Resistivity, Doping Concentrations, and Carrier Mobilities in Compensated n- and p-Type Czochralski Silicon: Comparison of Measurements and Simulations and Consistent Description of Material Parameters

Silicon crystals made from solar-grade feedstock, in general, contain boron and phosphorus atoms. Due to the resulting compensation effects, resistivity measurements on a single wafer alone are not sufficient to describe the electrical transport characteristics of the material, and existing standard models are not applicable. In this paper, guidelines for a consistent description of material parameters in compensated silicon are presented. It is shown that the mobility along the whole ingot is described more precisely by a recently published advanced mobility model accounting for compensation than by Klaassen's mobility model, especially for high compensation. Thus, a consistent description of the material parameters along the ingot may be achieved from only Scheil's equation, as well as the advanced mobility model, if the initial dopant concentrations in the melt are known. It is demonstrated that the set of material parameters may be consistently derived from resistivity measurements, only with no complex measurements of additional parameters within an error of 11% for compensation ratios $C_{{\rm R}} , if the base resistivity is measured at several positions along the crystal and if the simulations are based on Scheil's equation and the advanced mobility model.