Fröhlich electron–phonon interaction Hamiltonian and potential distribution of a polar optical phonon mode in wurtzite nitride triangular nanowires

Abstract

Polar optical phonon modes of wurtzite triangular nanowires (NWs) with three different cross sections, including the hemi-equilateral triangle (HET), the isosceles right triangle (IRT), and the equilateral triangle (ET), are deduced and analyzed using the dielectric continuum model. The exact and analytical phonon states of exactly confined (EC) modes in nitride NWs with HET, IRT, and ET cross sections are derived. The characteristic frequency of EC phonon modes in the triangular nitride NW systems is specified. Fröhlich electron–phonon interaction Hamiltonians in wurtzite NWs with three types of triangular cross sections are obtained. It is found from the numerical results that, among the three types of GaN NWs, the electron–phonon coupling of EC modes in NWs with an HET cross section is the weakest one, that in NWs with an ET cross section is the strongest one, and that in NWs with an IRT cross section is in the middle. The electrostatic potentials of EC modes in HET NWs are neither symmetric nor antisymmetric. The potential functions of EC modes in the ET NW structures have one (three) symmetric axis (axes) as the quantum numbers [Formula: see text] and [Formula: see text] take fractions (integers). The potential functions of EC modes in IRT NWs behave either symmetrically or anti-symmetrically, which are closely dependent on the parities of the quantum numbers [Formula: see text] and [Formula: see text]. With the increase of order-number of EC modes, the electron–phonon coupling becomes weaker and weaker. This reveals that cross-sectional morphology of quantum structures has an important influence on the symmetries of phonon modes and electron–phonon coupling strengths in low-dimensional quantum systems.