A microscopically accurate continuum model for void formation during semiconductor silicon processing

A predictive continuum model for void growth in crystalline silicon is presented based on extensive atomistic calculations of vacancy cluster thermodynamic and structural properties. It is shown that the previously neglected internal configurational entropy of clusters dramatically alters the high temperature formation free energies and capture radii of small clusters, which in turn strongly impact the predicted evolution of the vacancy size distribution during Czochralski crystal growth. The new model is shown to resolve an outstanding discrepancy between experimentally measured and predicted void nucleation temperatures while at the same time providing an excellent representation of the final size distribution and void density under a variety of crystal growth conditions. All thermophysical parameters for describing point defect transport and thermodynamics used in the model were obtained independently using regression to other experimental systems. The results of this work demonstrate the potential utility, and perhaps necessity, of atomistic simulations for quantitatively accurate process modeling of complex solid-state aggregation phenomena.