Cabrera—Mott approach to thermal oxidation

Suppose that some ionic species i is strongly rate-limiting and that the rapid flow of an electronic species produces a constant voltage VB across the oxide, independent of oxide thickness L. Furthermore, assume the electric field in the oxide to be due primarily to surface charge, such that space-charge effects are negligible. Then the electric field, E(x), in the oxide can be written as a constant E0 

If this field provides a driving force much greater than the driving force of the concentration gradient of the ionic species and if the behaviour of the ionic species is ohmic in this field, then the ionic current can be written as 

Employing now the assumption made by Cabrera and Mott [30] of a constant voltage VB, the growth rate can be written as 

Integration of this growth-rate expression then yields the parabolic growth law 

---