  A self-doping effect between outer and inner CuO$_2$ planes (OPs and IPs) in
multi-layer cuprate superconductors is studied. When one considers a
three-layer tight-binding model of the Hg-based three-layer cuprate derived
from the first principle calculations, the electron concentration gets to be
large in the OP compared to IP. This is inconsistent with the experimental fact
that more hole carriers tend to be introduced into the OP than IP.We
investigate a three-layer Hubbard model with the two-particle self-consistent
approach for multi-layer systems to incorporate electron correlations. We
observe that the double occupancy (antiferromagnetic instability) in the IP
decreases (increases) more than the OP, and also reveal that more electrons
tend to be introduced into the IP than OP to obtain the energy gain from the
on-site Hubbard interaction. These results are consistent with the experimental
facts, and this electron distribution between the OP and IP can be interpreted
as a self-doping effect arising from strong electron correlations.
