Doping Engineering in Multicrystalline Silicon: Accounting Incomplete Ionization and Charge Carrier Mobility

This paper presents a model for calculating the resistivity profiles in p-type multicrystalline silicon ingots doped with boron, phosphorus and gallium. The purpose of this study was to determine the initial concentrations of impurities that minimize the variation in resistivity values. The incomplete ionization of impurities and mobility of the majority charge carriers in silicon leads to an increase in resistivity along the height of the ingot. This study proposes a methodology to solve this problem by optimizing the initial impurity concentrations. The empirical formulas for determining the calculated value of the target resistivity and the required gallium concentration in the resistivity range 0.5 - 2.0 Ohm-cm are obtained. The results of the calculations allowed the authors to obtain quasi-planar resistivity profiles considering both the incomplete ionization of impurities and the mobility of the charge carriers. The MATLAB and Engee software packages were used to perform the calculations.