Chapter 3   : Fabrication of CMOS Integrated Circuits

Basics of Diffusion

A drop of color in a glass of water spreads from concentrated region to surroundings. This occurs because of the diffusion of color molecules. Similar situation take place when free charge carriers spread in a semiconductor and dopant atoms diffuse in semiconductor at elevated temperature. In this section we use the term diffusion in the later sense. In general, the diffusion is motion of species in solids in the direction of concentration gradient. The chemical process of diffusion is described by the second order differential equation known as Fick's laws.

Fick's first law is used in steady state diffusion , i.e., when the concentration within the diffusion volume does not change with respect to time (Fin=Fout).

Where F is the diffusion flux (in number of dopants cm-2 s-1), D is the diffusion coefficient or diffusivity (in cm2 s-1), n is the concentration of dopants (in cm-3), x is the position (cm).