Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Melt Convection in a Czochralski Crucible

2d-axisymmetric of natural and forced convection in the melt of a Czochralski equipment has been performed. The influence of the flow on the shape of the interface has been studied.     

Numerical study of influences of buoyancy and solutal Marangoni convection on flow structures in a germanium‐silicon floating zone

This paper presents a numerical study of Marangoni flows in a floating zone of germanium‐silicon crystals, which was performed by using a commercial finite element program FIDAD^TM. The numerical results point out that for fluids with a small Pr number the influence of buoyancy forces cannot be ignored in the numerical model. Furthermore, the competition between the thermocapillary (TC) and solutocapillary (SC) flows in the floating zones was qualitatively examined. If the TC flow is as strong as that in the Si‐rich floating zone, the SC flow may be restricted to the bottom area near the free surface. Otherwise, the SC flow may overcome the TC flow and induce a surface transfer of species. The numerical predictions agree well with the previous experiment results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent flow through bifurcated nozzles

A finite-element model has been used to study steady-state turbulent flow through bifurcated submerged-entry nozzles with oversized ports typical of those used in the continuous casting of steel. Both 2D and 3D simulations have been performed with the commercial code FIDAP, using the standard K–? turbulence model. Predicted velocities from 3D simulations compare reasonably with experimental measurements using a hot-wire anemometer conducted in a physical water model, where severe turbulent fluctuations are present. Results show that a 2D simulation can also capture the main flow characteristics of the jet existing the nozzle and requires two orders of magnitude less computer time than the 3D simulation. A model combining the nozzle and mould was set up to study the effect of the outlet boundary conditions of the nozzle on the jet characteristics. This modelling technique will assist in the design of submerged-entry nozzles, especially as applied to enhance steel quality in the continuous casting process. Further, the model will provide appropriate inlet boundary conditions for a separate numerical model of the mould.     

Analysis of Fluid Flow and Heat Transfer in a Gas Phase Crystal Growth Furnace

Steady-state simulations of fluid flow and temperature field are presented for an equipment that is used to grow Zinc Selenide single crystals from the gaseous phases via physical (PVT) or chemical vapour transport (CVT). Due to the horizontal arrangement of the air-filled furnace pipe calculating the natural convection in the air requires a 3D (three-dimensional) treatment of the problem. The simulations have been done by applying the commercial finite-element package FIDAP. The Navier-Stokes equation is solved with the Boussinesq approximation. The heat transfer analysis comprises also internal radiation wall-to-wall exchange. Due to the presence of the ampoule in the pipe, the development of vortices with higher velocities is restrained, so that the maximum velocity is roughly 1/4 of that in the case without an ampoule.     

Optimization of thermal conditions during crystal growth in a multi‐zone resistance furnace

The thermal condition is one the of most important control parameters for crystal growth. In this paper we present an effective numerical method in detail for optimizing thermal conditions in multi‐zone crystal growth facilities, especially for crystal growth by the float zone (FZ) technique. A furnace function Ω is introduced to integrate the character of a growth furnace into a linear equation system. The desired power distribution can be therefore approached by solving the linear equation system iteratively. An expert systemlike algorithm has been developed in order to obtain a more suitable solution for practical applications. This method was used to investigate thermal parameters for experiments of SiGe/GeSi single crystal growth by the FZ technique. It is an individual program which can be combined with any commercial finite element/finite volume (FE/FV) program such as FIDAP^TM.     

Use of Labels and Loops for the FIDAP Mesh Generation

The use of do-loops in connection with variables for the FIDAP mesh generation is demonstrated. Special focus is drawn on the advantage of labeling objects explicitly especially for more complicated meshes. These concepts are illustrated with the mesh generation for a three zone resistance furnace.     

Modelling of the Transport Processes in Bridgman grown Gallium Antimonide

In this work the thermal, velocity and species fields in the melt during the crystal growth by the vertical Bridgman method, has been studied. The simulations were focused on the special case of GaSb, which is a semiconductor of high technological importance. The simulations have been carried out both in 2 and 3‐D. In both cases the momentum (Navier‐Stockes), energy and mass transport equations were solved. The wall‐to‐wall radiation has also been included. In the two‐dimensional case an axisymmetric global model was developed taking into account the different elements present inside the real Bridgman growth system. In order to study the transport processes in the whole system during a complete growth process, the time dependence has also been considered. In the three‐dimensional case, the mathematical domain is restricted to the melt. These simulations were developed in order to study the influence of the ampoule tilting on the dopant distribution in the melt.