Multi-scale modeling and control of fluidized beds for the production of solar grade silicon

In this paper we develop a multi-scale model to describe the growth of silicon particles due to chemical vapor deposition (CVD) in a fluidized bed reactor (FBR). The reactor system is designed to make poly-silicon for solar cell applications by thermal decomposition of silane. The complex interplay between the continuous and the disperse phases and CVD onto the silicon particles in the FBR is modeled using three modules — Computational Fluid Dynamics (CFD), Reaction Module and Population Balance Module (PBM). The Computational Fluid Dynamics (CFD) module describes the hydrodynamics via momentum, mass and heat transfer between different phases. The reaction module describes the homogeneous gas phase reactions and deposition on polycrystalline silicon particles. The population balance represents the dynamic evolution of the particle size distribution. By coupling together the modules, we provide a complete multi-scale model for the particulate CVD process. The resulting nonlinear, multi-scale model is solved using COMSOL Multi-physics and MATLAB. The results from the proposed model match the experimental data obtained from a pilot scale reactor. An inventory controller maintains the void fraction and in turn the average diameter of the silicon particles at the exit.