Dispersive Spectra of Fröhlich Phonon Modes in Wurtzite Nitride Nanoholes with Circular and Square Cross Sections

Semiconductor nanoholes have garnered significant interest due to their unique nanotopological structures, which can result in distinct physicochemical characteristics. This study delves into the properties of crystal vibrations in nanohole structures. The analytic Fröhlich phonon state and dispersion relationship in wurtzite nanoholes, with circular and square cross sections (CS), are derived using the macroscopic dielectric continuum model. It is found that two types of phonon modes, surface optical (SO) and half‐space (HS) modes, coexist in wurtzite nitride nanohole structures. These phonon modes and their dispersive behaviors in nanoholes significantly differ from those in nanowires due to the different nanotopological structures. Furthermore, the Fröhlich electron–phonon interaction Hamiltonians for SO and HS phonon modes in nanoholes are obtained based on a field quantization scheme. Numerical calculations on wurtzite AlN nanoholes reveal that the shape of the CS has a remarkable influence on the dispersive spectra of SO and HS phonon modes. Additionally, it is found that the dielectric medium significantly affects the dispersive features of SO modes, while its influence on the dispersive behavior of HS modes is negligible. The profound physical mechanisms behind these observations are deeply analyzed.