Debye length
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 ).
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
- λ _{D is} the Debye length
- λ _{De is} the electron Debye length
- λ _{Di is} the ion debye length (for singly charged ions)
- T _{e} , T _{i is} the temperature of the electrons or ions
- n _{e} , the particle density of the electron
- ε _{0 is} the electric field constant
- k _{B is} the Boltzmann constant
- e is the elementary charge, i.e. the charge of an electron.
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
- the permittivity
- the Avogadro constant
- I is the ionic strength of the electrolyte.
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.