Debye length

Plasma physics is the screening length, named after Peter Debye Debye length or Debye radius, the characteristic length over which the electric potential of a local excess charge on the times falls (: Euler's number ).

In the vicinity of a charge located by the electrostatic repulsion or attraction as a statistical average of a few carriers of the same polarity as those of opposite polarity. Thereby, the charge is shielded from the outside. By the thermal motion of the particles, the order is disturbed and thus weaken the shielding effect. The resulting screening length is a key parameter in the Debye- Hückel theory. Their value depends on the given conditions of the symmetry of the problem: from screening length is called at a flat charge distribution of Debye radius in spherical symmetry.

The principle of shielding of a charge by free charge carriers is applicable to plasmas, electrolytes, and semiconductors.

Debye length in plasmas

In equilibrium, the following applies:

It is

  • The Debye length? d
  • λDe electron Debye length
  • λDi the ion Debye length ( for singly charged ions)
  • Te, Ti, the temperature of the electron or ion
  • Ne the number density of electrons
  • ε0 the electric field constant
  • E is the elementary charge, that is the charge of an electron.

In a low particle density plasma, the electrons are often much hotter than the ions and therefore more evenly distributed in the presence of electric fields. Then:

Conversely, the mobility of the ions is too low in a dense plasma, or with rapidly changing fields in order to adjust its density to the field. Then, the ion term can be neglected:

Debye length in the electrolyte

In the electrolyte applies:

In which

For aqueous solutions of 1:1 electrolytes such as sodium chloride is obtained at room temperature in 0.1 -molar solution a Debye length of 0.96 nm, in 0.001 -molar solution are 9.6 nm

Debye length in semiconductors

For an n -type semiconductor applies:

And for a p -type semiconductor:

It is

  • The dielectric constant of the semiconductor,
  • The thermal voltage
  • And the equilibrium carrier density of the semiconductor.
  • Electrochemistry
  • Plasma Physics
Thermal energy Thermodynamic temperature Electron mobility
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