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Modeling of Crystal Growth and Devices

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Features Added in Virtual Reactor 5.4

Brief summary. For more information see Release Notes 5.4.

Implementation of Full Navier-Stokes Flow Model

Two models of flow dynamics are implemented in Virtual Reactor 5.4, namely, full Navier-Stokes model and model of hyposonic flow. In the earlier versions of Virtual Reactor, the latter model was only available.

Extension of Output Information

Additional diagnostics about the species transport was added into the computation log file. The following quantities are reported:

  • Integral mass fluxes on boundaries of the growth chamber (in kg):
    • Total mass flux
    • Chemical fluxes for each species (on all catalytic boundaries)
    • Filtration fluxes for each species (on porous walls and thin slits)
    • Sum Fluxes for each species (sum of chemical and filtration fluxes)
  • Average growth rate for each boundary (on all catalytic boundaries). Positive value corresponds to growth/deposition, negative to sublimation/etching
  • Mass of all blocks at the current time step (in kg)

Changes in Solution Monitor

The following options were added to the solution monitor:

  • Runtime modification of the computational parameters
  • Specification of the Axis Ranges
  • Normalization of Residuals

Changes in Specification of the Porous Wall Parameters

The option of automatic calculation of wall thickness in specification of Porous Wall and Thin Slit boundary conditions is made user defined. In the earlier versions, the wall thickness on internal boundaries was always calculated automatically from the adjacent solid block geometry, which imposed some restrictions on specification of the adjacent blocks. Now the user can always set the wall thickness explicitly.

Fixing Errors

Several found errors have been fixed.


Features Added in Virtual Reactor 5.3

A new model of graphitization of evaporated polycrystalline source in PVT growth of SiC crystals has been implemented in the software package Virtual Reactor. For more information see History Notes 5.3.

Features Added in Virtual Reactor 5.2

Support of Gas-Gas Interfaces

Support of decomposition of complex gas domains into several gas blocks was implemented. This allows efficient meshing of gas domains that involve elongated rectangular zones, which can be meshed using quadrilateral mesh, as well as an irregular zone in the vicinity of the growing crystal which should be triangulated.

Acceleration of the Computation

Evaluation of the local gas mixture parameters was modified to reduce the generation of the linear set of equations and, as a result, the total computation time.

Modification of the Residual Plotter

  • Visualization of the residual variation during the computation run was optimized to eliminate the CPU time consumption by the residual drawing.
  • Continuous update of visual data during reading large log files was implemented.


Features Added in Virtual Reactor 5.1

Modeling SiC Growth by CVD

Release of VR-CVD SiC designed for modeling of SiC bulk crystal growth by Chemical Vapor Deposition.

Modeling Semi-Bulk GaN Crystals by HVPE

Implementation of full Virtual Reactor functional options, including long term growth modeling with crystal shape evolution, into HEpiGaNS (Hydride Epitaxial GaN Simulator) designed for modeling of GaN crystal growth by hydride vapor phase epitaxy.

Simplification of Assigning the Temperature Fitting Parameters

An option Default was added to settings of temperature fitting to simplify the use of temperature fitting. The exact values of the default parameters are assigned by the program depending on the other user-defined parameters.


Features Added in Virtual Reactor 5.0

Model of Glue Seed Mounting

To simulate the seed mounting, an advanced boundary condition to the elastic stress problem in the growing crystal accounting for the stress relaxation in an intermediate glue layer between the seed backside and graphite seed holder has been implemented.

The model assumes that the crystal is attached to the graphite seed holder through a glue layer. No displacement normal to the boundary is allowed, while the local radial displacement depends on the crucible displacement, glue layer thickness, glue parameters, heating time and current time instant. The following parameters should be specified by the user: thickness of the glue layer,.parameters of the glue relaxation time as a function of temperature, glue shear stress modulus, reference temperature and the duration of the heating process.

Quadrilateral Mesh and Automatic Mesh Generation

Meshing with either triangular or quadrilateral grid cells is available. Triangular mesh provides high flexibility allowing meshing of complex domains of an arbitrary shape and topology. Quadrilateral mesh can be only applied to convex blocks whose shape is topologically close to a rectangle. When quadrilateral mesh can be used, it provides higher accuracy and faster computation compared to triangular mesh.

Incorporation of Solid Source Evaporation

To predict the shape evolution of solid polycrystalline source, Solid Source block subtype was added. Interfaces of blocks of the following types of blocks can be moved in the virtual growth run: Crystal, Deposit and Solid Source.


User-defined specification of the material density was incorporated, which allows, in particular, assignment of different densities to the growing single crystal and evaporating polycrystalline source.

Relaxation of Static Pressure Variation

Relaxation of the variation of static pressure was incorporated, which improved stability of convergence of computation at low external pressure at high temperature, i.e. when the pressure drop between the growth chamber and external domains exceeds the external pressure value.

Acceleration of Each Iteration

Computational time consumed by both heat and mass transfer iterations is decreased.

New Variables in the Output

The C/Si ratio was added into the output in both 2D and 1D files. In VR_PVT SiC the C/Si ratio is defined as .

Fixing Errors

  • An error with treatment of the user-defined value of the emissivity on Ambient Heat Exchange boundary condition has been fixed. In Virtual Reactor 4.9, Emissivity = 1 was always used in the computation which resulted in a slight under-evaluation of temperature at a fixed power. Correct assignment of the default value Emissivity = 0.8 results in temperature increase of about 10 degrees.
  • Some errors in heat and mass transport computation and treatment of the crystallization front shifting have been fixed.
  • Some errors in operation of the graphical user interface have been fixed.


Features Added in Virtual Reactor 4.9.2

Fixing Errors

  • An error in Rescan operation. In Virtual Reactor 4.9.0 and 4.9.1, this error might result in an error message at saving the file after rescanning blocks after deleting some exterior domains so that some internal solid-gas interfaces turn external boundaries.
  • An error in the treatment of the inductor material change using the material specification by manual selection of the material name in the materials tree in the Block settings dialog for each inductor block.
  • An error in the initial visualization of the 2D distributions in Show Only One Zone From The List mode in Virtual Reactor 4.9.1, which resulted in simultaneous visualization of all zones in Powder Evolution, Growth Cell, Thermal Elastic Stress and RF (in case of multiple coil heating) regimes.


Features Added in Virtual Reactor 4.9.1

Fixing Errors

  • An error in the implementation of the Projection method in the computation of radiation heat transfer was fixed. The accuracy of the radiation heat transfer computation using Projection method was increased compared to older versions. In Virtual Reactor 4.9.1 use of the Projection method is recommended, since it works faster than the Ray Tracing method.
  • An error with assignment of the Poly-SiC material emissivity to the boundary where poly-SiC deposition is predicted is fixed.
  • An error with assignment of the Poly-SiC material emissivity to the boundary where poly-SiC deposition is predicted is fixed.
  • An error with assignment of temperature fitting parameters to new time steps automatically inserted in the virtual process was fixed.
  • An error in visualization of mixture viscosity at boundaries gas and powder blocks was fixed.
  • Several errors arising in the displacement of the crystal interface were fixed.
  • An error with automatic enabling of the Powder Evolution option after pressing the Cancel button was fixed.

Visualization of the Residual History

Visualization of old residuals files in the residual plotter was implemented. A file res-plotter.vrlog is written during the computation.

Visualization Module

Several improvements have been introduced into the Visualization module:

  • In the Streamlines section, Remove Last Streamline tool was added.
  • Several default visualization settings were modified.
  • Automatic selection of the first block in the list was eliminated.
  • An individual block in the Zones list single can now be selected or deselected by clicking the right mouse button. If one block (for example, the first one in the list) is selected, clicking on it with right mouse button clears selection of all blocks, which provides a unified boundary representation.


Features Added in Virtual Reactor 4.9.0

Acceleration of the Heat Computation in a Multi-Heater System

A new fitting algorithm has been implemented, which provides an efficient solution of the temperature fitting problem in a multi-heater system at much smaller number of iterations.

Implementation of a View-Factor Mechanism of Radiation Transfer

The View-Factor model is also available along with the Gebhart model. Usually, it consumes much less memory, which can be critical for growth systems with long perimeter of the gas blocks, in particular, in blocks with several long channels. So one can prescribe mesh in the channels that is enough fine for modeling the mass transport.

Visualization of the Streamlines

The built-in visualization tool was updated to provide adequate presentation of the flow pattern.

Acceleration of Each Iteration

Computational time consumed by both heat and mass transfer iterations is decreased.

Fixing Errors

  • An error was fixed with treatment of semitransparent gas boundaries with Ambient Heat Exchange boundary conditions.
  • Divergence of the heat and mass transfer An error with boundary cross-sections arisen at crystal etching was fixed.
  • Several errors in operation of the graphical user interface have been fixed.
  • The error diagnostics was made more detailed and clear.


New features in Virtual Reactor 4.8 with respect to Virtual Reactor 4.6

Fixing Errors

  • Errors found in the older release have been fixed. Robustness of the code operation was increased.
  • The computation procedure was optimized to reduce the computation time and memory usage. In particular, the computation of mass transport accounting for the crystal faceting was noticeably accelerated.

Error Diagnostics

  • The error diagnostics was made more detailed and clear.
  • Divergence of the heat and mass transfer solution is now identified at earlier stages, which is provided by analyzing the final residuals when the computation stops at reaching the maximum number of iterations.

New features in Virtual Reactor 4.6 with respect to Virtual Reactor 4.4

Assigning the Materials

A new interface of the specification of the materials properties has been implemented into Virtual Reactor 4.6.

In the previous version of Virtual Reactor, the materials database was only used as an external source of materials whose properties could be copied to the blocks, so that the actual values of the material properties used in the computations were those specified in the corresponding blocks.

In Virtual Reactor 4.6, the properties are always stored in the materials rather than in the blocks. Each block now has a reference to its material. So if the user changes the properties of a material in the database after he assigned this material to some blocks, he does not need to reassign the block properties.

Using references to materials provided an easy and pictorial assigning materials to the blocks. The user can select a material in the list of available materials and just click all the blocks to which the material should be assigned with left mouse button. The material is assigned to all needed blocks.

The blocks of the same materials are filled with the same color in the Graphics Window, which provides a clear identification of all blocks in the Graphics Window. A new block to which no material is still not assigned is not filled, which provides a clear identification of such blocks.

The Mass Loss Model

A new model predicting the total internal pressure and the mass loss has been implemented.

To describe semi-opened growth systems, two individual models are introduced: model of porous walls and model of thin slits on the contacts of adjacent crucible parts.

  • Model of the porous wall deals with microscopic pores assuming the mass transport to occur under free-molecular conditions. This model is designed to describe mass transport in a SiC system with crucible made of porous graphite.
  • Model of the thin slit deals with relatively large channels assuming the mass transport to occur under diffusion conditions. This model is designed to describe mass transport in a system with crucible made of dense materials.

So two different types of the mass transport boundary conditions are available:

  • Porous Wall. A boundary type that represents a solid surface permeable for the convective and diffusion mass transport through the pores. If the interface of the growth cell with the crucible is of Porous Wall type, the total pressure in the growth cell is calculated by the code.
  • Thin Slit. A boundary type that represents a small opening at a non-tight contact of adjacent solid parts of the crucible permeable for the convective and diffusion mass transport.

As a result, in the case of using the porous wall model, the average partial pressure of the carrier gas in the growth chamber is equal to the external pressure, while the pressure drop is caused by the reactive species partial pressures. In case of using the slit model, the partial pressure of the carrier gas in the growth chamber may vary from in a wide range.

Multi-Coil Heating

Module "Two-coil RF Heating" for modeling of heat transfer in a growth system heated by two inductor coils has been implemented into Virtual Reactor.

Virtual Reactor is supplemented by an option allowing the user to model the heat transfer in a growth system heated by several inductor coils with temperature monitoring made in several reference points. Normally, this should be used to model systems with two coils.

The user can prescribe two independent inductor coils, specifying the current frequency and generated power for each coil. Then the code computes the temperature distribution in the whole system. In addition, using two coils allows temperature fitting at two reference points. In this case, the code automatically adjusts the power generated by each inductor to meet the required temperatures.

Each coil may have an arbitrary number of turns (windings). An individual turn of any coil is represented by an Inductor block. All inductor blocks that have the same material are considered as blocks of the same coil. Blocks with different material are considered as blocks of different coils. The number of coils in the system is determined as the number of Inductor materials assigned at least to one Inductor block.

For each coil the user can either assign the total power generated in the coil or specify that the power should be varied to maintain temperature in the reference points. To provide the temperature fitting, the number of reference points should not exceed the number of independent heaters (coils or resistive heaters).


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