Process Design and Modeling of the Horizontal Ribbon Growth Method for Continuous Production of Silicon Wafers
This thesis contains theoretical development and experimental verification of the Horizontal Ribbon Growth (HRG) method for continuous silicon wafer manufacturing. In the HRG process, heat is removed through the top surface of the molten silicon pool, meanwhile, a thin silicon solid sheet is produced and extracted continuously, in this way minimizing material losses. We assessed three technical issues regarding the design and operation of the proposed process using mathematical modeling approaches: the overall process modeling, corrugated wavy interface, and front wedge formation. A Mathematical field model that governs the mass, momentum and energy balances is developed to provide a platform for alternative cooling/heating setups evaluation, as well as, various candidate process designs. The results of our study showed a relationship between the pulling velocity and the thickness of the ribbon that is qualitatively in agreement with available experimental results. A linear stability theory is used to investigate the wavy instability occurred at the wafer-melt interface. The conditions for the onset of stability were identified theoretically and numerically on the basis of diffusion-convection equations for the thermal, solutal fields coupled with the Navier-Stokes equation describing the flow field in the molten pool near the interface. The interface stability conditions of the system under different operating conditions were examined to establish the optimal range of operation. A cellular automata algorithm is coupled with finite difference scheme to study to evolution of crystallization for the system. The formation of dendrites at the crystal front, non-smooth/unstable solid-liquid interface, and sharp wedge were simulated. We demonstrate a more homogeneous segregation of impurities in the bottom portion of the resulting wafer, while an aggressive cooling rate results in an unsmooth interface formation. Two experimental pilot facilities were developed and utilized to validate theoretical findings and study the scale-up of the proposed process. In particular, an ice machine was built as a prototype to examine the feasibility of the process and test different preliminary design ideas, while a silicon pilot facility is utilized for experimenting with extracting silicon wafers continuously from the melt.