If the Diffusion Model property is set to
Global the model equations solved are greatly simplified because the spatial information of the different quantities in the plasma reactor are treated as volume-averaged. Without the spatial derivatives the numerical solution of the equation set becomes considerably simpler and the computational time is greatly reduced. This type of model is useful when investigating a broad region of parameters with complex plasma chemistries.
For a mixture consisting of k = 1, …,
Q species and
j = 1, …,
N reactions the mass-fraction balance equations for the first
Q − 1 species is given by
The sum in the last two term is over surfaces where species are lost or created. The fourth term on the right-hand side accounts for surface reactions of the kth species. The last term on the right-hand side is introduced because the species mass-balance equations are written in the nonconservative form and it is used in the mass-continuity equation to replace the mass density time derivative.
where QSCCM is the total mass flow given in number of SCCM units,
is the mean molar mass of the feed, and
NStd is the standard number density computed at 1 atm and 273.15 K.
In the Reactor property it is possible to choose three different types of reactor models. If the
Reactor type is set to
Closed reactor the mass-flow feeds are set to zero
and Equation 6-29 is solved to take into account possible mass changes in the system caused by surface reactions.
If the Reactor type is set to
Constant mass the outlet mass-flow is set such that the feed and surface reactions cannot change the mass of the system
If the Reactor type is set to
Constant pressure Equation 6-29 is not solved and the outlet mass-flow feed is set such that the mass feed and surface reactions cannot change the mass of the system
where Te is the electron temperature (V).
When the Motz–Wise correction option is set to
On
and when the Motz–Wise correction option is set to
Off, the forward rate constant is given by
Equation 6-37 is an estimation of the diffusive losses to the wall where
Λeff is the effective diffusion length, and
Dk.m is the mixture-average diffusion coefficient of species
k.
Surface reactions can be adjusted using the Correction factor hl. It is common practice to correct the surface ion losses by a factor that takes into account the ion spatial profile. Models for the ion correction factor can be found in the literature
Ref. 2 and
Ref. 3.
where Cp is the specific heat at constant pressure of the mixture,
T is the gas temperature,
hf,k is the enthalpy of species
k in the feed,
hk is the enthalpy of species
k. The heat source (SI unit: W/m
3) is given as
where Δεj is the electron energy loss from reaction
j (SI unit: V) and
F is the Faraday constant (SI unit: C/mol). The last term in the equation above is only added for electron impact reactions to account for the energy loss or gain by the electron. Note that the electron enthalpy is set to zero and does not contribute to
Hj. For electron impact reactions resulting in excitation and ionization
Δεj corresponds to the energy of the excited state being excited/deexcited or ionized, for attachment
Δεj is set to zero, and for elastic collisions
where me and
mk are the electron and heavy species mass in kg,
Te is the electron temperature in eV, and
Tgas is the gas temperature in K. Heat losses by transport are including in a simplified form:
where k is the thermal conductivity of the mixture,
TS is the surface temperature, and
ΛS is the diffusion length.
where Pabs is the power absorbed by the electrons (SI unit: W), and
e is the elementary charge. The last term on the right-hand side accounts for the kinetic energy transported to the surface by electrons and ions. The summation is over all positive ions and all boundaries with surface reactions,
εe is the mean kinetic energy lost per electron lost,
εi is the mean kinetic energy lost per ion lost, and
Na is Avogadro’s number.
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