Thermal history-driven void formation in silicon crystals: A discrete model approach

As the growth rate rises to achieve more substantial production rates in silicon crystal growth through the Czochralski (CZ) process, vacancy agglomeration leading to void defect formation becomes particularly notable due to the elevated ratio of growth rate to thermal gradient (V/G). To explore this phenomenon, a computational platform was developed that integrates a fully transient three-dimensional finite-element (FE) model and a cellular automaton (CA) model to simulate void nucleation and growth. This study offers a new discrete model for simulating void formation during the CZ process. It delivers a thorough analysis of the thermal dynamics within the furnace, the morphology of the solid-liquid interface, and the spatial distribution of point defects, including vacancies and interstitials. The model accounts for transient phenomena such as the synchronized movement of the crystal and crucible, the thermal capacity of furnace components, the thermal inertia of the solidification interface, and the evolving suspect formations governed by time-dependent conditions. The CA model, combined with the FE framework, evaluates void formation based on point defect concentration, temperature distribution, and nucleation density criteria. Experimental validation was carried out using wafers extracted from silicon ingots at different growth stages (50 mm, 250 mm, and 600 mm). Wafer cleaning and etching procedures were employed to increase defect visibility, and defect detection was carried out using a laser-based particle counting system. The results confirmed the presence and spatial distribution of voids, which accord with the simulation predictions.