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.
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.
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