Polar interface optical phonon modes and Frohlich electron-phonon interaction Hamiltonians in an arbitrary layer-number quantum well system

By using determinant method as in our recent work, the IO phonon modes, the orthogonal relation for polarization vector, electron-IO phonon Frohlich interaction Hamiltonian, the dispersion relation, and the electron-phonon coupling function in an arbitrary layer-number quantum well system have been derived and investigated within the framework of dielectric continuum approximation. Numerical calculation on seven-layer AlxGa1 -xAs/GaAs systems have been performed. Via the numerical results in this work and previous works, the general characters of the IO phonon modes in an n-layer coupling quantum well system were concluded and summarized. This work can be regarded as a generalization of previous works on IO phonon modes in some fixed layer-number quantum well systems, and it provides a uniform method to investigate the effects of IO phonons on the multi-layer coupling quantum well systems.