Data-assisted physical modeling of oxygen precipitation in silicon wafers

Abstract

A quantitative continuum model for oxide precipitation in silicon is presented that accounts for vacancy absorption and shape change as mechanisms of precipitate stress relief. All model parameters except one, the Si/SiO2 interface free energy, are fixed at values established in prior studies of microdefect formation. The interface free energy is described by an 8-parameter function, whose functional form and dependencies were based on an analysis of electronic structure calculations of small oxide cluster thermodynamics. The interface energy function parameters are regressed, using global optimization, to an experimental benchmark consisting of 13 wafer thermal anneals, with different temperature-time histories and resulting in widely varying measured final oxide precipitate densities. We demonstrate that the model is able to capture the benchmark features well with multiple parameter combinations and that additional constraints are required to fully specify a unique solution. We also show that a simple, single-parameter, constant interface free energy model cannot fully capture the diverse experimental benchmark, highlighting the complexity of oxide precipitation. The precipitation model is used to analyze the mechanisms responsible for several features of oxide nucleation and growth during wafer annealing.