Potential distribution of polar optical phonons and their electron–phonon coupling properties of a wurtizite GaN-based trianglar quantum dot

Polar optical phonon modes of a wurtzite nitride trianglar quantum dot (QD) are deduced and analyzed by using the dielectric continuum model. Based on a method of nonseparable variables, the Laplace equation of electristatic potential of the structure is solved, and the exact and analytical phonon states of exact confined (EC) modes are derived. It is found that the frequency of EC modes in the nitride trianglar QD systems can take both the longitudinal optical phonons in [Formula: see text]-direction [Formula: see text] and the longitudinal optical phonons in [Formula: see text]-plane [Formula: see text], which is obviously different from the cases of EC modes in wurtzite GaN quantum wells and quantum wires due to their different confined dimensions. The polarization eigenvectors and their orthogonality relations for the EC phonon modes are derived, which could form a set of orthogonal and completed basis vectors. By using the orthogonality relations of polarization eigenvector and field quantization method, the free phonon field of EC modes and the corresponding Fröhlich electron–phonon interaction Hamiltonian are obtained. Numerical calculations on a wurtztie GaN trianglar QD are performed. The spatial distributions of phonon potentials of EC phonons both in [Formula: see text]-plane and in [Formula: see text]-direction as well as the electron–phonon coupling strength are plotted and discussed. It is observed that the potential of these EC phonon modes is strictly confined within the trianglar QD ranges. The dependence of symmetries and electron–phonon coupling strength on the quantum numbers [Formula: see text] and [Formula: see text] in [Formula: see text]-plane, and the quantum number [Formula: see text] in [Formula: see text]-direction are analyzed in detail. The relationship of the total number of peaks and troughs with these quantum numbers are also discussed and induced.