We summarize our studies on neutrino-driven nucleosynthesis in He shells of early core-collapse supernovae with metallicities of Z < 10~(-3) Z_⊙. We find that for progenitors of~ 11-15 M_⊙, the neutrons released by ~4He(ve, e~+n)~3H in He shells can be captured to produce nuclei with mass numbers up to A~ 200. This mechanism is sensitive to neutrino emission spectra and flavor oscillations. In addition, we find two new primary mechanisms for neutrino-induced production of ~9Be in He shells. The first mechanism produces ~9Be via ~7Li(n, y)~8Li(n, y)~9Li(e~v_e)~9Be and relies on a low explosion energy for its survival. The second mechanism operates in progenitors of~ 8 M_⊙, where ~9Be can be produced directly via ~7Li(~3H, n_0)~9Be during the rapid expansion of the shocked Heshell material. The light nuclei ~7Li and ~3H involved in these mechanisms are produced by neutrino interactions with ~4He. We discuss the implications of neutrino-induced nucleosynthesis in He shells for interpreting the elemental abundances in metal-poor stars.
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