Energy-dependent electron scattering via interaction with optical phonons in wurtzite crystals and quantum wells

A formalism for the calculation of the scattering rate in wurtzite-type crystals and quantum wells (QW's) is developed taking into account features of the optical phonon spectra in an optically anisotropic medium. The electron-scattering rate due to the interaction with infrared/Raman-active polar optical phonons in GaN, bulk material, and heterostructures, is investigated. To determine the dependence of scattering rate on optical anisotropy and dimensionally induced transformation of the phonon spectra, three cases are considered: (a) bulk material with different orientations of the electron wave vector with respect to the optical axis; (b) a system in which bulk phonons interact with electrons confined in a QW; and (c) free-standing and embedded QW's where the effects of confinement of both electron and phonon subsystems are taken into account. It is found that the scattering rate depends weakly on the initial orientation of the electron wave vector. Exceptions are the energy intervals which correspond to the threshold values for emission of both TO-like and LO-like bulk phonons. Our results reveal a complex and strong dependence of the electron-scattering rate on the dispersion of a particular mode. Moreover, this dependence is found to be the main factor which determines electron-phonon scattering in wurtzite heterostructures, in particular, through the relation between phonon phase and group velocities. For the optically anisotropic media considered, the effect of spatial localization of the phonon modes on the scattering rate is found to be as strong as the effect of electron confinement.