For gas-phase reactions, the reaction rate is defined on a volumetric basis and the net rate of creation and destruction of chemical species becomes a source term in the species conservation equations. For surface reactions, the rate of adsorption and desorption is governed by both chemical kinetics and diffusion to and from the surface. Wall surface reactions therefore create sources and sinks of chemical species in the gas phase, as well as on the reacting surface.
Theoretical information about wall surface reactions and chemical vapor deposition is presented in this section. Information can be found in the following sections:
For more information about using wall surface reactions and chemical vapor deposition, see Wall Surface Reactions and Chemical Vapor Deposition in the User's Guide.
Consider the 
th wall surface reaction
written in general form as follows:
 | (7–73) |
where 
, 
, and 
represent
the gas phase species, the bulk (or solid) species, and the surface-adsorbed
(or site) species, respectively. 
, 
, and 
are the total
numbers of these species. 
, 
,
and 
are the stoichiometric
coefficients for each reactant species 
, and 
, 
, and 
are the stoichiometric coefficients for each product
species 
. 
and 
are
the forward and backward rate of reactions, respectively.
The summations in Equation 7–73 are for all chemical species in the system, but only species involved as reactants or products will have nonzero stoichiometric coefficients. Hence, species that are not involved will drop out of the equation.
The rate of the 
th reaction is
 | (7–74) |
where 
represents molar concentrations of surface-adsorbed
species on the wall. 
and 
are the rate exponents for the 
gaseous
species as reactant and product, respectively, in the reaction. The
variables 
and 
are the rate exponents for the 
site
species as reactant and product in the reaction. It is assumed that
the reaction rate does not depend on concentrations of the bulk (solid)
species. From this, the net molar rate of production or consumption
of each species 
is given by
 | (7–75) |
 | (7–76) |
 | (7–77) |
The forward rate constant for reaction 
(
) is computed using
the Arrhenius expression,
 | (7–78) |
| where, | |
|
| |
|
| |
|
| |
|
|
You (or the database) will provide values for 
, 
, 
, 
, 
, 
, 
, 
, and 
.
To include the mass transfer effects and model heat release, refer to Including Mass Transfer To Surfaces in the Continuity Equation, Wall Surface Mass Transfer Effects in the Energy Equation, and Modeling the Heat Release Due to Wall Surface Reactions in the User's Guide.
If the reaction is reversible, the backward rate constant for
reaction 
, 
is computed from the forward
rate constant using the following relation:
 | (7–79) |
where 
is the equilibrium constant
for 
th reaction computed from
 | (7–80) |
where 
denotes the atmospheric
pressure (101325 Pa). The term within the exponential function represents
the change in the Gibbs free energy, and its components are computed
per Equation 7–26 and Equation 7–27.
is the number of different types of sites, 
is the site density of site type 
. 
and 
are the stoichiometric coefficients of the 
th site species of type 
in reaction 
.
Ansys Fluent has the option to modify the surface reaction rate
as a function of species site coverages. In such cases, the forward
rate constant for the 
th reaction is evaluated
as,
 | (7–81) |
In Equation 7–81, the three
surface coverage rate modification parameters for species 
in reaction 
are 
, 
and 
. These parameters default
to zero for reaction species that are not surface rate modifying.
The surface (coverage) site fraction, 
is the fraction
of surface sites covered by species 
, and is defined as,
 | (7–82) |
where 
is the surface site concentration and 
is the surface site density
(see Equation 7–87).
Reactions at surfaces change gas-phase, surface-adsorbed (site) and bulk (solid) species. On reacting surfaces, the mass flux of each gas species due to diffusion and convection to/from the surface is balanced with its rate of consumption/production on the surface,
 | (7–83) |
 | (7–84) |
The mass fraction at the wall 
is related to concentration by
 | (7–85) |
is the net rate of mass deposition or etching as
a result of surface reaction; that is,
 | (7–86) |
is the site species concentration at the wall, and
is defined as
 | (7–87) |
where 
is the site density and 
is the site
coverage of species 
.
Equation 7–83 and Equation 7–84
are solved for the dependent variables 
and 
using a point-by-point coupled Newton solver. When the Newton
solver fails, Equation 7–83 and Equation 7–84 are solved by time marching in an ODE solver until
convergence. If the ODE solver fails, reaction-diffusion balance is disabled,
is assumed equal to the cell-center value 
, and only the site coverages 
are advanced in the ODE solver to convergence. You can manually
disable reaction-diffusion balance with the text interface command
define/models/species/reaction-diffusion-balance.
The effective gas-phase reaction source terms are then available for solution of the gas-phase species transport Equation 7–1.
The diffusion term in Equation 7–83 is calculated as the difference in the species mass fraction at the cell center and the wall-face center, divided by the normal distance between these center points. Ansys Fluent models the reactions that take place inside catalyst structures by introducing the Surface Area Washcoat Factor. Generally, a washcoat is a carrier in which the catalytic materials are suspended. These materials increase the surface area compared to the bare substrate by forming a rough and irregular surface; increasing the catalytically active reacting area available for surface reaction. To utilize the available reacting surface, Ansys Fluent provides an option to define a washcoat factor. This coefficient is multiplied by the reacting surface to calculate the available reacting surface which modifies the surface reaction rates linearly. Ansys Fluent can also model surface chemistry on unresolved walls using a porous media model. This model is appropriate for catalytic tube-banks or porous foam matrices where it is not feasible to resolve the individual walls. When surface reaction is enabled in porous cell zones, the Surface-to-Volume Ratio must be specified. The wall normal distance required for the diffusion term in Equation 7–83 is calculated as the inverse of the surface-to-volume ratio.
Most semiconductor fabrication devices operate far below atmospheric pressure, typically only a few millitorrs. At such low pressures, the fluid flow is in the slip regime and the normally used no-slip boundary conditions for velocity and temperature are no longer valid.
The Knudsen number, denoted 
, and
defined as the ratio of mean free path to a characteristic length
scale of the system, is used to quantify continuum flow regimes. Since
the mean free path increases as the pressure is lowered, the high
end of 
values represents free molecular flow and the low end the continuum regime.
The range in between these two extremes is called the slip regime
(0.01<
<0.1) [63] In the slip regime, the gas-phase velocity at
a solid surface differs from the velocity at which the wall moves,
and the gas temperature at the surface differs from the wall temperature.
Maxwell’s models are adopted for these physical phenomena in Ansys Fluent for
their simplicity and effectiveness.
velocity slip
(7–88)
(7–89)
Here,
and 
represent the velocity components that are tangential and
normal to the wall, respectively. The subscripts 
, 
and 
indicate gas, wall and cell-center velocities.
is the distance from cell center to the wall.
is the characteristic length. 
is the momentum accommodation coefficient of the gas
mixture and its value is calculated as mass-fraction weighted average of
each gas species in the system.
(7–90)
The mean free path,
, is computed as follows:
(7–91)
(7–92)
is the Lennard-Jones
characteristic length of species 
. 
is the Boltzmann
constant, 
.Equation 7–88 and Equation 7–89 indicate that while the gas velocity component normal to the wall is the same as the wall normal velocity, the tangential components slip. The values lie somewhere between the cell-center and the wall values. These two equations can be combined to give a generalized formulation:
(7–93)
where
(7–94)
temperature jump
(7–95)
or equivalently
(7–96)
where
(7–97)
is the thermal accommodation
coefficient of the gas mixture and is calculated as 
.
Important: The low-pressure slip boundary formulation is available only with the pressure-based solver.