【作者】 王进；

【导师】 关小军；

【作者基本信息】 山东大学 ， 材料加工工程， 2015， 硕士

【摘要】 随着电子工业的蓬勃发展和社会信息化的不断深入,微电子技术在人类生产生活的方方面面发挥着越来越重要的作用。硅单晶是电子器件制造的基础材料,其质量直接关系和决定着现代电子信息产业的发展速度和潜能。实验研究和实际生产中人们主要通过直拉法生长获得硅单晶。硅单晶直拉法生长过程中,大量的固有点缺陷和杂质在固液界面处引入硅单晶基体并随着拉晶过程演化成各种微缺陷。这些微缺陷,如空洞、位错环、氧-空位复合体、氧沉淀等,严重影响硅单晶的质量,进而制约着微电子器件的使用性能和发展潜力。因此,开展直拉硅单晶生长过程中微缺陷演化的研究工作势在必行。近些年来,随着计算机技术的发展,硅单晶微缺陷演化的数值模拟和仿真研究发展迅速,成为深入认识微缺陷动力学和预测缺陷大小和分布的重要研究途径。其中,相场法是近年来发展起来的一种研究材料微观组织演变的的数值模拟方法。不同于传统的尖锐界面模型,相场模型无需时刻跟踪界面即可模拟微观结构的演化过程,近些年来广泛应用于介观尺度下材料微观结构演变的模拟工作。本文以直拉硅单晶中的空洞型缺陷为研究对象,依据材料热力学、统计物理学和朗道相变理论构建了空洞演化行为的相场模型,通过数学建模、程序编写和图像可视化实现了空洞动态演化过程的仿真模拟,在晶体生长热力学和缺陷演化动力学的范畴内深入研究和认识硅单晶生长过程中空洞的形成机理,探索将相变理论应用于微缺陷演化动力学研究的新途径。首先,通过分析直拉硅单晶中空位、间隙硅原子的动力学行为和空洞的演化机制,基于材料热力学等相关知识和朗道相变理论,建立了直拉硅单晶过程中空洞演化的二维相场模型,包括构建系统自由能方程、描述空位扩散的保守场方程和空洞演化的非保守场方程等。然后,基于数值分析、计算机编程和图像可视化技术,开发了相场模型模拟硅单晶生长中空洞演化的应用程序。采用有限差分法和显式欧拉迭代法对空洞演化的控制方程进行了离散和数值求解,在给定的相场模拟假设、初始条件和边界条件的前提下,利用Matlab语言编制了空洞演化的主程序,以及函数优化、模拟结果处理和图像可视化输出等辅助程序。最后,利用所建立的空洞演化的相场模型及其模拟程序,研究了直拉硅单晶中单空洞长大动力学、空洞-基体界面演化动力学和双空洞长大动力学等三个方面,通过大量的模拟实验在多个层次深入探讨了空洞的演化机理以及相关参数对演化动力学的影响规律。结果表明,本文所建立的相场模型和开发的模拟程序能够有效展现空洞演化的动力学过程及其基本特征,模拟结果可依据热力学理论进行合理分析和解释。此外,相关热力学和动力学参数对空洞演化过程的影响规律与相关文献中的报道相吻合,有助于深入认识直拉硅单晶中空洞演化的物理机制,并进一步验证了所建相场模型的可靠性。更多还原

【Abstract】 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.更多还原