Conductivity
Electricity and Magnetism

## Conductivity, electrical

Glossary Definition for 16-19 #### Description

The electrical conductivity of a material is an intrinsic, bulk property that, together with the spatial dimensions and shape of a sample of the material, determines the electrical conductance (and therefore electrical resistance) of that sample.

Electrical conductivity is usually represented by the symbol σ.

Electrical conductivity is defined by the equation

σ = LR A

where R is the electrical resistance of a sample of material of length L and uniform cross-sectional area A.

Conductivity is the reciprocal of resistivity:

σ = 1ρ

where ρ is the electrical resistivity of the material.

#### Discussion

A model of electrical conduction in solids, known as band theory, can account for the huge range of conductivities seen in different materials. In this model, electrons in a solid can only have certain ranges of energy, called energy bands.

An electric current in a solid involves electrons that are free to move through the solid and are not associated with any particular atomic nucleus. These electrons are known as conduction electrons and they have energies in the so-called conduction band.

In the presence of an electric field, the conduction electrons acquire a drift velocity along the field direction and this motion constitutes an electric current. The greater the number density of conduction electrons, the greater the current for a given electric field, and hence the greater is the conductivity.

Electrons that remain bound to particular atoms and are not free to move through the material are known as valence electrons. Valence electrons have lower energies than conduction electrons; their energies lie in the valence band. Between the conduction band and the valence band there is a range of energies that are ‘forbidden’ – electrons in the solid cannot have energies in that range. The energy difference between the valence and conduction bands is called the band gap. A valence electron may be promoted to the conduction band if it acquires additional energy that is at least as great as the band gap.

In metals, the conduction and valence bands overlap, each atom contributes one or more electrons to the conduction band, and the conductivity is high. Transferring energy to a metal (e.g. by heating) does not result in any significant increase in the number of conduction electrons.

In a semiconductor, there is a smaller number density of conduction electrons than in a metal – on average much less than one per atom. So the conductivity is lower. However, semiconductors are characterised by having a small band gap. It is relatively easy to promote valence electrons to the conduction band (e.g. by heating or illuminating the material), which increases the conductivity. It is also possible to alter the energy band structure by combining two or more semiconducting elements (e.g. GaAs) and/or by ‘doping’ a semiconductor with small amounts of impurities – and thus to make ‘designer’ semiconductor materials with particular properties.

Insulators have very few conduction electrons as their band gaps are very large. They have very low conductivity.

S m-1

kg-1 m-3 s3 A2

Ω-1 m-1

#### Mathematical expressions

• σ = LR A
• where R is the electrical resistance of a sample of material of length L and cross-sectional area A
• σ = 1ρ
• where ρ is the electrical resistivity of the material

#### In context

Solid materials with conductivities greater than about ~ 105 S m-1 are classed as conductors, those with conductivities between about ~ 105 S m-1 and ~ 10–6 S m–1 are semiconductors, and those with lower conductivities are classed as insulators. Silver has the highest conductivity of any metal element. Table 1 below lists electrical conductivities of various materials at 20°C, illustrating the enormous range of values.

 Material Conductivity σ / S m-1 Silver 6.30 × 107 Copper 5.96 × 107 Titanium 2.38 × 106 Constantan 2.04 × 106 Nichrome 9.09 × 106 GaAs 5 × 10-8  to 103 Amorphous carbon 1.25 to 2 × 103 Sea water 4.8 Silicon 1.56 × 10-3 Glass 10-11 to 10-16 Sulphur 10-16 Paraffin wax 10-18 Teflon 10-23 to 10-26
###### Conductivity
appears in the relation σ=1/ρ G=σA/L