Stability of a weakly bound impurity center

Abstract

By employing the scalar model, the stability of a weakly bound impurity center in a three-dimensional crystal is analyzed. It is demonstrated that, for a weakly bound impurity center, the increase in the atomic displacement of the defect can bad to a violation of the harmonic approximation and then to an instability of the defect in the host crystal lattice. Resulting restrictions on the coupling stiffness of the impurity turn out to be rather severe if the anharmonic effect in the host system is significant. These restrictions also impose a lower limit on the resonance frequency induced by the bond weakening.