How can solar panels become cheaper? Part of the cost is in the production of silicon, which is manufactured in electrode-heated furnaces through a reaction between carbon and naturally occurring quartz rock. Making these furnaces more efficient could lead to a reduction in the financial cost of silicon and everything made from it, including computer chips, textiles, and solar panels. Greater efficiency also means reduced pollution.
Oxford Mathematics' Ben Sloman is working with colleagues Colin Please, Robert Van Gorder, and collaborators at Norwegian silicon production company Elkem to better understand how the furnaces behave.
One problem in silicon production is the formation of a solid crust, which clogs up the furnace and prevents the raw materials from falling down the furnace to the hot region, where the necessary chemical reactions occur. Due to the high temperatures involved (around 2000 kelvin) it is difficult to observe how this clogging happens, so Elkem have carried out experiments. A mathematical model developed by Ben and colleagues captures the evolution of gas flow, temperature, and chemical reactions in these experimental furnaces. Numerical simulations demonstrate that the position of crust formation is largely driven by temperature, with the location moving upwards as the furnace becomes hotter. This effect is quantified in an asymptotic analysis of the model . The furnace operators can change the type of raw materials used in the process and the energy input into the electrodes. Simulations of the model show that using more reactive carbon particles (for example charcoal) reduces the amount of silicon monoxide gas escaping from the furnaces, allowing more silicon to be produced from the quartz, and also reducing the build up of the furnace crust.
The image shows a sketch of a silicon furnace, reproduced from The Si Process Drawings, by Thorsteinn Hannesson.
 B. M. Sloman, C. P. Please, and R. A. Van Gorder. Asymptotic analysis of a silicon furnace model. Submitted. (2017).
The research is funded by the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling here in Oxford in collaboration with Elkem.