By high-energy (\ensuremath{\sim}2.5-MeV) heavy-ion ${(}^{75}$${\mathrm{As}}^{+}$, $^{84}\mathrm{Kr}^{+}$, $^{131,132}\mathrm{Xe}^{+}$, etc.) beam irradiation, the amorphous Si layers on the crystalline Si substrates formed by low-energy (\ensuremath{\sim}100-keV) ion implantation or by chemical-vapor deposition could be crystallized epitaxially at very low substrate temperatures (120--300 \ifmmode^\circ\else\textdegree\fi{}C, in the 2.5-MeV $^{75}\mathrm{As}^{+}$ irradiation case), far below the ordinary solid-phase (\ensuremath{\sim}600 \ifmmode^\circ\else\textdegree\fi{}C) or liquid-phase (\ensuremath{\sim}1400 \ifmmode^\circ\else\textdegree\fi{}C) epitaxial growth temperatures. Layer-by-layer amorphization of amorphous Si layers on the crystalline Si substrates also occurred at low temperatures (\ensuremath{\le}120 \ifmmode^\circ\else\textdegree\fi{}C, in the 2.5-MeV $^{75}\mathrm{As}^{+}$ irradiation case). The author elucidates the low-temperature (120--300 \ifmmode^\circ\else\textdegree\fi{}C) crystallization mechanism and the low-temperature (\ensuremath{\le}120 \ifmmode^\circ\else\textdegree\fi{}C) amorphization mechanism. The thermal diffusion of vacancies towards the amorphous layer, produced by nuclear scattering of incident heavy ions in the crystalline substrate, plays an important role in the low-temperature crystallization. High incident energies also contribute to the enhanced vacancy diffusion due to their large electronic scattering. Whether crystallization or amorphization occurs depends on the balance at the crystalline-amorphous interface, between the vacancy concentration supplied from the crystalline substrate toward the amorphous layer via thermal diffusion and the interstitial Si-atom concentration supplied from the amorphous layer toward the crystalline substrate via recoil by incident heavy ions.
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