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 z-direction omega(z,L) and the longitudinal optical phonons in xy-plane omega(t,L), 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 Frohlich 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 xy-plane and in z-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 p and q in xy-plane, and the quantum number m in z-direction are analyzed in detail. The relationship of the total number of peaks and troughs with these quantum numbers are also discussed and induced.

Automated summary

This study deduced and analyzed the polar optical phonon modes of a wurtzite nitride triangular quantum dot using the dielectric continuum model. The exact and analytical phonon states of exact confined modes were derived, and it was found that the frequency of these modes in the nitride triangular quantum dot systems could take both the longitudinal optical phonons in the z-direction and in the xy-plane. The spatial distribution and electron-phonon coupling strength of these modes were discussed, showing that their potential is strictly confined within the triangular quantum dot ranges.