Chlorine Discharge Global Model

Plasma discharges containing Chlorine are commonly used to etch semiconductors and metals in microelectronics fabrication. Cl2 has low dissociation energy and very low threshold energy for dissociative attachment, and atomic chlorine has large electron affinity. As a consequence a Cl2 plasma has substantial levels of electronegativity and dissociation. Quantification of the negative ion and atomic chlorine density is important to understand the reactor operation. In particular Chlorine atoms are accepted to be a main reactant for plasma etching.

In this study are presented model results of chlorine and electron density for absorbed powers between 25 and 600 W and for working pressures between 1 and 100 mTorr. To explore such a large parametric region it is used a global (volume-averaged) model since it can run simulations in a fraction of the time of a space dependent model while retaining the tendencies of volume-averaged physical quantities.

Model results of several relevant quantities such as atomic chlorine density, electron density, and electron temperature are in good agreement with measurements performed in inductively coupled plasma reactors found in the literature.

The reader can find more information about global models and Chlorine plasmas in Ref. 1, Ref. 2, and Ref. 3 and in the references therein.

Model Definition

The model used in this work considers that the spatial information of the different quantities in the plasma reactor can be treated as uniform or can be introduced using analytic models. Without the spatial derivatives the numerical solution of the equation set becomes considerably simpler and the computational time is reduced. In the following it is taken advantage of the fast computational time to investigate a broad region of parameters with a complex plasma chemistry.

When using a plasma global model the species densities and the electron temperature are treated as volume-averaged quantities. Detailed information on the global model can be found in the section Theory for Global Models in the Plasma Module User’s Guide. For heavy species the following equation is solved for the mass fraction

where ρ is the mass density (SI unit: kg/m3), wk is the mass fraction, wf,k is the mass fraction in the feed, mf and mo are the mass-flow rates of the total feed and outlet, and Rk is the rate expression (SI unit: kg/(m3·s)). The fourth term on the right-hand side accounts for surface losses and creation, where Al is the surface area, hl is a dimensionless correction term, V is the reactor volume, Mk is the species molar mass (SI unit: kg/mol) and Rsurf,k,l is the surface rate expression (SI unit: mol/(m2·s)) at a surface l. The last term is introduced because the species mass balance equations are written in the nonconservative form and it used the mass-continuity equation to replace for the mass density time derivative. In the last term Mf,l is the inward mass flux of surface l (SI unit: kg/(m2·s)). The sum in the last two terms is over all surfaces where there are surface reactions.

To take into account possible variations of the system total mass or pressure the mass-continuity equation can also be solved

The electron number density is obtained from electroneutrality

and if using the local energy approximation (LEA) the electron energy density nε (unit: V/ m3) is computed from

where Rε is the electron energy loss due to inelastic and elastic collisions, Pabs is the power absorbed by the electrons (SI unit: W), and e is the elementary charge. The last term on the right side accounts for the kinetic energy transported to the surface by electrons and ions. The summation is over all positive ions, 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. If using the local field approximation (LFA) the electron mean energy equation is not solved and the electron mean energy can be: (i) provided as a function of the electric field; or (ii) obtained by solving the Boltzmann equation in the two-term approximation.

The rate coefficients for electron impact reactions can be computed by appropriate averaging of cross sections over a EEDF. The EEDF can be either analytic or can be obtained by solving the steady state Boltzmann equation in the two-term approximation coupled with the equation system (The Boltzmann Equation, Two-Term Approximation Interface in the Plasma Module User’s Guide). When solving for the EEDF the coupling between the equations is as follows: (i) if the LEA is used the electron mean energy obtained from the electron mean energy equation is given as input to the Boltzmann solver; (ii) if the LFA is used the reduce electric field must be given as input to the Boltzmann solver and the electron mean energy comes from averaging over the computed EEDF.

This study uses the LEA and a Maxwellian EEDF to computed the electron impact rate coefficients.

In this work are simulated cylindrical reactors with several dimensions corresponding to inductively coupled plasma reactors used by different experimental groups. The simulations are performed for a reactor operating at constant pressure. Moreover, the mass-flow rate of the outlet is found by assuming that the feed and the surface reactions cannot change the total mass of the system

Note that the surface reactions used in these simulations do not change the mass of the system.

However the mass-continuity equation is not solved, the mass density can still change as a result of a change in the mean molar mass, thus accounting for changes in the number density (due to dissociation and association) to maintaining a constant pressure.

The expressions used for the mean kinetic energy lost per electron lost and the mean kinetic energy lost per ion lost are deduced from theory and numerical solution and are explained in Ref. 1and references therein. The gas temperature is a function of pressure and absorbed power and is based on experimental data Ref. 1.

plasma chemistry

It is used the plasma chemistry suggested in Ref. 2 and presented in Table 1that consists of 10 species and 44 reactions.

Table 1: table of collisions and reactions modeled.
reaction	formula	type
1	e+Cl2=>e+Cl2	Momentum	0
2	e+Cl=>e+Cl	Momentum	0
3	e+Cl2=>Cl+Cl+e	Dissociation	4
4	e+Cl2=>2e+Cl2+	Ionization	11.5
5	e+Cl2=>2e+Cl+Cl+	Ionization	14.25
6	e+Cl2=>3e+2Cl+	Ionization	28.5
7	e+Cl2=>Cl+Cl-	Attachment	0
8	e+Cl2v1=>Cl+Cl-	Attachment	0
9	e+Cl2v2=>Cl+Cl-	Attachment	0
10	e+Cl2v3=>Cl+Cl-	Attachment	0
11	e+Cl2=>Cl++Cl-+e	Ionization/Attachment	14.25
12	e+Cl2=>e+Cl2v1*	Excitation	0.07
13	e+Cl2=>e+Cl2v2*	Excitation	0.14
14	e+Cl2=>e+Cl2v3*	Excitation	0.21
15	e+Cl2v1=>e+Cl2v2*	Excitation	0.07
16	e+Cl2v2=>e+Cl2v3*	Excitation	0.07
17	e+Cl2v1=>e+Cl2v3*	Excitation	0.14
18	e+Cl2+=>2Cl	Excitation	0
19	e+Cl=>e+Cl12*	Excitation	1.35
20	e+Cl=>e+Cl52*	Excitation	10.17
21	e+Cl=>Cl++2e	Ionization	14.25
22	e+Cl12=>Cl++2e	Ionization	10.18
23	e+Cl52=>Cl++2e	Ionization	4.08
24	e+Cl-=>Cl+2e	Ionization	2.36
25	e+Cl-=>Cl++3e	Ionization	16.61
26	Cl52=>Cl	Radiation decay	0
27	Cl2++Cl-=>3Cl	Ion-ion recombination	0
28	Cl2++Cl-=>Cl+Cl2	Ion-ion recombination	0
29	Cl++Cl-=>2Cl	Ion-ion recombination	0
30	Cl2+Cl+=>Cl+Cl2+	Charge exchange	0
31	Cl2v1+Cl+=>Cl+Cl2+	Charge exchange	0
32	Cl2v2+Cl+=>Cl+Cl2+	Charge exchange	0
33	Cl2v3+Cl+=>Cl+Cl2+	Charge exchange	0
34	2Cl+Cl2=>2Cl2	Association	0
35	2Cl+Cl=>Cl2+Cl	Association	0
36	Cl+Cl2v3=>Cl+Cl2v2	Deexcitation	0
37	Cl+Cl2v2=>Cl+Cl2v1	Deexcitation	0
38	Cl+Cl2v1=>Cl+Cl2v0	Deexcitation	0

*The reaction set includes the inverse reaction with the rate coefficient obtained by detailed balance.

The model also include the surface reactions presented in Table 2.

Table 2: table of surface reactions.
reaction	formula	Sticking Coefficient
1	Cl2+=>Cl2	1
2	Cl+=>Cl	1
3	Cl2v1=>Cl2	1
4	Cl2v2=>Cl2	1
5	Cl2v3=>Cl2	1
6	Cl12=>Cl	1
7	Cl52=>Cl	1
8	Cl=>0.5Cl2	Ref. 1

The rate at which positive ions are lost to the wall is computed from the Bohm velocity and the density that an ion have near the surface. The ion density at the surface is estimated from theory Ref. 1 and Ref. 3 and is introduced in the model using the correction factor hl. Negative ions are assumed to be confined in the plasma bulk.

The rate at which neutral species are lost to the wall involves the information of diffusional losses, of the particle mean velocity, and of the sticking coefficient Ref. 1 and Ref. 3. The wall recombination of neutral chlorine atoms is an important aspect of chlorine containing discharges since it influences the degree of dissociation of the discharge. The sticking coefficient for the recombination of Cl at the surface is obtained by fitting experimental data Ref. 1. All other neutral excited species revert to ground state with sticking coefficient equal to one.

Results and Discussion

In this section are presented simulations results that can be compared with measurements and simulations reported in Ref. 1. The measurements are for inductively coupled plasma reactors with radius R and length L, operate at a given volumetric flow (Qf), and sweep either the input power or the pressure. The power absorbed by the plasma that is used in the simulations is estimated in Ref. 1. The parameters used in the simulations are summarized in Table 3, and are labeled with the name of the authors that perform the measurements. Overall the numeric results are consistent with those of Ref. 1 and agree well for most experimental conditions.

Table 3: Reactor parameters used in the simulations.
author
Corr et al	10	8.5	10	25-300 300	10 1-100
Malyshev and Donnelly	18.5	20	100	50-650	10
Efremov et al	15	14	20	300	1-100

Figure 1 and Figure 2 present electron and Cl number density as a function of the absorbed power for the experimental conditions of Corr et al and Malyshev and Donnelly. The atomic Chlorine density for the conditions of Corr et al and the electron density for the conditions of Malyshev and Donnelly (Figure 2) agree well with measurements. The electron density for the conditions of Corr et al (Figure 1) is highly overestimated when compared with measurements but is consistent with the simulation results of Ref. 1. The electronegativity, also presented in Figure 1, only agrees well with measurements at higher absorbed powers.

Figure 3 presents electron and Cl number density as a function of the reactor pressure for the experimental conditions of Corr and others. There is a fair agreement for all conditions with the model capturing the tendencies but slightly underestimating the Cl density and overestimating the electron density.

Figure 4 presents the electron temperature as a function of the reactor pressure for the experimental conditions of Efremov and others. The model agrees well with measurements capturing the decrease of the electron temperature with pressure. However, the measured temperature decreases at a faster rate with pressure at higher pressures.

Figure 1: Model results for the electron and Cl densities, and for the electronegativity as a function of the absorbed power for the conditions of Corr et al: P=10 mTorr, Qf=10 sccm, R=10 cm, and L=8.5 cm.

Figure 2: Model results for the electron and Cl densities as a function of the absorbed power for the conditions of Malyshev and Donnelly: P=10 mTorr, Qf=100 sccm, R=8.5 cm, and L=20 cm.

Figure 3: Model results for the electron and Cl densities as a function of pressure. The Cl density is for the conditions of Corr et al: Pabs=300 W, Qf=10 sccm, R=10 cm, and L=8.5 cm. The electron density is for the conditions of Efremov et al: Pabs=300 W, Qf=20 sccm, R=25 cm, and L=14 cm.

Figure 4: Model results for the electron temperature as a function of pressure for the conditions of Efremov et al: Pabs=300 W and Qf=20 sccm, R=15 cm, and L=14 cm.

References

1. E.G. Thorsteinsson, and J.T. Gudmundsson, “A global (volume averaged) model of a chlorine discharge,” Plasma Sources Sci. Technol., vol. 19, p. 015001 (15pp), 2010.

2. E. Kemaneci, E. Carbone, J-P. Booth, W. Graef, J. van Dijk, and G. Kroesen, “Global (volume-averaged) model of inductively coupled chlorine plasma: influence of Cl wall recombination and external heating on continuous and pulse-modulated plasmas,” Plasma Sources Sci. Technol., vol. 23, p. 045002 (14pp), 2014.

3. M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, John Wiley & Sons, 2005.

Plasma_Module/Global_Modeling/chlorine_global_model

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Root

Construct a cylindrical reactor with radius Rad and length L. The values of Rad and L are set in the node.

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type Rad.

In the text field, type L.

Global Definitions

Add parameters to be used in the simulations. The pressure and absorbed power need to be set here to be available to do a parameter sweep.

The different studies performed use different parameters so that before each new study (after the first study) it is necessary to change some of the parameters values.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Rad	10[cm]	0.1 m
L	8.5[cm]	0.085 m
Pabs	25[W]	25 W
Qfeed	10	10
p0	0.01[Torr]	1.3332 Pa

Definitions

Import the file containing the energy levels to be used when defining the reactions.

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file chlorine_global_model_variables_1.txt.

Import the file containing the variables used to define the gas temperature, the plasma and sheath potential, and the hl correction factors.

Variables 2

In the window, right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file chlorine_global_model_variables_2.txt.

Choose to use a global model for the following simulations and set the model to work at constant pressure.

Plasma (plas)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Set the background gas temperature, the working pressure, the total mass flow, the power absorbed, the mean kinetic energy lost per ion and electron lost.

The mole fraction of each species in the mass flow is set later in the species node.

Plasma Model 1

In the window, under click .

In the window for , locate the section.

In the T text field, type Th.

In the pA text field, type p0.

Locate the section. In the Qsccm text field, type Qfeed.

Locate the section. In the Pabs text field, type Pabs.

In the εe text field, type Epsilon_e.

In the εi text field, type Epsilon_p+Epsilon_s.

Add reactions relevant for the Chlorine plasma chemistry. There are about 40 volume reactions that need to be added.

For electron impact reactions it is needed to set the collision type, the rate constant and the energy loss in the collision.

For reactions between heavy species it is only necessary to set the rate constant.

Electron Impact Reaction 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>Cl+Cl+e.

Locate the section. From the list, choose .

In the Δε text field, type ediss.

Locate the section. In the kf text field, type 1.04e-13*plas.Te^(-0.29)*exp(-8.84/plas.Te)*N_A_const.

Electron Impact Reaction 2

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>2e+Cl2+.

Locate the section. From the list, choose .

In the Δε text field, type eionCl2.

Locate the section. In the kf text field, type 5.12e-14*plas.Te^(0.48)*exp(-12.34/plas.Te)*N_A_const.

Electron Impact Reaction 3

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>2e+Cl+Cl+.

Locate the section. From the list, choose .

In the Δε text field, type eionCl.

Locate the section. In the kf text field, type 2.14e-13*plas.Te^(-0.07)*exp(-25.26/plas.Te)*N_A_const.

Electron Impact Reaction 4

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>3e+2Cl+.

Locate the section. From the list, choose .

In the Δε text field, type 2*eionCl.

Locate the section. In the kf text field, type 2.27e-16*plas.Te^(1.92)*exp(-21.26/plas.Te)*N_A_const.

Electron Impact Reaction 5

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>Cl+Cl-.

Locate the section. From the list, choose .

Locate the section. In the kf text field, type (3.43e-15*plas.Te^(-1.18)*exp(-3.98/plas.Te) + 3.05e-16*plas.Te^(-1.33)*exp(-0.11/(plas.Te+0.014)))*N_A_const.

Electron Impact Reaction 6

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v1=>Cl+Cl-.

Locate the section. From the list, choose .

Locate the section. In the kf text field, type (14.06e-15*plas.Te^(-1.18)*exp(-3.98/plas.Te) + 12.51e-16*plas.Te^(-1.33)*exp(-0.11/(plas.Te+0.014)))*N_A_const.

Electron Impact Reaction 7

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v2=>Cl+Cl-.

Locate the section. From the list, choose .

Locate the section. In the kf text field, type (30.18e-15*plas.Te^(-1.18)*exp(-3.98/plas.Te) + 26.84e-16*plas.Te^(-1.33)*exp(-0.11/(plas.Te+0.014)))*N_A_const.

Electron Impact Reaction 8

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v3=>Cl+Cl-.

Locate the section. From the list, choose .

Locate the section. In the kf text field, type (46.31e-15*plas.Te^(-1.18)*exp(-3.98/plas.Te) + 41.18e-16*plas.Te^(-1.33)*exp(-0.11/(plas.Te+0.014)))*N_A_const.

Electron Impact Reaction 9

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>Cl++Cl-+e.

Locate the section. From the list, choose .

In the Δε text field, type eionCl.

Locate the section. In the kf text field, type 2.94e-16*plas.Te^(0.19)*exp(-18.79/plas.Te)*N_A_const.

Electron Impact Reaction 10

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>e+Cl2v1.

Locate the section. From the list, choose .

In the Δε text field, type ev1.

Locate the section. In the kf text field, type 3.99e-12*plas.Te^(-1.5)*exp(-7.51/plas.Te-0.0001/plas.Te^2)*N_A_const.

Electron Impact Reaction 11

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>e+Cl2v2.

Locate the section. From the list, choose .

In the Δε text field, type ev2.

Locate the section. In the kf text field, type (3.28e-17*plas.Te^(-1.12)*exp(-0.37/plas.Te) + 2.86e-17*exp(-(log(plas.Te)+0.99)^2/(2*1.06^2)))*N_A_const.

Electron Impact Reaction 12

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2=>e+Cl2v3.

Locate the section. From the list, choose .

In the Δε text field, type ev3.

Locate the section. In the kf text field, type (1.3e-17*plas.Te^(-1.24)*exp(-0.41/plas.Te) + 6.08e-18*exp(-(log(plas.Te)+0.94)^2/(2*1.02^2)))*N_A_const.

Electron Impact Reaction 13

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v1=>e+Cl2v2.

Locate the section. From the list, choose .

In the Δε text field, type ev2-ev1.

Locate the section. In the kf text field, type (3e-16*plas.Te^(-1.0)*exp(-0.37/plas.Te) + 4.61e-16*exp(-(log(plas.Te)+1.04)^2/(2*1.10^2)))*N_A_const.

Electron Impact Reaction 14

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v2=>e+Cl2v3.

Locate the section. From the list, choose .

In the Δε text field, type ev3-ev2.

Locate the section. In the kf text field, type (3e-16*plas.Te^(-1.0)*exp(-0.37/plas.Te) + 4.61e-16*exp(-(log(plas.Te)+1.04)^2/(2*1.10^2)))*N_A_const.

Electron Impact Reaction 15

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v1=>e+Cl2v3.

Locate the section. From the list, choose .

In the Δε text field, type ev3-ev1.

Locate the section. In the kf text field, type (1.25e-16*plas.Te^(-1.13)*exp(-0.36/plas.Te) + 1.06e-16*exp(-(log(plas.Te)+1.01)^2/(2*1.06^2)))*N_A_const.

Electron Impact Reaction 16

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2+=>2Cl.

Locate the section. From the list, choose .

In the Δε text field, type -eionCl2.

Locate the section. In the kf text field, type 9e-14*plas.Te^(-0.5)*N_A_const.

Electron Impact Reaction 17

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl=>e+Cl12.

Locate the section. From the list, choose .

In the Δε text field, type eCl12.

Locate the section. In the kf text field, type 4.55e-14*plas.Te^(-0.46)*exp(-2.01/plas.Te-0.001/plas.Te^2)*N_A_const.

Electron Impact Reaction 18

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl=>e+Cl52.

Locate the section. From the list, choose .

In the Δε text field, type eCl52.

Locate the section. In the kf text field, type (7.03e-17*plas.Te^(0.55)*exp(-2.15/plas.Te-1.5/plas.Te^2-2.05/plas.Te^3))*N_A_const.

Electron Impact Reaction 19

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl=>Cl++2e.

Locate the section. From the list, choose .

In the Δε text field, type eionCl.

Locate the section. In the kf text field, type 3.17e-14*plas.Te^(0.53)*exp(-13.29/plas.Te)*N_A_const.

Electron Impact Reaction 20

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl12=>Cl++2e.

Locate the section. From the list, choose .

In the Δε text field, type eionCl-eCl12.

Locate the section. In the kf text field, type 3.17e-14*plas.Te^(0.53)*exp(-13.29/plas.Te)*N_A_const.

Electron Impact Reaction 21

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl52=>Cl++2e.

Locate the section. From the list, choose .

In the Δε text field, type eionCl-eCl52.

Locate the section. In the kf text field, type (4.33e-14*plas.Te^(0.55)*exp(-0.15/plas.Te-0.85/plas.Te^2))*N_A_const.

Electron Impact Reaction 22

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl-=>Cl+2e.

Locate the section. From the list, choose .

In the Δε text field, type eatt.

Locate the section. In the kf text field, type 9.02e-15*plas.Te^(0.92)*exp(-4.88/plas.Te)*N_A_const.

Electron Impact Reaction 23

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl-=>Cl++3e.

Locate the section. From the list, choose .

In the Δε text field, type eatt+eionCl.

Locate the section. In the kf text field, type 3.62e-15*plas.Te^(0.72)*exp(-25.38/plas.Te)*N_A_const.

Electron Impact Reaction 24

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v1=>e+Cl2.

Locate the section. From the list, choose .

In the Δε text field, type -ev1.

Locate the section. In the kf text field, type 3.99e-12*plas.Te^(-1.5)*exp(-7.51/plas.Te-0.0001/plas.Te^2)*N_A_const*exp(ev1/plas.Te).

Electron Impact Reaction 25

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v2=>e+Cl2.

Locate the section. From the list, choose .

In the Δε text field, type -ev2.

Locate the section. In the kf text field, type (3.28e-17*plas.Te^(-1.12)*exp(-0.37/plas.Te) + 2.86e-17*exp(-(log(plas.Te)+0.99)^2/(2*1.06^2)))*N_A_const*exp(ev2/plas.Te).

Electron Impact Reaction 26

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v3=>e+Cl2.

Locate the section. From the list, choose .

In the Δε text field, type -ev3.

Locate the section. In the kf text field, type (1.3e-17*plas.Te^(-1.24)*exp(-0.41/plas.Te) + 6.08e-18*exp(-(log(plas.Te)+0.94)^2/(2*1.02^2)))*N_A_const*exp(ev3/plas.Te).

Electron Impact Reaction 27

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v2=>e+Cl2v1.

Locate the section. From the list, choose .

In the Δε text field, type -(ev2-ev1).

Locate the section. In the kf text field, type (3e-16*plas.Te^(-1.0)*exp(-0.37/plas.Te) + 4.61e-16*exp(-(log(plas.Te)+1.04)^2/(2*1.10^2)))*N_A_const*exp((ev2-ev1)/plas.Te).

Electron Impact Reaction 28

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v3=>e+Cl2v2.

Locate the section. From the list, choose .

In the Δε text field, type -(ev3-ev2).

Locate the section. In the kf text field, type (3e-16*plas.Te^(-1.0)*exp(-0.37/plas.Te) + 4.61e-16*exp(-(log(plas.Te)+1.04)^2/(2*1.10^2)))*N_A_const*exp((ev3-ev2)/plas.Te).

Electron Impact Reaction 29

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl2v3=>e+Cl2v1.

Locate the section. From the list, choose .

In the Δε text field, type -(ev3-ev1).

Locate the section. In the kf text field, type (1.25e-16*plas.Te^(-1.13)*exp(-0.36/plas.Te) + 1.06e-16*exp(-(log(plas.Te)+1.01)^2/(2*1.06^2)))*N_A_const*exp((ev3-ev1)/plas.Te).

Electron Impact Reaction 30

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl12=>e+Cl.

Locate the section. From the list, choose .

In the Δε text field, type -eCl12.

Locate the section. In the kf text field, type 4.55e-14*plas.Te^(-0.46)*exp(-2.01/plas.Te-0.001/plas.Te^2)*N_A_const*exp((eCl12)/plas.Te).

Electron Impact Reaction 31

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type e+Cl52=>e+Cl.

Locate the section. From the list, choose .

In the Δε text field, type -eCl52.

Locate the section. In the kf text field, type (7.03e-17*plas.Te^(0.55)*exp(-2.15/plas.Te-1.5/plas.Te^2-2.05/plas.Te^3))*N_A_const*exp((eCl52)/plas.Te).

Reaction 1

In the toolbar, click