The content and uniformity of carbon and silicon carbide (SiC) precipitates have an important impact on the efficiency of solar cells made of multicrystalline silicon. We established a dynamic model of SiC particle precipitation in molten silicon based on the Si-C phase diagram. Coupling with a transient global model of heat transfer, computations were carried out to clarify the characteristics of carbon segregation and particle formation in a directional solidification process for producing multicrystalline silicon for solar cells. The effects of impurity level in silicon feedstock and solidification process conditions on the distributions of substitutional carbon and SiC precipitates in solidified silicon ingots were investigated. It was shown that the content of SiC particles precipitated in solidified ingots increases markedly in magnitude as well as in space with increase in carbon concentration in silicon feedstock when it exceeds 1.26×1017 atoms/cm3. The distribution of SiC precipitates can be controlled by optimizing the process conditions. SiC precipitates are clustered at the center-upper region in an ingot solidified in a fast-cooling process but at the periphery-upper region for a slow-cooling process.A1. Computer simulation; A1. Directional solidification; A1. Impurities; A2. Growth from melt; B3. Solar cell

A series of computations were carried out to study the effect of crystal rotation rate on the melt-crystal interface shape and temperature gradient at the interface during CZ-Si crystal growth in a transverse magnetic field (TMCZ). A three-dimensional (3D) global model was used in this study. It was found that the interface deflection changes from non-uniformity in the azimuthal direction to an axisymmetric distribution with increasing crystal rotation rate. The mechanism of this effect is mainly attributed to the spatial fluctuations of local growth rate, which is derived as a function of crystal rotation rate and non-uniformity of interface deflection in the azimuthal direction. It contributes to the formation of the shape of the melt–crystal interface through the heat release of solidification at the melt–crystal interface. Even though the melt–crystal interface shape is nearly axisymmetric at a high crystal rotation rate, local growth rate fluctuations are still noticeable and play an important role in the characteristics of heat transfer and impurity segregation at the melt-crystal interface.

Three-dimensional (3D) analysis was carried out for oxygen transport in silicon melts of a Czochralski (CZ) growth process with electromagnetic fields. The system with electromagnetic fields was established with a transverse magnetic field and an injected electric current applied on the melt surface. The melt flow and thermal field in the growth furnace were numerically obtained with a recently developed 3D global model. The influence of electrode position and electric current direction on the oxygen distribution and concentration in the melt as well as on the growth interface was investigated. The heat transfer and mass transfer in the melt were also analyzed to clarify the mechanisms. The results showed that control of the oxygen distribution and concentration on the crystal growth interface is possible by appropriate positioning of the electrode on the melt surface and appropriate selection of the electric current direction. The results also showed that an electromagnetic CZ process (EMCZ) is superior to a transverse magnetic field-applied CZ process (TMCZ) and a conventional CZ process for controlling oxygen distribution in a silicon crystal grown from melt.

The casting method is a key method for large-scale production of multi-crystalline silicon for use in highly efficient solar cells in the photovoltaic industry. Since the efficiency of solar cells depends on the quality of the multi-crystalline silicon, it is important to optimize the casting process to control temperature and iron distributions in a silicon ingot. We developed a new transient global model for the casting process and carried out simulations to study the temperature and iron distributions in a silicon ingot during solidification. Conductive heat transfer and radiative heat exchange in a casting furnace and convective heat transfer in the melt in a crucible are coupled to each other. These heat exchanges were solved iteratively by a finite-volume method in a transient way. Time-dependent distributions of iron and temperature in a silicon ingot during the casting process were numerically studied.

Numerical and experimental analyses revealed the enhancement of diffusion of oxygen and boron by laser irradiation. We studied the effect of laser irradiation on the enhancement of diffusion of boron and oxygen including both isotopes of 16O and 18O. The study clarified that the diffusion of the impurities was enhanced by laser irradiation by about 2.5-8 times more than that in the case without laser irradiation in the temperature range from 990 to 1200℃. We confirmed from temperature measurements of the samples that such enhancement was not based on temperature increase caused by laser irradiation but was based on the effect of irradiation of the laser. The effect of frequency of the laser on the diffusion was observed by changing the wavelength of the laser.

A novel model for three-dimensional (3D) global simulation of heat transfer in a Czochralski (CZ) furnace for silicon crystal growth was proposed. Convective, conductive and radiative heat transfers in the furnace are solved together in a conjugated way by a finite control-volume method. A mixed 2D/3D space discretization technique was developed, and concepts of 2D domain and 3D domain for a CZ furnace were proposed. This technique enables 3D global simulations to be conducted with moderate requirements of computer memory and computation time. A 2D global simulation was carried out to obtain good initial conditions for 3D global modeling to speed up the global iteration. The model was demonstrated to be valid and reasonable.

The mechanism of formation of boron distribution in silicon crystals grown by the Czochralski method was numerically investigated. The diffusion processes in both the crystal and the melt were taken into account. The transient model involves the seed holding process and the crystal growth process. A Lagrangian method was developed for the computation in order to reduce numerical diffusion. A technique of grid cell generation was adopted for the adaptive mesh to track the crystal-melt interface. The results of computational analyses showed that the diffusion processes in the seed and grown crystals play an important role in the formation of the boron distribution in the grown crystals. The effects of concentration difference between the seed and the melt, the annealing treatment, the seed holding time and the crystal growth rate on the formation of impurity distribution during the seeding process were numerically investigated. The computation results are in good agreement with the experimental data.

A series of computations were performed for Czochralski silicon crystal growth in a transverse magnetic field with different crystal growth rates by using a recently developed three-dimensional global model. The effects of the transverse magnetic field and crystal growth rate on the melt–crystal interface were numerically investigated. It was found that the interface shape is three-dimensional when the crystal is not rotating, while it becomes nearly twodimensional when the crystal is rotating, even at a low rotation rate. The temperature gradient in the axial direction at the melt-crystal interface increases with increase in crystal growth rate except near the crystal edge, where it changes oppositely.