Model overview

CrysMAS is able to compute the convective and diffusive transport of the multiple species in the gas and melt media on block-structured mesh. No implementation for the unstructured mesh is available at the moment.

The transport properties of the gas mixture can be computed in dependence on the partial pressures of the transported gas components. The properties of each transported species in the transport medium without any other transported species will be accounted in the transport medium according to the Wilke approximation, see Kleijn in Bibliography .

The considered chemical species can be liquid or solid. Liquid species are transported in the predefined transport medium. Their distribution is computed as a mass fraction. It can be recomputed into the mass percent or concentration or partial pressure. The transport problem with boundary conditions is formulated for liquid species.

The second type of the species are solid. Solid species are not transported inside of the transport medium. They are localized at the predefined interfaces. The solid species in the model indicate deposited layers or etched surfaces. Their value has a meaning of the deposited layer thickness if the time-dependent simulation is done for the chemical reactions. Or it is a deposition or etching rate, if a stationary state is computed. The deposition velocity (it may be e. g. the crystal growth velocity for the epitaxial process) is resulted from the reaction rates which are computed using the boundary conditions of the transport problem.

Chemical reactions can be defined and applied either for the transport medium or for the interface between two materials. One of the materials in the pair should serve as a transport medium in the global transport model in the second case.

The reaction in the transport medium are the homogeneous reactions. They produce additional generation and dissipation source terms in the transport equation for the species number i which participates in the chemical reaction:  .

The source term includes the volumetric reaction rate R of each homogeneous chemical reaction with participation of the species number i either as the reacting agent or as produced chemical species. The volumetric reaction rate builds a product with the molar mass of the species for the mass fraction formulation. The computed transported mass fraction of the species is then designated as "omega".

Homogeneous chemical reactions can be defined being also endothermic or exothermic. The reaction heat is consumed or released. The chemical model will be coupled with the heat transport. The species transport problem together with chemical reactions is computed together with global heat transport iteratively by the segregated method.

Heterogeneous chemical reactions are defined for the external boundary of the transport medium. The medium is identified by the combination of the materials (in the transport medium and outside). All interfaces which satisfy to the contact condition are assumed to be reactive. The heterogeneous chemical reaction is treated as a flux boundary condition for the liquid species which participate in the reaction as products or reactants. The diffusive flux of the liquid species at the external boundary of the transport medium is set equal to the net result of all heterogeneous chemical reactions running at the selected interface where the considered species takes part.

It is possible to define and execute also the heterogeneous reactions at the interface between two transport media, whereby the reacting species and the reaction products are located in both transport media. The example of such reaction is the silicon monoxide evaporation from the silicon melt.

The including of the solid species into the heterogeneous reaction is also possible. The solid species can be treated as the reaction product. Then it contributes to the layer deposition at the interface. Or the solid species can be treated as a reacting substance. Then the condensed medium will be consumed at the external boundary of the rheological domain.

On the current development stage the reaction rates are the only generally unknown parameter which should be entered by the user in order to define the chemical kinetics. Reaction rates can be only prescribed as constant values or as functions of temperature. Reaction rates can be adjusted using the literature data, theoretical models or own calibration experiments. Later the online computation of the reaction rates based on first thermodynamics principles is indented for implementation.