Diffusion of dopants into solids under the application of an electric field often requires the introduction of a composition-dependent diffusivity to account for the phenomenon of “elastic drift”...

Diffusion of dopants into solids under the application of an electric field often requires the introduction of a composition-dependent diffusivity to account for the phenomenon of “elastic drift” where the solid resists the introduction of additional atoms into its lattice by a kind of mechanical, or spring-like, force [3]. Following the discussion in Section 4.6.1, assume that we can express elastic drift using a linear expression for diffusivity as a function of concentration. Initial impression might suggest that the diffusivity should decrease with increasing dopant concentration. Show that this idea cannot work and that to actually increase the resistance, the diffusivity must increase with dopant concentration (i.e., we need a less steep profile at equilibrium). The total flux consists of two components, one due to diffusion and another due to drift within the electric field that can be written simply as a velocity times a concentration (flux = velectricc).