Polar optical phonons at $GaAs|Al_{(x)}Ga_{(1-x)}As$ interfaces:   influence of the concentration of Al
  We study long-wavelength polar optical modes at semiconductor interfaces of GaAs|Al_{(x)}Ga_{(1-x)}As and take into account influence of the Al concentration. We have considered two cases in which the interface is kept at unfixed and fixed electrostatic potential. The spectrum of excitation then shows existence of localized and resonant modes to depend on the concentration of Al. For the case of a fixed electrostatic potential, a splitting of the resonant mode near the transverse threshold is found for certain ranges of the concentration x. The existence of these modes has been obtained by computing the spectral strength through the Surface Green Function Matching (SGFM) method. 
A. E. Chubykalo, D. A. Contreras-Solorio and M. E. Mora-Ramos   (Universidad Aut\'onoma de Zacatecas)