On the Mott-Cabrera oxidation rate equation and the inverse-logarithmic law

Abstract

It is shown that the often cited inverse-logarithmic oxidation law, X -1∝ -logt, where X is the oxide thickness and t the observation time, is not an asymptotic solution of the rate equation derived by Mott and Cabrera in their theory of low temperature oxidation. Thus whether or not the inverse-logarithmic law is experimentally verified has no bearing on the validity of this theory. A correct solution is presented, and it is shown that for thin oxide films a plot of X-1 vs log(t/X2) should yield straight lines. Vermilyea's data on Ta is reexamined according to this analysis and yields reasonable results for the activation energy of defect solution (1.59 eV) and for the potential across the oxide (1.79 V).