Numerical analysis of Oxygen control during growth of Czochralski silicon single crystals
In the present work, a set of 2D global furnace simulations accounting for oxygen dissolution and transport have been used to predict Oi content along the produced Silicon crystal. It is shown that Oi content is sensitive to several growth parameters (melt level, crucible rotation, etc.). Results indicate Oxygen tends to increase at the end of the crystal due to a combination of weakening of turbulence and planar velocity in addition to decrease of the melt free surface. Crucible rotation is the most influencing parameter at low melt level. Argon gas pressure and flow have a limited impact at low melt level.
Development of oxygen transport model in Czochralski growth of silicon crystals
Oxygen is one of the most important impurities in Czochralski (Cz)-grown silicon crystals. The precise control of oxygen concentration in growing crystal, both in radial and in axial directions, is required to obtain silicon wafers with necessary electronic properties. A modified numerical model of oxygen transport as a way of prediction of oxygen concentration in growing Si crystals is described in this paper. Test calculations for the updated model were performed for a Cz setup with a small crucible diameter and weak turbulent melt flow. The calculated oxygen profile along the crystallization front is compared with available experimental data. 2-D and 3-D calculation results have evaluated the number of finite volumes in 3-D grid, required for precise description of oxygen transport in the small growth system.
Global model of Czochralski silicon growth to predict oxygen content and thermal fluctuations at the melt-crystal interface
Abstract A computational model combining calculations of global heat and mass transfer in the entire CZ system with Large Eddy Simulation (LES) of turbulent melt convection is presented. Global heat and mass transport is calculated using an axisymmetrical quasi-steady-state approximation with accounting for radiative heat exchange, heat conduction in solid parts, inert gas flow, and turbulent melt convection. The global transport calculations provide adequate boundary conditions for comprehensive investigation of melt turbulent convection using 3D LES. The LES of the melt flow describes the temperature distribution and impurity transport in the melt much better than 2D turbulent flow models. Moreover, the 3D calculations provide complete information with respect to thermal fluctuations in the melt and to non-uniformity of the crystallization process at the melt–crystal interface.