Construction and validation of C₃F₈ electron impact and heavy particle reaction scheme for modeling plasma discharges Open Access

Perfluorocarbons (PFCs) are extremely stable compounds with unique physical and chemical properties that make them usefully suited for some specialized applications. PFCs such as CF₄, C₂F₆, C₃F₈, and C₄F₈ are widely used in the etching of dielectrics such as silicon dioxide (SiO₂) and silicon nitride (Si₃N₄) because these chemistries exhibit the desired etch selectivities over silicon or mask layers [i.e., amorphous carbon layers and photoresist] by forming upon them a fluorocarbon polymer of sufficient thickness for selective etching.^1–3 One of the most commonly used among these gases is C₄F₈ and its mixtures.^4–7 This is due to the linear temporal growth of the film in the plasma of a given gas and its attractive chemistry properties. C₃F₈ does not have this advantage; however, the qualitative composition of the film obtained when using this gas is very similar to C₄F₈. So, it is commonly used in silicon, SiO₂, glass, and Si₃N₄ etching.⁸ Moreover, C₃F₈ is considered a less dangerous greenhouse gas, since it has a relatively small atmospheric lifetime² and significantly higher utilization, i.e., a greater percentage of C₃F₈ is destroyed in the plasma, than other gases.⁹ In addition to that, C₃F₈ has good thermal and chemical stability, low toxicity, and relatively high vapor pressure. It is used for atomic layer deposition (ALD) of thin films, for example, Al₂O₃¹⁰ and cleaning.⁹ C₃F₈ is also used as a polymer-forming gas in the atomic layer etching (ALE).

Despite its widespread use in industry, there are very little published experimental and theoretical data on RF discharges in this gas.

In addition to the classical data of Christophorou on the cross sections of electronic processes in C₃F_8,¹¹ given, for example, in the book on data for gaseous electronics,¹² there are relatively recent works in the literature devoted to this issue. Thus, in Ref. 13, a set of cross sections is given, normalized to the drift velocity from swarm experiments in C₃F₈ with the addition of argon. The authors of Ref. 13 have added three vibrational cross sections with given thresholds by analogy with C₂F₆ in the absence of similar data in C₃F₈. This gives reasonable agreement between calculations and experiments. Furthermore, in the work,¹⁴ the authors, using this set as a basis, added two inelastic excitation cross sections to describe their swarm experiments both in pure C₃F₈ and with the addition of argon. In both works, the Boltzmann equation solver in the multiterm approximation was used to calculate the drift velocity. Furthermore, in work,¹⁵ the authors again improved this set, separating neutral dissociation from total dissociation, which also includes dissociative ionization. This was done based on works.^16,17 In Ref. 16, the accurate fitting between the last experimental point (22 eV) and threshold of dissociation (10 eV) was received and verified by comparing experimental swarm parameters with those calculated using the Boltzmann equation solver in the two-term approximation (TTA). In Ref. 17, the total and neutral dissociation and total ionization (which is, in fact, all dissociative ionization) cross sections were measured experimentally. In Ref. 15, calculations carried out using the Boltzmann equation solver in the TTA were compared with swarm experiments in pure C₃F₈ and in mixtures with N₂ and CO₂. Rather good agreement with the experiment was obtained. The set of cross sections presented in this work is the most relevant in the published papers. Also, there are recent ionization cross-sectional data,¹⁸ based on the calculation using the binary-encounter Bethe (BEB) method. Based on all of these data, a set of electronic reactions was built in the present paper.

To supplement it with reactions between radicals and ions, sets of zero-dimensional models in C₄F₈^19–24 were taken as a basis. To determine which radicals may be present in the reaction scheme, data on dissociative ionization channels^25,26 were used. Furthermore, dissociation of radicals was also taken from works on C₄F₈. Information on dissociative attachment channels^27,28 and cross sections^27,29 was also used to separate the dissociative attachment cross section from the total attachment cross section and define the main dissociative attachment channel.

We were unable to find any data on plasma characteristics (electron density and temperature, electronegativity, radical density) in the C₃F₈ ICP discharge. The only data on the density of electrons and negative ions in the pressure and power ranges of interest were reported for the CCP discharge.³⁰ In this work, the density of electrons and negative ions (using laser photodetachment) was measured at pressures of 30–120 mTorr and powers of 7–35 W using the noninvasive method of microwave cavity resonance spectroscopy.

This paper is organized as follows: Sec. II provides a brief description of the models used in the calculation of RF discharges. Section III, containing results and discussions, is divided into three parts: validation of electron impact C₃F₈ cross-sectional set and construction of full reaction scheme, calculations in the CCP discharge, and comparison with experiment and calculations in the ICP discharge. Section IV ends the paper with the main results and conclusions.

The two-dimensional (2D) hydrodynamic drift-diffusion ICP model used in this work has been described in detail elsewhere.^31,32 Next, we briefly describe the main points of this model. The plasma parameters (particle densities, electron temperature, fluxes, and others) were found by solving the next set of equations:

1. The continuity equations for the particle densities (electrons, ions, and neutrals):

   $∂ n ∂ t + ∇ · ( n v ) = ∑ j R j ,$

   (1)

   where n is the density and $v$ is the particle flow velocity. On the right-hand side, there is the sum of the production and loss rates of particles in the jth reaction.

2. The conservation equations for the particle momentum in drift-diffusion approximation both for ions and electrons:

   $J = μ n E − D ∇ n ,$

   (2)
   where $μ = q / m ν m$ is the particle mobility, ν_m is transport frequency, q is the particle charge, and $D = μ k B T e / q$ is the diffusion coefficient, where $k B$ is the Boltzmann constant. Also, it is possible to calculate a full ion momentum equation if it is needed.³² In our calculations, electron mobility was specified as a function of the mean electron energy, calculated in the BOLSIG+ program.³³ For ions, the mixture-averaged diffusion coefficient was first found, and then, the mobility was found using Einstein's relation. The input data for this approach are the parameters of the Lennard–Jones potential. A more detailed description of mixture-averaged diffusion approximation can be found in Ref. 34 or in COMSOL Reference Manual.³⁵ The boundary conditions for the electron flux are³⁶ as follows:

   $n · J e = 1 2 v t h n e ,$

   (3)
   where v_th is the electron thermal velocity. The boundary conditions for the $k th$ heavy particle flux are as follows:

   $n · J k = M k R surf , k + M k c k μ k z k ( n · E ) ,$

   (4)
   where $J k$ is mass flux on surface, $M k$ is molar mass, $c k$ is molar concentration, $μ k$ is mobility, and $z k$ is particle charge. $R surf , k$ is defined as follows:

   $R surf , k = ∑ i ν k , i 1 4 γ i 1 − γ i / 2 8 R T π M k ,$

   (5)

   where $ν k , i$ is the stoichiometric coefficient, $γ i$ is the sticking coefficient, R is the gas constant, and T is the gas temperature. For neutral heavy particles $z k = 0$⁠, therefore for them, only the first term remains on the right-hand side of Eq. (4).

3. The energy conservation law for electrons:

   $∂ ∂ t ( 3 2 n k B T e ) + ∇ · q + e J e · E + ∑ j R j H j = 0 ,$

   (6)

   $q = − K ∇ T e + 5 2 k B T e J e ,$

   (7)
   where q is the heat flux, K is the thermal conductivity, and H_j is the enthalpy of the $j th$ reaction. The boundary condition for the electron energy density is³⁶ as follows:

   $n · q = 5 6 v t h n ϵ .$

   (8)

   For the ions, the energy conservation law is not solved. Following Ref. 37, it is assumed that the ion temperature was constant (on the order of 0.1–0.5 eV) throughout the chamber.

4. The distributions of the electromagnetic fields are described by Maxwell's equations, which are solved in the two-dimensional axisymmetric geometry:

   $1 μ 0 μ r ∇ 2 A + ε 0 ε r ω 2 A = − J s ,$

   (9)

   $∇ · ( ε 0 ε r ∇ V ) = − e ( Z i n i − n e ) ,$

   (10)
   where A and V are the vector and scalar electric potentials, and $J s$ is the current density generated by an inductive coil. In this and previous studies, the power applied to the coils is the input parameter and determines $J s$⁠.³¹ The metal walls of the chamber are assumed to be grounded, and boundary conditions for the quartz walls are as follows:

   $− n · D = ρ s , ∂ ρ s ∂ t = n · J i + n · J e .$

   (11)
   The boundary conditions for the vector potential at the outer boundaries of the simulated volume are as follows:

   $n × A = 0 ,$

   (12)

   which means magnetic insulation.

5. To correctly describe the gas temperature distribution, the heat balance equation for neutral gas is solved:

   $ρ C p ∂ T ∂ t + ρ C p u · ∇ T + ∇ · q = Q ,$

   (13)

   $q = − κ ∇ T ,$

   (14)

   where ρ is the mass density, C_p is the heat capacity at constant pressure, u is gas velocity, κ is the thermal conductivity, and Q is the heat source of chemical reactions. More information about term Q can be found in Ref. 31. The boundary conditions for the gas temperature are $T = 313 K$ on all chamber walls. Accounting for gas heating is especially important when studying processes in ICP discharges of mixtures containing molecular gases.³⁸ 

6. To take into account the gas flow, the Navier–Stokes equations are included in the model assuming the absence of turbulence and volumetric forces

   $ρ ∂ u ∂ t + ρ ( u · ∇ ) u = − ∇ p + ∇ ( μ ( ∇ · u + ( ∇ · u ) T ) − 2 3 μ ( ∇ u ) I ) ,$

   (15)

   $ρ ∇ u = 0 ,$

   (16)

   where ρ is the gas density, p is the pressure, μ is the dynamic viscosity, the subscript T on the right-hand side denotes transposition, and I is the unit matrix. The boundary conditions for the velocity of neutral gas at the chamber walls are $u = 0$⁠. Here, in Eqs. (15) and (16), u is the mass-averaged velocity over all heavy particles.

7. The rate coefficient of electron reactions is obtained as follows:

   $k j = ∫ 0 ∞ σ i ( ε ) u e ( ε ) f ( ε ) d ε ,$

   (17)

   where σ_j is the scattering cross section for the jth process, $f ( ε )$ is the electron energy distribution function (EEDF), u_e is the absolute value of the electron velocity, and $ε = m e u e 2 / 2$ is the electron energy. In this study, the EEDF in ICP discharge under given conditions is assumed to be Maxwellian and normalized to unity. This is a common starting assumption for molecular gases in the present pressure range (10–50 mTorr). It is possible to add a solver of the Boltzmann equation in a two-term approximation for a more realistic EEDF (in future work). The electron impact and heavy particle reactions with their rate coefficients are discussed in detail in Sec. III.

In addition to the two-dimensional ICP model described above, a one-dimensional hydrodynamic drift-diffusion CCP model was used in this work. There are practically no experimental data on plasma characteristics in the C₃F₈ discharge. The only work in which the density of electrons and negative ions was measured as a function of discharge power and gas pressure was performed in a CCP discharge. Therefore, to test the set of reactions in C₃F₈ created during this work on the CCP experimental data, this one-dimensional model was used. The governing equations are almost the same as in the ICP model except for Eqs. (4)–(7). Due to the one-dimensionality of the model, the equations for gas heating and Navier–Stokes equations for gas flow were not included. Also, the gas heating is not as big in a CCP discharge as in ICP³⁹ and the temperature could be considered uniform in a one-dimensional model. Instead of two Maxwell's equations (9) and (10), only the Poisson equation (10) in one-dimensional form is solved in the CCP discharge model. The boundary conditions for this equation are: $V = V 0 cos ( ω t )$ on the powered electrode and V = 0 on the ground electrode.

The EEDF shape in model for CCP discharge is also considered to be Maxwellian one. However, at pressures below 100 mTorr, non-local effects may appear that affect the EEDF shape and the results of calculations using this model.

The above sets of differential equations for both models were solved by the finite element method with the help of the COMSOL software package, Plasma Module.³⁵ 

Before constructing a reaction scheme, it is necessary to determine a reliable set of electronic cross sections. The most suitable starting set was chosen from work.¹⁵ In addition to the elastic cross section, the cross sections of three vibrational and two electronic excitations, the attachment cross section, the neutral dissociation, and ionization cross sections are also separated in this set (it is known that all ionization reactions in C₃F₈ are dissociative). However, the work provides comparisons with the results of the swarm experiment for pure C₃F₈ and mixtures with N₂ and CO₂, without using the data in mixtures with Ar from.¹⁴ Also, the calculations were carried out in the TTA Boltzmann equation solver. Therefore, in this work, drift velocities were compared with the experimental data from¹⁴ both in pure C₃F₈ and in a mixture with Ar. The only change made to that set was the replacement of the total ionization cross section with a more recent one calculated using the binary-encounter Bethe (BEB) method.¹⁸ Solutions of the Boltzmann equation were carried out both in the two-term approximation using the Bolsig program³³ and the Monte Carlo (MC) method using the METHES package.⁴⁰  Figure 1 shows the drift velocity in pure octafluoropropane calculated both in the TTA and by the MC simulation, and experimental points from¹⁴ are also shown.

As described in Ref. 15, the present set shows reasonable agreement of the drift velocity calculated in the TTA with the experimental points. Moreover, MC simulation shows results similar to the TTA. Figure 2 shows the drift velocity calculated in the two-term approximation and by the Monte Carlo simulation in comparison with the experiment for two compositions of argon and octafluoropropane mixtures—0.526% and 5.05% of C₃F₈ in Ar. Cross sections for electron interactions with argon were taken from Ref. 41 and include elastic, metastable excitation (11.56 eV) and ionization (15.8 eV) cross sections.

The given set in these calculations shows reasonable agreement with the experimental data in both approaches. All characteristic features of the drift velocity dependence on the reduced field are reflected in the calculation results. Swarm experiments in dilute mixtures with argon are typical when studying molecules inelastic processes with a low energy threshold. The maximum of these inelastic processes cross sections is located near the Ramsauer minimum of Ar elastic cross section. This leads to the high impact of these inelastic cross-sectional absolute values on swarm parameters in a mixture with argon. In our case, these are the cross sections of vibrational excitations, which did not change in the work,¹⁵ remaining the same as in Ref. 14. However, in the original work,¹⁴ calculations were carried out in a multiterm approximation of the Boltzmann equation, while our calculations show that the two-term approximation also describes the experimental dependence quite well. Moreover, the Monte Carlo method for the calculation of swarm parameters was not used in any of these works. So, we additionally made the MC calculations of swarm parameters in pure C₃F₈ and its mixture with Ar, shown in Figs. 1 and 2. As a result, the set from Ref. 15, taking into account the ionization cross section from Ref. 18, describes all the features of the drift velocity both in pure octafluoropropane and in its mixtures with argon. The separation of total cross sections of ionization, dissociation, and attachment by channels and corresponding reactions are discussed below.

To construct a complete reaction scheme for such a complex molecular gas as C₃F_8, it is necessary to determine which radicals and ions will be present in the plasma. Radicals and ions appear due to such electronic inelastic processes as ionization, dissociation, attachment, dissociative ionization, and dissociative attachment. In C₃F₈ gas, all ionization processes are dissociative; therefore, the formation of the C₃F₈⁺ ion is not included in our scheme. All other processes were divided into channels with the formation of various radicals and ions. The resulting radicals and ions can also further break down into smaller particles. To take these processes into account, it was decided to use similar schemes for C₄F_8,²² where all the radicals and ions of interest are present. The complete list of particles taken into account in our scheme is given in Table I.

Table II shows all the electronic reactions present in our scheme.

Based on the structure of the molecule, the most likely channel of neutral dissociation was chosen to be C₃F₈ + e → C₂F₅ + CF₃ + e (reaction R7). Other possible channels are not included in our study to not overcomplicate the scheme with the purely known reaction rates.

Based on the work,²⁶ where partial ionization cross section in C₃F₈ was measured by Fourier Transform Mass Spectrometry (FTMS) in cubic ion cyclotron resonance (ICR) trap cell, it was chosen six dissociative ionization channels (see Table II, reactions R10–R15). Their cross sections^25,26 were normalized to match in sum the total dissociative ionization cross section from Refs. 16 and 18. The normalized partial ionization cross sections are shown in Fig. 3.

The radicals obtained in these reactions were subsequently used to construct a complete reaction scheme.

It is also important to separate dissociative and non-dissociative electron attachment processes. The cross sections for total and dissociative attachment are presented in the paper.²⁷ Possible channels of dissociative attachment are also indicated there. The work²⁸ shows the relative intensities of signals from five negatively charged radicals in C₃F₈: F⁻, C₂F₅⁻, CF₃⁻, C₂F₃⁻, and C₃F₇⁻. However, the signal intensity from F⁻ is at least 10 times greater than from the others. The work²⁹ provides a cross section for dissociative attachment in C₃F₈ with the formation of F⁻, which matches the total cross section for dissociative attachment from the work.²⁷ Thus, in our reaction scheme, there is a dissociative attachment cross section with the formation of F⁻ (R9) and a non-dissociative attachment cross section (R8) equal to the difference between the total attachment cross section and the dissociative attachment cross section. The reaction R55 for electron detachment from C₃F₈⁻ is taken similarly to C₄F₈⁻ from Ref. 22.

Heavy particle reactions such as neutral recombination, ion–ion recombination, ion charge exchange, and others were also taken from the detailed reaction scheme in C₄F₈²² for radicals and ions present in C₃F₈ plasma. The complete list is given in Table III. The reaction R131 for C₃F₈⁻ is taken similarly to C₄F₈⁻ from Ref. 22. The reaction R133 means that the X⁺ and Y⁻ ions are neutralized into the corresponding molecules X and Y without dissociation, where X⁺ and Y⁻ are combinations of all possible ions listed in Table I. Thus, R133 corresponds to 27 reactions in total.

Sticking coefficients of reactions on the walls were set based on the works²² and²¹ and presented in Table IV. $X +$ in Table IV is representing all possible positive ions, listed in Table I, and $X$ is representing corresponding neutral species. There are nine surface reactions concerning positive ions in total. In future work, the particle wall loss should be corrected for the particular experiment conditions. The sticking coefficients should be obtained either experimentally or from model estimations taking into account the experimentally measured radical densities.

Once a reaction scheme has been constructed, it must be validated against data from experimental setups. Since we did not find data on ICP discharges in C₃F₈ in the literature, we had to use data from the CCP discharge from the work³⁰ for validation. This paper presents electron and negative ions densities measured using the noninvasive method of microwave cavity resonance spectroscopy at pressures of 30–120 mTorr and powers of 7–35 W. In this experiment, the capacitively coupled rf plasma was produced within a cylindrically shaped microwave cavity. Part of the cavity wall was RF powered (13.56 MHz RF source), and the rest was grounded. The electrode separation was 20 mm. The radius of RF-driven electrode was 62 mm, and the inner radius of the cavity was 87.5 mm. A detailed description of this geometry can be found in Ref. 42. To obtain plasma characteristics in this configuration, we used a 1D hydrodynamic model, where the computational region corresponded to the gap between the electrodes (20 mm), the corresponding voltage was applied to one end of the interval (representing the power electrode), and the other one was grounded. The gas temperature was set to be constant along the interval and was equal to 300 K. The calculation results are shown in Fig. 4.

The obtained power dependencies [Figs. 4(a) and 4(c)] qualitatively describe the experimental data. The densities of electrons and negative ions differ quantitatively by less than 2 times. While their ratio - electronegativity - differs by no more than 10%, except for the last point. The last experimental point at a power of 35 W quite sharply changes the dependence of the density of negative ions on power, which may be due to inaccuracy of the measurements. In this case, the slope of the curve would practically fit with the calculated one and would intersect with the electron density curve also only in the region of 23 W. Taking into account the complexity of the reaction scheme and the absence of any experimental data on the degrees of dissociation and concentrations of separate radicals, we can say, as a first approximation, that the model adequately estimates the densities of charged particles in the C₃F₈ plasma at a given pressure and in a given power range.

The dependences on pressure look different. At high pressures (>80 mTorr), the differences in concentrations are also of the order of 40%, and in electronegativity is no more than 10%. At low pressures, only the concentration of negative ions differs within 40%, while the electron concentration and electronegativity at 30 mTorr differ by 8 times. Moreover, the qualitative dependences differ dramatically. In the experimental data, there is practically no dependence on pressure, while in the obtained results the electron concentration is minimal at low pressure and increases, gradually approaching the experimental values. Following this, the electronegativity dependence has the opposite tendency. This can be explained by the fact that the hydrodynamic drift-diffusion model cannot correctly describe the CCP discharge at low pressures.

So, the resulting model adequately describes the few experimental data that are available in the literature at pressures of the order of 100 mTorr.

For completeness, Fig. 5 shows the dependence of the C₃F₈ dissociation degree on power.

As we can see, in the CCP discharge of octafluoropropane, the number of radical molecules does not exceed one-fifth of the total molecules. Thus, we have a strongly electronegative discharge (under all calculated conditions, the electronegativity is much greater than 1), while the main molecule does not dissociate much under the calculated conditions.

Figure 6 shows diagrams of the concentrations of radicals and ions in C₃F₈ CCP plasma at a pressure of 120 mTorr and a power of 25 W.

It can be seen that the main radicals are heavy C₃F₇, C₂F₆, and C₂F₅, which is also a consequence of the weak dissociation of these molecules under these conditions. The main negative ion is F⁻, and its concentration is 30 times higher than the electron concentration. The main positive ions under these conditions can be considered heavy C₃F₇⁺ and C₂F₅⁺, as well as the relatively light CF₃⁺. Similar distributions are observed in other conditions considered in this work. These concentrations of radicals were obtained without any normalization to experimental values. Therefore, when such data appear, the reaction scheme (mainly wall loss coefficients) presented in this work will need to be modified to match the real experimental conditions. This is the very first attempt to create a proper scheme for C₃F₈.

Since octafluoropropane is also used in ICP discharges, we carried out calculations using our two-dimensional hydrodynamic ICP model taking into account neutral gas heating and flow.^31,32 Calculations were carried out using an experimental chamber from our laboratory as a reference. A detailed description of this geometry is given in Ref. 32. Below we briefly describe the main points. It is a cylindrical metal volume 10.4 cm in height and 16.2 cm in radius. At the bottom, there is an electrode with a radius of 6 cm, which in our calculations is under a floating potential. The top of the chamber is covered with quartz glass 1.5 cm thick, on which there are four turns of a copper coil. The frequency of the signal supplied to the coil is 13.56 MHz. Calculations were carried out at a pressure of 10 mTorr, typical for ICP discharges, and in the power range of 200–750 W, typical for this facility.

The results are presented in Fig. 7 as 2D distributions of electron density, main negative ion (F⁻) density, main positive ion (CF₃⁺) density, and gas temperature for a discharge power value of 500 W.

From the pictures, it can be seen that the density of negative ions is concentrated in the center of the discharge and at the peak is slightly higher than the density of electrons. Thus, electronegativity is greater than unity only in a small region in the center of the discharge. As will be shown below, at higher powers, the discharge ceases to be electronegative at all. The electron density is distributed more uniformly in the bulk of the discharge. The density of positive ions follows the profile of negative ions in the center and transfers to the profile of electrons, providing quasi-neutrality. This distribution of profiles is associated with a complex relationship between the mobilities of charged particles of different masses in non-own gas. In this work, ion mobility was calculated through the Einstein relation from the mixture-averaged diffusion coefficient.³⁵ The maximum gas temperature distribution is in the center and at the peak is about 800 K, which correlates with experimental data, for example, in ICP discharges in CF₄ gas.³⁸ 

Figure 8 shows the dependence of electronegativity and the degree of dissociation on the power at the center of the chamber. It can be seen that at low powers, there are almost twice as many negative ions as electrons, but with increasing power, the discharge ceases to be electronegative. Also, almost all initial molecules of C₃F₈ are dissociated in all power ranges. This result differs significantly from the results in the CCP discharge, where under all conditions considered, the electronegativity was high (no less than 20) and the degree of dissociation was low (no more than 20%).

A high dissociation degree may occur because the electron temperature under the coil reaches 5–6 eV, while in the CCP discharge in the plasma bulk, it was about 3 eV.

Thus, electronegativity is so low because the original molecule strongly dissociates and the discharge sustains in a mixture of radicals (mainly CF₂). The attachment cross-sectional peak for CF₂ is an order of magnitude lower (∼2 × 10⁻¹⁸ cm²)⁴³ than in C₃F₈ (∼1 × 10⁻¹⁷ cm²), and in our scheme, this reaction (R52) is written as a process rate (3 × 10⁻¹¹ cm³/s), by analogy with C₄F₈ schemes. Accordingly, with the used attachment, cross-sectional reactions (R8) and (R9) have a total rate of about ∼2–3 × 10⁻¹⁰ cm³/s depending on conditions which is an order of magnitude higher than the rate of (R52).

Figure 9 shows diagrams of radicals and ions concentrations in C₃F₈ ICP plasma at a pressure of 10 mTorr and a power of 500 W.

Unlike the discharge in the CCP, here we see a different picture of charged and neutral species relative composition. Due to higher T_e value in ICP discharge, not only the main molecule but also its large radicals actively dissociate. Therefore, the main radicals are CF₂, CF₃, and C₂F₆. The main molecule dissociates so strongly that 7 of its radicals exceed it in concentration. Thus, it turns out that the discharge burns not in C₃F₈ gas, but in a mixture of its radicals, which significantly complicates accurate calculations. The main negative ion remains F⁻, but the concentration of electrons increases significantly compared to CCP discharge. The composition of positive ions has also changed, now lighter ions (CF₃⁺ and CF₂⁺) of basic radicals are prevailing.

Although CCP and ICP plasma results are compared in this section, it should be noted that the purpose of the present paper is not the direct comparison of ICP and CCP discharges, but the simulation of C₃F₈ plasma in the typical discharge parameters of CCP and ICP. The power densities of the two studied discharge configurations are similar (0.023–0.088 W/cm³ for ICP, 0.0146–0.073 W/cm³ for CCP). The surface area to discharge volume ratios are different (1.2 cm⁻¹ for CCP and 0.3 cm⁻¹ for ICP). Direct comparison of ICP and CCP at the same specific powers and S/V ratio is a separate task and may not be the useful one, because of different typical geometries of ICP and CCP in their real applications. The ICP discharge is hardly ignited in the typical CCP geometry with the small electrode gap and large electrode diameter. The CCP excitation is not practically useful in the studied ICP geometry due to poor spatial uniformity, which are crucial in CCP discharge applications.

In this work, a set of electronic and heavy particle reactions was constructed to simulate plasma discharges in C₃F₈. For this purpose, a set of electron collision cross sections for C₃F₈ was taken from the literature and additionally validated on swarm parameters. Based on the reaction channel information, a scheme of electronic reactions was compiled. A complete reaction scheme was constructed for all the ions and radicals under consideration by analogy with C₄F₈. Calculations were carried out for the CCP and ICP discharges in C₃F₈ in one-dimensional and two-dimensional hydrodynamic drift-diffusion models, respectively, using the resulting reaction scheme. A comparison with the available experimental data on the CCP discharge showed the adequacy of the constructed scheme and reasonable agreement was obtained on electron and ion density data in the region of model applicability (neutral gas pressure higher than 80 mTorr). The dissociation degree and ion and radical compositions were additionally obtained as a function of power for both the CCP and ICP discharges. The spatial distributions of charged particles are shown for an ICP discharge. The results obtained in ICP and CCP discharges differ significantly. Thus, in CCP, the degree of dissociation was low (no more than 20%), and the electronegativity was high (no less than 20). In ICP, the opposite trend is observed. The main molecule C₃F₈ dissociates to a large extent, and the discharge burns in a complex mixture of its relatively light radicals. In this case, the electronegativity at low powers only reaches 2, and at high powers, the discharge ceases to be electronegative. This can be explained by a difference of approximately an order of magnitude in the peak of the attachment cross sections and the corresponding electron reaction rates of the dominating C₃F₈ component in the CCP case and the main radical CF₂ in the ICP case.

The constructed model, as far as the authors know, is the first attempt to describe the chemical scheme of reactions in octafluoropropane. Therefore, in the future, if appropriate experimental data in an ICP discharge will be available (concentrations and fluxes of charged particles, radical composition), this scheme can be improved and supplemented.

This work was done with the support of MSU Program of Development, Project No. 23A-SCH06-06.

The authors have no conflicts to disclose.

Andrey Kropotkin: Data curation (lead); Formal analysis (equal); Investigation (lead); Software (lead); Validation (equal); Visualization (lead); Writing – original draft (lead). Dmitry Voloshin: Conceptualization (lead); Data curation (lead); Funding acquisition (lead); Methodology (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.