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# Charge transport

Electrical conductivity in materials is usually probed by the application of an electrical potential (e.g. the voltage from the contact pads of a battery) to opposite faces of the material. If we are able to measure the flowing current we can determine the conductance by applying Ohm's law. In order to be independent of the particular dimensions of the material we want to use the applied electric field E (voltage across a length) and the current density j (current flowing through a certain cross section). Then, Ohms's law reads:

j = σ E

The proportionaliy constant σ is called specific conductivity and is a material inherent property. The inverse of the specific conductivity is the specific resistivity ρ.

ρ=1/σ

Metals are generally good conductors with low resistivities in the range of μΩcm because every metal atom contributes its valence electrons for the charge transport. For example, in copper the specific resistivity is 1.58 μΩcm at 0oC and increases linearly to 2.26 μΩcm at 100oC.

Semiconductors live up to their name, they are usually less conductive than metals. Their conductivity is conveniently expressed by the product of three quantities; the number of charge carriers n, their mobility μ, and their charge e.

σ = n e μ

The need for the definition of these quantities arises because the conductivity of semiconductors can be vaired over several orders of magnitude by controlling the number and type of charge carriers (this is called doping). The mobility turns out to be less accessible to external control. On the following pages we will develop some ideas about charge carriers in semiconductors, for mobility there is a separate chapter.

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