Ultrasonic study of vacancy in single crystal silicon at low temperatures

We have performed ultrasonic measurements at low temperatures in order to investigate vacancy in single crystal silicon. The longitudinal elastic constants of non-doped and boron-doped silicon grown by a floating zone method exhibit appreciable softening with decreasing temperature down to 20 mK. The softening of boron-doped silicon is easily suppressed in applied magnetic field up to 2 T, while the softening of non-doped silicon is robust in fields even up to 16 T. The softening of elastic constants in high-purity crystalline silicon is certainly caused by the coupling of elastic strains of the ultrasonic waves to electric quadrupoles of the vacancy orbital.