CGSim Version 8.12 Reference Guide by MissZhu

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									Semiconductor Technology Research, Inc.




          CGSim

Crystal Growth Simulator

             Version 8.12




     Software for Modeling of
  Crystal Growth from the Melt




   Graphical User Interface

        Reference Guide
                                     Semiconductor Technology Research, Inc.


Table of contents


1    Introduction ............................................................................................................. 5
2    Installation............................................................................................................... 5
3    Getting Started ........................................................................................................ 5
    3.1    CGSim Operation ............................................................................................. 5
    3.2    Geometry Specification .................................................................................... 6
    3.3    Material Specification ...................................................................................... 6
    3.4    Generation of 1D grids along block boundaries (splitting) .............................. 8
    3.5    Generation of 2D grids in blocks...................................................................... 8
    3.6    Boundary condition specification..................................................................... 8
    3.7    Problem mode specification ............................................................................. 9
    3.8    Computation execution..................................................................................... 9
    3.9    Result visualization .......................................................................................... 9
    3.10      Automatic geometry reconstruction .............................................................. 9
4    Main Menu ............................................................................................................ 10
    4.1    File .................................................................................................................. 10
    4.2    Edit ................................................................................................................. 12
    4.3    Fragment......................................................................................................... 13
    4.4    Picture............................................................................................................. 13
    4.5    Options ........................................................................................................... 14
    4.6    Statistics.......................................................................................................... 15
    4.7    Functions ........................................................................................................ 16
    4.8    Materials ......................................................................................................... 17
    4.9    Tools ............................................................................................................... 20
    4.10      RUN ............................................................................................................ 22
    4.11      Version ........................................................................................................ 23
5    Geometry Window ................................................................................................ 24
    5.1    Geometry Toolbox.......................................................................................... 24
    5.2    Selected Object/New object window.............................................................. 33



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    5.3      Bottom panel................................................................................................... 33
    5.4      Pop-up menu................................................................................................... 35
6     Blocks Window ..................................................................................................... 35
    6.1      Information mode ........................................................................................... 36
    6.2      Set material mode ........................................................................................... 36
7     Grid Window......................................................................................................... 37
    7.1      Details............................................................................................................. 37
    7.2      Grid................................................................................................................. 37
    7.3      Auto grid generator......................................................................................... 40
    7.4      Auto split ........................................................................................................ 41
8     Gas Window.......................................................................................................... 42
    8.1      Details............................................................................................................. 42
    8.2      Grid................................................................................................................. 43
    8.3      Boundaries ...................................................................................................... 43
    8.4      Miscellaneous ................................................................................................. 44
9     Radiation Window................................................................................................. 44
    9.1      Details............................................................................................................. 45
    9.2      External boundaries ........................................................................................ 45
    9.3      Surface Emissivity.......................................................................................... 46
    9.4      Splitting .......................................................................................................... 47
    9.5      Internal boundaries ......................................................................................... 48
      9.5.1        Cuvettes ................................................................................................... 48
      9.5.2        Boundary.................................................................................................. 49
10        Solid Window .................................................................................................... 49
    10.1.       Details ......................................................................................................... 50
    10.2.       Grid.............................................................................................................. 50
    10.3.       External boundaries..................................................................................... 50
    10.4.       With gas....................................................................................................... 51
    10.5.       Heat source.................................................................................................. 51
    10.6.       Anisotropy................................................................................................... 52



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   10.7.       Internal boundaries...................................................................................... 53
11       CZ (LEC) Window ............................................................................................ 54
   11.1.       Details ......................................................................................................... 54
   11.2.       Grid.............................................................................................................. 55
   11.3.       Properties..................................................................................................... 56
   11.4.       Interface....................................................................................................... 56
   11.5.       Growth......................................................................................................... 57
12       Crystal Position Window ................................................................................... 57
   12.1        Properties..................................................................................................... 60
   12.2        Pedestal ....................................................................................................... 60
   12.3        Holder.......................................................................................................... 61
   12.4        Specification................................................................................................ 62
   12.5        Crystal position ........................................................................................... 63
13       Solver ................................................................................................................. 66
Appendix 1. System Requirements.............................................................................. 74
Appendix 2. Theory description .................................................................................. 75
   A2.1.       Materials classes.......................................................................................... 75
   A2.2.       Basic Equations ........................................................................................... 76
   A2.3.       Specification of materials properties........................................................... 77
   A2.4.       External Boundary Conditions .................................................................... 77
   A2.5.       Internal Boundary Conditions ..................................................................... 79
   A2.6.       Conditions at Gas Block Boundaries .......................................................... 80
Appendix 3. Tools for Moving and Zooming a Picture............................................... 82
References.................................................................................................................... 83




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1 Introduction
CGSim code is a specialized software aimed for Czochralski crystal growth modeling. The
present version has been designed for global heat transfer and gas convection simulation in the
axisymmetrical approximation. The simulation of the heat transfer in the growth system involves
radiative and conductive heat transport. The code reconstructs automatically the crystal, melt,
and encapsulant geometries in CZ and LEC growth for various crystal positions allowing serial
computations. Defects Module predicts distribution of thermal-elastic stresses and point
defects producing in the crystal. The results obtained by the CGSim code can be analyzed
using CGSim View program which is a part of the package.


2   Installation
To install CGSim package on an Intel processor-based PC running Windows, the user should
run the file setup.exe. During the installation, the user should assign the home directory to
install the package. Installation wizard, in particular, creates a shortcut to the CGSim shell and
assigns associations for the CGSim project files (.gm) to the CGSim shell.


3 Getting Started

3.1 CGSim Operation
User work with the CGSim package includes the following stages:
       Prescription of the growth system geometry
       Material specification
       Generation of 1D grids along block boundaries (splitting)
       Generation of 2D grids in blocks
       Boundary condition specification
       Problem mode specification
       Computation execution
       Result visualization




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3.2 Geometry Specification
Specification of the two-dimensional axysimmetric geometry of the growth system is the first
stage of simulation process. The geometry should be represented as a set of boundaries
forming closed non-overlapping contours bounding blocks that correspond to constructive
elements of the growth system, such as insulation, heater, crystal, crucible, melt, etc. The block
recognition is carried out by the code automatically.



3.3 Material Specification
Material Specification in the CGSim includes the following steps:
       Specification of materials involved in the computations (selection of a class and
       prescription of physical properties). Materials can also be imported from the material
       database file;
       Assigning a material to each block.
   The following classes of the materials are available: None, Vacuum, Solid, Gas, Melt,
Crystal, Encapsulant. Different physical processes are simulated in the block depending on
the class assigned (Table 1). Each class requires prescription of a respective set of material
properties. The properties can be specified as a constant, a polynomial function, a piecewise
linear function, a A+B/T function, and a user-defined function. Note that None and Vacuum are
specified in the CGSim by default.




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 Table 1
              Radiation   Conductive
                                                     Required material
   Class        heat         heat      Convection                            Specific features
                                                         properties
              transport    transport
   None          –             –           -                 –                         –
 Vacuum          +             –           -                 –                         –
                                                    thermal conductivity,              –
   Gas           +             +           +             viscosity,
                                                          density
                                                    thermal conductivity,              –
   Solid         –             +           -
                                                     surface emissivity
                                                    thermal conductivity,   Specific       boundary
                                                     surface emissivity,    conditions;       Block
                                                    melting temperature,    geometry varies if
   Melt          –             +           -
                                                        latent heat,        automatic geometry
                                                          density           reconstruction           is
                                                                            prescribed
                                                    thermal conductivity,   Specific       boundary
                                                     surface emissivity,    conditions;       Block
                                                          density           geometry varies if
  Crystal        –             +           -                                automatic geometry
                                                                            reconstruction           is
                                                                            prescribed


                                                    thermal conductivity,   Specific       boundary
                                                     surface emissivity     conditions;       Block
                                                                            geometry varies if
Encapsulant      –             +           -
                                                                            automatic geometry
                                                                            reconstruction           is
                                                                            prescribed




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3.4 Generation of 1D grids along block boundaries (splitting)
1D grids along all boundaries of Gas and Vacuum blocks should be created for radiation heat
transport computations. Both automatic and manual splitting are supported.



3.5 Generation of 2D grids in blocks
The user should generate a 2D grid inside the block manually or using the automatic grid
generator built-in in the program. The CGSim generator can create quadrangular (Q-grid) and
triangular (Т-grids).
      Non-matched grids are supported by the CGSim, allowing different grid roughness in two
blocks adjacent to a common boundary. This simplifies manual grid specification and enables
automatic point insertion at boundaries by the triangular grid generator.
      The problem of crystallization front correction requires a special grid design: the melt and
the crystal should have a block with quadrangular grid, which contains the melt-crystal interface.
The number of intervals on the melt-crystal interface should be equal or large than 15.
      Note that the 2D grid is not required in Vacuum blocks.



3.6 Boundary condition specification
Boundary conditions used in heat transfer computations are specified at external boundaries of
the computational domain. By default, the conditions of heat fluxes and temperature continuity
(Ideal boundary conditions) are used at the internal boundaries, except the melt-crystal
interface, where heat flux has a jump proportional to the crystallization rate. Besides, the user
can set specific internal boundary conditions.
      Boundary conditions used in gas convection computations are specified at gas block
boundaries. By default, the conditions of zero velocities (Wall boundary conditions) are used at
the solid-gas boundaries. Besides, the user can set specific gas boundary conditions.
      Usually, CZ and LEC problems require setting constant temperature at the external
boundaries of the growth system.




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3.7 Problem mode specification
The user should select a problem which will be solved by the CGSim code. There are three
problem modes in CGSim:
       Direct heat computation. In this mode, heat transfer is computed in the whole growth
       system with the heater powers and the crystallization front shape assigned by user.
       Heater power adjustment to provide the required crystallization rate. In this mode, the
       heater powers are adjusted by the CGSim solver to provide the crystallization rate
       prescribed by the user, the crystallization front shape is assigned by the user. Heater
       power adjustment is available if a heater is specified as a leading and the Find Power
       flag turned on.
       Crystallization front geometry computation. In this mode, both the crystallization front
       shape and the heater powers are adjusted by the CGSim code. Crystallization front
       geometry computations are available if a heater is specified as leading and both Find
       Power and Find interface shape flags are turned on. The CGSim code predicts (i) the
       leading heater powers providing the crystallization rate prescribed by the user and (ii)
       the crystallization front shape.



3.8 Computation execution
The computational module is invoked in a separate console window. The computations stop
automatically as soon as convergence is reached or the maximum number of iterations has
been performed.



3.9 Result visualization
The results are visualized with CGSim View program as 2D distributions and 1D plots.



3.10 Automatic geometry reconstruction
The automatic reconstruction allows fast creation of the CZ and LEC growth setup geometries
with various crystal heights. It includes two main stages:
       Pedestal and holder specification;
       Specification of the boundary of the reconstructed zone.



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After that, any geometry with smaller crystal height is automatically generated by the code. New
geometry requires only grid generation in the reconstructed blocks (the melt, crystal, crucible,
encapsulant, and seed blocks). Other parameters (material specification, boundary conditions,
heater powers, etc.) are taken from the original problem.




4 Main Menu
The Main Menu is placed at the top.


4.1 File
The options available with the File menu allow the user to open an existing project (.gm) file, to
save the current project to a .gm file, and to import geometry information from .txt or .dxf files. A
.gm file contains geometry and all information about a problem (grids, boundary conditions,
materials properties, heat sources etc.). Lines and points can be exported to a .txt file.




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New                              To start a new.gm file, click on the New option in the File
                                 menu.
Open                             This option is used for opening an existing .gm file.


Save                             This option is used for saving the current .gm file.


Save as                          This option is used for saving the current .gm file with another
                                 name.
Notes                            Using the Notes option, the user can make notes, which will be
                                 saved in the .gm file.
Import                           This option can be used for import of a geometry from .txt or
                                 .dxf files. A line in a .txt file should contain point coordinates
                                 for point creation or coordinates of two points for line creation.
                                 The user can select the necessary lines in the .dxf or .txt file
                                 (Fig. 4.1a). Besides, it is possible to rotate the imported
                                 geometry    and/or   transform    units   (convert     meters   into
                                 millimeters). The Auto splitting option splits the lines at cross-
                                 points. If the lines lie closer than DeltaSplit, they will be
                                 interpreted as a single line. The option works only in the
                                 Geometry window.
Export                           The geometry can be saved in a .txt file as a set of lines
                                 (coordinates of two points) and in a .dxf format.
List       of                    The File menu provides the user with a list of the most recently
.gm file                         opened .gm files (Fig. 4.1b).
Exit                             To close the CGSim code, click on Exit in the File menu (or on
                                    button in the window right top).




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        Fig. 4.1a                                    Fig.4.1b



4.2 Edit
Select all                  To select all geometrical objects, click on Select all in the Edit
                            menu (this option is available only in the Geometry window).
Unselect all                To unselect all, click on Unselect all in the Edit menu (this option
                            is available only in the Geometry window).
Remove          3d          This option is for removing the 3d arcs (ellipses) used to see the
arcs                        picture as 3d (this option is available only in the Geometry
                            window).
Align to grid               It is possible to align the geometry to the grid specified in the
                            Options menu (this option is available only in the Geometry
                            window).
Scale        and            The user can move geometric object and change its size using
Move                        the Scale option (Fig. 4.2).




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       Fig. 4.2


4.3 Fragment
Geometrical objects can be translated into other .gm files by using a .fgm file.
Write fragment                        To save geometrical objects (lines, points, splines, arcs) in a
                                      .fgm file, select the objects and click on the Write fragment.
Read fragment                         To import objects from a .fgm file to the current .gm file, use
                                      the Read fragment option.



4.4 Picture
Background picture                                The background picture can help to create
                                                  geometry, using a file presenting the growth
                                                  system geometry, prepared in bmp graphic
                                                  format.
   •   Load       from                            This option is for reading a picture from a .bmp
       file                                       file.
   •   Set size                                   The user can set the background picture size and
                                                  position with the Set size option (Fig. 4.3).
                                                  Besides, it is possible to choose the Geometry
                                                  window side (left, right), where the picture will be
                                                  located.
   •   Remove                                     The option removes the background picture.




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         Fig. 4.3


Save to .bmp file                                    One can save the working area as a picture in a
                                                     .bmp file with 50, 100, 200, or 400 % scaling.
Copy to clipboard                                    One can copy the working area in the clipboard
                                                     with 50, 100, 200, or 400 % scaling.



4.5 Options
The Options menu (Fig. 4.4) is used to set the following parameters:
   Task mode                    axisymmetric problem is solved by default;
   Picture Sizes                size of the area, which is contoured by the white dashed line;
                                this area does not effect the geometry, but can be useful for
                                geometry drawing;
   Grid                         grid step specification is used to snap an object to the grid;
   X, Y to display              number of digits after point coordinates;
   Points                       point attributes: shape, size, and width;
   Put      point    to    the distance, within which points are put to the symmetry axis;
   symmetry axis
   Marking points               marking point size;
   Lines                        line width;
   3d-ellipses                  3D imagination;
   Margin visible               margin visibility;
   Zoom scale by mouse          rate of picture zoom with mouse.




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       Fig. 4.4



4.6 Statistics
The Statistics menu contains information about the geometry such as Block Name, Material,
Class (solid-(s), gas-(g), melt-(m), crystal-(c), encapsulant-(e), vacuum-(v), none-(n)), Area,
Volume, Grid Type (structured, unstructured), and the number of Nodes (Fig. 4.5). Besides, the
user can find data on a total number of blocks and nodes related to each material class.




       Fig. 4.5




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4.7 Functions
This menu is aimed for function programming using the CGSim built-in language (Fig. 4.6). The
Editor, Debugger and Graph tabs in the Functions window allow creation of any analytical or
piecewise-linear function. It is possible also to import functions from another .gm file.




       Fig. 4.6




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4.8 Materials
Edit                                One can create and edit information on materials
                                    data with the Edit option
Properties                          of materials (density, dynamic viscosity, conductivity,
                                    emissivity, melting temperature, latent heat, electric
                                    conductivity etc.) are specified in the Properties tab
                                    (Fig. 4.7a); any property can be specified as a
                                    constant, a polynomial function, a piecewise linear
                                    function    of   temperature,    A+B/T    function,   an
                                    expression, or as a user-defined function, which is
                                    programmed with the Function menu by the user.
Class                               (solid, gas, melt, encapsulant, and crystal) and type
                                    of hatching (Mono mode or Colored mode) can be
                                    set in the Materials tab (Fig. 4.7b); if special
                                    CZ(LEC) options will be applied (automatic geometry
                                    reconstruction for several crystal heights, heat power
                                    adjustment to provide a required crystallization rate,
                                    calculations of crystallization front geometry), it is
                                    necessary to use the melt (for CZ and LEC), crystal
                                    (for CZ and LEC) and encapsulant (for LEC) classes.
Edit     materials                  This option allows edition of the materials database
files                               .mt file.
Import                              This option is used for .mt file import (Fig. 4.8).

Export                              This option is used for .mt file export (Fig. 4.9).
Clear                               Using this option, the user can remove data on
                                    materials properties from the opened .gm file.




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   Fig. 4.7a




      Fig. 4.7b




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      Fig. 4.8




      Fig. 4.9




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4.9 Tools
Maitence CP list       The option allows the user to operate with geometries (CPs) created
                       using    Crystal Position Window (see Sec.12 Crystal Position
                       Window, 12.5 Crystal position)


If crystallization front geometry computation mode is set (see Sec. 11 CZ (LEC) Window, 11.4
Interface), the CGSim program saves a Name interface.txt file, with the interface shape
computed by the code (Name is the name of the original .gm file).


New crystal            The user can import the crystallization front geometry using this option
interface              (Figs. 4.10a and 4.10b). At that, the grid will be automatically
                       reconstructed.




       Fig. 4.10a




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      Fig. 4.10b




Meniscus shape      This option is used to compute meniscus shapes for the current crystal
                    geometry (Fig. 4.11). The following sequence of operations should be
                    executed:
      choose one of the Melt surface or Encapsulant surface options;
      select the crystal surface adjacent to the triple point (melt-crystal-gas for the CZ growth or
      melt-crystal-encapsulant for the LEC growth) ; a spline curve corresponding the meniscus
      shape will arise;
      move the spline curve at a required position and press the Put button.




   Fig. 4.11



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Note:    Meniscus shape computation requires setting a wetting angle WANGLE (deg), surface
         tension STENSION (N/m), melt density (for CZ and LEC) and encapsulant density (for
         LEC) RHO.




Make Id_Bnd file     This option can be used to save a set of numbers of boundaries selected
                     by the user. The data are further used by the CGSim solver to create a file
                     employed by the Flow Module (.bnd file). The following steps are required
                     to make limited .bnd file for further computations of the crystallization zone
                     with Flow Module:
        select all needed boundaries (surrounding the crystallization zone);
        go to Tools / Make Id_Bnd file / Yes.

At the end of the computation, the CGSim solver will write into the .bnd file only selected
boundaries.



4.10 RUN
Run                  One can start the CGSim computations using the Run option in the
                     RUN menu or the pressing Ctrl+F9 hot key. See Sec. 13 Solver for
                     more information.
Defect module        Use this option to start the module Defects.
CGView               Click on this option, to start CGSim View visualization tool.




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  4.11 Version
  Version number                        Using this tab, the user can check the CGSim version.
  Registration                          This option is used to register the CGSim program. To
                                        get an activation key for the license on a computer where
                                        the CGSim program was installed, one needs to send the
                                        original key value from the computer to cgsim-
                                        support@semitech.us via E-mail. If the activation key is
                                        available, paste it in Activation key area and press

                                                 (Fig. 4.12).




   Send the key value to
cgsim-support@semitech.us               Paste the activation key here
        via E-mail                              and press Ok.



                 Fig. 4.12




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5 Geometry Window

5.1 Geometry Toolbox




                              Geometry is prescribed with a set of tools within the Geometry
                              toolbox (Fig. 5.1). If the toolbox is selected, a set of icons is
                              available. The icons can be used by the user to create and
                              manipulate geometric entities, such as points, lines, curves, arcs,
                              etc. Two modes are available (selected using the mode option at

                              the window left bottom): “elastic” lines and arcs       and point-to-

                              point lines and arcs        . In the former mode, lines are plotted
                              during their creation. In the latter mode, lines become visible only
                              after setting of the end points.
         Fig. 5.1


Select object       . This button is used to activate selecting geometrical entities. To unselect an
entity, press this button again or press the space on the keyboard.


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Select objects in the rectangle           . This option is used to select objects lying within a
rectangle that appears on the screen after pressing this button and whose size can be changed
by the user.


Unselect all      . Pressing this button unselects all objects selected.


Point. There are several options dealing with point operation.
       Create point      . The button serves for point creation.
       Put point to grid     . The option allows the user to put the selected point to the grid.
       Intersection point     . This option provides splitting of the objects at an intersection point.
       For this purpose, select sequentially the objects to split and put the Intersection point
       button. After that, click on one of the object next to the intersection position. The

       intersection point can also be created by using the Split line, arc, …             button (see
       below).
        Note: To split lines, the user needs only to select two lines and push the button.
The points can also be created and edited using Selected Object/New object tabs (see Sec. 5.2
Selected Object/New object window)


Line. The code provides several capabilities to create a line.
       Create line     . This option creates a line connecting two points.
       Vertical or horizontal line       . This option assists the user in an easier creation of
       horizontal or vertical lines.
In addition, using Selected Object/New object tabs (see Sec. 5.2 Selected Object/New object
window), the user can edit the coordinates of the onset and the end of the line.


Rectangle       . The option can be used for rectangle creation. If this is made in the point-to-point
lines and arcs mode, only two opposite corner points are required to create a rectangle. Note
that the coordinates of all four points of the rectangle can be edited so that the rectangle can be
transformed to an arbitrary quadrangle.


Arc. There are five options in the code related to the creation of arcs and their further
modification.



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       3-point arc     . The 3-point arc option puts an arc on three points selected by the user.
       Explicit definition of the arc parameters using Selected Object/New object tabs is
       illustrated by Fig. 5.2. The following arc parameters have to be assigned: the center
       coordinates (xc, yc), the arc radius (r), and the arc begin and end angles (α1 and α2).
       Center-and-2-point arc       . This option is used for creation an arc from its central point
       and two other points belonging to the arc.
       Concentric arc      . Using this option, one can create an arc concentric to an existing one.
       Move arc point       . This option is aimed at modifying the parameters of an existing arc.
       The positions of the point forming the arc can be changed either moving a point with the
       left mouse button or by explicit changing its coordinates.
       Change arc radius        . Like in the previous option, the arc radius can be changed with
       the left mouse button or explicit definition of the radius.




       Fig. 5.2.


Spline. This tool includes three options.
       Spline      . This option creates a spline using the points picked sequentially by the user.
       Add point to spline       . The user is allowed to add points to a spline. The spline is
       reconstructed automatically, as new points are added.
       Continue spline      . A spline can be continued by picking new points outside the spline.
       The spline will be continued starting from its end.


Polyline. There are three options available for work with polyline:
       Polyline      . This option creates a polyline using the points picked sequentially by the
       user.
       Add point to polyline      . The user is allowed to add points to a polyline. The polyline is
       reconstructed automatically, as new points are added.
       Continue polyline        . A polyline can be continued by picking new points outside the
       polyline. The polyline will be continued starting from its end.



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Convert spline <->polyline         . The user can use this option for conversion of a spline to the
polyline and vice versa for conversion of a polyline to the spline.


Options related to splitting and creating perpendiculars
       Point as perpendicular          . This option creates a new point that is the result of
       intersection of the selected entity and a perpendicular dropped to this entity from the
       selected point. The perpendicular line itself is not shown.
       Create perpendicular line       . This option is similar to the previous one, but it additionally
       creates the perpendicular line.
       Split line, arc, …    . This option provides splitting of the object at a point specified by the
       user. This option can also be used for splitting objects at an intersection point by putting
       the button and clicking the mouse in vicinity of the intersection point.
       Split line with perpendicular     . This action is similar to the creation of perpendicular line,
       but the selected entity is split at the point of its intersection with the perpendicular.
       Perpendicular with splitting       . This option is similar to the previous one with one
       exception: the perpendicular line is not drawn.


Text related options. To create/edit text blocks, the user can operate with the following
options:
       Text    . This option adds text to the picture.
       Text with a marginal note        . With this button, it is possible to create a text block with
       marginal note.
       Edit text   . This option is used to edit the existing text block.
       Increase font size     . Option for increasing the text size.
       Decrease font size      . Option for decreasing the text size.


Move/translate. This tool provides translation of entities without duplication or multiplication.
       Move selected entity      . With this option, the selected entity can be moved using the left
       mouse button.
       Move horizontally      . The purpose of this option is to easily move the selected object
       horizontally.




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       Move vertically     . The purpose of this option is to easily move the selected object
       vertically.
       Translate by explicit distances     . Using this option, the user is able to move or copy an
       entity by explicitly specified distances in X and Y directions. To do this, select Action and
       specify distances (Fig. 5.3).




       Fig. 5.3.


       Point-to-point moving       . Select entities (lines, splines, polylines etc.) for moving, press
       the Point-to-point moving button and then click an attachment point. The selected
       objects will attach to the point (Fig. 5.3a). This tool is convenient for putting meniscus
       shapes (Fig. 5.3b).




                                                     B                               B
 A                             A

Fig. 5.3a                                           Fig. 5.3b


Multiply/duplicate. This tool provides a possibility to multiply/duplicate geometrical entities.
       Multiply selected entities      . This option allows you to multiply selected entities. After
       pressing the corresponding button, a special window appears (Fig. 5.4), where the user
       is to select the multiplication direction (up, down, left, or right), the number of the copying
       repetition, and the copying step.


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       Fig. 5.4.


       Duplicate selected entities      . This option provides translation and duplication of the
       selected entity. For this purpose, the user should select the object and select two points.
       The object will be translated and duplicated along the direction specified by two points
       and the distance between them. Note that the two points defining the translation
       distance and direction may be positioned anywhere on the page area.


Duplicate and translate. This tool includes three buttons.
       Duplicate and translate       . Press this button and translate the selected entity (it will
       become white and move slightly from the original object) to the desired position using
       the left mouse button.
       Duplicate and translate horizontally     . The purpose of this option is to easily translate
       (with duplication) the selected object horizontally.
       Duplicate and translate vertically     . The purpose of this option is to easily translate
       (with duplication) the selected object vertically.


Approximation of arcs and splines with lines                . Selecting this option, the user may
substitute an arc or spline by a set of straight lines by specifying the number of approximation
intervals as shown in Fig. 5.5. Pressing the Fix button confirms the entity splitting.




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        Fig. 5.5.


Put flag      . This option allows the user to put a flag on the picture to mark some parts of the
geometry, if they will require modifications in the future, or with some other purposes.


Draw 3D ellipse       . This option is aimed at imagining how the current geometry looks in three
dimensions. To draw the ellipse, pick any point, the angle of view of the obtained “3D” picture
may be regulated using 3D angle option on the bottom panel of the window. 3D ellipses can be
switched on/off by the      button on the bottom panel of the window. If the user needs to delete
the 3D ellipse, one again clicks the option and picks the point.


Merge/unmerge points. This option deals with merging/unmerging points.
        Merge points     . To merge points, the user is to select at least two points and press this
        button.
        Merge points in the window        . This option allows the user to merge all points lying
        within a special window that appears on the screen after pressing this button. To get
        more/less points within the window, zoom out/in the picture.
        Unlink objects    . This option is used to unmerge objects at the point of their junction.


Align horizontally/vertically. The purpose of this option is to align points horizontally or
vertically.
        Align points horizontally    . Two or more selected points may be aligned horizontally by
        pressing this button.
        Align points vertically     . Two or more selected points may be aligned vertically by
        pressing this button.




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Grouping. The operations of moving, translation, duplication, etc. can be performed with groups
of objects. To select one object in a group, press the Shift button on your keyboard and select
an object by the left mouse button.
       Add selected items into group      . Select entities you would like to integrate into a group
       and press this button. A special window appears (Fig. 5.6) to specify the group name
       (new or selected form the name list).




       Fig. 5.6.
       Edit group list    . Each group can be removed from the group list, as well as its name
       can be changed.
       Select group      . Each group can be selected either using the Select object button or by
       choosing the group from the group list within this option.


Find entities with one contact        . This option analyses topology of the geometry and shows
coincident lines and lines that do not belong to any closed object (block).


Geometry information        . By pressing this button, the user gets information about the current
status of the geometry created (the number of points, the minimum distance between points, the
number of lines, the minimum line length, the numbers of arcs, splines, texts, flags, and chains).
An example of the Information window is given in Fig. 5.7a.




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            Fig. 5.7a                             Fig. 5.7b


Calculate distance and angle        . Using this option, the user can calculate distance between
any two points and orientation angle of the line connecting these points:
       press the Calculate distance and angle button;
       select two points by mouse clicking;
       the Measure window with information appears (Fig. 5.7b).


Zoom in      . This option is for zooming in a fragment of the picture: select the fragment by the
rectangular and apply the zooming by the double click.


Restore object size after zooming in        . This option restores the previous picture size after
zooming in a fragment of the picture.


Delete selected           . To delete selected object use this button or the Del button on the
keyboard.


Undo/Redo.
       Undo       . Use this option for Undo operation.
       Redo       . Use this option for Redo operation.


ID options. Each geometrical entity belonging to the current picture has a unique number Id
which can be used for geometry analysis.
       Point Id    . Activating this option, the user may see on the screen the numbers of all
       point forming the picture.


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       Entity Id      . Activating this option, the user may see on the screen the numbers of all
       entities forming the picture.
       Find entity by number        . The user may find an object by its number, specifying this
       number in a special window that appears after pressing the corresponding button. Note
       that several entities can be found at a time by setting several IDs for searching.


5.2 Selected Object/New object window
This option is aimed at explicit specification and editing of the coordinates of various
geometrical entities. For example, if the user needs to create a point with coordinates (100;100),
one is to choose the point among objects that can be created using the New object tab (Fig.
5.8) and then to specify its coordinates, as demonstrated in Fig. 5.9. Similarly, the coordinates
of an existing entity can be modified using the Selected Object tab.




           Fig. 5.8                                         Fig. 5.9




           Fig. 5.10



5.3 Bottom panel
Service buttons on the bottom panel. There are several additional options assisting the user
in geometry creation, located on the bottom panel of the Geometry window (Fig. 5.10):
       Show grid       . Pressing this button enables showing the grid.
       Draw with affixment to grid       . By pressing this button, the user activates the drawing
       mode with affixment to the grid.

       Show/hide background picture        . This option is to show/hide the background picture.
       Show points        . Activating this option, the user can see points forming geometrical
       entities.




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        Show points forming curves       . All curves (like splines, arcs, etc.) consist of two kinds of
        points: “green” or “red” points (shown with green (points belonging to entities forming
        closed contours) or red color) and “gray” ones (shown with gray color), as shown in
        Fig. 5.11. The points of the first kind can be used for further geometry creation (to create
        lines, curves, etc.), whereas the points of the second kind are allowed only for editing
        their coordinates. So, this option is to show such points forming curves.




        Fig. 5.11.
        Create entity using existing points       . The option is aimed at creating an entity (line,
        curve, spline) using only existing points.
        Affixment to entities     . The option allows the affixment of points created in various
        ways (as an intersection point, end of a line, curve, etc.) to existing entities.
        Select points only      . Pressing this button, the user activates the mode when selection
        of points only is allowed.
        Show frame around close points          . With this option, the user can see frames around
        points located close to each other under the current zooming of the picture.
        Show axes      . This option is to show axes.
        Show new position of axis origin        . To change the position of the origin of the axes,
        press this button and specify the new position of the axes by clicking the left mouse
        button.
Note:    This tool facilitates specification of coordinates relative to a specific point. In particular,
         it can be useful for specification of sizes of some units of the reactor.


        Reset axis origin    . This option restores the initial position of the axis origin.
        Left side, Right side, Both sides                . CGSim is designed for solving of 2D
        axisymmetric problems. The problem is solved in the domain ranging in the radial
        direction from the symmetry axis (zero radial coordinate) to the outer surfaces of the
        reactor (maximal radial coordinate). This looks like a “half” of the real reactor. The user
        may work with the geometry in either left or right half-plane, i.e. to the left or to the right




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       of the symmetry axis. The Left side, Right side, Both sides tool allows choosing in which
       half-plane (or in both simultaneously) the user prefer to specify the geometry.


5.4 Pop-up menu
The menu is used for fast access to some options: click by the right mouse button in the
Geometry window.

       Unselect all               . Pressing this button unselects all objects selected.

       Connect selected points                         . Use this option to connect two points by a
       line.
       Align horizontally      . Two or more selected points may be aligned horizontally by
       pressing this button.
       Align vertically     . Two or more selected points may be aligned vertically by pressing
       this button.
       Merge points       . To merge points, the user is to select at least two points and press this
       button.

       Increase grid step                    . The option is used for increasing a step of the grid
       used for align of geometry.

       Decrease grid step                     . The option is used for decreasing a step of the grid
       used for align of geometry.

       Undo           . This option is used to Undo the latest operations.

       Main geometry only (allowed only for the Main geometry)                             . To mark
       an object as a main geometry object, select it and choose Main geometry only in the
       pop-up menu.

       All geometers (allowed only for the Main geometry)                        . An object will be
       marked as active in all geometries.


6 Blocks Window
The Blocks window is used for analysis of the geometry topology, automatic division of the
geometry into blocks and specification of block materials. The sign “?” near the cursor indicates
that the Information mode is active, the “list” sign shows that the Set material mode is on.




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Note:    Before using the Problems window, the user has to assign material properties in the
         Materials menu (see Sec. 4.8 Materials).



6.1 Information mode
The user can check matching of the blocks and the materials in the Information mode. If the
user selects a material, blocks of this material will be shown. Contrary, if one selects a block,
the block material will be marked (Fig. 6.1).




                                                                       Material list




        Fig. 6.1


6.2 Set material mode
To make specification, select the Set material mode and click by the left mouse button on a
material in the material list in the right part of the window, then click the same mouse button on
a geometry block.




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7 Grid Window

7.1 Details
The tab checks matching of the blocks and the materials. If the user selects a material, the
respective blocks material is displayed. And vice versa, if the user selects a block, the
respective material is marked.



7.2 Grid
Grid generation is performed in the Grid tab. Normally, grid generation is performed using the
Auto grid generator tab (see Sec. 7.3 Auto grid generator). Two grid types are available:
quadrangular (Q-grid) and triangular (T-grid). There is a possibility to use non-matched grids
(Fig. 7.1).




        Fig. 7.1
Quadrangular grid (Q-grid)
To generate a quadrangular grid, use the following instructions:
        Select a block with the left mouse button.
        Click Face Create in the Q-grid option. If the block has only 4 points, faces will be
        created automatically and the Edge Create option will be active. If a block has more than
        4 lines, the user should select 4 points (with the left mouse button) to specify the faces,
        then the Edge Create option will become available (Fig. 7.2).




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                     If block has more
                   than 4-point splitting
                     lines, user should
                     select 4 points to
                       specify faces




        Fig. 7.2


        Click Edge Create option; select a face or faces and specify a number of intervals. This
        splitting can be applied to the selected face or to all faces of the block (Fig. 7.3). A grid
        can be refined by selection of a power and a refinement type (forward, backward, and
        symmetry). One can create the same number of intervals as on the adjacent face in a
        neighbour block by using the From neighbor button (Fig. 7.3). If numbers of nodes at the
        opposite faces are equal, a quadrangular grid will be generated automatically after
        clicking the Store button.
Note:    The power can take on values less than 1.0. This leads to refinement in the middle of
         the line if symmetry refinement is selected.


Triangular grid (T-grid)
Using the Grid option, one can specify a method employed by the code for triangular grid
generation:
        Advancing front;
        Delaney.
To generate a Triangular grid, use the following instructions:



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      click Edge Create, select a face or faces and specify the number of intervals , this
      splitting can be applied to the selected face or to all faces of the block. A grid can be
      refined by selection of a power and a type (forward, backward, and symmetry) of
      refinement. It is possible to create the same number of intervals as on the adjacent face
      in a neighbour block by using the From neighbor button (Fig. 7.3).
      click Grid Create and a grid will be generated. The grid generator may add some nodes
      for creating a more uniform grid.




                Balance
            shows number
            of the intervals
                                                             From neighbor button
             at the faces


       The splitting can be                                   Specify the number of
         applied to the                                            intervals and
       selected face or to                                   refinement parameters
         all faces of the
               block



              Fig. 7.3




   There are three buttons, which can be useful for grid generation:

      Select entities without splitting     . This option selects the faces without splitting in the
      current block.

      Show entities without intervals        . The faces without splitting will be marked in the
      current block.

      Kill grid    . This option deletes the grid in the current block.




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7.3 Auto grid generator
Auto grid generator allows the user to generate quickly a grid for the whole system. The user
needs to select All, set a distance between the grid points Delta, and press the Create grids
button (Fig. 7.4). Besides, this tab provides the user several options, facilitating the choice of
blocks and grid types for the automatic grid generation.


Note:      The user can customize later the grid manually in selected blocks (see Sec. 7.2 Grid).




Fig. 7.4                                                      Fig. 7.4a


Selection of blocks where grids are to be generated automatically (Fig. 7.4a):
        Choice of blocks where grids will be automatically created:
               All (grids will be generated in the whole computational domain);
               Solid (grids will be generated in all solid blocks);
               Gas (grids will be generated in all gas blocks);
               Melt (grids will be generated in the melt and crystal blocks);
               Empty (grids will be generated in blocks, where grids have not generated yet);
               Selected (grids will be generated in selected blocks). To select several blocks,
                press Ctrl+Shift and click the respective blocks.


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       Prescription of the grid type:
               try to create Q- grid (the generator will create Q-grids in the quadrangle blocks
                  and T-grids in other blocks),
               all grids should be T-grids (the generator will generate T-grids in all blocks);
       Set of distance between the grid points Delta in millimeters;
       Press of the Create grids button.



7.4 Auto split
For the radiative heat modeling, 1D grids should be created along all transparent block
boundaries. The Auto split tab is used for automatic 1D grid generation (splitting) (Fig. 7.5). The
following steps are required:
       Selection of boundaries for which 1D grids will be created:
               All (1D grids will be created for all boundaries of the transparent blocks);
               Empty (1D grids will be created for the boundaries, which have not splitted yet);
               Selected (1D grids will be created for selected boundaries);
       Set of a distance between 1D grid points Delta in millimeters;
       Press of the Apply splitting button.




       Fig. 7.5




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Note:     1D grids for the radiative heat modeling can also be created manually (see Sec. 9
          Radiation Window, 9.4 Splitting).




8 Gas Window
The Gas window is used for the gas flow problem statement and contains the following tabs:
        Details
        Grid
        Boundaries
        Miscellaneous



8.1 Details
The user can check matching of gas blocks and gas materials. If one clicks on a block, the
respective material will be displayed in the material list. And vice versa, if a material is selected
in the material list, the respective blocks will be marked (Fig. 8.1).




        Fig. 8.1




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8.2 Grid
Use this tab for gas block grid creation (Fig. 8.2). The respective steps are described in Sec. 7
Grid Window, 7.2 Grid.




       Fig. 8.2



8.3 Boundaries
Use the tab to specify boundary conditions. The boundaries, for which conditions are not set,
are marked by “?”.These boundaries are considered as walls. To specify conditions, click at a
boundary or boundaries and select a boundary condition from the condition list (Fig. 8.3).
There are several condition types:
       Wall
       Inlet
       Outlet
       Rotation
The details of each type of boundary condition are described in Appendix 2. Theory , A2.46
Conditions at Gas Boundaries




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                                          Boundary
                                          condition




       Fig. 8.3


8.4 Miscellaneous
Use the tab to specify atypical gravity (Fig. 8.4).




       Fig. 8.4


9 Radiation Window
This window provides tools for Radiation problem statement. Here gas and vacuum blocks are
active. The following tabs in the right part of the Radiation window are available (Fig. 9.1):


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       Details
       External boundaries
       Surf. Emiss
       Splitting
       Internal boundaries



9.1 Details
The user can check matching of transparent blocks and materials. If one clicks on a block, the
respective material will be displayed in the material list. And vice versa, if a material is selected
in the material list, the respective blocks will be marked (Fig. 9.1).




                                                                                                Tabs in the
                                                                                             Radiation window


                                                                                                Material list




       Fig. 9.1



9.2 External boundaries
Use the tab to specify external boundary conditions. The boundaries, for which conditions are
not set, are marked by “?”. If boundary condition is not assigned for an external boundary, the




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CGSim solver generates an error message. Click at a boundary or boundaries and select a
boundary condition from the condition list (Fig. 9.2).
There are several condition types:
       T=const
       Convective
       Radiative
       Generalized
       Adiabatic with transmission




                                                                                          Boundary
                                                                                          condition
                                                                                             list




       Fig. 9.2
The details of each type of boundary condition are described in Appendix 2. Theory , A2.4
External Boundary Conditions.


9.3 Surface Emissivity
The tab is used if it is necessary to set a boundary emissivity differing from a corresponding
block material emissivity. By default, a solid block emissivity is used (Fig. 9.3).




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       Fig. 9.3




9.4 Splitting
For the radiative heat modeling, 1D grids should be created along all transparent block
boundaries. It can be done with the Splitting tab (Fig. 9.4) following instructions below:
       Select a boundary or boundaries with the left mouse button;
       Set a number of intervals; (select it from the offered numbers by clicking an appropriate
       button or set a number with the keyboard);
       Click Apply.




                                                                                       Select entities
                                                                                          without
                                                                                          splitting

                                                                                         Show entities
                                                                                        without splitting




   Fig. 9.4


There are three buttons, which can be useful for splitting:


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       Select entities without splitting    . This option selects the faces without splitting in the
       current block.

       Show entities without intervals        . If the user presses this button, the faces without
       splitting are marked in the current block.

       Apply to all objects remaining                                . Press this button to apply the
       splitting step to all objects, which have not yet splitted.



9.5 Internal boundaries
This tab allows working with inner entities: cuvettes and boundaries inside a transparent area.


9.5.1 Cuvettes
All transparent blocks form cuvettes consisting of adjoining gas blocks. The user can give name
to a cuvette by using the Name button (Fig. 9.5).




                                                                                            The Name
                                                                                            button




       Fig. 9.5




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9.5.2 Boundary
In this context, a boundary is a line inside a cuvette, which can be treated as a shield or a
delimiter (Fig. 9.6). An alone thin unit, such as a heat shield in the CZ growth, can be drawn as
a line and specified as a shield with an emissivity Emissivity and number of thin screens N
(Fig. 9.6). A delimiter is a line dividing a cuvette, which can be adiabatic or absolute black.




         Fig. 9.6




10 Solid Window
This window provides tools for Solid problem statement. There are following tabs in the window
right:
         Details
         Grid
         External boundaries
         With gas
         Heat sources
         Anisotropy
         Internal boundaries


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10.1. Details
The user can check matching of solid blocks and solid materials. If one clicks on a block, the
respective material will be displayed in the material list. And vice versa, if a material is selected
in the material list, the respective blocks will be marked (Fig. 10.1).




       Fig. 10.1



10.2. Grid
Use this tab for solid block grid creation. This tab is similar to the respective tab in the Grid
window (see Sec.7 Grid Window, 7.2 Grid).



10.3. External boundaries
Several boundaries types for external boundaries of solid blocks are available:
       Adiabatic



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       T=const
       q=const
       Convective
       Radiative
       Generalized
The details of each type of boundary condition are described in Appendix 2. Theory , A2.4
External Boundary Conditions.



10.4. With gas
One of three condition types can be chosen for a boundary between solid and gas blocks:
       Ideal
       T=constant
       Convective



10.5. Heat source
The Heat source tab is used to prescribe heater powers (Fig. 10.2). Power assignment can be
done by two ways:
       Specification of Volumetric heat source (W/cm3);
       Specification of Total heat source (W).
If heater(s) are marked as Leading heater, its power(s) in computations is(are) varied to provide
the required crystallization rate (see Sec. 11 CZ (LEC) Window, 11.5 Growth).




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       Fig. 10.2



10.6. Anisotropy
This tab is used for specification of material anisotropy in a solid block. The material set for this
block in the Problem window is called basic material, and its properties are used along principal
direction. An alternative material can be selected from materials defined in the Materials menu.
CGSim computation requires refined grids in blocks with anisotropic characteristics.
The user can specify anisotropic material properties in two ways:
       XY model (Fig. 10.3a) The X-axis is the principal direction, and characteristics of the
       basic material specified for this block in the Problem window will be used along it;
       alternative material properties will be accounted along the Y-axis. It is possible to rotate
       the anisotropy axes using Angle of axis inclination, which is degree measure of the
       angle between the X-axis and a new basic axis. This method can be applied for a solid
       block with quadrangular and triangular grid.
       BFC model (Fig. 10.3b) Directions are chosen to be along the block boundary. The bold
       arrow marks the principal direction. This approach is applicable only for a solid block
       with quadrangular grid.




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       Fig. 10.3a                                  Fig. 10.3b



10.7. Internal boundaries
This tab works with boundaries which are the solid-solid interfaces. The following types can be
chosen (Fig. 10.4):
       Ideal
       Adiabatic
       Contact resistance
       T=const
       Nonideal contact
       Heat source
The details of each type of boundary condition are described in Appendix 2. Theory , A2.5
Internal Boundary Conditions.




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       Fig. 10.4



11 CZ (LEC) Window
In this window only melt, crystal and encapsulant blocks are active. To specify a block as melt,
crystal and encapsulant, set an adequate class for the material in the Material menu. It is
necessary to define a density (RHO), a latent heat (LHEAT), and the melting temperature
(TMELT) for the melt, and the crystal density (RHO).
The CZ (LEC) window contains the following tabs:
       Details
       Grid
       Properties
       Interface
       Growth
       Encapsulant



11.1. Details
The tab checks matching of the blocks and the materials for the melt, crystal and encapsulant
blocks. If one selects a material, the blocks of this material will be shown. On the contrary, if one
selects a block, the block material will be marked (Fig. 11.1).




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         Fig. 11.1



11.2. Grid
This tab is used for the grid generation in the melt and the crystal blocks. The grid creation
process is the same as in the Grid window (see Sec. 7 Grid Window, 7.2 Grid). If an interface
task will be included in the computation, the grid should fit the following requirements (Fig.
11.2):
         The melt should have a block with quadrangular grid, which contains the melt-crystal
         interface;
         The crystal should have a block with quadrangular grid, which contains the melt-crystal
         interface;
         The melt-crystal interface should be a single continuous line;
         The numbers of the nodes on the melt-crystal interface should the same in the melt and
         in the crystal blocks;
         The numbers of the nodes on the melt-crystal interface should be larger than 15.
The blocks with quadrangular grid will be reconstructed during interface shape computations.




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11.3. Properties
The user can see the information about the melt and the crystal:
       the melt and crystal densities (kg/m3)
       the melting temperature (K)
       the latent heat (J/kg)
       the crystal weight (kg)
       the melt weight (kg)
       the charge weight (kg)




                Blocks with
                quadrangular grid




                      Fig. 11.2



11.4. Interface
This tab formulates the melt-crystal interface correction problem (Fig. 11.3). The user can
change following parameters of the interface correction problem:
       Relaxation coefficient
       Max number of iterations



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        Residuals (if the current residual of the interface correction problem is less than the
        Residual the computation of the interface will stop)
        Find interface shape (use this button for the interface shape computation).


Note:    The interface correction task can be computed only with the heater power fitting (see
         Sec. 11 CZ (LEC) Window, 11.5 Growth).


Note:    To compute the interface shape, the specific grid should be created (see Sec. 11 CZ
         (LEC) Window, 11.2 Grid).



11.5. Growth
This tab sets the task of leading heater power correction to obtain the required crystallization
rate (Fig. 11.4). The user can set a required crystallization rate and choose its units (mm/h or
mm/min). Also, there are computational parameters for the heater power fitting:
        Maximum number of iterations;
        Residual (if the current residual of the Find power problem is less than the Residual, the
        fitting of the power will stop).
To include this task in the computation, set Find power.




                    Fig. 11.3                                        Fig. 11.4




12 Crystal Position Window
This window allows easy creation of several geometers with various crystal positions. The user
should create a geometry (main geometry) for a highest crystal position in the Geometry window
(see Sec. 5 Geometry Window), which will be automatically reconstructed for smaller crystal


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positions by changing crystal, the melt, the crystal holder, and pedestal blocks. The geometry
should contain a crystal holder and a pedestal, which have simple rectangular blocks with
quadrangular grids (Fig. 12.1). These blocks will be resized, which allows geometry
reconstruction.
      It is efficient to create grids in all solid blocks and make boundary splitting (see Sec. 7
Grid Window) before using the Crystal Position window. In this case, the grids will be inherited
by new geometries.
      A created geometry with a new crystal height will be accessible in all windows except the
Crystal Position window. New geometries are independent of each other, but they automatically
inherit main geometry changes, except crystallization zones. So, it is possible to vary facility
geometry (shields, heaters, etc.) for all crystal positions by changing the main geometry. If it is
necessary, the user can mark an object as a main geometry object and it will not be translated
into other geometries: select an object in the Geometry window, click by right mouse button and

choose                     in the pop-up menu. To unmark an object, use the
option in the same pop-up menu.




                                crystal holder




                                                                      the simple rectangular
                                                                          block with the
                                                                        quadrangular grid
                                   pedestal



                   Fig. 12.1


The code permits independent heat source specification for the main geometry and geometries
with new Crystal Positions (CPs). If heat sources have been yet assigned and the user
continues his work with the project, the following algorithm is used for heat source inheritance:


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       If a new block with a heat source is created in the main geometry, its heat source is
       copied into all CPs. The respective message appears.
       If an existing block with a heat source is modified (for example, inner lines are specified)
       in the main geometry, its heat source is copied into all CPs. The respective message
       appears.
       If the volume of an existing block is changed, the specified Volumetric heat source
       remains unchangeable and Total heat source is calculated and vice versa (Fig.12.1a).




                                                                                       The
                                                                                       calculated
                                                                                       heat source




                                     The
                                     specified
                                     heat source

Fig. 12.1a



The Crystal position window has the following tabs:
       Properties
       Pedestal
       Holder
       Specification
       Crystal position




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12.1 Properties
The user can see the following information about the melt and the crystal:
       the melt and crystal densities (kg/m3)
       the melting temperature (K)
       the latent heat (J/kg)
       the crystal weight (kg)
       the melt weight (kg)
       the charge weight (kg)



12.2 Pedestal
Using this tab, one can specify a pedestal consisting of solid blocks which adjoin the melt
(Figs. 12.2):

       click on                              ; the all solid blocks connected through other with the
       melt will be selected (Fig. 12.2a);

       click on                          and unselect unnecessary blocks (Fig. 12.2 b);

       click on                               and select a block in the pedestal, which will be
       changed in height to move the crucible (Fig. 12.2c); this block should be a simple
       rectangular block with a quadrangular grid.
      Besides, the user can specify a law of pedestal motion:
       fixed pedestal position (the parameter defined below is equal to zero);
       fixed melt free surface (the parameter equals unity);
       user defined melt free surface (the user can specify the parameter in the range 0 ÷ 1);
       simple (a constant melt depth and fixed melt free surface).




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           Fig. 12.2a                       Fig. 12.2b                       Fig. 12.2c




12.3 Holder
The Holder tab is used to specify a crystal holder consisting of several blocks connected with
the crystal:

        click on                           ; all solid blocks connected through other with the
        crystal will be selected;

        click on                          and unselect unnecessary blocks;

        click on                          and select a block in the holder, which will be changed
        to move the holder; this block should be a simple rectangular block with a quadrangular
        grid and should not adjoin the crystal.




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12.4 Specification
It is necessary to specify the melt and crystal zones, which will be changed accounting for the
conservation of mass. The Specification guide provides this by clicking on the required lines and

pressing               button. Use the instructions below for specification:
       Crystallization front (Fig. 12.3a);
       Crystal surface (Fig. 12.3b);
       Crystal/seed;
       Crucible internal surface (Fig. 12.3c);
       Melt/encapsulant (Fig. 12.3d);
       Encapsulant/ gas (Fig. 12.3e);
       Encapsulant/seed (outer surface of the seed, which will be contacted with encapsulant
       at a small crystal height) (Fig. 12.3f).

The user can return to previous position of the Specification guide using              button. If
any changes have been made in the geometry, Specification should be restarted.




                  Fig. 12.3a                                           Fig. 12.3b




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                  Fig. 12.3c                                            Fig. 12.3d




                  Fig. 12.3e                                            Fig. 12.3f




12.5 Crystal position
If the user has passed through Specification, CGSim is ready to automatically generate a
geometry with a lower crystal height (Fig. 12.4). To change a crystal position (CP), the user can
choose one of the following ways:

       set the crystal length (in mm) in the Crystal position window and press

       use        and           for increasing and decreasing of a crystal height
The   current   position       will   be   displayed   in   the   special   window,   for   example

                           .




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                                                                             the Crystal position
                                                                                   window




              Fig. 12.4



Add current CP                                . After selection a certain position, the user can
save the current geometry using this button. The saved geometry becomes active in all
windows, except the Crystal Position window (Fig. 12.5). Before start of computations for a
saved geometry, it is necessary to create grid and 1D radiation grid (Splitting) in reconstructed
blocks.




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   Saved geometries
       with new
    crystal positions




                        Fig. 12.5

Maintence CP list                                . This option allows the user to change CP
names, to copy CPs or delete them (Fig. 12.6).




               Fig. 12.6

Note:   CP list can be opened in the Tools menu.




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13 Solver
Three computational modes are available in the program: (i) direct heat transfer computations,
(ii) heater power adjustment, and (iii) crystallization front geometry computation. Note that gas
convection can be accounted or not in all described above cases. Below, the respective
algorithms built-in in the code are described in detail.
      Direct heat transfer computations. In this mode, heat transfer in the system is computed
with the heater powers and the crystallization front shape assigned by the user in GUI.
Boundary condition of the first order is specified at the interface suggesting that the interface
temperature is equal to the melting temperature. Local growth rate may deviate significantly
(even signs of the rates can be different).
      The computations are realized as global iteration process. During the each iteration, a
problem of radiative heat transport is solved, the code calculates the materials properties
dependent on temperature, constructs a matrix of linear set of equations, and solves it with the
bi-conjugate gradients method. Generally depending on the problem complexity, from few tens
to few thousands iterations are necessary for convergence. The iterative procedure is finished if
a prescribed residual or a maximum number of iterations assigned by the user is achieved.
      Heater power adjustment. In this mode, heat transfer in the system is computed with the
growth rate and the crystallization front shape assigned by the user in GUI. Boundary condition
of the second order is specified at the interface suggesting that the heat flux through the
interface is governed by the growth rate, crystal properties, and the local interface slope.
      Powers of heaters marked in GUI as “leading heaters” are varied until the temperature of
the triple point crystal-melt-gas becomes equal to the melting temperature. The algorithm of
heat power adjustment is following:
       First, the computation is performed at fixed heater power. If the temperature residual
       becomes        less      than    the     Relative Residual      criterion   (specified    in
       Heater Power/Relative Residual of the Settings tab of GUI) multiplied by the initial value
       of the residual, the heater power is changed on the assumption of linear relationship of
       the crystallization rate in the triple point and the heater power.
       At the moment of the heater power change, the temperature residual rises greatly. Then
       the computation is performed at new heater power. If the residual becomes less than the
       Relative Residual criteria multiplied by the maximum residual obtained during the
       previous heater power correction, new heater power correction occurs.




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        Global iterations are finished if both the convergence occurs and the triple point
        temperature reaches the melting temperature within Relative Accuracy (specified in
        Heater Power/Relative Accuracy of the Settings tub of GUI).
    Crystallization front geometry computation. In this mode, the heater power adjustment
algorithm is the same as in the previous section described. The crystallization front geometry is
found to minimize variations of the local crystallization rate.
      If the crystallization rate in the triple point becomes close to the required value within
Max Accuracy (specified in Interface Correction/Max Accuracy of the Setting tub of GUI) due to
the power adjustment, the crystallization front shape is varied so that the Stefan condition is met
at each point of the interface (see Eq. A2.2 in Appendix 2, Theory description). The iterative
procedure is finished if the temperature residuals and the founded powers and local
crystallization   rates   are   within   the   required   accuracy   (Stop Criteria/Relative Residual,
Interface Correction/Relative Accuracy, and Heater Power/Relative Accuracy in the Setting tub
of GUI, respectively).




        Fig. 13.1a




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Start of computations

     To start computations, click on Run in RUN menu or use Ctr+F9. The Solver window will
be started for the active geometry (crystal position) (Figs. 13.1a). The Solver window has the
Run tab showing the created tasks. The red marked problems will be ignored because the
solver cannot formulate task for them (Fig. 13.1a). Press the Run Solver Manager button to run
the Solver Manger.




       Fig. 13.1b


    The Solver Manager window has several tabs, which allows the user to control all
computation steps (Fig. 13.1b). To run the solver, press the Start button; to stop the solver,
press Save&Stop or Stop.




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Setting tab
   The user can specify the solver parameters in the Settings tab of Solver Manger (Fig.
13.1b).
          General:
                Problem. This tab indicates what problems will be solved.
                It can be
                       conductivity Heat transport,
                       Radiation heat exchange,
                       gas Flow computations,
                       Turbulence of gas flow,
                       Interface Correction,
                       Heater Power;
                Interface Correction Parameters. For most problems, the parameters by default
                 are appropriate; we recommend to change the parameters only if the interface
                 correction does not converge.
                       Max Local Curvature. This parameter limited the melt/crystal interface
                            curvature. If the local curvature is larger than the parameter, the front
                            shape will be smoothed. The parameter value of 1 corresponds to a
                            maximum angle between adjoining faces of          90°. The zero value is for
                            zero curvature, i.e. straight.
                       Max Accuracy. The parameter is a maximum difference of the
                            crystallization rate in the triple point and the required rate. The
                            crystallization front correction procedure is activated if the difference of
                            the crystallization rate in the triple point and the required rate is within
                            the parameter value.
                       Relative Accuracy. The parameter defines the accuracy for the difference
                            between the local crystallization rates and the required crystallization
                            rate. The melt/crystal interface correction is finished if the maximum
                            relative difference of the local crystallization rate and the required rate is
                            within the accuracy.




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              Heat Power. For most problems, the parameters by default are appropriate. We
                recommend to change the parameters only if the heater power correction does
                not converge.
                       Relative Residual: The parameter defines the relative temperature
                        residual drop after the previous power correction, at which next heater
                        power correction occurs.
                       Relative Accuracy: The parameter defines the relative difference between
                        the crystallization rate in the triple point and the required rate. The
                        heater power adjustment is finished if the relative difference between
                        the required and local crystallization rate in the triple pint is within the
                        accuracy.
      Stop Criteria:
              Number is the number of global iterations;
              Relative Residual: If the residual ratio of the current iteration and the first iteration
                is less than the Relative Residual the computation will stop;
              Absolute Residual: If the residuals for all variables is less than Absolute
                Residual, the computation will stop ;
      Initial Conditions:
              Restart type: New Simulation, Restart, or Continue;
              Initial values of variables;
      Output:
              Output type: Specified Interval or End of Simulation;
      Convergence parameters:
              Inertia for considered values;
              Relax for considered values;
      Additional parameters:
              Linear Solver
                       NumSweeps is the maximal number of linear solver sweeps;
                       Relative Residual. If the residual ratio of the current iteration and the first
                        iteration is less than the Relative Residual the linear solver will stop;
                       Absolute Residual. If the residuals is less than Absolute Residual, the
                        linear solver will stop;
              Limits are limits for considered values.




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Output tab
   This tab shows the solver output, containing solver information and variable residual values
(Fig. 13.2a).




       Fig. 13.2a


Residual plotter tab
       This tab graphically shows variable residuals (Fig. 13.2b). It is possible to turn off/on a
residual graphic by clicking a variable name in the right part of the tab.




       Fig. 13.2b


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2D tab
This tab presents 2D distributions of the computed variables (Fig. 13.2c):
         Coordinates X, Y, Z (mm);
         Velocity components Vx, Vy (m/s);
         Density (kg/m3);
         Heat capacity cp (J/(kgּK));
         Conductivity (W/m/K);
         Heat source TSu (J/s);
         Temperature Residual Res_T .
         To regenerate the picture in the 2D window, press the Update button in the upper part of
the window.
         It is possible to visualize the computational mesh (select the Mesh option) and the
variable legend (select the Legend option).




         Fig. 13.2c



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Interface tab
       This tab shows profile of the crystallization front (the red line Y) and distribution of the
crystallization rate (the blue line Vgr) along the front (Fig. 13.2d). It is possible to turn off/on a
graphic by clicking a variable name in the right part of the tab.




       Fig. 13.2d




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Appendix 1. System Requirements
The system requirements for installation and use of the CGSim 6.0 software are listed below.


Minimum configuration
       Intel Pentium III
       128 MB RAM
       16 MB Video card
       1024*768 resolution
       Microsoft® Windows® 2000 Professional , Windows XP® Professional




Recommended configuration
       Intel Pentium IV 2000MHz
       1024 MB RAM
       64 MB Video card
       1280*960 resolution
       Microsoft® Windows® 2000 Professional , Windows XP® Professional




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Appendix 2. Theory description
This section provides the user with a brief description of the governing equations employed by
Crystal Growth Simulator (CGSim). The code permits a self-consistent solution of
axisymmetric heat transfer problem accounting for the heat transfer via conduction and heat
exchange between solid surfaces by radiation. Gas flow effect can be considered with CGSim
also. Due to relatively low crystallization rates used in industrial CZ growth systems, the quasi
steady state approximation is applied to compute the long term crystal growth. The heater
power is adjusted in the calculations to provide a required pulling rate. The melt/crystal interface
geometry is also found by the code. Besides, the module Defects built in the code allows
simulation of elastic stresses produced in the crystal. For silicon crystals grown by the
Czochralski technique, the software predicts behavior of point defects and clusters [1].



A2.1. Materials classes
Assignment of block properties in CGSim involves prescription of a material class. There is an
unambiguously relation between the problem solved in the block and the class of material
selected for the block. There are 7 classes of materials distinguished by the CGSim program:
Vacuum, Gas, Solid, Melt, Crystal, Encapsulant, and None. Depending on the selected
material class, the code generates a set of problems executed further by the CGSim solver in
the block:
       Vacuum: heat conduction is ignored, heat exchange between solid surfaces is
       simulated; the material is considered as a completely transparent medium;
       Gas: heat conduction, radiation heat exchange between solid surfaces and gas
       convection are simulated; the material is considered as a completely transparent
       medium;
       Solid: anisotropic or isotropic heat conduction is modeled; the material is suggested to
       be opaque;
       Melt: isotropic heat conduction is considered; the material is suggested to be opaque;
       Crystal: isotropic heat conduction is simulated; the material is suggested to be opaque;
       Encapsulant: isotropic heat conduction is modeled; the material is suggested to be
       opaque;




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       None: assignment of the block material to this class results in exclusion of the block
       from the computational domain. No physical processes are simulated in such a block.
      Some specific features of heat transfer problem governed by a specified class are
discussed below.
      If a block is prescribed as Melt, its volume is recalculated by the code automatically,
assuming the side boundary of the cylindrical crystal part to be vertical and according to crystal
positions assigned by the user. The code corrects automatically position of an Encapsulant
block following the geometry of the block specified as Melt (the Encapsulant bottom adjoins the
Melt top).
      The user can prescribe a volumetric heat source Q (W/m3) or a total heat source Qt (W) in
Solid medium.



A2.2. Basic Equations
Generally, the heat transfer is described by the following equation:
                                    − ∇ ⋅ (λik ∇T ) = Q .                                       (A2.1)

Where T is the temperature, λik is the thermal conductivity tensor.
      Radiative heat exchange between any solid surfaces through a non-participating medium
is computed in terms of gray-diffusive surface radiation. The total radiative flux incoming to a
given surface element is calculated using the configuration factors Fij (the view factors). The
calculation of view factors in a complex geometry via integration over emitting area accounting
for the shadowing effect is described in details in [2]. Then the total radiative flux incoming to
the elementary surface element i (i = 1, N e , where Ne is the total number of elementary surfaces

on the boundary) can be calculated as qiin =   ∑q   out
                                                    j     Fij , where qiin is the radiation flux incident to

the i-th surface element, qiout = qiem + (1 − ε i )qiin is the radiation flux outgoing from the i-th

surface element, qiem = ε iσT 4 is the heat emission from the i-th surface element, ε i is the

emissivity of the i-th surface element, σ is the Stephan-Boltzman constant.
      Gas convection is considered within Naver-Stocks equations written for subsonic gas flow
in an axisymmetrcal case. An algebraic model is applied for turbulent gas flow.
      For numerical implementation of the formulated model, a finite-volume numerical
algorithm has been developed to be used on unstructured grids. An implicit scheme for the
energy equations was employed. A large non-linear set of equations is obtained as a result of


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the discretization. A steady-state solution is established as a limit of a relaxation process. The
solution of the linearized set of equations at each iteration during the relaxation process is
obtained by biconjugated gradient method.




A2.3. Specification of materials properties
The user should prescribe properties of all materials involved in the computations. Generally the
properties are the temperature dependent functions which can be specified in CGSim code in
different ways:
        const

Materials properties are suggested to be temperature independent.
        polynomial

Materials properties are computed by the code using the polynomial function, which coefficients
are prescribed by the user.
        piecewise linear

Materials properties are computed by the code using the A and B parameters prescribed by the
user.
        A + B/T

Materials properties are computed by the code using the A and B parameters prescribed by the
user.
        function.

In the latter case, a user-defined function is used by the code to compute the respective
materials properties.



A2.4. External Boundary Conditions
Boundary conditions specified at external boundaries (walls) of the computational domain
depend on the problem specified for the block. There are 3 classes of material for which
external boundaries can be prescribed in CGSim: Solid, Gas, and Vacuum.

Boundary conditions on an external boundary of a Solid block can be prescribed as
        Adiabatic


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Setting of this condition corresponds to zero heat flux through the boundary (adiabatic
boundary).
        T = const
The T = const type is intended for specification of an external wall with a fixed temperature
distribution. The user can specify a thin wall in vicinity of the boundary (a computational grid is
not required for this wall). In this case, a wall thickness Delta (m), a wall thermal conductivity
Conductivity (W⋅m-1⋅K-1), and an external temperature of the wall Ta (K) should be also
prescribed. The code will solve heat transfer inside the wall automatically. If the wall thickness is
equal to zero, heat transfer problem is not computed. Besides, the user can prescribe Ta as a
variable parameter using a function specified a priori.
        q = const
On a boundary of this type, the outward heat flux (W/m2) at the wall should be prescribed.
Setting a positive heat flux corresponds to heat supply from the outside. Setting a negative heat
flux corresponds to heat release from the system to the outside. Besides, the user can prescribe
heat flux as a variable parameter using a function specified a priori.
        Convective
This type of boundary condition is aimed for modeling of heat exchange between a boundary
and ambient. The heat transfer is characterized by the ambient temperature Ta (K) and the heat
transfer coefficient a (W⋅m-2⋅K-1). Besides, the user can specify a thin wall in vicinity of the
boundary (a computational grid is not required for this wall). Specification of parameters
required for thin wall modeling is the same as for a T = const boundary (see above).
        Radiative
The Radiative type is intended to account for external heat transfer via radiation. The heat flux
at the wall is calculated as q w = σε w (Tr4 − Tw ) , where Tr (K) is the ambient temperature, Tw (K)
                                                 4



is the wall temperature, σ is the Stefan-Boltzmann constant, and ε w is the wall emissivity. The

user has to specify an ambient temperature and an emissivity. Besides, the user can specify a
thin wall in vicinity of the boundary (a computational grid is not required for this wall).
Specification of parameters required for thin wall modeling is the same as for a T = const
boundary (see above).
        Generalized
The Generalized type is intended to account for external heat transfer via convection and
                                                                               4
radiation. The heat flux at the wall is calculated as q w = q s + σε w (Tr4 − Tw ) + a ⋅ (Ta − Tw ) , where Tr




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(K) is the radiative ambient temperature, Tw (K) is the wall temperature, σ is the Stefan-

Boltzmann constant, and ε w is the wall emissivity, Ta (K) is the ambient temperature, a is the

heat transfer coefficient (W/m2⋅K), and q s is the heat flux unchanging fraction (W/m2). Besides,

the user can specify a thin wall in vicinity of the boundary (a computational grid is not required
for this wall). Specification of parameters required for thin wall modeling is the same as for a
T = const boundary (see above).

     There are 5 types of boundary conditions which can be applied for an external boundary of
a Gas or Vacuum block. Specification of parameters required for T = const, Convective,
Radiative, Generalized boundaries is the same as for respective boundaries assigned for a
Solid block (see above).
         Adiabatic
The Adiabatic type is intended to simulate a wall which is transparent for radiation but is
adiabatic for the heat conduction. The user has to preset an emissivity ε w and a boundary

transmittance f.



A2.5. Internal Boundary Conditions
Normally, conditions of heat flux and temperature continuity are used in the code by default at
the internal boundaries with an exception at the melt–crystal interface, where the temperature is
taken to be equal to the crystal melting temperature prescribed by the user. The crystallization
rate is related to heat fluxes in the crystal and in the melt by the following expression known as
Stefan condition:

                                       ∂T        ∂T 
                       ρ cryst ∆Hu n =  λ  − λ       ,                                  (A2.2)
                                       ∂n  melt  ∂n  cryst
where u n is the local crystallization rate normal to the melt-crystal interface, ∆H (J/kg) is the

crystallization heat, ρ cryst (kg/m3) is the crystal density, λcryst (W⋅m-1⋅K-1) is the melt thermal

conductivity. The averaged crystallization rate ν is calculated by integrating the vertical
component uν of the local crystallization rate u n along the melt-crystal interface with the area S

         1
         S∫
as ν =       uν dS .
           s




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        Besides, the user can redefine the internal boundary picking out one from the following
list:
         Ideal
This condition means the equality of the heat fluxes. The ideal type is on default.
         Adiabatic
One can set the adiabatic boundary condition.
         Contact resistance
This type is used to simulate a heat source qv (W/m3) at a solid-solid boundary, which has a
thickness Delta (m) and a thermal conductivity Conductivity (W⋅m-1⋅K-1).
         T = const
To set a constant temperature at a boundary, apply the T = const type.
         Nonideal contact
This type of boundary condition is used for modeling of a gap between two solid blocks, for
example between two rough surfaces. The gap thickness is Delta (m) and the thermal
conductivity of the gas filling the gap Conductivity (W⋅m-1⋅K-1) should be specified. If the
emissivity of the gap surface differs from the block material emissivity, the user can assign the
surface emissivities ε1 and ε2 which are used by the code for effective emisssivity
ε eff = ε 1ε 2 /(ε 1 + ε 2 − ε 1ε 2 ) calculation (-1 means that the surface emissivity is equal to the block

emissivity). The parameter S indicates a serried portion.
         Heat source
The user can specify heat release at the boundary. If the boundary is marked as Leading
heater, the heat source will be adjusted.



A2.6. Conditions at Gas Block Boundaries

Boundary conditions on a boundary of a Gas block can be prescribed as
         Wall
This type of boundary condition is used for modeling of solid wall with zero velocity.
         Inlet
To set inlet boundary, specify inlet gas velocity components U and V (m/s).
         Outlet
One can set the outlet boundary condition.




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        Rotation
This type of boundary condition is used for modeling of wall rotation. Specify angular velocity of
wall in rad/s, rps, or rpm.
        Symmetry
This type of boundary condition is applicable only for vertical or horizontal external gas
boundaries.




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Appendix 3. Tools for Moving and Zooming a Picture
The user interface provides several options for moving and zooming the picture you see on the
screen.
Moving options include the following:
       The right mouse button (note that there is a small delay of 0.2 sec between pressing this
       mouse button and the start of moving) or the left mouse button;
       Keep the Shift key on your keyboard and move the mouse;
       The arrow keys on your keyboard;

       The red arrows        that are available in any window of the program and located on the
       bottom panel;

       Pressing the View button                (located on the top panel) or the F9 key (doing the
       same) opens a smaller window with a general view of the picture. In this window, the
       user may indicate (using the left mouse button) the part of the picture to be shown in
       details in the main window (this part has a lighter color in the small window).


Zooming options include the following:
       The middle mouse button or the mouse roll;
       The “plus” and “minus” keys are on your keyboard. Note that they zoom in or zoom out
       the picture with reference to the cursor position on the screen. These keys also operate
       in the “F9” mode (see item (5) in the previous paragraph), allowing the user to select a
       smaller or a larger fragment of the picture for a detailed view;

       The Zoom in and Zoom out buttons               on the bottom panel of each window;

       The Show all button       on the bottom panel of each window;

       The Show the whole page button          on the bottom panel of each window (the page can
       be specified in the Options menu (see Sec. 4 Main Menu, 4.5 Options);

       There are the special zoom options in the processing block: Block           and Initial state

            , which are available in the Blocks, Grid, Gas, Radiation, Solid, CZ(LEC) windows.
       An example is given in Fig. A3.1: select the desired block from the block list, click the
       Block button, and you will see this block occupying the whole screen. The Initial state
       button returns the working area in the initial state.


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                          Semiconductor Technology Research, Inc.




       –––

                                                         The Block       The Initial state
                                                         button          button
              Fig. A3.1




References
 [1] CGSim, Crystal Growth Simulator, Module “Defects”, Version 2.1, STR Inc. (2004).
 [2] F. Dupret, P. Nicodeme, Y. Ryckamans, P. Wouters, M.J. Crochet, Int. J. Heat Mass
    Transfer 33 (1990) 1849.




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