3. Diffusion and conductivity

Once the carrier density has been determined, the aim is to calculate the expression for the conductivity. This can be obtained by taking into account the phenomenon of diffusion.

In a conductor, the velocity of carriers is close to the Fermi speed (of the order of 10 ⁶ m/s). Let a surface S separate two regions with slightly different carrier densities ρ ₊ and ρ _–

Carriers move in either direction with equal probability, so when densities are equal on either side of S, the two currents from each side of S cancel each other out. Not so when the densities are different. A current then arises, directed from the higher to the lower density. To calculate this current, we take into account the time between two collisions as the...