Methods for modeling the impurity concentration of a single crystal silicon ingot
Methods for forming single crystal silicon ingots in which plural sample rods are grown from the melt are disclosed. A parameter related to the impurity concentration of the melt or ingot is measured. In some embodiments, the sample rods each have a diameter less than the diameter of the product ingot.
1. A method for modeling the impurity concentration of a single crystal silicon ingot, the method comprising:
pulling a first sample rod from a silicon melt disposed in a crucible, the first sample rod having a first sample rod diameter of less than 100 mm;
measuring a first sample rod parameter related to the impurity content of the first sample rod, the first sample rod parameter being selected from the group consisting of the phosphorous concentration, boron concentration, aluminum concentration, gallium concentration, arsenic concentration, indium concentration, antimony concentration, total impurity concentration, dopant concentration, and resistivity of the first sample rod;
pulling a second sample rod from the silicon melt, the second sample rod having a first sample rod diameter of less than 100 mm;
measuring a second sample rod parameter related to the impurity content of the second sample rod, the second sample rod parameter being selected from the group consisting of the phosphorous concentration, boron concentration, aluminum concentration, gallium concentration, arsenic concentration, indium concentration, antimony concentration, total impurity concentration, dopant concentration, and resistivity of the second sample rod; and
determining the impurity concentration of a single crystal silicon ingot based at least in part on a rate of change in the difference between the measured first sample rod parameter and the measured second sample rod parameter.
2. The method as set forth in claim 1 wherein the first sample rod parameter and the second sample rod parameter is the same parameter.
3. The method as set forth in claim 1 wherein the first sample rod diameter and the second sample rod diameter is each less than about 50 mm.
4. The method as set forth in claim 1 wherein the first sample rod diameter and the second sample rod diameter is each less than about 25 mm.
5. The method as set forth in claim 1 wherein the first sample rod diameter and the second sample rod diameter from about 5 mm to about 100 mm.
6. The method as set forth in claim 1 further comprising:
pulling a third, fourth, fifth, sixth, seventh, eighth, ninth and/or tenth sample rod from the melt, the diameter of each sample rod being less than about 100 mm; and
measuring a sample rod parameter related to the impurity content for each sample rod pulled from the melt.
7. The method as set forth in claim 1 wherein the impurity concentration of a single crystal silicon ingot is determined from a model, the first sample rod parameter and the second sample rod parameter being input into the model.
8. The method as set forth in claim 1 further comprising pulling a product ingot from the melt, the single crystal silicon ingot in which the impurity concentration is determined being the product ingot pulled from the melt.
9. The method as set forth in claim 1 wherein the melt is a first melt, the method further comprising:
pulling a first product ingot from the first melt; and
pulling a second product ingot from a second melt, the single crystal silicon ingot in which the impurity concentration is determined being the second product ingot pulled from the second melt.
10. The method as set forth in claim 9 wherein the diameter of the first and second sample rods are each less than 0.75 times the diameter of the product ingot.
11. The method as set forth in claim 1 wherein the impurity concentration is an impurity concentration of a portion of the single crystal silicon ingot.
12. The method as set forth in claim 1 wherein the impurity concentration is concentration of one or more impurities over the length of the single crystal silicon ingot.
13. The method as set forth in claim 1 further comprising annealing each sample rod in a thermal donor kill cycle prior to measuring the first and second sample rod parameters.
14. The method as set forth in claim 13 wherein the sample rods are annealed at a temperature of at least about 500° C.
15. The method as set forth in claim 14 wherein a length of the anneal is at least about 5 seconds.
16. The method as set forth in claim 13 wherein a length of the anneal is from about 5 seconds to about 5 minutes.
17. The method as set forth in claim 13 further wherein the sample rod is annealed at a temperature of at least about 650° C.