Size distribution modeling for fluidized bed solar-grade silicon production

This work addresses modeling size distribution of solar-grade silicon particles grown by thermal decomposition of silane gas in a fluidized bed reactor. Particles grow with heterogeneous chemical vapor deposition and by scavenging powder produced in homogeneous gas phase reaction. The model uses ordinary differential and algebraic equations that track particle movement through discrete size intervals to simulate changes in the size distribution. The model solves quickly and is easily tuned to fit experimental data. Validating the model with experimental data from pilot plant tests shows that this approach is useful for control system design and scale-up of the fluidized bed silicon production process. Combining the developed model with feedback control theory also provides a novel method for sensitivity analysis.