Abstract: Methods for producing single crystal silicon ingots are disclosed. The methods may involve modeling formation of thermal donors and target resistivity during downstream annealing processes such as during subsequent device manufacturing such as manufacturing of interposer devices. The model may output a pre-anneal wafer resistivity target range. The single crystal silicon ingot production process may be modeled to determine a counter-doping schedule to achieve the pre-anneal wafer resistivity target range across a longer length of the main body of the ingot.