Electric-field screening

In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas), electrolytes, and charge carriers in electronic conductors (semiconductors, metals). In a fluid, with a given permittivity $ε$ , composed of electrically charged constituent particles, each pair of particles (with charges $q 1$ and $q 2$ ) interact through the Coulomb force as

\mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \varepsilon \left|\mathbf {r} \right|^{2}}}{\hat {\mathbf {r} }},

where the vector

r

is the relative position between the charges. This interaction complicates the theoretical treatment of the fluid. For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as

1/ r 2

, the average number of particles at each distance

r

is proportional to

r 2

, assuming the fluid is fairly isotropic. As a result, a charge fluctuation at any one point has non-negligible effects at large distances.

In reality, these long-range effects are suppressed by the flow of particles in response to electric fields. This flow reduces the effective interaction between particles to a short-range "screened" Coulomb interaction. This system corresponds to the simplest example of a renormalized interaction.^[1]

In solid-state physics, especially for metals and semiconductors, the screening effect describes the electrostatic field and Coulomb potential of an ion inside the solid. Like the electric field of the nucleus is reduced inside an atom or ion due to the shielding effect, the electric fields of ions in conducting solids are further reduced by the cloud of conduction electrons.

^ McComb, W.D. (2007). Renormalization methods: a guide for beginners (Reprinted with corrections, Reprinted ed.). Oxford: Oxford University Press. §1.2.1, §3.2. ISBN 978-0199236527.

[1] McComb, W.D. (2007). Renormalization methods: a guide for beginners (Reprinted with corrections, Reprinted ed.). Oxford: Oxford University Press. §1.2.1, §3.2. ISBN 978-0199236527.

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