Abstract
A theory of electron--optical-phonon interactions in quantum wells consisting of mixed crystals is reported. According to whether the well or the barrier is made of mixed crystals, quantum wells consisting of mixed crystals are divided into three types. The expressions of phonon frequencies of all phonon modes and the electron--LO-phonon interaction Hamiltonian of all the types of the quantum wells are obtained based on the dielectric continuum approach. As applications of the present theory, the concentration dependences and the dispersion relations of the interface-optical-phonon frequencies in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}\mathrm{As},$ ${\mathrm{Zn}}_{x}{\mathrm{Cd}}_{1\ensuremath{-}x}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e},$ and ${\mathrm{ZnS}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}/\mathrm{ZnS}$ quantum wells are calculated. The interaction energies of an electron in the lowest subband state with every optical phonon mode are also calculated. The features of the polaronic effect in quantum wells consisting of mixed crystals are discussed.
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