The Heavy Species Transport Interface
The Heavy Species Transport (hs) interface (), found under the Plasma >Species Transport branch (), adds electron impact reactions, gas phase reactions, and species and surface reactions to plasma models. The most convenient way to do this is to load a set of collision cross sections from a file in the Cross Section Import section from the Settings window for Heavy Species Transport.
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is hs.
Out-of-Plane Thickness (2D, 1d Axisymmetric, and 1D)
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For 2D components, enter a Thickness d (SI unit: m). The default is 1 m.
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For 1D axisymmetric components, enter a Vertical height dz (SI unit: m). The default is 0.01 m.
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For 1D components, enter a Cross-section area A (SI unit: m2). The default is 0.01 m2.
Diffusion Model
Select a Diffusion model — Mixture-averaged (the default), Fick’s law, or Global. When using the Mixture-averaged or Global models, the mixture averaged diffusion coefficients are automatically computed based on the data specified for each species.
Transport Settings
The Migration in electric field check box is selected by default. The Migration term is part of the total mass flux vector. Select the check boxes for other transport mechanisms to Include — Convection, Calculate thermodynamic properties, Full expression for diffusivity, or Compute tensor ion transport properties. The selection changes the number of Model Inputs requiring values on the Settings window for Diffusion, Migration. Note the following:
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Convection of heavy species present in a plasma can often be neglected due to the low operating pressure.
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For Calculate thermodynamic properties select the thermodynamic properties of each reaction and species are computed automatically based on the thermodynamic properties of each species.
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For Full expression for diffusivity it computes a more accurate expression for the binary diffusion coefficients. Often the additional correction terms (the collision term, ΩD given by Equation 5-18 and used in Equation 5-17) are negligible in which case the expressions are much simpler and the time taken to assemble the Jacobian matrix is reduced.
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For Mixture diffusion correction additional terms are included in the definition of the mass flux vector to ensure that the same solution is obtained regardless of the choice of the species which comes from the mass constraint. This option makes the problem more non–linear and strongly coupled, and is only necessary when the molecular weights of the species differ substantially (such as a mixture of sulfur hexafluoride and hydrogen).
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For Compute tensor ion transport properties the tensor form of the ion transport properties when a static magnetic field is present are computed. This option only needs to be activated when a strong DC magnetic field exists and the operating pressure is very low (on the order of millitorr). When this option is activated an expression must be provided for the magnetic flux density which would typically be computed by another physics interface. This is set in the Convection, Migration, Diffusion feature.
When the Diffusion model is set to Global only the properties Calculate thermodynamic properties and Full expression for diffusivity are available.
Reactor
This section is available when the Diffusion model is set to Global. Select a Reactor type from the list — Closed reactor (the default), Constant mass, or Constant pressure.
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 Closed reactor solves a closed system where mass and pressure can change, for example, as the result of surface reactions and volume reactions of the associative/dissociative type.
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 Constant mass solves a system with mass-flow feed and outlet. The mass-flow outlet is set to keep the mass-density constant. 
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Constant pressure solves a system with mass-flow feed and outlet. The pressure is kept constant by adjusting the system mass-density if needed.
Electron Energy Distribution Function Settings
If cross-section data is used to define source coefficients in the model then an electron energy distribution function (EEDF) needs to be selected. These options are available.
For more information on the electron energy distribution function (EEDF), see the Theory for the Boltzmann Equation, Two-Term Approximation Interface.
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Maxwellian. This option assumes a Maxwellian EEDF which takes the form:
where
where is the mean electron energy (eV), ε is the electron energy (eV) and Γ is the incomplete gamma function.
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Druyvesteyn. This option assumes a Druyvesteyn EEDF which takes the form:
where
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For Generalized, it is a generalized distribution function where the EEDF is somewhere between Maxwellian and Druyvesteyn. Specify a power law; the number must be between 1 and 2. Mathematically, the EEDF takes the form:
where
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Function. If a two-dimensional interpolation function has been added to the model, it can be used for the EEDF. In this case, the x-data should be the electron energy (eV) and the y-data should be the mean electron energy (eV).
The two-dimensional interpolation function can be computed using a parametric sweep in The Boltzmann Equation, Two-Term Approximation Interface. This allows for modeling of discharges where the EEDF is far from Maxwellian. For step-by-step instructions on how to do this, refer to this blog entry: https://www.comsol.com/blogs/the-boltzmann-equation-two-term-approximation-interface/
In all these cases the rate constants in the model are automatically computed based on the selected EEDF using the formula:
(5-1)
The rate coefficients when computed using cross section data are a highly nonlinear function of the mean electron energy. COMSOL Multiphysics automatically computes the integral in Equation 5-1 and makes the result available for evaluation of the rate coefficient. The variation of the rate coefficient for any particular model can be plotted using <name>.kf_<reaction_number>. For example, for reaction number 3 in a Heavy Species interface, with name hs, the rate coefficient would be plotted using hs.kf_3.
Stabilization
To display this section, click the Show More Options button () and select Stabilization in the Show More Options dialog box.
If the Formulation is set to Finite element, log formulation (linear shape function) or Finite element, log formulation (quadratic shape function) then the solver can run into difficulties when the species mass fractions approach zero. The Reaction source stabilization check box (selected by default) adds an additional source term to the rate expression for each species. In the ι text field, enter a tuning parameter for the source stabilization. The default value is 1. This value is usually good enough. If the plasma is high pressure (atmospheric) then it can help to lower this number to somewhere in the range of 0.25–0.5.
surface chemistry
Use this to specify the Total surface site concentration (SI unit: mol/m2) which will be added on all boundaries. This setting only affects models which have surface species included in the surface chemical mechanism.
Discretization
Select Formulation — Finite volume (constant shape function), Finite element, log formulation (linear shape function) (the default) to solve the equations in logarithmic form, Finite element (linear shape function), Finite element, log formulation (quadratic shape function), or Finite element (quadratic shape function). The option with log formulation solve for the log of the dependent variables, ensuring that the mass fraction of any of the species is never lower than zero. This makes it more numerically stable but increases the nonlinearity of the equation system, and as such the model might take slightly longer to solve. The linear formulation solves the equations in the original form.
When the Diffusion model is set to Global the sections Stabilization and Discretization are not available.
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Stabilization
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Domain, Boundary, and Pair Nodes for the Heavy Species Transport Interface
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Theory for the Heavy Species Transport Interface
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Interpolation in the COMSOL Multiphysics Reference Manual
Surface Chemistry Tutorial Using the Plasma Module: Application Library path Plasma_Module/Chemical_Vapor_Deposition/surface_chemistry_tutorial