Oxide precipitation at silicon grain boundaries

Oxygen precipitates at various grain boundaries in crystalline silicon, formed after prolonged high temperature annealing, grow within a narrow size distribution. This narrow size distribution appears to depend on the specific grain boundary. On the basis of this observation a model is derived which is based on the energy balance between grain boundary energy, ${\mathrm{Si/SiO}}_2$ interface energy, and an additional term describing the energy of the ledges of the faceted precipitates. This model predicts an energy minimum for a defined size of the precipitates.