Charge Screening in an Electron Gas of Arbitrary Degeneracy

Utilizing the dielectric response formulation, analytic expressions are obtained for the screening field around a localized point charge in a non‐interacting Fermi‐Dirac electron gas of arbitrary degeneracy. Screening field features suggested by the analytic forms are discussed. In the non‐degenerate case, the field is a modified Brooks‐Herring one; the predominant form of the screening factor is inverse exponential with a transition to Gaussian in the range k B Tr 2 ≪1.