Kinetics of dry oxidation of silicon. I. Space-charge-limited growth

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Abstract
Recent studies of the kinetics of dry oxidation of silicon have shown that the time dependence is more precisely described by a power-of-time law than by a linear-parabolic expression. This study shows the power law to be correct. This follows from the interdependence of the experimental linear and parabolic rate constants. The linear-parabolic expression appears to be equivalent to the first terms of a series expansion of the power-of-time law. The omission of higher-order terms gives systematic deviations known as the ‘‘anomalous’’ initial regime. An ionic space-charge-limited growth model is introduced, based on the classical oxidation theory of Wagner and accounting for the effect of internal fields on conduction. First, it is shown that both the magnitude of ionic and electronic conduction are sufficiently high, which is illustrated for an oxide layer of 300 Å growing at 870 °C. It is made plausible that the oxide-fixed charge density, Qf, is sufficiently large at high temperatures to cause large internal fields. An expression is derived which accounts for the mutual Coulomb repulsion of charges in very dense space-charge layers. The excellent fit of the derived expression and its application will be discussed in part II.