Project description
Objective O1
Modeling of heat transport in a Cz configuration for 200mm silicon crystals growth
First the geometry for a melt-crystal system in a Cz configuration will be defined. A 200 mm diameter crystal and a 490 mm diameter crucible will be considered for the numerical investigation. Time dependent computations will be carried out using the STHAMAS3D software that has already been validated by experiments for Cz-Si process. The discretization procedure of STHAMAS3D is based on the finite volume method. A flux blending between central differencing scheme (CDS) and upwind differencing scheme (UDS) was used for the convective fluxes. A higher percentage (~100%) of CDS is unable to handle high-frequency turbulent fluctuations. A lower percentage of CDS (~0%), due to the numerical diffusion, will suppress the mechanical instabilities. Using a flux blending of 80% CDS along with UDS, physically meaningful solution can be predicted. The SIMPLE algorithm is applied for pressure correction and the implicit Euler method for the time integration. The computational block-structured non-orthogonal is subdivided into 16 blocks consisting of control volumes. Two types of boundary conditions can be used: Neumann boundary (specifies a constant flux density of the variable normal to the line) and a Dirichlet boundary (specifies fixed values for the variable along the line). The boundary conditions used in the numerical investigations will mirror the experimental conditions from a set-up used at SINTEF. An important issue for the quality of the numerical modeling is the choice of the grid. A grid refinement at the walls is necessary to solve the boundary layers. The thickness of the boundary layer, for laminar conditions is: δ =4.64⋅L⋅Re-1/2, where L is the distance from the leading edge and Re is the Reynlods number. Different levels of refinement will be taken into consideration in order to determine the number of control volumes that need to be used so that the obtained solution will not be dependent on the grid. The simulation will start with the coarse grid (only 2-3 nodes in the boundary layer) and will be refined to include 4-5 nodes in the boundary layer or even more if the simulations indicate that this level of refinement is not enough. Once a suitable grid is identified, simulations will be done for several values of the temperature gradient in order to estimate how the temperature fluctuations near the solid-liquid are related to the crystals striations observed experimentally. For this investigations the crystal and crucible rotation rate will be considered fixed. Temperature fluctuations in the melt can also arise due to the rotation rates of the crucible and of the crystal. In order to evaluate their influence, simulations will be done with a fixed temperature gradient and considering different values of the rotation rates.
Objective O2
Modeling of impurity transport in a Cz configuration for 200mm silicon crystals growth
The numerical model described in Objective O1 will be further developed to include the impurities transport. A similar investigation, with the one that was presented in Objective O1, for the grid refinement will be done for this set-up. The thickness of the diffusive boundary layer (δD) is different from the thickness of the convective boundary layer (δ), the relationship between the two being: δD=δ⋅Sc-1/3, where Sc is the Schmidt number. It can be seen that the diffusive boundary layer depends on the diffusion coefficient, D, therefore a study of the influence of the grid refinement of the solution obtained for the concentration fluctuations is mandatory for all types of impurities. There are three main sources of impurities for Si ingots that need to be considered. First, the natural impurity content in the feedstock (P and B dopants). Another source, are the impurities originating from the crucible. Usually silica crucible are used for the Czochralski growth of Silicon crystals. At very high temperatures, the dissolution of the silica crucible occurs and oxygen impurities are released into the melt. Since silica crucibles cannot be used for more than one growth, alternatives for crucible materials are investigated, and Si3N4 has proved to be an important candidate. By introducing this crucible material, several improvements and cost reductions could be achieved, including the possibility of crucible reuse. This is of special importance for "Cz-multi-pulling" of sc-Si-ingots. The multi-pulling method is a technology where several silicon crystals can be manufactured from a single process cycle using a recharging unit. This method can be fully exploited, if adequate crucibles properties, like silicon nitride are available. The advanced inert material properties provide a great potential of a large number of reuse during silicon ingot crystallization - for both, mc-Si and sc-Si technology. The Eco-Solar company aims for reuse of the crucible by more than 10 times, without deteriorating the silicon material quality. Employment of reusable silicon nitride crucibles, instead of single-use silica ones, will reduce the crucible costs by 2/3 and result in less resource consumption. However, the corrosion of the silicon nitride crucible will contaminate the melt with nitrogen impurities. When the solubility limit of oxygen and nitrogen are exceeded, Si3N4 and Si2N2O precipitates are formed in the melt and this can have a detrimental effect on the quality of the grown crystals. Therefore, the study of the O and N distribution in the melt will allow us to better understand the precipitation formation process. Many parts of the heating elements of a Czochralski set-up are made from graphite. Therefore, carbon is also a potential candidate for contamination of the melt and hence the crystal. Numerical studies will be done to investigate the concentration fluctuation for the most common impurities found in the Silicon melt: B, P, O, N, C. The influence of crystal and crucible rates on the concentration fluctuations will also be investigated for different type of impurities.
Objective O3
Influence of different types of magnetic fields on the impurities transport
Magnetic fields are largely used in Cz growth of silicon crystals in order to control the melt flow and impurities distribution. The numerical model of the 200 mm Cz Silicon crystal developed in Objective O2 will be extended to include the influence of static magnetic fields: vertical magnetic field, horizontal magnetic field and cusp magnetic field. The impurity distribution in the melt and the dopant concentration fluctuations in the presence of various types of magnetic fields will be investigated.