The free energy density can have a contribution from the electric energy. Therefore, the chemical potential in Equation 3-293 can depend on the electric potential V as

where z is the charge number of the transported species, and F is Faraday constant. The flux due to electromigration is then defined as a function of the chemical potential

with the mobility M and the electric field E = −∇V.

For linear mobility, M is related to the diffusion coefficient D as

Replacing Faraday constant with the elementary charge and Avogadro number, F = eNA, and the gas constant in terms of Boltzmann constant, R = kBNA, gives the electromigration flux