Modeling of Resistivity Profiles in Multicrystalline Silicon

This paper presents the results of modeling the resistivity profiles of multicrystalline silicon ingots doped with boron, phosphorus, and gallium. All calculations were performed using MATLAB software by solving a system of linear equations. To obtain homogeneous resistivity profiles across the height of the ingot and controlled conductivity inversion profiles, a method of calculating initial impurity concentrations was used. The effects of incomplete ionization of the acceptor impurities on the resistivity variations along the ingot are briefly described. For ingots with homogeneous resistivity distribution, empirical relationships between gallium and phosphorus concentrations and the amount of boron in the source material have been discovered.