(522b) Multi-Scale Modeling and Control of Particulate Cvd for Production of Solar Grade Silicon In Fluidized Beds

In this paper we develop a multi-scale model to describe 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. It is expected that the new FBR system will reduce the cost of solar grade silicon relative to the energy intensive decomposition of Tri-Chloro-Silane in the Siemens process, which dominates the market at present.

The complex interplay between continuous and disperse phases and CVD onto the Silicon particles in the FBR is modeled using three computational modules. The Computational Fluid Dynamics (CFD) module describes simplified hydrodynamics via momentum exchange, mass and heat transfer between different phases. The CFD system is assumed to have fast dynamics relative to the deposition rate so that we can use the quasi-steady state approximation. The reaction module describes the heterogeneous and homogeneous gas phase reactions which allow Silane gas to decompose and deposit on poly-crystalline silicon particles. Hydrogen escapes the system and carries with it fine silicon particles. The formation of fines represents a yield loss. It should be minimized by optimizing the process conditions. The mechanism for fines production is modeled in the reaction module. Finally, we have developed a novel approach to discretize and solve the population balance equations. This last module is used to represent the dynamic evolution of the particle size distribution function. The reaction and population balance models are implemented and solved in the MATLAB modeling environment, whereas the fluid bed system is solved using FEMLAB multi-physics modules.

The simulation studies show that the dynamics of the open loop model is very sensitive to external perturbations and that very long time (24 hours or more) is needed before the system reaches steady state. Control is therefore needed to stabilize the particle size distribution and optimize yield. The control problem is difficult since it involves a wide range of time-scales, ranging from seconds to several days. The dynamics are highly interacting and nonlinear.

In the paper we show how a simple feedback-feedforward control strategy allows the system dynamics to stabilize at desired operating points by changing system parameters like temperature and seed flow. We furthermore show that the controller maintains the particle mass hold up by adjusting silicon product outlet rate while the temperature inside the reactor is kept constant to maintain expected recovery through manipulating heat input through the wall of the fluid bed reactor. The particle size distribution and average product size is controlled using the seed rate and seed distribution functions.

The paper will review briefly results from an industrial pilot plant system which are used to verify the model system and we will demonstrate the effectiveness of the closed loop control system in simulation studies. The overall stability of the control system has been verified using the passivity-based theory based on thermodynamic storage functions which we have developed in our research group.