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

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概要

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• 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.

• 2013-12-15

著者

• Goto Terutaka

  Graduate School Of Science And Technology Niigata University

• Nemoto Yuichi

  Graduate School Of Science And Technology Niigata University

• Akatsu Mitsuhiro

  Graduate School Of Science And Technology Niigata University

• MITSUMOTO Keisuke

  Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

• Baba Shotaro

  Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

• Saito Yoshihiko

  Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

• Yamada-Kaneta Hiroshi

  Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan

• Yamada-Kaneta Hiroshi

  Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushyu 804-8550, Japan

• Okabe Kazuki

  Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

• Saito Hiroyuki

  GlobalWafers Japan Co., Ltd., Seirou, Niigata 957-0197, Japan

• Kashima Kazuhiko

  Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

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