Long-wavelength polar optical modes in GaAs semiconductor layered structures

A long-wavelength model of polar optical modes coupling the vibration amplitude u (the relative displacement vector) and the electrostatic potential phi leads to a system of coupled differential equations. This system is here solved for a quantum well without approximations and with simultaneous satisfaction of mechanical and electrostatic matching boundary conditions. Explicit solutions for u and phi are given, and the resulting eigenmodes for GaAs-based quantum wells are studied in detail. The model gives modes with a mixed character describing the coupling between u and phi . Thus one single model yields confined quasi-longitudinal (strictly longitudinal for in-plane wavelength vector kappa =0), confined quasi-transverse (strictly transverse for kappa =0) and interface modes. The dynamical structure, spectral strength and spatial dependence of the relevant amplitudes are studied in detail. The results are in good agreement with available Raman experimental data and have all the basic features present in microscopic calculations. Some comments are made on the limitations of purely dielectric or purely mechanical models.