Multi-Objective and Robust Optimal Control of a CVD Reactor for Polysilicon Production

Traditionally, high-grade polysilicon is produced in the so-called "Siemens" reactor. The process is based on the Chemical Vapor Deposition (CVD) of silicon from a gaseous mixture of silanes and hydrogen on silicon rods. To obtain the crystal growth on the rod surface high temperatures are needed. The rods are heated internally by the Joule effect, i.e., an electrical current induces heating due to the electrical resistance of the silicon material. The Joule effect allows for a tight temperature control but, it also makes this process extremely energy intensive. In this work an existing model is improved by accounting for the reflectivity of the wall and the radiative absorption of the bulk. Additionally, the uncertainty on the thermal conductivity parameter of the silicon rods is taken into account. Hence, a robust optimal control problem is formulated and solved based on the evaluation of Lyapunov equations. Finally, the trade-off among productivity and energy cost is studied via a multi-objective (MO) scalarization method.