Modeling thermal donor formation and target resistivity for single crystal silicon ingot production

A method for producing a single crystal silicon ingot from a silicon melt held within a crucible, the method comprising:

• determining a post-anneal target resistivity for wafers sliced from the single crystal silicon ingot, the post-anneal target resistivity being the target resistivity of the wafers after an anneal of the wafers;
• modeling thermal donors generated during the anneal of the wafers sliced from the single crystal silicon ingot to determine a pre-anneal wafer resistivity target range, the pre-anneal wafer resistivity target range being a resistivity target range of the wafers before the anneal;
• modeling a dopant profile of the melt during single crystal silicon ingot growth to determine a counter-doping schedule in which the silicon melt is doped with a first dopant and a second dopant is added to the silicon melt in two or more cycles during ingot growth, the counter-doping schedule resulting in at least a portion of the single crystal silicon ingot being within the pre-anneal wafer resistivity target range;
• adding polycrystalline silicon to the crucible;
• heating the polycrystalline silicon to cause the silicon melt to form in the crucible;
• adding the first dopant to the crucible, the first dopant being p-type or n-type;
• contacting the melt with a seed crystal;
• withdrawing the seed crystal from the melt to form the single crystal silicon ingot;
• and
• adding the second dopant to the silicon melt while forming the single crystal silicon ingot based on the counter-doping schedule, the second dopant being of a type different from the type of the first dopant, the second dopant being added in two or more cycles.