Dispersions and frohlich electron-phonon interaction hamiltonian of propagating optical phonon modes in quasi-one-dimensional wurtzite GaN-based quantum well wires

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the propagating (PR) optical phonon modes and the Frohlich-like electron-PR phonon interaction Hamiltonian in a quasi-one-dimensional (Q1D) wurtzite quantum well wire (QWW) structure are deduced and analyzed. Numerical calculations on AlGaN/GaN/AlGaN wurtzite QWW are performed. Results reveal that the dispersive frequencies of PR modes are the continuous functions of free wavenumber k(z) in z-direction and discrete functions of azimuthal quantum number m. The reduced behavior of the PR modes in wurtzite quantum systems is obviously observed. From the discussion of the electron-PR phonon coupling functions, it is found that the low-order PR modes in the case of small kz and m play a more important role in the electron-PR phonon interactions. Moreover, a detailed comparison of the PR modes in Q1D QWW structures with those in quasi-two-dimensional quantum wells are also carried out. The physical reasons resulting in the relationship and distinction in the two types of systems are also analyzed deeply.