Diffusion

· The chemical reaction at the oxide interface is fast and the oxygen or material concentration is constant during growth. A "steady state" situation governed by Fick's first law describes the process:
J_x = -D(dc/dx); D = D₀exp(-Q/kT)

· The Rate of Oxide Growth depends on the oxygen flux :
(dx/dt) = AJ_X= - AD(dc/dx)
· Separate Variables and Integrate:

which yields: x² = AD (c_S - c_I) t, or x = B (D t)^1/2
· Oxide growth is parabolic as a function of time.