Figure 1 AlN crystal grown by PVT

Modeling of PVT AlN using Virtual Reactor software

VR-PVT AlN predicts the crystal shape evolution in
sublimation AlN growth by simulating the global heat transfer in the growth system
coupled with species diffusion and convective flow in the growth
Below, we’ll have a closer look at the respective modules
incorporated in the Virtual Reactor software tool.


Part 1: Heat Transfer Modeling

Modeling of the global heat transfer problem in a system for AlN 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 AlN 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.

Fig. 2.
Local streamline patterns and supersaturation
distributions near the slit under the crucible
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.

Convective heat transfer simulation can be added to the thermal
module on the customer request. The subject will be implemented
in two weeks after request confirmation.

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

  • Diffusion of Al and N2 species.
  • 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.
  • Thin slits at the contacts of the crucible elements
    allowing for mass leakage from the growth chamber.
  • Inlets and Outlets.

Fig. 3.
Al mass fraction distribution in the gas cell.
Modeling of mass transport in the AlN powder charge. The model
includes a set of mass transport equations accounting for
heterogeneous chemical reactions at the surface of AlN granules.
The powder characteristics (porosity, granule size) can be
specified independently for several powder regions.

Crystal evolution during the growth within the quasi-stationary approximation described above. Powder evolution during the growth, which includes prediction of the temporal variation of all powder characteristics (local porosity, granule size, and graphitization degree).

Additional Modules that can be added to the Basic Version of the VR-AlN code

1. Module for analysis of dislocations dynamics

A module providing analysis of the propagation of threading {1010}<1210> and {1010}<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.

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