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 mediums, such as ionized gases (classical plasmas), electrolytes, and electronic conductors (semiconductors, metals).
For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable.
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.
[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.
Consider a fluid composed of electrons moving in a uniform background of positive charge (one-component plasma).
Viewed from a large distance, this screening hole has the effect of an overlaid positive charge which cancels the electric field produced by the electron.
Only at short distances, inside the hole region, can the electron's field be detected.
[2]: §5 If the background is made up of positive ions, their attraction by the electron of interest reinforces the above screening mechanism.
The screened potential determines the inter atomic force and the phonon dispersion relation in metals.
The screened potential is used to calculate the electronic band structure of a large variety of materials, often in combination with pseudopotential models.
The first theoretical treatment of electrostatic screening, due to Peter Debye and Erich Hückel,[3] dealt with a stationary point charge embedded in a fluid.
For simplicity, we ignore the motion and spatial distribution of the ions, approximating them as a uniform background charge.
This simplification is permissible since the electrons are lighter and more mobile than the ions, provided we consider distances much larger than the ionic separation.
Let ρ denote the number density of electrons, and φ the electric potential.
After the system has returned to equilibrium, let the change in the electron density and electric potential be Δρ(r) and Δφ(r) respectively.
In the Debye–Hückel approximation,[3] we maintain the system in thermodynamic equilibrium, at a temperature T high enough that the fluid particles obey Maxwell–Boltzmann statistics.
The former condition corresponds, in a real experiment, to keeping the metal/fluid in electrical contact with a fixed potential difference with ground.
The chemical potential μ is, by definition, the energy of adding an extra electron to the fluid.
If the temperature is extremely low, the behavior of the electrons comes close to the quantum mechanical model of a Fermi gas.
The Fermi energy for a 3D system is related to the density of electrons (including spin degeneracy) by
This result follows from the equations of a Fermi gas, which is a model of non-interacting electrons, whereas the fluid, which we are studying, contains the Coulomb interaction.
Therefore, the Thomas–Fermi approximation is only valid when the electron density is low, so that the particle interactions are relatively weak.
On using the linearized motion of the electrons in their own electric field, it yields an equation of the type
is the plasma permittivity, or dielectric function, classically obtained by a linearized Vlasov-Poisson equation,[6]: §6.4
In physics, this phenomenon is known as Friedel oscillations, and applies both to surface and bulk screening.
In each case the net electric field does not fall off exponentially in space, but rather as an inverse power law multiplied by an oscillatory term.
Theoretical calculations can be obtained from quantum hydrodynamics and density functional theory (DFT).
