  Metal enrichment by the first-generation (Pop III) stars is the very first
step of the matter cycle in the structure formation and it is followed by the
formation of extremely metal-poor (EMP) stars. To investigate the enrichment
process by the Pop III stars, we carry out a series of numerical simulations
including the feedback effects of photoionization and supernovae (SNe) of Pop
III stars with a range of masses of minihaloes (MHs), M_halo , and Pop III
stars, M_PopIII . We find that the metal-rich ejecta reaches neighbouring
haloes and external enrichment (EE) occurs when the halo binding energy is
sufficiently below the SN explosion energy, E_SN . The neighbouring haloes are
only superficially enriched, and the metallicity of the clouds is [Fe/H] < -5.
Otherwise, the SN ejecta falls back and recollapses to form enriched cloud,
i.e. internal enrichment (IE) process takes place. In case that a Pop III star
explodes as a core-collapse SNe (CCSNe), MHs undergo IE, and the metallicity in
the recollapsing region is -5 < [Fe/H] < -3 in most cases. We conclude that IE
from a single CCSN can explain the formation of EMP stars. For pair-instability
SNe (PISNe), EE takes place for all relevant mass range of MHs, consistent with
no observational sign of PISNe among EMP stars.
