Phase Field Model And Simulation Of The Evolution Behavior Of Void-type Defects During Czochralski Silicon Single Crystal Growth

With the vigorous development of electronic industry and deepening of society informatization, microelectronic technology plays an increasingly important role in almost every aspect of human activities. Silicon single crystal, whose quality determines the development speed and potentiality of modern electronic information industry, is the basic material in electronic device manufacture. Czochralski crystal growth process is the most common method to obtain silicon single crystal in experimental study and practical production. In the CZ process, vast intrinsic point defects and impurities are introduced into the melt/crystal interface and aggregate into various microdefects with the pulling of crystal. These microdefects such as void, dislocation loop, oxygen-void complex, and oxygen precipitate, significantly affect the quality of silicon crystal, and restrict the performance and development potentiality of microelectronic devices. Therefore, research work on the microdefect evolution in CZ silicon crystal growth is imperative.In the past decades, along with the development of computer technology, the simulation research on microdefect evolution in CZ silicon crystal develops so rapidly that numerical modeling becomes one of the important research approaches to understanding microdefect dynamics thoroughly as well as predicting the microdefect size and distribution. Phase field modeling is a burgeoning numerical simulation method developed in recent years and is usually applied to microstructure evoltuion in materials. Unlike traditional sharp interface model, phase field model is capable of modeling the evolution process of microstructures without real-time tracking of the interface movement. Thus, it is widely used in the simulation research of the material microsiructure evolution at mesoscopic level.In the present thesis, void-type microdefect was made the research object. Based on the knowledge of material thermodynamics, statistical physics, and the Landau theory of phase transitions, phase field model describing void evolution behaviour was established. On the basis of numerical modeling, programming and image visualization, dynamic simulation of void evolution was realized. This research focused on the thorough understanding and studying of formation mechanism of voids in CZ silicon crystal growth in the theoretical system of crystal growth kinetics and microdefect evolution dynamics, to which a new way of applying phase thransition theory was explored.Firstly, the diffusion behaviour of vacancies and interstitial silicon atoms, as well as the mechanism of void evolution were analyzed. Based on the relevant knowledge of material thermodynamics and the Landau theory of phase transitions, a two-dimensional phase field model of void evolution in CZ silicon crystal growth was established, including the construction of free energy equation of the system, Cahn-Hilliard equation discribing vacacy diffusion and Allen-Cahn equation discribing void evolution.Then, on the basis of numerical modeling, comput programming and image visualization, the application program of the phase filed model for simulating the void evolution in silicon crystal growth was developed. The kinetic equations of void evolution were discreted and solved numerically using a central finite difference scheme with forward Euler marching scheme in time. Under the premise of given simulation assumption, initial condition and boundary condition, the main program of void evolution, as well as the auxiliary programs of function optimization, simulation result processing and image visualization output were written in Matlab programming language.Finally, growth dynamics of the single void and double voids, as well as the evolution kinetics of void-matrix interface during Czochralski silicon growth were simulated by the established phase field model and the corresponding program code. Besides, the void evolution mechanism and the influence laws of relevent factors on void evolution dynamics were also studied and disscussed at multitude levels through a great number of simulation experiments. The results show that the phase field model built and program code written in this research is capable to capture the dynamics process and basic features of the void evolution, and the simulation results can be analyzed and interpreted reasonably based on the thermodynamics theory. Also, the influence laws of relevent thermodynamic and kinetic parameters on the void evolution process coincide well with reports in related literature, which contributes to understanding the physical mechanism of void evolution in CZ silicon growth thoroughly, and enhances the reliability evaluation of the constructed phase field model.