Point-defect generation during oxidation of silicon in dry oxygen. I. Theory

In this paper, we consider how oxidation in dry O2 influences the point-defect densities in silicon. By using relationships based on the continuity equations in the oxide and applying a proposed set of boundary conditions to the oxidizing Si-SiO2 system, we derive an analytic expression for the supersaturation of interstitials during oxidation. The analysis results in an expression having the experimentally observed sublinear dependence on oxidation rate without requiring any assumptions of nonlinearity. In addition, through observations of the dependence of the linear rate constant in the linear-parabolic model of oxidation on ambient oxygen pressure, it is possible to predict how the interstitial supersaturation will vary with oxidation rate at a given temperature. A companion paper [J. Appl. Phys. 59, 2551 (1986)] compares the predictions of the model with experimental results.