitively depend on kz and m. When kz and m are relatively large, with the increasing of kz 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 kz and m have analogous effects on the frequencies and the electrostatic potentials of the IO phonons.