Absolute Value Determination of Vacancy Concentration in Silicon Crystals Using Low-Temperature Ultrasonic Measurements

For the samples taken from the void region of the CZ silicon crystal grown with the same solidification condition and different thermal histories after the solidification, we measure the magnitude S of the elastic softening which is proportional to the concentration of the single vacancies [V]. For these samples, we also measure the size distribution of the void density by using the infrared light-scattering tomography, to evaluate the concentration [Vc] of the vacancies consumed for the void formation. From these two experiments, we find a sum rule [Vc] + a S= C, where C depends only on the solidification condition and is independent of the thermal history after the solidification. This enables us to find the conservation rule of the vacancies [Vc] + [V] = C. The value of the proportionality constant a in the relation [V] = a S is determined. Demonstration of determining the absolute values of [V] from the measured S is given. An estimate is made for the value of the quadrupole-strain coupling constant.