Optimizing cooling strategies in the Czochralski process for large-diameter silicon ingots

As the semiconductor industry shifts towards larger wafer sizes, such as 300 mm and 450 mm, controlling defects is crucial to ensure device performance and yield. Conversely, a high cooling rate is essential for achieving higher production rates. Therefore, finding the optimal cooling strategy is critical to maintaining high production rates while ensuring high-quality wafer production. This paper employs a simulation model to investigate the impact of various cooling strategies on point defect formation during the CZ process for 450 mm diameter silicon ingots. Using the 3D energy equation coupled with the Navier-Stokes equation and moving mesh theory, the transient CZ process is simulated, incorporating defect evaluation equations. Beside original CZ puller configuration, two cooling strategies are examined: one with a small gap and long cooling jacket (Case II) and another with a large gap and short cooling jacket (Case III), compared against a baseline setup (Case I). The simulations reveal that Case II, while enhancing the crystallization rate, increases non-uniformity. Conversely, Case III produces a flatter solid-liquid interface and lower defect concentrations, achieving a maximum Cv-Ci of 0.4 × 10¹⁴ cm⁻³, compared to 1.1 × 10¹⁴ cm⁻³ and -2.5 × 10¹⁴ cm⁻³ in Case I and II. These findings suggest that adjusting cooling strategies can significantly impact the quality and uniformity of large- diameter silicon ingots.