Practical method and physics of evaluation for vacancy concentration of silicon crystals by measuring low-temperature elastic softening

The paper reports the recent progress of our research on the vacancies in boron-doped (B-doped) as-grown silicon crystals of commercial-base quality achieved by means of the low-temperature ultrasonic measurements. The paper also demonstrates how our research-base technique for the vacancy observation is established as the practical tool of evaluating the vacancy concentration of the commercial silicon crystals and wafers. An emphasis is made on the confirmation of the following findings obtained in our previous experiment for the elastic softening by the vacancies in boron-doped silicon crystals: (1) the steep softening that suddenly starts at 2-4 K in the cooling process, and (2) the complete disappearance of the softening by a weak magnetic field of 4 T applied along [111] direction. We further investigate in detail how the low-temperature softening at a fixed temperature responds to the applied magnetic field, to find the following characteristic anisotropy: The manner of disappearance of the softening strongly depends on the direction of the magnetic field. For the magnetic field imposed along [1-10] direction, nearly 60% of the full softening still remains even at a strong magnetic field of 8 T, in contrast to the case of the magnetic field applied along [111] direction.