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Excavation rate of silicon surface nanoholes
8.For example, Y. Li, Y. Kanamori, and K. Hane, Microsyst. Technol. 10, 272 (2004).
11.Y. Ohno, S. Takeda, T. Ichihashi, and S. Iijima (unpublished).
12.On surfaces in a conventional microscope, the sputtering of surface atoms, oxidization, and contamination take place simultaneously under electron irradiation. When is high, the first process is most probably predominant and so the surface is virtually free from oxidation and contamination (Ref. 11).
13.The flux was about , and the irradiated surface received electrons of throughout TEM observation. The dose needed for observation was much smaller than that for irradiation (above about ).
15.It is known that vacancies are introduced inside the crystal at by the irradiation of electrons whose energy is above (Ref. 16). This indicates that the migration of surface vacancies, that can be introduced by the irradiation of electrons with lower energy (down to about ), toward the inside of the crystal could be negligible. Also, even when is above , effects of the vacancies inside the crystal could be negligible in the present work, since the number density of vacancies introduced inside the crystal is small (less than of the number density on the surfaces even at ).
17.K. Urban and A. Seeger, Philos. Mag. 30, 1395 (1974).
18.We do not discuss quantitatively the infilling rate of surface nanoholes in the present study, since the number of surface vacancies introduced per an area on an electron entrance surface is unclear. It is considered that the number is rather small for flat electron entrance surfaces hit normally by electrons. However, it is proposed that many surface vacancies are introduced on real electron entrance surfaces irradiated by high-energy electrons (Ref. 19), presumably due to effects of steps existed on the surfaces.
19.K. Torigoe, T. Ichihashi, and S. Takeda (unpublished).
20.M. Kiritani and H. Takata, J. Nucl. Mater. 69–70, 277 (1978).
21. for a surface can be estimated, with the threshold energy for formation of vacancies on the surface, with the McKinley-Feshbach’s formula (Ref. 22). The threshold energy is estimated to be (Ref. 11), and it is close to the sublimation energy of a silicon surface [e. g., for a (111) surface (Ref. 23)].
23.K. Yagi, Scan Electron Microsc. 1982, 1421 (1982).
24.The phenomenological parameter , that is so called a correlated recombination factor, describes the probability that a displaced atom returns to the vacant site from which it originates. for displacement of atoms in semiconductors is the order of (Ref. 25).
26.Since is independent of at an UHV [Fig. 2(a)], is independent of on deoxidized surfaces. may depend on when is low at a low vacuum [Fig. 2(b)], due to effects of oxidization and contamination. The effects are ignored in this paper.
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