# What are nonlinear resistances

#### Non-linear current-voltage characteristics

A large number of two-pole elements with the property "resistance" have a non-linear current-voltage relationship.

The non-linear resistance depends on a physical quantity:

• Temperature-dependent resistors (NTC thermistors, silicon resistors, PTC thermistors);
• Voltage-dependent resistors (varistors);
• Magnetic field-dependent resistances (field plates);
• Light-dependent resistors (photo resistors).

The dependency is indicated in the resistance symbol by an inclined line, at the end of which is the corresponding physical variable.

The manufacturers use characteristic curves to indicate the properties that are important for use in circuits.

Nonlinear resistors are single-layer semiconductor components.

#### Conduction mechanisms in semiconductor materials

The experimental results show opposite temperature behavior of the conductivity compared to metals: the conductivity increases exponentially with increasing temperature.

At low temperatures the conduction band is empty. Purest silicon z. B. is an insulator at low temperatures. All electrons are fixed in the valence band. Only at higher temperatures are bonds broken, which corresponds to the lifting of an electron from the valence band into the conduction band. A hole, a defect electron, has formed at the broken bond. In an applied electric field \ (\ vec {E} \) the electrons move in the conduction band, while the holes in the valence band are passed on to neighboring atoms in the direction of the field strength.

The electrical conduction is bipolar, it is only carried by the grid's own electrons and defect electrons. One speaks of self-management.

The following applies to the conductivity (see equation (40)):

 \ (κ = n _ {+} \ mathrm {e} b _ {+} + n _ {-} \ mathrm {e} b _ {-} \) (64)

where \ (n _ + (n _ {-}) \) and \ (b _ + (b _ {-}) \) mean the number density or mobility of the holes and electrons.

Because of the charge neutrality is

The intercalation (doping) of foreign atoms in the base material creates the effect of extraneous conduction or impurity conduction. If the tetravalent basic material silicon (i.e. there are four valence electrons on the outer shell) is doped with pentavalent elements such as phosphorus, arsenic, antimony, which are called electron donors or donors, the fifth electron of the foreign atom is not required for valence bonding. It is available as a free electron. The number density of these electrons dominates at low and medium temperatures compared to the thermal pair formation (hole, electron).

Because of the predominantly negative free charge carriers (majority carriers) the material is called \ (n \) - conductive.

When doped with trivalent elements such as aluminum, indium or boron, which are called electron receivers or acceptors, the trivalent element tries to steal electrons from the tetravalent element silicon in order to complete its bonds in the lattice. This creates movable defect electrons, the material becomes \ (p \) -conducting.

The temperature dependency of the conductivity of semiconductor single-layer components differs between self-conduction and external conduction.

If one plots the temperature dependence \ (\ left (\ dfrac {1} {T} \ right) \) on the \ (x \) axis and the conductivity logarithmically on the \ (y \) axis, two straight lines result that are assigned to the internal line area (I) and the external line area (II).

The following picture also shows an original measurement on silicon:

Temperature dependence of the resistance