We calculate nucleosynthesis in Population III supernovae (SNe) and compare the yields with various abundance patterns of extremely metal-poor (EMP) stars. We assume that the observed EMP stars are second-generation stars, which have the metal-abundance patterns of Population III SNe. Previous theoretical yields of Population III SNe cannot explain the trends in the abundance ratios among Fe-peak elements (Mn, Co, Ni, Zn)/Fe or the large C/Fe ratio observed in certain EMP stars with [Fe/H] -2.5. In this paper we show that if we introduce higher explosion energies and mixing fallback in the core-collapse SN models of M ~ 20-130 M☉, the above abundance features of both typical and C-rich EMP stars can be much better explained. We suggest that the abundance patterns of the [Fe/H] ~ -2.5 stars correspond to supernova yields with normal explosion energies, while those of the carbon unenhanced ([C/Fe] 1) stars with [Fe/H] -4 to -3 correspond to high-energy supernova yields. The abundance patterns of the C-rich ([C/Fe] 2) and low [Fe/H]( -5.5 ~ -3.5) stars can be explained with the yields of faint SNe that eject little 56Ni as observed in SN 1997D. In the supernova-induced star formation model, we can qualitatively explain why the EMP stars formed by the faint or energetic supernovae have lower [Fe/H] than the EMP stars formed by normal supernovae. We also examine how the abundance ratios among Fe-peak elements depend on the electron mole fraction Ye and conclude that a large explosion energy is still needed to realize the large Co/Fe and Zn/Fe ratios observed in typical EMP stars with [Fe/H] -3.5.
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