Electron optical-phonon coupling in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells due to interface, slab, and half-space modes

The electron optical-phonon coupling is studied in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells as due to the interface modes, the confined slab modes in the well, and the half-space modes in the barriers. The polaron binding energy and effective mass are calculated and the relative importance of the different phonon modes is investigated as a function of the width of the quantum well. The full energy spectrum, i.e., the discrete energy levels in the well and the continuum energy spectrum above the barrier, are included as intermediate states. The polaron binding energy and effective mass go continuously from the three-dimensional (3D) ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As to the 3D GaAs results when the well width varies from zero to infinity.