Growth Instabilities and Thermo-elastic Stresses in Czochralski Process for Silicon Single Crystal

Abstract

Silicon single crystal pulling process by Czochralski method is a multi-scale problem from atomistic scale defects up to several meters. This process involves several sources of instabilities e.g. crystal diameter perturbation, turbulent melt flow, pulling rate fluctuation, heating power oscillation. A wide range of growth instabilities is studied with a special focus on the melt/crystal interface shape and thermo-elastic stresses as key parameters in crystal growth process.

Energy, mass and momentum conservation equations are solved by means of numerical simulations. The axisymmetric Czochralski furnace is implemented in a global model in which the melt flow complexities and all heat transfer aspects are included. In order to ensure the fidelity of numerical simulations, a set of sensitivity analyses is initially performed with respect to thermo-physical properties of furnace components. The impact of uncertainties in the material properties on the key growth parameters is investigated. Interface tracking scheme is used to obtain the melt/crystal interface shape under different growth conditions. Evolution of interface shape is studied with regards to crystal and crucible rotation rates. The interaction of various driving forces in the melt flow is studied. In particular, formation of W-shape interface type is explored with respect to the flow structure. The map of thermo-elastic stresses is calculated regarding the interface shape instabilities.

Another source of growth instabilities is crystal diameter fluctuations during the course of growth process. The map of temperature and thermo-elastic stress fields associated with diameter fluctuations is evaluated for isotropic and anisotropic silicon properties. The excess resolved shear stress from critical value is calculated for 12 dislocation slip systems. As one main objective is to grow dislocation-free crystal for PV applications, the probability of dislocation generation is examined along the grown crystal.

Finally, a transient model is developed to simulate crystal advection using an expanding mesh scheme. An Eulerian-Lagrangian approach is adopted to calculate the thermal field and thermally induced stresses dynamically. The two-phase medium is treated by employing Cpequivalent method. The crystal pulling rate fluctuation, as an inevitable feature of crystal growth, is applied for growing a fixed diameter crystal. The interface curvature is captured as the crystal grows. Combining the interface shape and pulling rate instabilities, thermo-elastic stresses are calculated dynamically in this part of thesis.