The paper presents results of 2D axisymmetric mathematical modelling of laboratory CZ model facility that corresponds well to a large industrial silicon CZ growth system. The purpose of the investigation is to examine turbulent melt flow features that develop in the model crucible, when various dynamic magnetic fields (travelling, alternating) are applied, and to test the applicability of the modified low Re k–ε turbulence model for the calculation of flows in these cases by extensive comparisons between calculated and measured data. The electromagnetic field is calculated with a self-developed program, and the calculations of the melt motion are carried out with the user modified hydrodynamic program package CFD-ACE. Extremely fine grid and the modified low Re k–ε turbulence model are used in hydrodynamic calculations. The flow features and temperature fields are investigated, and the influence of dynamic field strength and crucible and crystal rotation is shown. A comparison between calculation results and temperature measurements in a corresponding laboratory model with low-temperature InGaSn eutectic has shown good agreement.

The paper proposes Monte-Carlo method-based 2D and 3D models of vacancies and interstitials in a cubic crystal. The model exploits the concept of lattice gas with covalent bounds between neighbour nodes. Two lattices shifted by half-period serve as nodes for atoms of the main crystal and interstitials. Distribution of particles between both lattices characterizes the entropy of the crystal. Successfully chosen interaction energies between main and sub-lattices allows the authors to detect a phase transition solid–liquid as well as to study the production of crystal defects/their agglomeration as a function of cooling/heating rate. Although the introduced 3D modification of the model contains several rough assumptions, this gives all results of the 2D case as well as reflects some 3D specificities. All the results obtained agree qualitatively with experimental observations on crystals.

The fully transient axisymmetric model has been developed for calculation of phase boundaries in large (up to 200mm diameter) industrial floating zone (FZ) silicon single crystal growth with the needle-eye technique. The transient model is implemented in a specialized computer program. The model and program are based on a previously developed model and program for steady-state FZ process calculations. This transient approach allows studying of such substantially time-dependent process phases as the growth of the starting and ending cones of the crystal rod, which are particularly important for growth of large crystals in practice. Numerous calculations are carried out and the results for reducing crystal diameter during growth process are presented.

This paper presents a comparison between numerically calculated and measured temperature distributions in turbulent flow in a laboratory model for a CZ large silicon single crystal industrial growth system with a horizontal DC magnetic field. The laboratory model consists of an electrically heated 20” crucible with low-temperature InGaSn melt, a water-cooled metallic crystal model, and a magnet system creating a horizontal magnetic field in the range 0–0.16T. Distributions of time-averaged temperature values in various cross sections in the melt are obtained from measurements by a multichannel thermocouple system. A 3D numerical model for the scalar potential induced in the melt by the velocity field in the horizontal DC magnetic field is implemented in the HD program package CFD-ACE+TM(V2003). For 3D HD calculations, moderate grids and the RNG k-ϵ turbulence model are used. Comparisons between calculated and measured temperature distributions in various cross sections are carried out for the cases with and without crucible and crystal rotation and with and without the magnetic field. The agreement is generally good, but some local discrepancies appear in the cases with the crystal rotation.

We present an updated version of the combined 2D/3D model of heat transfer and turbulent melt convection for industrial Czochralski (CZ) crystal growth. The 3D computational domain consists of silicon melt, crucible and crystal, and is extended by including gas blocks. To provide boundary conditions for the 3D domain, global heat transport is calculated within a 2D steady approach. Several computed melt/crystal interface geometries are compared with available experimental data for 100 and 300mm diameter CZ crystals. The temperature distribution along the melt/crucible boundary and unsteady temperature fluctuations in the melt bulk are compared with the respective measurements. The computations are performed using an improved version of the crystal growth simulator (CGSim) program package allowing 3D unsteady analysis with high approximation orders.

A model approach for a modification of the effective heat conductivity in the turbulent melt flow simulation for 28″ Si CZ crucibles is presented, which helped to overcome deficiencies in the growth interface shape prediction for industrial 300mm Si CZ growth. The model has been incorporated into a CZ simulation tool based on the simulation software codes FEMAG for the global heat transfer and CFD-ACE for the turbulent melt flow simulation. The model predictions are compared to results from 300mm Si CZ growth experiments with 200kg charge weight in 28″ crucibles in a growth parameter range covered by standard industrial processes. The model is an engineering approach. Nevertheless, some physical background is briefly discussed on a phenomenological basis, including results of recent model experiments.

Silicon wafer manufacturing is one of the key processes that determine the yield and the profitability in semiconductor device production. The present paper gives an overview on various applications for numerical modeling in the wafer manufacturing process. It starts with thermal and convection models for the crystal growth process, both by the Czochralski (CZ) and the Floating Zone (FZ) method. Within this field, in particular modeling of electromagnetic field influence on melt flow has become an an indispensable means for the puller design and the process development for both methods. A further chapter is devoted to model approaches for predicting crystal defects, like grown-in voids, self-interstitial aggregates or oxygen precipitates. The defect modeling connect the crystal growth directly to the device manufacturing processes, as crystal defects may be detrimental or beneficial to microelectronic devices, produced on the silicon wafer. A last chapter points briefly to more recent applications of numerical modeling in auxiliary processes, like wafer heat treatment steps, epitaxial growth or wafer cleaning.

The paper presents an investigation of features of turbulent flow in CZ silicon crystal growth system with horizontal DC magnetic field by 3D mathematical modelling and comparison with experiment in a laboratory system. The 3D model for the scalar potential in the melt induced by horizontal DC magnetic field together with corresponding boundary conditions is implemented in the HD program package CFD-ACE(V2002). For the 3D HD calculations moderate grids and the k-ε standard turbulence model are used. The features of the flow and temperature field structure are investigated and the influence of magnetic field strength and crucible and crystal rotation is shown. The comparison between calculation results and measurements in the corresponding laboratory model with low temperature melt has shown good agreement.

The paper presents an investigation of the turbulent flow features in a CZ crystal growth system with a horizontal DC magnetic field by 3D mathematical modelling. A laboratory model with InGaSn eutectic and with a 20″ crucible is considered. The model corresponds to an industrial silicon crystal growth system. A 3D model for the scalar potential induced in the melt by a horizontal DC magnetic field is implemented in the HD program package CFD-ACE(V2003) together with the corresponding boundary conditions. For 3D HD calculations, moderate grids and the RNG k–ε turbulence model are used. The features of the flow and the temperature field structure in different cases (only thermogravitational convection, flow with rotation influence) under the magnetic field are investigated. It is shown that the flow and temperature distributions in all cases are strongly influenced by the magnetic field of 0.08–0.16T. The crucible and crystal rotation together with the horizontal DC field creates flow and temperature distribution with a very complicated 3D structure.

The melt flow in large diameter crucibles during the growth of silicon (Si) single crystals of 300mm diameter is characterized by turbulent large-scale velocity and temperature fluctuations. Strong efforts of the crystal growth industry are dedicated to the control of the interface shape and the related point defect distribution in the crystal, of the oxygen and particle transport in the melt, of the crucible overheating and of the conditions for dislocation free growth. Static and time-dependent electromagnetic fields offer new possibilities to meet the continuously increasing demands on crystal quality and yield improvement. Numerical simulation helps to investigate a wide range of possible process conditions, and to reduce experimental costs and time to market significantly. Depending on the required accuracy and available computation resources, two-dimensional (2D) or three-dimensional (3D) models are used. Temperature measurements in the melt, carried out during crystal growth and in model facilities, provide data for the verification of the numerical models, for direct process optimization and for a better understanding of the heat and mass transport behavior.

The paper describes a numerical simulation tool for heat and mass transfer processes in large diameter CZ crucibles under the influence of several non-rotating AC and CUSP magnetic fields. Such fields are expected to provide an additional means to influence the melt behaviour, particularly in the industrial growth of large diameter silicon crystals. The simulation tool is based on axisymmetric 2D models for the AC and CUSP magnetic fields in the whole CZ facility and turbulent hydrodynamics, temperature and mass transport in the melt under the influence of the electromagnetic fields. The simulation tool is verified by comparisons to experimental results from a laboratory CZ setup with eutectics InGaSn model melt.

Turbulent silicon melt flows are studied in large diameter Czochralski crucibles under the influence of alternating, steady and combined magnetic fields. The investigations are based on the experimentally verified two-dimensional axisymmetric mathematical models. The influence of steady, alternating and combined magnetic fields on the flow pattern and temperature field is investigated. Global heat transfer and melt flow calculations are coupled and the influence of melt convection on the interface shape is studied and compared with experimental data.

The paper describes a numerical simulation tool for heat and mass transfer processes in large diameter CZ-crucibles under the influence of several non-rotating AC and CUSP magnetic fields. Such fields are expected to provide an additional means to influence the melt behaviour, particularly in the industrial growth of large diameter silicon crystals. The simulation tool is based on axisymmetric 2D models for the AC and CUSP magnetic fields in the whole CZ-facility and turbulent hydrodynamics, temperature and mass transport in the melt under the influence of the electromagnetic fields. The simulation tool is verified by comparisons to experimental results from a laboratory CZ set-up with eutectics InGaSn model melt.

The results of an investigation of energy requirements and ways of saving energy in the production process of photovoltaic modules are reported. The investigation was carried out as a process chain analysis. It contains a comprehensive collection of process step data, from the reduction of SiO2 up to the completed module. Analysis and comparison results include conventional mono- and multicrystalline silicon modules as well as MIS-I modules and thin film solar cells based on amorphous silicon. The investigation includes model cases of an expanded production volume and its implications for energy requirements. Modifications of the production process in pursuit of the goal of improved cell efficiency need to be reviewed taking into account the accumulated energy requirements of the whole module. The data framework presented in the report provides a reliable, fast and flexible measure that enables researchers to meet this condition.