Debye length

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In the plasma physics is screening length by Peter Debye Debye length or Debye radius called the characteristic length on which the electric potential of a local excess charge on the fold decreases ( : Euler's number ).

Ion distribution in a solution

Due to the electrostatic repulsion or attraction, there are, on a statistical average, fewer charge carriers of the same polarity than those of opposite polarity in the immediate vicinity of a charge . This shields the load from the outside (see illustration). The thermal movement of the particles disrupts the order and thus weakens the shielding effect. The resulting shielding length is a central variable in the Debye-Hückel theory . Under given conditions, its value depends on the symmetry of the problem: one speaks of shielding length in the case of a plane charge distribution, of Debye-Radius with spherical symmetry .

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

Debye length in plasmas

The following applies in equilibrium:

In it is

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

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


Debye length in electrolytes

The following applies in electrolytes:


in which

For aqueous solutions of a 1: 1 electrolyte such as common salt , the Debye length in 0.1 molar solution is 0.96  nm at room temperature , and 9.6 nm in 0.001 molar solution.

Debye length in semiconductors

For an n-type semiconductor :

and for a p-type semiconductor:

It is

  • the dielectric constant of the semiconductor
  • the temperature stress
  • or the equilibrium charge carrier density of the semiconductor.