Extrinsic conductivity

Extrinsic conductivity refers to the proportion of conductivity of a solid that is caused by the incorporation of foreign atoms into the crystal lattice . ${\displaystyle \sigma }$

Conductivity as a function of temperature and degree of doping

The introduction of foreign atoms is called doping . These foreign atoms cause an increase in conductivity, as they - depending on the number of their valence electrons - introduce additional vacancies or additional freely moving charges into the solid.

The extrinsic conductivity is almost independent of temperature at low temperatures and is contrary to the intrinsic conductivity even at 0  K . As a result, the extrinsic conductivity dominates at low temperatures, while it is covered by the intrinsic conductivity when the temperature rises.

The mathematical relationship results from the Arrhenius equation :

${\displaystyle \sigma =\sigma _{0}\cdot \exp \left(-{\frac {E_{\mathrm {A} }}{R\cdot T}}\right)}$

With

• the activation energy ${\displaystyle E_{\mathrm {A} }}$
• the universal gas constant ${\displaystyle R}$
• the temperature ${\displaystyle T}$
• the factor for a reference variable ${\displaystyle \sigma _{0}}$ ${\displaystyle \sigma }$

In the shape

${\displaystyle \Leftrightarrow \ln {\frac {\sigma }{\sigma _{0}}}=-{\frac {E_{\mathrm {A} }}{R}}\cdot {\frac {1}{T}}}$

For this type of solid-state conductivity , straight-line Arrhenius graphs are obtained , the slope of which is proportional to the activation energy.

Since thermal excitation is necessary for intrinsic lattice defects , the activation energy for intrinsic conduction is usually twice as large as that of extrinsic conduction. Depending on the degree of doping, families of straight lines with different slopes are obtained for the extrinsic line (not shown).

example

When doping sodium chloride  NaCl with manganese (II) chloride  MnCl ₂ , the stoichiometric composition of the compound changes depending on the degree of doping:

${\displaystyle {\text{Na}}_{1-2x}}$ ${\displaystyle {\text{Mn}}_{x}}$ ${\displaystyle {\text{L}}_{x}}$ ${\displaystyle {\text{Cl}}_{1}}$

L denotes the cations vacant , which are necessary for the maintenance of the charge balance .

The doping has the consequence that a cation vacancy is created for each Mn ion. Excess Cl ions are located at a different location (e.g. surface) of the crystal because of the charge neutrality . The chloride cannot be in the vicinity of the manganese ion - for example in an interstitial space - since interstitial spaces in the NaCl lattice cannot be occupied by chloride. ${\displaystyle ^{2+}}$ ${\displaystyle ^{-}}$

See also

• Defect depletion

Individual evidence

1. ^ AB Lidiard: Ionic Conductivity . In: S. Flügge (Hrsg.): Electrical Conductivity II / Electrical Line Phenomena II (=  Handbook of Physics ). tape XX , no. 4 . Springer, Berlin / Göttingen / Heidelberg 1957, p. 246-349, here 280 .