Phenomenological models of dielectric functions and screened Coulomb potential

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).