The effect of Frenkel defect formation on spherical SiO2 precipitate growth in silicon wafers

Abstract

A general analytic solution is given to the sphere-growth problem which includes (1) oxygen and point defect transport, (2) interface reaction kinetics, (3) surface energy, and (4) strain energy storage. Short, intermediate, and long time behaviors are given. In the long time domain, where the Peclet number for oxygen is constant provided the far field conditions are constant, the growth rate is dominated at low and intermediate temperatures primarily by silicon interstitial formation and somewhat by strain energy storage. At high temperatures (≳1150 °C), these effects become small and the interface begins to approach the thermodynamic equilibrium state. However, at all lower temperatures, the supersaturation of silicon interstitials at the SiO2/Si interface is very large and the interface is far from the thermodynamic equilibrium. Extension of the mathematical approach to precipitates of other shapes is also given.