Phenomenological models of dielectric functions and screened Coulomb potential

TL;DR

This paper develops phenomenological models linking dielectric functions and screened Coulomb potential variations with doping, emphasizing the role of ionization energy and Fermi-Dirac statistics in these processes.

Contribution

It introduces models that connect ionization energy to dielectric and Coulomb screening behaviors, providing a theoretical basis for doping-dependent evolutions.

Findings

Screened Coulomb potential varies with doping as derived theoretically.

Ionization energy influences static dielectric functions significantly.

Models recover known potentials in specific limits of ionization energy.

Abstract

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).