If a concentration gradient of mobile particles exists, there will be a flow of such particles – diffusion – from the region of high concentration to the region of low concentration:

where f is the particle flux through a plane parallel to the surface, in numbers per square metre per second. D is a constant of proportionality – the diffusion constant – and $\partial N/\partial x$ is the concentration gradient.

Since N is also a function of time during the diffusion process, Fick’s second law can be derived from the first law and is given as:

Diffusion also takes place in the y- and z-directions, parallel to the plane of the surface, as soon as a concentration gradient is established below the surface. Diffusion flow will continue until the concentration becomes uniform across the specimen.

This effect is utilized in producing a desired impurity profile in a particular specimen of semiconductor. At normal temperatures the impurity atoms are immobile until heated to a high temperature. A concentration gradient is formed by heating the semiconductor wafer in a gaseous atmosphere of the impurity atoms so that a high concentration exists at the surface. Under such conditions the impurity atoms diffuse into the semiconductor. In practice the diffusion process is stopped by reducing the temperature when the desired profile has been achieved.