Dispersion of polar optical phonons in wurtzite quantum wells

Dispersion relations for polar optical phonon modes in wurtzite quantum wells (QW’s) are obtained in the framework of the dielectric continuum model. It is found that anisotropy of the dielectric medium causes a number of qualitative peculiarities in the phonon spectra. Among these are the absence of the proper confinement for the oscillatory waves located in the QW, inversion of the order of symmetric and antisymmetric quasiconfined optical modes, formation of the finite energy intervals where such confined modes—which are found to be dispersive—can exist, penetration of the half-space phonons into the QW, etc. Some additional peculiarities, such as appearance of propagating modes, strong dispersion of long-wavelength half-space modes, and reduction of the number of interface modes, arise as a result of overlapping characteristic phonon frequencies of the surrounding material and the material of QW. Predicted phonon behavior leads to the conclusion that dependence of dielectric properties of ternary-binary low-dimensional wurtzite heterostructures on composition can serve as a powerful tool for the purposes of phonon spectrum engineering. In order to illustrate these results, the optical phonon spectra are calculated for an ${\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N}/\mathrm{GaN}/{\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N}\hspace{0.5em}\mathrm{QW},$ an $\mathrm{AlN}/\mathrm{GaN}/\mathrm{AlN}\hspace{0.5em}\mathrm{QW},$ and for a $\mathrm{GaN}$ dielectric slab.