  The evolution of static dielectric constants and polarization with doping are
analyzed and discussed using established experimental results. The variation of
screened Coulomb potential with doping is derived theoretically to justify the
said evolutions. The latter justification arises due to the influence of
ionization energy ($\mathcal{E_I}$) on the static dielectric functions. The
bare Coulomb potential and the Thomas-Fermi screened potential with finite
carrier density were recovered when $\mathcal{E_I} \to \infty$ and
$\mathcal{E_I} \to E_F^0$ respectively. Basically, these phenomenological
models are associated with the ionization energy based Fermi-Dirac statistics
(iFDS).
