Strong Quadrupole-Strain Interaction of Vacancy Orbital in Boron-Doped Czochralski Silicon

• Published in: Journal of the Physical Society of Japan 2013-12, Vol.82 (12), p.124604-124604-8
• Main Authors: Okabe, Kazuki, Akatsu, Mitsuhiro, Baba, Shotaro, Mitsumoto, Keisuke, Nemoto, Yuichi, Yamada-Kaneta, Hiroshi, Goto, Terutaka, Saito, Hiroyuki, Kashima, Kazuhiko, Saito, Yoshihiko
• Format: Article
• Language: English
• ISSN: 0031-9015; 1347-4073
• DOI: 10.7566/JPSJ.82.124604

We have carried out ultrasonic measurements of a boron-doped silicon ingot grown by the Czochralski method in order to determine the quadrupole-strain interaction constant of a vacancy orbital. The low-temperature softening of the elastic constant $C_{44}$ shows a remarkable variation depending on positions of the ingot, which reflects the distribution of vacancy concentration $N$ in the ingot. An infrared laser scattering tomograph was employed to measure the density and size of voids in the silicon wafers by determining the vacancy concentration $N_{\text{cons}}$ consumed in void formation. Using a combination of laser scattering tomography and low-temperature softening, we have found a sum rule in which the initially created vacancy concentration $N_{\text{total}}$ corresponds to the sum of the residual vacancy concentration $N$ and the consumed vacancy concentration $N_{\text{cons}}$ as $N_{\text{total}} = N + N_{\text{cons}}$. Taking account of the sum rule, we deduce the interaction constant $g_{\Gamma_{5}} = (2.8\pm 0.2)\times 10^{5}$ K for the quadrupole-strain interaction $H_{\text{QS}} = -g_{\Gamma_{5}}O_{zx}\varepsilon_{zx}$ of the vacancy orbital. The huge deformation energy of $1.6\times 10^{5}$ K per vacancy with the $\Gamma_{8}$ ground state for unit strain $\varepsilon_{zx} = 1$ verified the strong electron--lattice interaction of the vacancy orbital. Employing the one-to-one correspondence between the softening of $\Delta C_{44}/C_{44} = 1.0\times 10^{-4}$ down to 30 mK and the vacancy concentration of $N = 1.5 \times 10^{13}$ cm -3 , we can determine the vacancy concentration by low-temperature ultrasonic measurements. The present work surely puts forward a novel semiconductor technology based on low-temperature ultrasonic measurements for evaluating vacancy concentration in silicon wafers.