Surface acoustic wave diagnosis of vacancy orbital with electric quadrupoles in silicon

We demonstrate ultrasonic diagnosis of vacancies in boron-doped silicon wafers currently used in device manufacturing. The low-temperature softening of elastic constants measured by surface acoustic waves (SAW) as well as bulk ultrasonic waves is caused by a coupling of elastic strains to electric quadrupoles of the vacancy orbital in silicon wafers. Using interdigital transducers with a comb gap of 2.5 μm on a piezoelectric ZnO film deposited on the (001) surface of the wafer, we observed the softening of 1.9×10−4 in relative amount of the elastic constant Cs below 2 K down to 23 mK. Taking account of the strong quadrupole-strain interaction, we deduced a small vacancy concentration 3.1×1012 cm−3 in the surface layer of the wafer within a penetration depth 3.5 μm of the SAW.