Applied Science and Convergence Technology 2020; 29(6): 125-132
Published online November 30, 2020
https://doi.org/10.5757/ASCT.2020.29.6.125
Copyright © The Korean Vacuum Society.
Dhanoj Gupta^{*}
Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot-7610001, Israel
Correspondence to:E-mail: dhanojsanjay@gmail.com
A brief review of the electron collision studies of perfluorocarbons and SF6 relevant to plasma is presented. The use of these gases in various applications of plasma is highlighted, and their possible replacement with gases that have a low global warming potential is suggested. The results for a few simple fluorocarbons are presented, i.e., C_{2}F_{2}, C_{3}F_{4}, and C_{4}F_{6} for elastic scattering and C_{2}F_{6} for ionization, and the requirement for further investigation is highlighted. This review is not extensive; however, it presents an important step towards understanding the lack of cross-section data for numerous fluorocarbon molecules/radical species. In addition, it highlights the requirement for the detailed study of fluoroketones and fluoronitriles, which are possible substitutes for SF6 for various electron collisional processes other than ionization.
Keywords: Electron collision, Perfluorocarbons, Cross-section data, Plasma
The collisions of electrons with atoms, molecules, ions, and surfaces are of fundamental importance in low-temperature plasmas (LTPs), with numerous applications in plasma science and technologies. LTPs represent a unique state of matter consisting of neutral atoms and molecules, radicals, ions, electrons, and excited states. They are used in the semiconductor industry for etching, depositing materials, synthesizing nanomaterials, and cleaning reaction chambers and in the field of plasma medicine [1]. Electron collision data are important in the fields of astrophysics, astrochemistry, aeronomy, radiation physics, gas discharge, electron beam lasers, and plasma processing devices for auroras and solar plasma [2]. Plasma–wall interactions are one of the major challenges in the realization of plasma reactors. These interactions are important for the physical and chemical processes in all plasmas with technological applications. Perfluorocarbons (PFCs) are extensively used as feedstock gases for various applications in plasma processing [3,4]. PFC gases, such as CF_{4}, C_{2}F_{6}, and C_{3}F_{8}, have been widely used for plasma etching applications [3]. SF_{6} is widely used in high-voltage gas-insulated switchgears and gas-insulated lines [5] and as an etchant [6]. However, the global warming potential (GWP) of SF_{6} is 22800 times larger than that of CO_{2}, and it is extremely difficult to decompose in the atmosphere [7]. This has led to interest in finding a suitable replacement for this gas. Moreover, owing to the requirement of the Kyoto Protocol [8] for the reduced emission of PFCs and SF_{6}, research is being actively conducted on new gases with a low GWP, which can be suitable substitutes for existing plasma gases in various plasma applications. Hence, it is desirable to find alternative gases that are environment friendly with a relatively low GWP but with a potential similar to SF_{6} or other currently used PFCs. For this purpose, the detailed electron collision studies of possible substitute gases at the molecular level is important at energies ranging from 0–100 eV. In LTPs (3–5 eV), the energy of electrons can reach up to 100 eV. Hence, the collision cross-section data in the range of 3–100 eV are important. Moreover, to experimentally analyze electron heating mechanisms [9,10], scattering and excitation cross- section data are required up to a minimum of 25 eV but desirable up to a maximum of 100 eV.
The literature survey shows that there is still a lack of electron collision cross-section data for numerous PFCs and their fragments. The ionization cross sections (
The literature survey for the low and intermediate energies for electron scattering elastic, differential, momentum, excitation, and total cross sections for PFCs shows the lack of complete cross-section data. Various elastic and total cross sections for PFCs and SF_{6} have been experimentally measured [36-52]. Szmytkowski and Możejko have compiled the measurements of the total cross sections from a range of molecules from 2009–2019 [53]. The low and intermediate energies cross-section calculations for various collision processes for several fluorocarbons have been theoretically predicted [54–59]. In recent years, the scarcity of cross-section data for simple fluoro- carbons has led to studies on the low-energy cross section of fluoro- carbons, such as C_{2}F_{2} [60], C_{3}F_{4} [61], and C_{4}F_{6} isomers [62], for various elastic and inelastic processes using the R-matrix method. At inter- mediate and high energies, differential and total cross sections have been computed using the single-center approach for C_{4}F_{6} isomers [63].
Goswami and Antony [64] have recently calculated cross-section for elastic and inelastic processes for an extensive range of energies for SF_{6} using the R-matrix and spherical complex optical potential (SCOP) [32,33] methods. They have provided detailed references for various cross-section studies on SF_{6} in their article; hence, readers are directed to their article for more information about SF_{6}. In the aspect of finding potential substitutes for SF_{6}, fluoroketones and fluoronitriles have been extensively studied over the past few years owing to their low GWP compared to SF_{6} [65–68]. These studies have focused on the insulation properties of these gases under different conditions. Furthermore, these gases have received considerable attention for the study of electron impact ionization because this is an important parameter for examining electron avalanche and gas breakdown mechanisms. Wang
In the current scenario, it is widely recognized that there are new technological advances in plasma processing and the utilization of plasmas in general, ranging from plasma medicine to material processing. These developments are based on the manipulation of plasma properties. This highlights the requirement for a detailed understanding of the atomic and molecular processes within plasmas. It is well known that theoretical calculations are important for providing data over a com- prehensive range of energies [80]. Even though there is active research worldwide on the experimental determination of electron collision cross sections for several atoms/molecules/radicals, the data for nu- merous other important targets are still unknown [81]. In the next section, a brief description of the theoretical methods used by the author is presented along with recent results obtained using each method.
There are various theoretical methods for studying low-energy electron molecule collisions. This subsection presents a brief over- view of the
The UK polyatomic R-matrix codes [87] have been implemented in the Quantemol-N software [88], which can be used by specialists and nonspecialists with a background in scattering theory. Quantemol- N has been used for several years for successfully calculating various low-energy cross sections for a variety of molecules [89–101]. The fixed nuclei approximation has been employed in all calculations performed by the author. The basis of the R-matrix method is the division of a configuration space into an inner region and outer region. The inner region should be selected such that it contains the wave function of a target, where the center of mass of the target coincides with the origin of the coordinate system. The interaction potentials originating from the static, exchange, polarization, and correlation between the target and projectile must be included in the inner region. The advantage of the inner region problem is that a precise solution can be obtained using quantum chemistry codes. The inner region problem is energy independent, and hence, it must be solved only once. This makes the R-matrix method computationally affordable and easy to use. All target properties are calculated in the inner region.
The wave function constructed inside the inner region for the (
where
A set of MOs is constructed from occupied and virtual target MOs using the Hartree–Fock self-consistent-field calculation augmented with Gaussian type orbitals and the continuum orbitals of Faure
Moreover, differential cross sections and momentum transfer cross sections can be acquired using the
The SCOP and CSP-ic methods are widely used theoretical formalisms for calculating elastic and inelastic cross sections at inter- mediate to high energies. The total cross section is the sum of elastic and inelastic cross sections. These methods have been successfully used to calculate various electron collision cross section for atoms [108–114] and molecules [115–124] at intermediate to high energies. In addition, they have been adapted to study positron collisions with atoms and molecules [125]. In the SCOP method, complex optical potential (
The first term of Eq. (3) accounts for all elastic processes, and the second term represents absorption processes, which account for the loss of flux into various inelastic channels. Real potential consists of static (
The static potential and charge density of a target are obtained from the parameterized Roothan–Hartree–Fock wavefunction of the Cox and Bonham parameters [126]. Exchange potential is obtained from the parameter-free Hara [127] free electron gas exchange model, and the model potential of Zhang
Once the complete interaction potential given by Eq. (3) is obtained, the Schrödinger equation is solved using the partial wave approximation to obtain the complex phase shifts (
Here,
The sum of elastic and inelastic cross sections from Eqs. (5) and (6) provides the total cross section, which is expressed as
The detailed derivation of the equations are provided in [130].
The inelastic cross section calculated using the SCOP method can be utilized to obtain
where the first term represents the total excitation cross section for all dipole-allowed electronic transitions and the second term represents all ionization processes (single, double, inner shell, etc.) induced by a projectile electron. The contribution of excitation decreases as the contribution of ionization increases with incident energies.
The BEB method is combination of the Bethe theory and Mott cross section. Kim and Rudd [28] and Hwang
where
Here,
A recent article by Karwasz
This section discusses the recent results obtained by Gupta
Figure 1(a) shows the application of the R-matrix and SCOP methods at low, intermediate, and high energies to calculate the elastic cross section, as studied by Gupta
Figure 2 shows the results for the R-matrix calculation of the elastic and excitation cross sections for the three isomers of C_{4}F_{6}, i.e., 1,3-C_{4}F_{6}, c-C_{4}F_{6}, and 2-C_{4}F_{6}. Even though the molecular formulae for all isomers are the same, their elastic scattering cross sections are quite different below 8 eV as depicted in Fig. 2(a) owing to the different molecular geometry of the targets. The shape resonance is detected for all three isomers, 1,3-C_{4}F_{6}, c-C_{4}F_{6}, and 2-C_{4}F_{6} at 2.95, 2.57 and 3.20 respectively. The experimental results of the elastic cross section obtained by Hoshino
Figure 2(b) depicts the excitation cross section of the first excited state of the three isomers. The thresholds for the first exci- tation energy of 1,3-C_{4}F_{6}, c-C_{4}F_{6}, and 2-C_{4}F_{6} are at 4.88, 5.84, and 6.74 eV for the ^{3}B, ^{3}B_{2} and ^{3}A'' states, respectively. The isomer effect is not sufficiently strong in the case of the electronic excitation cross section. The sharp feature is observed at approximately 9.6 eV for 1,3-C_{4}F_{6} and 2-C_{4}F_{6}, which may be owing to the Feshbach resonances detected at the same energy range for these isomers. A recent study by Bharadvaja
Figure 3 shows the
The BEB results of Gupta
The author would like to thank the Weizmann Institute of Science, Israel, for the prestigious Dean of Faculty Fellowship and Prof. Daniel Zajfman and Dr. Oded Heber from the Weizmann Institute of Science for their support. The author would also like to thank his collaborators, Dr. Jung Sik-Yoon, Dr. Mi-Young Song, Dr. Deuk Chul Kwon, and Dr. Heechol Choi from National Fusion Research Institute, South Korea, Prof. Bobby Antony from the Indian Institute of Technology (Indian School of Mines) Dhanbad, India, and Dr. Suvam Singh from the Max Plank Institute for Nuclear Physics, Germany.