On the Motthyphen;Cabrera oxidation rate equation and the inversehyphen;logarithmic law

摘要

It is shown that the often cited inversehyphen;logarithmic oxidation law,Xminus;1prop; minus;logt, whereXis the oxide thickness andtthe 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 inversehyphen;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 ofXminus;1vsloglpar;tsol;X2rpar;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).