Observation of vacancy in crystalline silicon using low-temperature ultrasonic measurements

We have successfully observed isolated vacancies in crystalline silicon using low-temperature ultrasonic measurements. The floating zone (FZ) silicon exhibits softening in longitudinal elastic constants consisting of transverse C₄₄ and (C₁₁ - C₁₂)/2 in part with decreasing temperature below 20 K down to 20 mK. The applied magnetic fields of up to 16 T at the base temperature 20 mK show no effect on the low-temperature softening in non-doped FZ silicon, while the fields of up to 2 T suppress the low-temperature softening in boron-doped FZ silicon. This experiment suggests that isolated vacancies with non-magnetic charge state V⁰ in the non-doped FZ silicon and with magnetic charge state V⁺ in the boron-doped FZ silicon lead to the low-temperature softening. We have also observed the low-temperature softening in the Pv-region of non-doped Czochralski (CZ) silicon ingot, which indicates vacancy distribution. A coupling of electric quadrupoles of triplet state of vacancy orbital to the elastic strains of the sound waves is discussed for description of the low-temperature softening.