Effect of dynamics on the elastic softening of vacancies in Si

Recently, elastic softening at temperatures below 20 K has been observed in nondoped floating zone silicon. From the experimental analysis, it has been suggested that this softening is caused by an intrinsic vacancy defect through the Jahn-Teller (JT) effect. We have theoretically studied the relations between softening and the vacancies. The ground state of the JT distortion is stiff. However, by considering atomistic dynamical and anharmonic effects, it is found that low-energy excitations exist in the E-mode distortion and that different polarizations of the E-distortion can be easily interchanged. The calculated energy barriers for the reorientation of JT distortions are consistent with other experiments and calculations. This low-lying mode can be the cause of softening in the elastic responses