Surface Reaction
The Surface Reaction node () sets up reactions involving gas phase, surface, and bulk species on surfaces. Surface reactions play an important role in the overall characteristics of a discharge. This typically involves first-order reactions on surfaces where excited or ionic species transition back to their ground state.
Reaction Formula
The first thing to input after creating a new reaction is the Reaction Formula. The reaction can only be irreversible. Valid species names consist of a case-sensitive combination of letters, numbers, and “+” or “-” signs. With the exception of the “+” and “-” signs, which are used for ions, special characters are not allowed as species names or part of species names (for example, [], *, #, and _). In addition, the first character in a species name must be a letter to avoid confusion with the stoichiometric coefficients in the reaction formula. Ions are labeled with one plus or minus sign per species charge added directly after the species name.
For surface reactions, use the notation (s) to denote surface species or (b) to denote bulk species. (Bulk surface species is not to be confused with gas phase species.) The species is then called name_surf or name_bulk depending on the species type. For example, using Si(s) in the reaction formula creates a surface species with the name Si_surf and Si(b) creates a surface species with the name Si_bulk.
Under Specify reaction using select whether to specify the surface reaction using Sticking coefficient or Rate coefficient. If the Diffusion model property is set to Global, and the reaction is first order, the surface reaction can also be specified using Sticking coefficient and diffusion. If the reactant species has the Species type set to Ion, the surface reaction can also be specified using Bohm velocity. Sticking coefficients are typically easy to estimate intuitively and must be between 0 and 1. Rate coefficients require specification of a rate constant, which can be obtained in the appropriate literature.
Under Motz–Wise correction select whether to include this correction in the expression for the rate constant. This option is only available when the reaction is specified using sticking coefficients. When the Motz–Wise correction is set to On, Equation 5-19 is used to compute the rate constant. When set to Off, Equation 5-20 is used.
Only irreversible surface reactions are supported.
Arrhenius Parameters
This section is available when a valid formula for the surface reaction is entered.
Choose whether or not to use Arrhenius expressions to compute the sticking coefficients. When this option is activated, the expression for the sticking coefficient is automatically computed using:
where Asf is the frequency factor, nsf is the temperature exponent, and Esf is the activation energy (SI unit: J/mol).
Include Yield
Choose whether or not to include yield parameters to compute the reaction rates for the species involved in this surface reaction. This is mostly used in plasma etching simulations.
This option can only be selected if there are exactly two reactant species including one gaseous species and one surface species.
Reaction Parameters
The options available in this section depends on the Diffusion model property. If it is set to Fick’s law or Mixture Averaged, the following options are available.
When Specify reaction using is set to Sticking coefficient and the Use Arrhenius expressions checkbox is not selected, enter a Forward sticking coefficient for the surface reaction. This value should be between 0 and 1. When the value is zero, the surface reaction rate is zero, and the surface reaction feature is not necessary. For neutral radicals, a typical value is 1E-3. For highly reactive species, like ions or electronically excited atoms or molecules, a value of 1 is more appropriate. If the Use Arrhenius expressions checkbox is selected, enter the following:
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A value or expression for the Forward sticking coefficient frequency factor Afs (SI unit: 1). This should typically be a number between 0 and 1, since it is used to compute a sticking coefficient.
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A value or expression for the Forward sticking coefficient exponent nfs (SI unit: 1). A nonzero value is only necessary if the sticking coefficient varies with temperature.
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A value or expression for the Forward sticking coefficient activation energy Efs (SI unit: J/mol). A nonzero value is only necessary if the sticking coefficient varies with temperature.
When Specify reaction using is set to Rate coefficient and the Use Arrhenius expressions checkbox is not selected, enter a Forward rate constant for the surface reaction. The unit changes depending on the order of the reaction. The Forward rate constant could be dramatically different depending on the surface reaction. Entering unphysical values can lead to numerical instabilities when solving, so only well known values from the literature should be used. If the Use Arrhenius expressions checkbox is selected, enter the following:
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A value or expression for the Forward surface frequency factor af (SI unit: m/s for first-order reactions). This unit will change depending on reaction order.
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A value or expression for the Forward surface exponent bf (SI unit: 1). A nonzero value is only necessary if the rate constant varies with temperature.
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A value or expression for the Forward surface activation energy ef (SI unit: J/mol). A nonzero value is only necessary if the rate constant varies with temperature.
If the Diffusion model property is set to Global, the following options are available in addition to the ones listed above.
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A value or expression for the Correction factor hl (SI unit: 1). A value other than one only needs to be specified when the reactant is an ion. In that case, typical values range from 0.1–0.3. This can be thought of as a correction to the surface area where the reaction occurs. Values for specific reactions can be found in the literature.
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When Specify reaction using is set to Sticking coefficient and diffusion, enter an Effective diffusion length Λeff (SI unit: m). A smaller value will increase the surface reaction rate.
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If the Include yield option is selected, the Yield parameters subsection will be available. Within the subsection, the first item is a selectable input, Specify yield using, where the available options are Incoming species energy and User defined.
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If the option Incoming species energy is selected, the following empirical equation is used to calculate the yield:
where the parameters are the Proportionality constant A0, Energy Ei, and Threshold energy Eth.
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If the option User defined is selected, the yield can be defined directly using either a constant, an expression of plasma parameters, or a function based on some table data such as an interpolation function.
The calculated yield will be used as a multiplier when calculating the reaction rates for all the species involved in this surface reaction, except for the incoming species itself and its corresponding species (same or neutralized species) in the products.
Secondary Emission Parameters
If the Heavy Species Transport interface is coupled to the Drift Diffusion interface, or the Plasma interface is being used, it may be necessary to include secondary electron emission in the model. This is typically only needed when ions are the reactant.
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Enter a value for the Secondary emission coefficient γi (SI unit: 1). The value should be between 0 (no secondary emission) and around 0.45, for ions and surface which produce a high yield of secondary electrons. Values for specific pairs of ions and surfaces are given in the literature.
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Enter a value for the Mean energy of secondary electron εi (SI unit: V). This value may be hard to find in the literature, so what is often used is the value for the ionization energy of the reactant minus twice the work function of the surface. So, for an Argon ion, with ionization energy of 15.8 V and a surface with a work function of 5 V, the mean energy for the secondary electron would be 5.8 V.