Effect of process parameters on stress development in two-dimensional oxidation

Abstract

A simplified viscoelastic analysis has been made of the stress evolution during two-dimensional (2D) oxidation of silicon substrates, with the objective of learning the effect of process parameters such as temperature and steam pressure. A cylindrical silicon surface was chosen for simplicity of analysis, and yet it still has most of the essential elements pertinent to practical problems such as, e.g., the oxidation of trench corners in silicon integrated circuits. With correlations between the viscosity and the hydroxyl content of SiO2, and between the hydroxyl content and the steam pressure, the analysis shows that stress reduction can be achieved by carrying out oxidation at high steam pressures. However, stresses remain rather high if the oxidation temperature is as low as 800 °C. For a linear-parabolic oxidation kinetics, both the oxide and the substrate stresses do not increase indefinitely with the increase of oxide thickness, but reach their respective peaks at oxide thicknesses that are dependent on process parameters. The present results should be useful in serving as guidelines in the selection of 2D oxidation conditions. The accuracy of a previous 2D oxidation model based on the viscous flow of an incompressible fluid has also been assessed with reference to the viscoelastic model. The incompressible-fluid model is found to be quite accurate at high temperatures ≳900 °C.