Two-dimensional distribution of vacancy concentration at cross points for the ingot length and the temperature gradients to largely reduce point defects and the growth of a dislocation-free NOC ingot for evaluation of its quality

Abstract

The noncontact crucible (NOC) method has a large and deep low-temperature region in Si melt to grow a uniform large Si single ingot. The cross point with the same concentration of vacancy (CV) and interstitial Si atom (CI) is very important to reduce the point defects in NOC ingot. The relation between the temperature gradient, G, the position and concentration of cross point was estimated using equations derived from Voronkov’ explanation. For NOC growth, two stages for temperature gradient are required as G1 at the growing interface and G2 at the melt surface. The linear T profile is useful for the two-stage growth. Concentration curve of vacancy and interstitial Si atom was calculated on the two stages as a function of the distance from the growing interface. A cross point appears above the melt surface even for the two-stage calculation with a long ingot inside the melt. By the two dimensional-distribution of CV at cross point for G2/G1 and d1, CV has a tendency to become higher as G2/G1 becomes larger. On the whole, the higher CV area appears in the larger G2/G1 and shorter d1 region, and the lower CV area appears in the smaller G2/G1 and longer d1 region. The latter condition is suitable for the NOC growth. Such trend of CV at cross points should be utilized to reduce the remained point defects in ingot. Lower CV and CI at the cross point can reduce the remained point defects in a NOC ingot using smaller G2/G1, smaller G1 and longer d1 near the critical point. To confirm the quality of NOC ingot grown using the present method, a dislocation-free Si single ingot was grown utilizing silica crucibles by the NOC growth method. The maximum diameter and total length of the grown ingot are 17.5 and 15.5 cm, respectively. A Si ingot was experimentally grown by the NOC method. The bottom of the NOC ingot had a convex shape in the growth direction which is very advantageous to NOC growth.It was confirmed by habit lines and etch-pit density of dislocation whether the ingot was dislocation-free or not. A dislocation-free Si single ingot was realized by the NOC method for the first time.