  Fermi-Dirac statistics has been utilized by introducing the average
ionization energy ($E_I$) as an additional anomalous energy gap in order to
derive the two-dimensional concentration of charge carriers and the
phenomenological resistivity model for the superconducting polycrystalline
materials. The best fitted values of $E_I$ and the charge carriers'
concentration ranges in the vicinity of 4 to 9 meV and 10$^{16}$ m$^{-2}$
respectively for the superconducting single crystal samples and polycrystalline
compounds synthesized with various compositions via solid-state reactions. The
phenomenological resistivity model is further redefined here based on the
gapless nature of charge-carriers' dynamics within the Cu-O$_2$ planes that
corresponds to anomalous Fermi liquid behavior, which is in accordance with the
nested Fermi liquid theory.
