Stochastic model for grain size versus dose in implanted and annealed polycrystalline silicon films on SiO2

160-nm polycrystalline silicon films were implanted at room temperature with 100-keV silicon ions and subsequently annealed. The final grain size was found to increase with implant dose. A model is presented here to account for the dose dependence of the grain size. Three mechanisms were presumed to account for the final grain size: statistical variations of area coverage by the implanted ions, ion channeling, and spontaneous nucleation. Model parameters were successfully fit to the experimental data.