Screening effect

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 q1 and q2 ) interact through the Coulomb force as E Φ = S {displaystyle {mathcal {E}}Phi =S} , ϵ ( k , ω ) Φ ( k , ω ) = S ( k , ω ) {displaystyle epsilon (mathbf {k} ,omega ),Phi (mathbf {k} ,omega )=S(mathbf {k} ,omega )} , 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 q1 and q2 ) interact through the Coulomb force as 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/r2, the average number of particles at each distance r is proportional to r², 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 (see sections 1.2.1 and 3.2 of ). 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). 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 N {displaystyle N} -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 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 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. The first theoretical treatment of electrostatic screening, due to Peter Debye and Erich Hückel, 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, this model is referred to as jellium. Let ρ denote the number density 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.