Observation of Low-Temperature Elastic Softening due to Vacancy in Crystalline Silicon

Abstract

In challenging a direct observation of the vacancy in crystalline silicon, we have carried out low-temperature ultrasonic measurements down to 20 mK. The longitudinal elastic constants of non-doped and B-doped crystalline silicons, which were grown by a floating zone (FZ) method in commercial base, reveal the elastic softening proportional to the reciprocal temperature below 20 K. The applied magnetic fields turn the elastic softening of the B-doped FZ silicon to a temperature-independent behavior, while the fields up to 16 T do not affect the elastic softening of the non-doped FZ silicon. We present a plausible scenario for this result. Namely the vacancy with the non-magnetic charge state V 0 in the non-doped silicon and the magnetic V + in the B-doped silicon is responsible for the low-temperature softening of the shear elastic constants ( C 11 - C 12 )/2 and C 44 , which can be described in terms of the quadrupole susceptibility due to the Jahn–Teller effect.