摘要
硅单晶是制造集成电路和光能转换产品的基础材料,对于21世纪信息产业和太阳能产业的发展起到关键的支撑作用。从2002年始,我国硅单晶产量由不足世界总产量的0.4%发展为今天以出口为主。但是,其品质还无法与国际上高纯度、高完整性、高均匀性、大直径的发展趋势同步。目前,直拉硅单晶缺陷已经成为制约其发展和应用的关键问题,然而,硅单晶中一些缺陷也有利于提高器件的成品率与电参数,对它们的认识亦由原来的“消除”转变为“控制、利用”,促使人们更加重视对其合理控制即“缺陷工程”的研究。鉴于直拉硅单晶直径逐渐增大的趋势及“缺陷工程”的兴起,揭示和控制硅单晶生长过程中空洞、氧沉淀等微观缺陷的演变规律和存在状态以确保其应用性能已成为当前不容忽视的实际问题。
近年来,采用计算机数值模拟作为辅助手段已成为直拉硅单晶缺陷研究的一种新趋势,直拉硅单晶缺陷研究已逐渐转向试验观察-理论分析与计算机数值模拟相并行。但是,目前的数值模拟研究只限于有限元法的宏观模拟,还不能对介观或微观区域中缺陷演变进行模拟,缺少深层次的仿真分析。探索宏观-介观-微观多尺度耦合的模拟方法、相应模型、应用程序及其关键模拟技术,实现直拉硅单晶缺陷多尺度数值模拟的研究势在必行。
相场法以Ginzburg-Landau自由能理论为基础,用微分方程来展现有序化势和热力学驱动的综合作用,是一种新型的材料微结构演化的数值模拟方法。经过20多年的发展,它已成为材料介-微观组织模拟的一种重要方法。目前,国内学者已经应用相场模型进行了枝晶长大、动态再结晶及单晶生长的模拟研究,但未见其用于单晶体缺陷模拟的报道。因此,本文尝试采用相场模型,模拟了直拉硅单晶中微缺陷的演变,这一研究具有重要的理论意义和实际价值。
首先,基于晶体生长物理学和相场模拟理论,全面考虑原始点缺陷的扩散和复合行为以及拉晶速度对空洞演化的影响,创建了直拉硅单晶空洞演化的单相场模型,并以时间为纽带,通过空间尺度转换、网格再划分等技术,将有限元软件CGSim所模拟的温度场、点缺陷浓度场导入相场模型,完成有限元方法与相场方法的耦合,实现硅单晶微缺陷的宏观分析和介观形态观察的有机结合。成功地模拟了Φ400mm直拉硅单晶轴线不同区域空洞演化,揭示了初始本征点缺陷浓度和拉晶速度对空洞演化的影响规律：初始本征点缺陷浓度较高时,空洞的数目、平均尺寸、面积分数普遍较大,孕育阶段缩短、形核和长大阶段延长；空洞的偏聚及合并、长大的现象明显；两种拉晶速度对于空洞演化历程影响不大,依然先后经历孕育-形核-长大-稳定四个阶段,拉晶速度较低时空洞的密度增加而平均尺寸减小。该相场模型及其模拟结果的可靠性得到了实验观察与有限元模拟结果的检验。
其次,基于直拉硅单晶生长时空洞演化单相场模型,创建了直拉硅单晶生长微缺陷演化多相场模型及其分析流程,完成了不同初始点缺陷状态对直拉硅单晶生长时轴向微缺陷演化影响的模拟研究及其相关机理的探讨,结果表明：①纯初始间隙氧原子浓度条件下,随着温度降低,氧沉淀密度单调增加,平均直径先增大后缓慢减小；随着初始间隙氧原子浓度增加,空洞平均直径增大(低温时更显著),空洞密度减小(低温时),而平均直径增大。②低温时,最小的和最大的初始空位浓度分别对应最小的多型空洞密度和空洞密度,最大初始空位浓度下空洞平均直径相对较大；随着初始空位浓度增大,氧沉淀密度基本不变,氧沉淀平均直径增大且随温度降低逐渐增强。③低温时,空洞密度与平均直径随间隙硅原子浓度增大而减小,初始间隙硅原子浓度对氧沉淀演变影响不大。该相场模型及其模拟结果的可靠性得到了相关的宏观模拟结果验证。
随后,考虑轴向和径向点缺陷对流、扩散的影响,进一步完善了空洞-氧沉淀演化多相场模型及其应用程序,通过宏观有限元模拟和介观多相场模拟,实现了晶体内部微缺陷全局演变的双层次仿真,揭示了拉晶速度对微缺陷存在状态影响的规律。结果表明：①晶体内不同轴向位置处空洞和氧沉淀的径向分布规律均相同,即除了晶体边缘空洞密度减小或无空洞区之外,随着径向半径增加,空洞密度增大而平均直径减小；氧沉淀密度沿径向大部分区域变化不大,仅在接近侧表面区域呈现先升高又急剧降低的变化,其平均直径沿径向减小且总体变化幅度大于空洞。②随着轴向位置升高,空洞密度降低,平均直径增大,无空洞区减小；氧沉淀密度径向变化减弱而平均直径径向变化增强。③拉晶速度对于微缺陷径向分布规律没有影响,随着拉晶速度加快,空洞密度曲线和平均直径曲线向侧表面平移,空洞密度减小、平均直径增加,无空洞区减小；氧沉淀密度和直径的径向变化趋势减小。④相场模拟结果不仅提供了微缺陷演变的形貌、分布状态等介观信息,而且显示了与有限元模拟相同的空洞径向演变规律,两种模拟的结合可实现直拉硅单晶生长时微缺陷演化的多尺度全局模拟。
最后,在空洞-氧沉淀多相场模型基础上,引入余差函数计算硅片热处理过程中点缺陷扩散,成功地模拟了硅片在炉冷、传统高-低-高三步等温退火、RTA退火和中子辐照退火过程中硅片微缺陷的演变规律,并与理论和实验进行了比较。模拟结果表明：①炉冷过程对于直拉硅单晶微缺陷分布规律没有影响,只使得空洞平均直径略有增加,氧沉淀尺寸减小、密度增大。②三步等温退火时,在第一步高温退火获得的合理间隙氧原子浓度分布前提下,通过后续的低温退火和高温退火,可在硅片中形成表面为洁净区和心部为氧沉淀聚集区的“内吸杂”结构,且第三步高温退火促进了心部氧沉淀聚集。③较高起始温度的Ramping退火硅片的微缺陷密度和尺寸要明显小于较低起始温度的Ramping退火硅片,同时洁净区厚度较大；RTP处理+Ramping退火后硅片的微缺陷密度、尺寸都小于传统的RTP处理+低-高两步退火,且空洞演变所受退火条件影响较氧沉淀更明显。④在合理的中子辐照空位浓度条件下,通过相场模拟可实现硅片心部高表面低的空位浓度分布状态。
Silicon crystal is the basic material of integrated circuit and light converse products, it plays a important role in the21th century information industry and solar industry. In2002, the silicon yield of China account for less than0.4%of the world, after ten years'development, single crystal industry of China has turned to export-oriented. However, it is still unable to keep up with international development trend of high purity, high integrity, high uniformity and large diameter. At present, CZ silicon defects becomes the main restrictive factor of its development and adhibition, but some defects in silicon crystal also help increase the yield and electrical parameter, people's cognition has turned from "eliminate" to "control, utilize", which impel people to focus more on the defect engineering. In view of the increase of silicon crystal diameter and the rise of defect engineering, indicating and managing the evolution law and existing state of silicon crystal defects such as voids and oxygen precipitation to guarantee the performance property of silicon crystal have become a practical problem that cannot be ignored.
Recently, using computer numerical simulation as a supplementary mean in defect engineering of CZ silicon has become a new trend, CZ silicon defect engineering has turned to experimental observation-theoretical analysis parallel with computer numerical simulation. However, computer numerical simulation is restricted to macro simulation which uses finite element method at present, it cannot be used in mesoscopic and microcosmic simulation of defect evolution. Exploring a macroscopic-mesoscopic-microcosmic multi-scale coupling simulation method, coupling model, application program and key simulation technology to realize CZ silicon defect multi-scale coupling simulation is imperative.
Phase-field method is based on Ginzburg-Landau free energy theory, using differential equation to show the comprehensive action of ordering potential and thermodynamics drive. After more than20years'development, it has become a very important method in mesoscopic-microcosmic simulation. At present, domestic scholars have been using phase-field method to simulate dendrite growth, dynamic recrystallization and single crystal growth, but using phase-field method to simulate the evolution of defects in single silicon crystal has not been reported. Therefore, this paper adopt phase-field method to simulate the evolution of CZ silicon defects, this research has great theoretical significance and actual value.
Firstly, based on crystal growth physics and phase-field simulation theory, fully considered the diffusion and compound behavior of point defects and the effect growth speed did to void defects' evolution, built phase-field model of single silicon void evolution, took time as the link, through scale transformation of spatial and mesh subdivision etc., temperature field and point defect concentration field which were simulated by finite element software (CGSim) were introduced into phase-field model so finite element method and phase-field method were coupled, in this way, the organic combination of the macroscopic analysis of silicon crystal and mesoscopic morphology observation could be realized. Successfully simulated the0400mm CZ silicon axial void defects evolution of different areas, revealed the effects of different intrinsic point defects concentration and different crystal growth speed do to the evolution of void defects:when intrinsic point defects concentration is high, the number, average size and area fraction of void defects were generally increased, incubation stage was shortened, nucleation stage and growth stage were both increased; the segregation, combination and growth of void defects were obvious; two different growth speed had little effect on the evolution of voids, void still followed incubation, nucleation, growth and static at different temperature intervals, the concentration increased and average size decreased with low growth speed. The reliability of phase-field model and the simulation result were verified by experimental observation and finite element simulation results.
Secondly, based on the phase-field model of void dynamics during CZ silicon crystal growth, created a multiple phase-field model of micro defects dynamics during CZ silicon crystal growth and analysis process, simulated the effects different state of initial point defects did to the evolution of axial micro defects and discussed the related mechanism, the results showed that:①under the condition of pure concentration of initial interstitial oxygen, as temperature decreased, concentration of oxygen precipitate increased, average diameter increased at first then decreased slowly; as concentration of initial interstitial oxygen increased, the average diameter of voids increased (more significantly at temperature), the density of voids decreased (low temperature), but average diameter enlarged.②under low temperature, the maximum and the minimum initial void defects concentration correspond to the maximum and the minimum multi-type void defects concentration, under the condition of maximum initial vacancy concentration, the average diameter of voids was relatively large; as initial vacancy concentration increased, oxygen precipitate concentration changed little, the average diameter of oxygen precipitate increased and got bigger when temperature fell.③under low temperature, concentration and average diameter of vacancies decreased as interstitial silicon concentration increased, interstitial silicon concentration did little effect on oxygen precipitate evolution. This phase-field model and simulation results were verified by the relative macroscopic simulation results.
Subsequently, In consideration of the axial and radial diffusion and convection of point defects, further perfected the vacancy-oxygen precipitate dynamics multiple phase-field model and its application program, through the finite element macroscopic simulation and multiple phase-field mesoscopic simulation, realized double level simulation of global micro defects dynamics in CZ silicon, revealed the influence low of micro defects state affected by growth speed and initial interstitial oxygen concentration. The results showed that:①The radial distribution laws of vacancy and oxygen precipitate in different axial position of silicon were the same, namely except for the decreasing of vacancy density on the edge of silicon or the zero-vacancy area, with the increasing of radial radius, vacancy density increased and average diameter decreased; oxygen precipitate density changed little along radial direction in most areas, only increased at first then dropped rapidly near the lateral surface, oxygen precipitate average diameter decreased along radial direction and its general change range was bigger than voids.②With axial position raising, vacancy density decreased, average diameter increased and zero-vacancy area decreased; the radial change of oxygen precipitate decreased and average diameter's change increased.③Growth speed did no effect on micro defects' radial distribution. As growth speed increased, vacancy density curve and average diameter curve moved toward lateral surface, vacancy density decreased, average diameter increased and zero-vacancy area decreased; the density and radial change trend of oxygen precipitate were both decreased.④The phase-field simulation results not only provided the morphology, distribution etc. mesoscopic information of micro defects, but also indicated the vacancy radial evolution law, which was the same as finite element simulation result, to combine the two simulations could realize multi-scale global simulation of micro defect dynamic during the growth process.
Finally, based on the void-oxygen precipitate multiple phase-field model, this paper introduced complementary function to calculate macroscopic point defects diffusion in CZ silicon heat treatment, simulated the silicon microscopic defects' evolution during furnace cooling, traditional High-Low-High temperature isothermal annealing, RTA annealing and neutron irradiation annealing and results were compared with theory and experiments. Defects evolution law in different annealing process:①Furnace cooling did no effect on CZ silicon micro defect distribution law, only made vacancy average diameter increased slightly, oxygen precipitate size decreased and oxygen precipitate density increased.②Under the condition of reasonable interstitial oxygen concentration distribution acquired from the first high temperature annealing, a intrinsic gettering structure of denuded zone on the surface and oxygen precipitate accumulation area in the core part could be made through subsequent high and low temperature annealing, the third step high temperature annealing could promote the accumulation of oxygen precipitate.③Silicon under high initial temperature annealing had much smaller micro defect density and size than which was under low initial temperature annealing and the thickness of denuded zone was larger at the same time; silicon after RTP annealing plus Ramping annealing had smaller micro defect size and density than that after traditional RTP annealing plus low-high temperature annealing, annealing condition had greater influence on vacancy dynamics than oxygen precipitate.④Under the condition of reasonable neutron irradiation vacancy concentration, the vacancy concentration distribution of high on the surface and low in core part could be realized by phase-field simulation.
引文
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