Importance of zero cross-point (Cp = 0) control between the vacancy and interstitial Si atom concentration curves to obtain a perfect Si ingot using Si melt growth

Abstract

The cross-point (Cp), which appears in the vacancy (CV) and interstitial Si atom (CI) concentration curves, is a simple controlling factor for ingot growth and provides a final goal to obtain a defect-free Si ingot using general Si melt growth. The importance of Cp is demonstrated using the noncontact crucible method (NOC), which has a relatively small temperature gradient due to an ingot grown inside the melt. The control of temperature gradient G at a constant growth rate v is simple for the actual ingot growth; thus, the present simulated results are expressed by G at a constant v. The concentration at the Cp point becomes smaller as G becomes smaller and finally becomes zero (Cp = 0), in which CV and CI are practically zero (CV=CI=0). The estimated G and temperature T at Cp = 0 for v = 0.000144 cm s−1 are 6.3, 12.5, and 18.5 K cm−1 and 1216 K (943 °C), 1354 K (1081 °C), and 1371 K (1098 °C), corresponding to each combination. At 1216 K, G should be precisely controlled within 6.3 ± 3 % K cm−1 in the region substantially close to Cp = 0 to maintain the remaining concentration of point defects substantially lower than 1.0 × 1013 cm−3. G should be changed during growth from larger G to smaller G, such as 6.3 K cm−1, to efficiently grow the ingot within the limited time. The changing point, x of G, is an important key parameter for the timing variation, where x denotes the normalized distance from the growing interface. The initial G is large; thus, the changing point of G approaches the growing interface. The growth condition necessary to obtain a defect-free Si ingot can be demonstrated using the Cp = 0 point, which is fully compatible with the perfect critical point where CV and CI are practically zero. The present results are mainly considered using the CV and CI concentration curves. However, these results largely help understand the approximate trend of G and v for the growth of defect-free ingot and the relation between Cp and the commonly used critical point between CV and CI.