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Modeling of Crystal Growth and Devices

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Figure 1. 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.

Figure 2. Crystal and deposit shape evolution animated


Part 1: Heat Transfer Modeling

Modeling of the global heat transfer problem in a system for SiC crystal growth, including

  • 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 granule size).
  • 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.

Figure 3. A typical temperature distribution in the growth system.
Computation of the thermal stress distribution in the crystal, including 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.


Figure 4 Animated mass fluxes at the early stage of SiC growth (click to open)

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.

Figure 5 Animated mass fluxes at the late stage of SiC growth (click to open)

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 of computations.

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 and <0001> 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.

Figure 7. Distribution of threading dislocations in a SiC wafer cut from the boule shown at the left hand side.



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