Impact of Thermal Stress on Intrinsic Point Defect in Czochralski Crystal Growth: Developing a Quantitative Model for Defect Formation and Distribution

The distribution of intrinsic point defects, comprising vacancies and self-interstitials, plays a pivotal role in determining the quality and properties of silicon wafers, with profound implications for their applications in the semiconductor industry. Previous research posits that the dominant defect type in Czochralski (Cz) Si can be manipulated by adjusting the ratio of the pulling rate (V) to the axial thermal gradient (G). The critical value of V /G establishes the equilibrium between vacancies and self-interstitials. However, conventional theories often consider ( V /G ) (crit) to be a constant based on the assumption of thermal equilibrium. In this study, we present evidence that the formation and diffusion of the intrinsic point defects are influenced by thermal stress, rendering ( V/ G ) (crit) dependent on thermal stress distribution. Through a combination of first-principles calculations and finite element simulations, we establish a quantitative theoretical model that considers thermal stress. Based on this model, the impact of thermal stress on the defect distribution during Cz Si growth and the value of ( V/ G ) (c rit) is elucidated. Our findings are validated through experimental growth of Cz Si and analytical testings. This work not only contributes to a deeper understanding of the microscopic mechanisms governing defect dynamics in Si but also advances Cz Si growth technology, ultimately enhancing the quality of the resultant Si wafers.