Czochralski_Silicon_Crystal_Growth-May_2013.webm

Download printable brochure with application examples. Last updated September 26, 2012.

The CGSim (Crystal Growth Simulator) code is specialized software for simulation of Czochralski (Cz), Liquid Encapsulated Czochralski (LEC), Vapor Pressure Controlled Czochralski (VCz), and Bridgman growth. The code provides information to growers on the most important physical processes responsible for crystal growth and quality. The CGSim package contains several modules such as Basic CGSim, Defects, Flow Module, and CGSim View.

Fig. 1. CGSim package

CGSim can be effectively applied to the following practical problems:

• Control and optimization of the crystallization front geometry and V/G distribution by adjustment of the hot zone and growth parameters.
• Increase of the crystallization rate with keeping high crystal quality.
• Control over stress and defects in the growing crystal. Defect engineering via accurate adjustment of the heat shields.
• Governing melt convection via crystal/crucible rotation rates, magnetic fields of various strength and orientation. Stabilization of convection in the melt while maintaining reasonable turbulent mixing.
• Analysis of impurity transport in both the melt and gas. Prediction of oxygen and carbon containing species concentrations in Si CZ growth. Adjustment of growth conditions and modification of the hot zone aimed at providing desired impurity concentrations.
• Adequate account of encapsulant, turbulent gas flow, and convective heat transport in liquid encapsulated growth.
• Modelling support for design and optimization of new crystal growth setups.

Capabilities of the CGSim package are illustrated through detailed application examples listed below:

• Modeling of casting process for silicon solar cells
• 100 mm Czochralski Silicon Growth
• 300 mm Czochralski Silicon growth
• Effect of magnetic fields in 400 mm Czochralski Silicon growth
• Numerical analysis of sapphire crystal growth by the Kyropoulos technique
• VCz growth of 100 mm GaAs
• High-pressure liquid-encapsulated Czochralski growth (HPLEC) of InP
• CsI crystal growth by continuous feed method
• Quartz crystal growth in hydrothermal autoclave
• Oxide Crystals
• Adjustment of heater power distribution during VGF growth of GaAs crystals
• HEM Sapphire crystal growth

Capabilities of Basic CGSim include:

• Radiative heat transport
• Conductive heat transport
• Heater power adjustment to provide the required crystallization rate
• Calculation of crystallization front geometry
• Automatic reconstruction of the geometry for several crystal positions
• Special models for anisotropic characteristics of materials

The Basic CGSim program is developed for industries and research teams. Graphical User Interface of the Basic CGSim code requires no special computational skills. All setup and computational steps are highly automated to minimize user efforts.

Work with Basic CGSim includes the following stages:

• Specification of the growth system geometry
• Specification of material properties
• Grid generation
• Boundary condition specification
• Computation process
• Visualization of the results

Below, we will have a closer look at some of these stages.

Fig. 2. Specification of the Growth System in the Graphical User Interface (GUI)

The Basic CGSim has a convenient tool for geometry specification. Any geometry can be constructed by creating and manipulating geometric entities, such as, points, lines, curves, etc. To facilitate the geometry creation, the toolbox contains extensive set of tools for selecting, moving, splitting, connecting, and duplicating objects as well as tools for creating splines, polylines, and perpendiculars. If any modifications are introduced into the complex multiblock geometry, the user only needs to regenerate the grid and specify the materials in those blocks that were modified, while the rest of the setup stays intact.

Advanced users familiar with AutoCAD can use it as an alternative geometry specification tool and then import the geometry into CGSim using the DXF format.

The CGSim code is a software designed specially for 2D axisymmetrical computations, so the user only needs to create a half of the reactor geometry.

The built-in geometry analyzer automatically recognizes closed contours as blocks, which substantially facilitates the geometry pre-treatment. This feature is also very useful as a diagnostics tool—if some area of the geometry, that stands for a separate construction element or a closed gas volume is not recognized as a block, it means that the contour representing its boundary is not closed. At the next step, the user can quickly generate a grid for the whole system using the auto grid generator. Since the automatic grid generator is very robust, the user only needs to set a parameter characterizing desired grid refinement to start the grid generation. GUI also provides the user with several options, facilitating the choice of blocks and grid types for the automatic grid generation. For instance, the user can choose the grid of some type to be generated in gas or solid blocks only.

Fig. 3. Examples of grids generated by Basic CGSim

Advanced users can customize the mesh manually in selected blocks or throughout the whole system. The grid generator supports triangular and quadrangular grids with both matched and mismatched interfaces. These capabilities are especially important for modeling of the crystallization front geometry, when structured grids are required on both sides of the interface. Local refinement of structured grids can be achieved through refining the node distribution on the respective edges towards one of the ends or symmetrically. For unstructured grids, refinement can also be regulated through the grid quality parameters.

Fig. 4. Assigning the Material Properties in GUI

The CGSim tool for setting characteristics of materials gives the user wide possibilities. One can choose a constant, a polynomial function, a piecewise linear function, expression, or an arbitrary function, which can be programmed in the Function window. Plots for all characteristics can be displayed in the same window. For example, the heat conductivity can be defined as a function of temperature and coordinates in an arbitrary way borrowed from literature. Incorporated programming language similar to Pascal, extended by preprocessor and visualization of the function, allows this for user.

After the geometry creation and the material specification, Basic CGSim calculates the crystal and melt weights, and the initial charge weight, which helps the user to draw crystallization zone geometry. Beside the global heat computations with the given heater powers, Basic CGSim allows searching the powers providing a certain crystallization rate and prediction of crystallization front geometry. The code permits automatic reconstruction of the geometry for several crystal positions. To make it, the user has to build only the geometry with the highest crystal position and to specify the crystal heights to be computed.

Fig. 5. 1D and 2D Visualization with CGSim View

CGSim View allows analysis of 2D and 1D distributions including heat and mass fluxes, V/G ratio and temperature gradient along the crystallization front. Additionally, 1D distributions along a boundary can be displayed as a plot and stored in a file on a hard disk. Built-in animation tools help to analyze features of 3D melt convection.

The present version of basic CGSim operates under Windows 2000 and Windows XP. The solver of Flow Module is available for parallel computations under Linux.

Demo version and code documentation are available upon request.