Patent ID: 8216362

Claim:
A process for growing a single crystal silicon ingot from a silicon melt wherein the melt/solid interface between the ingot and the silicon melt is not flat, the ingot comprising a central axis, a seed-cone, an end opposite the seed-cone, and a constant diameter portion between the seed-cone and the opposite end, said constant diameter portion having a lateral surface, a radius (R) extending from the central axis to the lateral surface, and a nominal diameter of at least about 150 mm, the ingot being grown in accordance with the Czochralski method, the process comprising: controlling (i) a growth velocity, v, and (ii) an effective average axial temperature gradient, G effective , during the growth of at least a segment of the constant diameter portion of the ingot over the temperature range from solidification to a temperature of about 1200° C., wherein G effective is defined by the following equation: G effectve = [ G corrected v ] x , flat × v x , iface and G corrected is defined by the following equation: 1 T corrected = ( 1 / T m ) + ( 1 / T m 2 ) ⁢ zG corrected , such ⁢ ⁢ that ⁢ ⁢ ∑ f ⁡ ( T - T corrected ) = 0 wherein: G effective represents a revision to G corrected , revised to account for the deviation in the interface shape from a flat profile; T is the temperature of at any fixed radial location, r, within the segment; T m is the temperature at the melt/solid interface; z is the axial distance from the interface at the given radial location; the function f denotes an acceptable statistical agreement between T and T corrected ; the subscript x denotes the critical value at which the predominate intrinsic point defect transitions between vacancy dominated and interstitial dominated material, such that [G corrected /v] x,flat is the ratio of G corrected /v at which the material transitions from interstitial dominated to vacancy dominated for a flat melt-solid interface and v x,iface is the critical value of v wherein G effective /v x,iface is the ratio at which the material transitions from interstitial dominated to vacancy dominated for the non-flat melt-solid interface; flat denotes a flat interface; iface denotes any non-flat interface; such that the ratio of v/G effective , at a given axial position within said segment, varies radially by less than about ±30%, relative to the critical value of v/G effective ; and, cooling said segment from the solidification temperature to about 750° C.