New resistivity/dopant density model for compensated-Si

Models establishing relationships between electrical resistivity and dopant densities of silicon wafers/bricks are not applicable for compensated-Si, such as upgraded metallurgical grade silicon UMG-Si. To date, no satisfactory theoretical model has been able to explain precisely the variety of new experimental results and observations related to compensated-Si. In this study, a new approach considering equilibrium ionisation constants according to electrolyte theory was proposed, which reproduce, for single-doped Si, Thurber's curves of charge carrier's mobilities. When more than one doping species are involved, as in compensated-Si, a numerical algorithm has to be used for solving multiple equilibrium systems. The study of such systems demonstrates a particular behaviour known from buffered solutions. Equilibrium constants were calculated from thermodynamic properties of chemical compounds, and a new general theory was proposed using available knowledge of electrochemistry (Nernst equation, Butler-Volmer equation). Considering that the silicon/dopant systems constitute a weak electrolyte solid solution, it is concluded that the electrolyte solution theory provides a good physical model and mathematical framework to get a better understanding of solar cell's behaviour.