  We calculate nucleosynthesis in Population (Pop) 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 the second generation
stars, which have the metal-abundance patterns of Pop III SNe. Previous
theoretical yields of Pop III SNe cannot explain the trends in the abundance
ratios among iron-peak elements (Mn, Co, Ni, Zn)/Fe as well as the large C/Fe
ratio observed in certain EMP stars with [Fe/H] <~ -2.5. In the present paper,
we show that if we introduce higher explosion energies and mixing-fallback in
the core-collapse SN models of M ~ 20 - 130 Msun, 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 un-enhanced
([C/Fe] < 1) stars with [Fe/H] =~ -4 ~ - 3 correspond to high-energy supernova
yields. The abundance patterns of the C-rich ([C/Fe]>~ 2) and low [Fe/H] (=~ -5
\~ -3.5) stars can be explained with the yields of faint SNe that eject little
56Ni as observed in SN1997D. 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 iron-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.
