In
physics, screening is the damping of
electric fields caused by the presence of mobile
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* '' Charge!!'', an album by The Aqu ...
carriers. It is an important part of the behavior of charge-carrying
fluids, such as ionized gases (classical
plasmas),
electrolytes, and
charge carriers
In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is use ...
in electronic conductors (
semiconductors,
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typica ...
s).
In a fluid, with a given
permittivity , composed of electrically charged constituent particles, each pair of particles (with charges and ) interact through the
Coulomb force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
as
where the vector 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 , the average number of particles at each distance is proportional to , assuming the fluid is fairly
isotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
. 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 (see sections 1.2.1 and 3.2 of).
In
solid-state physics, especially for
metals
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
and
semiconductors, the screening effect describes the
electrostatic field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
and Coulomb potential of an
ion
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conv ...
inside the solid. Like the electric field of the
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
* Atomic nucleus, the very dense central region of an atom
*Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucl ...
is reduced inside an atom or ion due to the
shielding effect
In chemistry, the shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron. The shielding effect can be defined as a ...
, the electric fields of ions in conducting solids are further reduced by the cloud of
conduction electrons
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in w ...
.
Description
Consider a fluid composed of electrons moving in a uniform background of positive charge (one-component plasma). Each electron possesses a negative charge. According to Coulomb's interaction, negative charges repel each other. Consequently, this electron will repel other electrons creating a small region around itself in which there are fewer electrons. This region can be treated as a positively charged "screening hole". 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. For a plasma, this effect can be made explicit by an
-body calculation (see section 5 of
). If the background is made up of positive ions, their attraction by the electron of interest reinforces the above screening mechanism. In atomic physics, a germane effect exists for atoms with more than one electron shell: the
shielding effect
In chemistry, the shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron. The shielding effect can be defined as a ...
. In plasma physics, electric-field screening is also called Debye screening or shielding. It manifests itself on macroscopic scales by a sheath (
Debye sheath) next to a material with which the plasma is in contact.
The screened potential determines the inter atomic force and the
phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical ...
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 screening effect leads to the
independent electron approximation, which explains the predictive power of introductory models of solids like the
Drude model, the
free electron model and the
nearly free electron model
In solid-state physics, the nearly free electron model (or NFE model) or quasi-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model i ...
.
Theory and models
The first theoretical treatment of electrostatic screening, due to
Peter Debye and
Erich Hückel
Erich Armand Arthur Joseph Hückel (August 9, 1896, Berlin – February 16, 1980, Marburg) was a German physicist and physical chemist. He is known for two major contributions:
*The Debye–Hückel theory of electrolytic solutions
*The Hücke ...
,
dealt with a stationary point charge embedded in a fluid.
Consider a fluid of electrons in a background of heavy, positively charged ions. 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. In
condensed matter physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the ...
, this model is referred to as
jellium.
Screened Coulomb interactions
Let ''ρ'' denote the
number density
The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects ( particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
of electrons, and ''φ'' the
electric potential. At first, the electrons are evenly distributed so that there is zero net charge at every point. Therefore, ''φ'' is initially a constant as well.
We now introduce a fixed point charge ''Q'' at the origin. The associated
charge density
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
is ''Qδ''(''r''), where ''δ''(''r'') is the
Dirac delta function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire ...
. After the system has returned to equilibrium, let the change in the electron density and electric potential be ''Δρ''(''r'') and ''Δφ''(''r'') respectively. The charge density and electric potential are related by
Poisson's equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with th ...
, which gives
: