Diffusion is the process whereby particles move from regions of higher concentration to regions of lower concentration.  Although this includes the self-diffusion phenomena, our interest is in the diffusion of impurity atoms.  Diffusion can be illustrated as the following figures:

Interstitial
 
n = 4n _oe^-Em/kT

   n _o = frequency of lattice vibrations
    Em = interaction energy involved
    T = temperature of the lattice in K
    V = frequency with which thermal energy fluctuations occur

Substitutional

n = 4n _oe^-Es/kT e^-En/kT

   Es = Schottky Vacancy energy
   En = potential barrier associated with the process

It can be shown that
    D = diffusion coefficient = diffusion constant = cm²/sec
 
D = n d²/6 where d is the lattice spacing

D = (4n _od²/6)e^-Em/kT

    general form
 
D = D_oi e^-Ei/kT
 
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