Shallow Impurity States in Ternary Mixed Crystals

Polaron bound to a shallow Coulomb impurity center in a polar ternary mixed crystal A x B 1-x C is studied by a perturbation variation method.The interaction between an electron and two branches of longitudinal optical phonon modes is taken into account by using the modified random element isodisplacement model and a so called effective phonon mode approximation method.The analytic expressions for the ground state energy and the binding energy of the polaron as functions of the composition x are obtained.The phonon screening,mass renormalization and self trapping effects are analyzed.The numerical results for several ternary mixed crystals show that the phonon screening effect is dominant and the binding energies of bound polarons are generally reduced by the electron phonon interaction.A non monotonous dependence of the phonon contributions to the binding energies on the composition x is found.The validity of the effective phonon mode approximation method is discussed.