From considerations of basic statistical and crystal-pulling functions, formulas have been developed which relate the quality and consistency of polycrystalline silicon batches (as expressed by the mean dopant concentration and the standard deviation of pulled sample crystals) to the probable resistivity yield of Czochralski-grown single crystals, in terms of the desired resistivity and the allowable resistivity range. A method which permits the independent determination of the standard deviation of the crystal-pulling equipment and of the polycrystalline silicon itself is presented.
These formulas and method may serve as a generally valid basis for the statistical evaluation of polycrystalline silicon batches.
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