Polar optical phonon states and their dispersive spectra of a wurtzite nitride superlattice with complex bases: Transfer-matrix method

Based on the dielectric continuum model and transfer-matrix method, the whole polar optical phonon states in a wurtzite GaN-based superlattice (SL) with arbitrary-layer complex bases are investigated. It is proved that 2n types of phonon modes may exist in a wurtzite nitride SL with n-layer complex bases. The analytical phonon states of these modes and their dispersive equations in the wurtzite GaN/AlxGa1−xN SL structures are obtained. Numerical calculations on a wurtzite SL with three-layer GaN/Al0.15Ga0.85N/AlN complex bases are performed. And the calculations focus on the dispersive spectra of phonon modes in the system. Results reveal that there are one type of interface-optical (IO) phonon modes and four types of quasi-confined (QC) phonon modes in the SL with three-layer GaN/Al0.15Ga0.85N/AlN complex bases. The dispersive spectra of phonon modes in complex bases SL form a series of frequency bands. The behaviors of QC modes reducing to IO modes are observed. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of phonon modes and their polaronic effect in wurtzite GaN-based SLs with complex bases.