Due to its electrical and thermal properties, aluminum nitride is a promising material for fabrication of insulating substrates for high-temperature and high-frequency electronic devices. Bulk AlN crystals are normally grown by the sublimation technique (Physical Vapor Transport) involving evaporation of AlN powder in the hot zone of a reactor followed by crystallization the reactive species on the seed placed in a colder zone. Due to kinetic limitation of the molecular nitrogen adsorption/desorption rate, the AlN growth requires temperatures higher than 1900 °C. Virtual Reactor capabilities for the modeling of this process include:

• Modeling of the mass transport in the clearance between the powder and the seed includes diffusion of Al and N₂ and convective flow.
• Prediction of the total vapor pressure inside the tightly closed or semi-closed growth chamber.
• 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 shape evolution during the long-term growth.
• Powder evolution during the growth, which includes prediction of the temporal variation of all powder characteristics (local porosity and granule size) and local values of physical properties that depend on these powder characteristics.

Heat Transfer Modeling

Modeling of the global heat transfer problem in a system for AlN crystal growth includes:

• 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. Anisotropic thermal conductivity in solid materials is assumed.
• 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. Solid blocks can be considered opaque for the radiation or semitransparent.

VR provides means for quick virtual furnace modifications to improve thermal fields, supports programmable power of the inductor(s), programmable shifting of the furnace elements. Inductor(s) power can also be set up to match certain assigned constant (or changing in time following the assigned recipe) temperature in the control point(s).

Modeling Mass Transport of the Reactive Species

When AlN is growing by the sublimation technique, its vapor usually consists of Al and N₂. The reactive species are produced by the AlN powder evaporation and then transported to the seed where they contribute to the single AlN growth. The surface mechanisms related to AlN growth differ significantly from those of SiC. The principal difference comes from the kinetic limitation of the adsorption/desorption rate of molecular nitrogen which is a major reactive vapor species along with atomic Al. To account for this effect, we use the temperature dependent N₂ sticking coefficient extracted from the data on free evaporation of AlN in vacuum.

A specific feature of AlN sublimation growth is a dramatic growth acceleration when the vapor becomes nearly stoichiometric, i.e P_Al ~ 2P_N2. Then the species transport occurs entirely via convection with the gas velocity limited only by the evaporation kinetics. The stoichiometric composition can be achieved at a low vapor pressure close to a critical pressure P_c(T) which is associated with drastic changes in the gas flow pattern from a quasi-one-dimensional, corresponding to the directional species transport from the source to the seed, to essentially two-dimensional, due to the species emerging from the crucible to the ambient. At P < P_c, the AlN growth on the seed changes to etching, which can be also alternatively obtained by raising the temperature.