定向凝固法由于生产成本低且对多晶硅原料等级要求较低，已成为目前太阳能用晶硅生产的主要方法。众所周知，晶硅太阳能电池的效率决定于硅片的质量，而硅片的质量又与晶硅中的夹杂物（包括杂质和颗粒）含量及分布密切相关。因此，研究定向凝固过程晶硅中杂质分布、颗粒形成及吞并过程非常重要。杂质及颗粒的分布主要受热驱动熔液对流、固液界面形状及长晶速度的影响。工业生产中定向凝固法制得的硅锭尺寸在不断加大，目前广泛应用的定向凝固系统可以生产270~500kg的硅锭，能生产800~1000kg硅锭的定向凝固系统也在研究之中。随着坩埚尺寸的增加，熔液流动、界面形状及长晶速度对夹杂物分布的影响变得更加重要。在本文的研究中，首先研究工业用定向凝固系统中热场部件对界面形状、长晶速度等决定晶体质量的参数的影响，提出热场改进优化方案。然后针对熔炉核心区域建立了能描述长晶过程热输运与组分输运的二维瞬态模型，研究熔液流动、界面形状等对杂质分布的影响。在此基础上建立了碳过饱和时碳化硅颗粒的生成及长大的模型。颗粒一旦生成，就会与周围的熔体交换动量。颗粒的速度及位置与颗粒上作用的力有关。当颗粒靠近固液界面时，颗粒与固液界面之间还会发生相互作用，导致颗粒被界面排斥或者吞并。本文考虑颗粒上作用的所有力（包括界面张力、粘性力、重力、马格努斯力、萨夫曼力、牵连附着流体运动的力），建立了一个颗粒的运动及吞并模型。此模型包括两部分：大范围熔体中的运动以及运动到界面前沿区域被界面吞并/排斥的模型。然后，计算模拟了一个工业用定向凝固系统中的碳分布、颗粒运动及分布情况，并对界面形状、熔液对流、原料初始杂质含量等对杂质、颗粒分布的影响进行了研究。研究结果表明通过改变热场部件可以有效改善铸锭炉内的热场分布从而改善硅锭质量，减少杂质的进入；通过控制温度边界条件可以控制计算区域中的温场分布，从而影响固液界面的形状；凹的固液界面导致杂质在中心聚集，中心区域最先出现过饱和，而凸的界面下，杂质聚集区在坩埚壁附近；凸固液界面下，杂质一旦聚集即被靠近坩埚壁很强的熔液对流带走，而凹的界面下，由于杂质聚集的中心区域是滞止区，很难被熔液带走，因此凹界面比凸界面对原料等级的要求高。长成的硅锭中颗粒的分布及尺寸受原料等级，温场、流场分布及长晶速度的影响。颗粒被吞并时的尺寸由晶体生长速度决定，低的生长速度对应大的颗粒尺寸，高的生长速度下，被吞并的颗粒尺寸很小。
Directional solidification is the most common method for producing silicon ingot for solar cells due to its low cost and low requirement for feedstock. It is well known that the efficiency of solar cell strongly depends on the quality of silicon wafers, while the quality of wafers is mainly affected by the contents and distributions of impurities and its precipitates. It is, thus, important to investigate the impurity distribution, particle formation and engulfment in the liquid phase during directional solidification process.The distribution of impurities and its precipitates is strongly affected by thermally driven flow, solid/liquid interface shape and growth rate. Currently, commercial 270–500 kg directional solidification systems are widely used in production and the systems capable of producing 800–1000 kg ingots are also being developed. As the size of crucible in the industrial directional solidification system becomes larger, the influence of melt flow, interface shape and growth rate on impurities distribution becomes much more significant. In this thesis, we will first study the relationship between thermal field components and crystal quality, and discuss the methods for system optimization are discussed. Then a 2D transient model of heat and mass transfer for the core area of directional solidification system is developed to investigate the effect of thermally driven flow and interface shape on the transport of carbon species. When the carbon concentration exceeds the local solubility limit, SiC particle is formed in the Si-melt. A computational model is developed which is capable of describing SiC particle formation and growth. Once the particle is formed, it exchanges momentum and energy with the local melt. The velocity and position of the particle are determined by the forces acting on it. If the particle is close enough to the solid–liquid interface, the engulfment and pushing transition occurs. The physical model are developed to describe particle movement and engulfment with the consideration of all forces acting on silicon carbide particles, such as interfacial force, drag force, gravitational force, magnus force and saffman force. The particle movement and engulfment model consists of two parts: a model for the particle motion in the melt and the particle engulfment and pushing (PEP) model for the particle engulfment. Calculations are carried out to investigate the carbon distribution and SiC particle transport in an industrial growth system. The effect of interface shape, thermal driven flow and the feedstock’ level on impurity and particle distributions are discussed.It is found that hot zone design and optimization are useful for silicon ingot improvement; the solid/liquid interface can be controlled by the temperature boundary condition; a concave interface leads to the carbon accumulation in the central region near the interface, while for convex interface, the carbon accumulation exists near the side crucible wall; the carbon accumulation place corresponds to supersaturation position. When the interface is concave, a stagnation zone of melt flow exists in the central region where the carbon accumulation occurs. The flow is not strong enough to take the carbon to the bulk liquid. When the interface is convex, the carbon concentration in the whole fluid field is much more uniform. This means when the interface shape is convex, the silicon solidification system has much better feedstock tolerance. The particle distribution in the as grown silicon ingot is mainly affected by feedstock level, thermal and flow field, growth rate. The size of the SiC particle when engulfed into solid Si is mainly determined by the solidification rate. The low solidification rate is not desirable for high quality Si crystal growth when the solid/liquid interface is concave.
