The Stress and Strength at the Neck of a Large Diameter Silicon Crystal during Growth

Abstract

Temperature, strength, and stress at the Dash thin neck of large diameter silicon crystals during Czochralski growth are analyzed. The combination stress from the crystal weight, the meniscus weight, and the surface tension are calculated for the initial crystal growth stage, including shoulder portion and the first 12.5 cm long of body growth. Two shoulder lengths, 2.5 and 10 cm with three diameter sizes, 200, 250, and 300 mm are calculated. A two‐dimensional, axisymmetric neat conduction model using a commercially available software, ANSYS® is used to calculate the temperature distribution in the crystals. The strength of the thin neck is obtained from the relationship between the upper yield strength of silicon and temperature. To maintain a dislocation‐free (DH) lattice structure, the strength of the thin neck must be higher than the combination stress acting upon the thin neck. The results indicated that the neck temperature increases with the crystal diameter and decreases with the shoulder length. The minimum neck diameter to maintain a DF structure for a 200 mm crystal is 3.7 mm with a 2.5 cm shoulder and 3.06 mm with a 10 cm shoulder. For a 250 mm crystal, the minimum neck diameter is 4.8 mm with a 2.5 cm shoulder and 4.1 mm with a 10 cm shoulder. For a 300 mm diameter crystal, the minimum neck diameter is 6.1 mm with a 2.5 cm shoulder and 5.2 mm with a 10 cm shoulder.