Charge carrier density

The charge carrier density denotes the number of charge carriers per volume. It is measured in m⁻³. As any density it can depend on position. It should not be confused with the charge density, which is the number of charges per volume at a given energy.

The carrier density is obtained by integrating the charge density over the energy that the charges are allowed to have.

The charge carrier density is a particle density, so integrating it over a volume V gives the number of charge carriers N in that volume

$N=\int_V n(\mathbf r) \,\mathrm{d}V$.

where

$n(\mathbf r)$ is the position-dependent charge carrier density.

If the density does not depend on position and is instead equal to a constant n₀ this equation simplifies to

$N=V\cdot n_0$.

The charge carrier densities enters equations concerning the electrical conductivity and related phenomena like the thermal conductivity.

Measurement

The density of charge carriers can be determined in many cases using the Hall Effect, the voltage of which depends inversely on the density [1].

Such measurements show that the density for silver is around 1 x 10^28 m^-3, or around 1.8 per atom.