Partly three-dimensional global modeling of a silicon Czochralski furnace. I. Principles, formulation and implementation of the model

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.