Crystal and deposit shape evolution
VR-PVT SiC predicts the crystal shape and the
powder source evolution in SiC sublimation growth by
simulating the global heat transfer in the growth system coupled with
species diffusion and convective flow in both the growth chamber and the powder charge.
Below, we’ll have a closer look at the respective modules
incorporated in the Virtual Reactor software tool.
Crystal and deposit shape evolution animated
Part 1: Heat Transfer Modeling
Modeling of the global heat transfer problem in a system for SiC crystal
- Inductive heating. The computation of the Joule heat sources
due to inductive heating is carried out by solving the Maxwell equations.
- Conductive heat transfer in solid materials and gas domains.
The thermal conductivity of the materials used in the growth system can
be prescribed by the user as a function of temperature. Anisotropic
thermal conductivity can be assigned.
- Heat transfer in the SiC powder. Effective heat conductivity
is calculated from the powder characteristics (local porosity and
- Convective and radiative heat transfer in transparent gas
blocks. The view-factor technique is used to model the radiation heat
exchange. All solid blocks are assumed to be opaque for the radiation.
A typical temperature distribution in the growth system.
the density of gliding dislocations in the crystal calculated on the
assumption of a full stress relaxation due to plastic deformation.
Visualization of the obtained results.
The software supply will include a Database of Material Properties,
User Manual, Context Help, and Sample files.
Part 2: Mass Transport Modeling
Modeling of the mass transport in the clearance between the powder
and the seed includes
- Multi-component diffusion of reactive species
(Si, Si2C and SiC2) in the presence of carrier gas.
- Convective flow.
Prediction of the total vapor pressure inside the tightly closed
or semi-closed growth chamber.
The following boundary conditions for the mass transport problem
to be solved in the gas cell are available:
- Chemically reactive surfaces of the seed, growing
crystal and the crucible. A quasi-thermodynamic model is used
to describe the mass exchange between the vapor and solid surface.
- Chemically reactive porous crucible walls allowing
for mass leakage from the growth chamber.
- Thin slits at the contacts of the crucible elements
allowing for mass leakage from the growth chamber.
- Inlets and Outlets.
Crystal evolution during the growth within the quasi-stationary
approximation described above.
Prediction of parasitic poly-SiC deposition on the crucible
walls, including deposit evolution during the whole process along
with the crystal growth and its effect on the growth enlargement.
Modeling of mass transport in the SiC powder charge. The model
includes a set of mass transport equations accounting for
heterogeneous chemical reactions at the surface of SiC granules
and granule graphitization during the growth run. Initial powder
characteristics (porosity, mean granule size, and graphitization
degree) can be specified independently for several powder regions.
Powder evolution during the growth, which includes prediction
of the temporal variation of all powder characteristics (local
porosity, granule size, and graphitization degree).
Visualization of the obtained results.
The software supply will include a Database of Material
Properties, User Manual, Context Help, and files with examples
Figure 6 Flow pattern and distribution of the Powder
Porosity (left) and Graphitization Degree (right)
Part 3: Additional Modules that can be added to
the Basic Version of the VR-SiC code
Module for analysis of faceting of the growing crystal
Account of the crystal faceting can be added to the mass
transport module on the customer request.
Module for analysis of dislocations dynamics.
A module providing analysis of the propagation of threading
dislocations can be implemented
into the basic version of the Virtual reactor on the customer
request. It is used as a post-processing tool. A pre-computed
sequence of consecutive crystal shapes corresponding to all time
instants of the virtual growth process, at which the heat- and
mass transport problems were solved, are used to start the
dislocation analysis. This option provides 2D propagation of
dislocations originating from the seed in a selected vertical
crystal cross-section and the dislocation outcrop mapping in
a set of horizontal crystal cuts.
Distribution of threading dislocations in a SiC wafer cut from the boule shown at the left hand side.