Optical vibration modes and electron-phonon interaction in ternary mixed crystals of polar semiconductors

Optical vibrations of the lattice and the electron-phonon interaction in polar ternary mixed crystals are studied in the framework of the continuum model of Born and Huang and the random-element-isodisplacement model. A normal-coordinate system to describe the optical vibration in ternary mixed crystals is correctly adopted to derive a new Frohlich-like Hamiltonian for the electron-phonon interaction including the unit-cell volume variation influence. The numerical results for the phonon modes, the electron-phonon coupling constants and the polaronic energies for several typical materials are obtained. It is verified that the nonlinearity of the electron-phonon coupling effects with the composition is essential and the unit-cell volume effects cannot be neglected for most ternary mixed crystals.