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A detailed numerical consideration is used as basic approach for calculating profiles of activation energy versus oxide thickness for various temperatures between 780 and 930 °C. Results presented here are intentionally not based on models of diffusion and reaction kinetics to avoid introducing correction terms due to the expansion of theory still under discussion. The statistical calculation gives the mean activation energy of 2.01 eV with standard deviation of 0.10 eV, very close to the overall activation energy of 2.05 eV [M. A. Rabie, Y. M. Haddara, and J. Carette, J. Appl. Phys. 98, 074904 (2005)]. More instructive features of the thermal oxidation of silicon have been disclosed directly from measurements of oxide thickness with time [M. A. Hopper, R. A. Clarke, and L. Young, J. Electrochem. Soc. 122, 1216 (1975) and J. Blanc, Philos. Mag. B 55, 685 (1987)]. Graphs of the natural logarithm of the growth rate versus oxide thickness, in the range between 2 and 65 nm, show that the oxide thickness influences the activation energy EA between 1.4 and 2.7 eV.

Thermal oxidation of silicon belongs to the most decisive steps in microelectronic fabrication because it allows creating electrically insulating areas which enclose electrically conductive devices and device areas, respectively. Deal and Grove developed the first model (DG-model) for the thermal oxidation of silicon describing the oxide thickness versus oxidation time relationship with very good agreement for oxide thicknesses of more than 23 nm. Their approach named as general relationship is the basis of many similar investigations. However, measurement results show that the DG-model does not apply to very thin oxides in the range of a few nm. Additionally, it is inherently not self-consistent. The aim of this paper is to develop a self-consistent model that is based on the continuity equation instead of Fick’s law as the DG-model is. As literature data show, the relationship between silicon oxide thickness and oxidation time is governed—down to oxide thicknesses of just a few nm—by a power-of-time law. Given by the time-independent surface concentration of oxidants at the oxide surface, Fickian diffusion seems to be neglectable for oxidant migration. The oxidant flux has been revealed to be carried by non-Fickian flux processes depending on sites being able to lodge dopants (oxidants), the so-called DOCC-sites, as well as on the dopant jump rate.