The use of Fick´s law in modeling diffusion processes

Fick´s Law treats the diffusion coefficient as the factor of proportionality between the flux and the spatial gradient of a diffusing species. A recent model for impurity diffusion in semiconductors computes the flux in a different way by taking the spatial gradient of the product of the diffusion coefficient and the density of diffusing species. The results of these two approaches are different for spatially dependent diffusion coefficients. The nature and significance of this difference are explored in terms of the random walk and thermodynamic derivations of the diffusion equation. It is concluded that Fick´s Law is the more fundamental and straightforward way to model diffusion processes