Electron Swarm Research Articles

Determination of the electron collision cross-section set for the C4F6 molecule by using an electron swarm study

A set of electron collision cross-sections for the C4F6 molecule has been successfully determined for the first time by using an electron swarm method with a two-term approximation of the Boltzmann analysis. The set is evaluated by fitting the calculated electron drift velocities in pure C4F6 and in C4F6-Ar mixtures to the experimental data in the E/N range of 0.35 — 1200 Td (1 Td = 10−17 Vcm2), where E/N is the ratio of the electric field (E) to the neutral number density (N). The set is confirmed to be reliable due to our ability to reproduce satisfactorily the electron drift velocities in pure C4F6 and in 0.1, 0.5, 1, 5, and 10% C4F6-Ar mixtures with deviations of ±5%. The set may be the best available so far for use in the quantitative numerical modeling of a4 plasma discharge for various processing procedures with materials containing C4F6 molecules.

Determination of the electron collision cross sections for the C2H4 molecule by using the electron swarm method

A set of low-energy electron-collision cross sections for ethene (C2H4) is necessary for quantitative numerical modeling of plasma discharges for processing procedures with materials containing C2H4 molecules. The set was derived from the measured electron transport coefficients for a pure C2H4 molecule by using an electron swarm study and a two-term approximation to the Boltzmann equation for energy. The electron transport coefficients, which were calculated by using the derived set, are in good agreement with the experimental values over a wide range of E/N ratios in pure C2H4 molecule, where E is the electric field and N is the neutral number density. The validity of the present set of the C2H4 molecule was not only checked by using a Monte Carlo simulation but also evaluated by comparison with another set.

Electron swarm transport in THF and water mixtures

The transport coefficients of electrons in mixtures of gaseous water and tetrahydrofuran (THF) are calculated using a multi-term solution of the Boltzmann equation. Electron transport coefficients at room temperature are presented over a range of reduced electric fields from 0.1–1000 Td, with significant differences between the behaviour in pure water and pure THF being found. The influence of the water to THF mixture ratio on the calculated transport coefficients is also presented.

Electron transport in CF3I and CF3I-N2 mixtures

Electron collision cross sections for CF3I are estimated using the electron swarm method. Electron drift velocity, effective ionisation coefficient, and longitudinal diffusion coefficient in CF3I are calculated using Monte Carlo method, and the calculated electron transport coefficients are compared with those measured. Calculated electron drift velocity agrees with measured data within the difference of 6% below 1600 Td, and calculated effective ionisation coefficient agrees with measured data within the difference of 10% above 460 Td. Further, those swarm parameters in CF3I–N2 mixtures are calculated, and calculated values of electron drift velocity and effective ionisation coefficient agree well with measured data in CF3I–N2 mixtures. This confirms the validity of the estimated set.

Electron swarm experiments in dense rare gases: a review

Swarm techniques have largely been used to investigate electron transport in very dilute gases in order to shed light on the electron-atom (molecule) scattering cross section and, hence, on the interaction potential. The theoretical basis for the analysis of these experiments is classical Kinetic Theory. However, electron transport in dense media, either in gaseous- or condensed phase, is a physical phenomenon of fundamental and practical interest. Dense rare gases are model systems for disordered media. They are particularly well suited to investigate how the dynamics and energetics of quasifree electrons change as the environment density is gradually increased. A review on the electron swarm experiments in dense rare gases is presented here.

시뮬레이션에 의한 SF6-He 혼합기체에서 전자에너지 분포함수

This paper describes the electron transport characteristics in SF6-He gas calculated E/N values 0.1～700[Td] by the Monte Carlo simulation and Boltzmann equation method using a set of electron collision cross sections determined by the authors and the values of electron swarm parameters obtained by TOF method. This study gained the values of the electron swarm parameters such as the electron drift velocity, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients for SF6-He gas at a range of E/N. A set of electron collision cross section has been assembled and used in Monte Carlo simulation to predict values of swarm parameters. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, Lucas and Carter. The swarm parameter from the swarm study are expected to sever as a critical test of current theories of low energy scattering by atoms and molecules.

Negative surface ionization electron affinities and activation energies of SFn

Sulfur hexafluoride (SF6 ) is the most frequently used standard for anion mass spectrometry because of its large temperature-independent cross-section for electron attachment. However, the kinetic and thermodynamic properties--the products of the reactions, and the number of negative ion states of the SF(n)--are presently in dispute. The electron affinities for SF(n) (n = 1-6) are predicted by assuming dissociation energies and ground-state electron affinities based on literature values. The temperature dependence of the 2012 negative surface ionization mass spectrometer data, and other negative ionization mass spectrometry, electron capture detector, and beam and magnetron data, are analyzed using a kinetic model. More precise and accurate activation energies for thermal electron attachment and electron affinities of SF6 , SF5 and SF4 are reported. The largest experimental electron affinities of SF, SF2 and SF3 are assigned to the ground states. Ionic Morse potentials for multiple states are calculated. A mechanism for the formation of the ionic products observed in negative surface ionization thermal electron attachment to SF6 is presented. Negative surface ionization on a hot filament with mass spectrometry is a relatively simple and effective method for determining electron affinities similar to the electron capture detector, magnetron, swarm and beam procedures. A new method of predicting the number of negative ion states from dissociation limits establishes targets for the data analysis. Pseudo one-dimensional anionic Morse potentials illustrate the mechanism for the reaction of thermal electrons with SF6 and the consecutive dissociation pathways.

A novel method to determine the concentration of VOCs at atmospheric pressure

A novel method to detect the concentration of electronegative VOCs based on the electron attachment rate at atmospheric pressure, through negative discharge in an ion drift tube, is introduced. When the carrier and drift gas in the drift tube are all high-purity nitrogen, electrons are formed by a negative discharge in the ion source, and are injected into the drift region through the shutter grid. When the electronegative sample molecules are continuously introduced into the drift tube from one end, the neutral molecules are ionized through a collision and capture process with the counterflowing swarm of electrons in the drift region. The electron swarm is exponentially diluted as it travels in the drift region. As a result, negative ions are formed in the drift region and a tail appears in the ion mobility spectrum. These spectra include information such as the intensity of the ions and electrons, the drift time, analyte concentration, the electron capture rate etc. The sample concentration can be calculated using the relative equation including information from the spectrum. As examples, in this work the concentration of electronegative samples of CCl4, CHCl3, and 1,1,1-C2H3Cl3 are studied when the electron energy is about 0.54 eV. The sample concentrations obtained in the experiment using this method are in good agreement with the initial concentrations created using a syringe pump. The comparison shows that the process of utilizing electron capture information to determine concentration is effective. This study provides a novel method to determine the concentrations of VOCs at atmospheric pressure.

Transport properties of electron swarms in tetrahydrofuran under the influence of an applied electric field

Using an almost complete set of electron impact cross sections for scattering from the important biomolecule tetrahydrofuran (THF), compiled as a part of this study, swarm transport coefficients are determined by solving the Boltzmann's equation over the range of applied reduced fields from 0.01 to 10 000 Td. The present investigation highlights the experimental issues associated with, and the real need for, measurements of the corresponding THF transport coefficients, so that the self-consistency of our proposed cross section set might be evaluated.

Electron attachment to molecules studied by electron beam and electron swarm experiments

Relative cross sections obtained in dissociative electron attachment (DEA) reactions from crossed beams experiment are often normalised using absolute rate coefficients obtained from electron swarm experiments. Both methods, however, are carried out under rather different pressure conditions, namely single collision conditions (beam experiments) and in a higher pressure environment (electron swarm experiments). The peculiarities of the DEA process are considered with respect to these different conditions. Results from both methods are compared by means of two case studies, namely electron attachment to CF2Cl2 (swarm, effusive beam, supersonic beam containing clusters) and CClF2COOH (swarm, effusive beam).

Response analysis of electron attachment rates to C3F8 and SF6 in buffer gases

Electron swarm methods are applied for investigating the effects of small amounts (⩽1.5%) of a strongly electronegative sample gas in the buffer gases Ar, N2 or CO2. A pulsed Townsend method, a Monte Carlo swarm method, and a solution of the Boltzmann equation are used to determine the effective ionization rate constants of the gas mixtures. The sensitivity of the effective ionization rate constant to changes of the mixing ratio is evaluated. Our methods are benchmarked with the analysis of Ar–SF6 and N2–SF6 mixtures, and subsequently used for the analysis of gas mixtures containing C3F8. The results based on the recommended C3F8 cross sections are shown to be inconsistent with the experimental data for N2–C3F8 and CO2–C3F8 mixtures.

Electron swarm coefficients and the limiting field strength of SF6–N2O mixtures

The electron drift velocities and the effective ionization coefficients have been measured with a pulsed Townsend apparatus for the SF6–N2O mixtures (1–75% SF6) over the combined density-normalized electric field strength, E/N, from 130 to 420 Td (1 Townsend = 10−17 V cm2). Strong electron detachment effects have been observed for gas pressure mixtures above 1 Torr due mostly to NO−, arising as a dissociation product of N2O. In contrast, the influence of detachment due to the negative ions from SF6 is shown to be very small. It has been found that the limiting electric field strength, E/Nlim, of the SF6–N2O mixture is slightly superior (25–5%) to that of SF6–N2 for SF6 amounts of 0–50%, respectively.

Electron Swarm Parameters and Electron Collision Cross Sections

An electron swarm study using molecular gas-rare gas mixtures is briefly reviewed, and the advantage of using these mixtures to evaluate inelastic electron collision cross-section data for molecules through electron swarm study is explained. This advantage also suggests a new procedure for deriving a consistent set of electron collision cross sections for molecules by using electron swarm data measured in pure molecular gas and in the molecular gas-rare gas mixtures alternately. The procedure is detailed by using an example of C2H4. The derived cross-section set for C2H4 covers the energy range where a conventional electron beam experiment is not practical and can be crucial for the quantitative modeling of relevant plasmas.

Characteristics of Electron Conduction in a Gas under a Quadrupole Magnetic Field and Radio-Frequency Electric Fields

Electron conduction in CF4 under a simplified model quadrupole magnetic field (QMF) and rf electric fields at f = 13.56, 27.12, and 40.68 MHz was analyzed using a Monte Carlo method, following the manner of electron swarm analyses. This field configuration simulated current paths of magnetic neutral loop discharge plasmas used for dry etching. The electron conduction therein was focused on as an elemental process of plasma power deposition. The electrons formed a star-shaped distribution with four rays along the separatrices of the QMF. The effective electron conductivity quantified as the amplitude of mean electron velocity was high around the central axis. The time-averaged mean electron velocities in the four regions of the QMF were biased under a rectification effect of the magnetic field. With increasing f, the high-conductivity region expanded and ionization was promoted. An enhancement of plasma power deposition under high driving frequencies was indicated.

Electron Collision Cross Sections for the BF3Molecule and Electron Transport Coefficients in BF3–Ar and BF3–SiH4Mixtures

A consistent set of low-energy electron collision cross sections for the boron trifluoride (BF3) molecule has been derived from the measured electron transport coefficients for a pure BF3 molecule using an electron swarm study and a two-term approximation of the Boltzmann equation for energy. The electron transport coefficients, which were calculated using the derived set, are consistent with the experimental data over a wide range of \(E/N\) values (ratio of the electric field \(E\) to the neutral number density \(N\)). The present set of electron collision cross sections for the BF3 molecule, therefore, is the best available so far for the quantitative numerical modeling of plasma discharges for processing procedures with materials containing BF3 molecules. The electron-transport coefficients for BF3–Ar and BF3–SiH4 mixtures were also calculated and analyzed in a wide range of \(E/N\) ratios for the first time. The presence of a remarkable synergism in the Townsend first ionization coefficient has been pointed out in BF3–SiH4 mixtures.

The effective ionization coefficients and electron drift velocities in gas mixtures of CF3I with N2 and CO2 obtained from Boltzmann equation analysis

The electron swarm parameters including the density-normalized effective ionization coefficients (α−η)/N and the electron drift velocities Ve are calculated for a gas mixture of CF3I with N2 and CO2 by solving the Boltzmann equation in the condition of a steady-state Townsend (SST) experiment. The overall density-reduced electric field strength is from 100 Td to 1000 Td (1 Td = 10−17 V·cm2), while the CF3I content k in the gas mixture can be varied over the range from 0% to 100%. From the variation of (α−η)/N with the CF3I mixture ratio k, the limiting field strength (E/N)lim for each CF3I concentration is derived. It is found that for the mixtures with 70% CF3I, the values of (E/N)lim are essentially the same as that for pure SF6. Additionally, the global warming potential (GWP) and the liquefaction temperature of the gas mixtures are also taken into account to evaluate the possibility of application in the gas insulation of power equipment.

Boltzmann analysis of electron swarm parameters in binary CF4+ Ar mixtures

The electron swarm parameters, namely electron mean energy, drift velocity, effective ionization coefficient and limiting values of number density reduced electric fields, E/N, are calculated in CF4+Ar mixtures for various CF4 concentrations that vary from 2 to 100% over a range of E/N from 50Td to 600Td by solving Boltzmann's equation. In this study Boltzmann's equation was solved using finite difference method under steady-state Townsend condition. One of the most important results of this study indicated that at higher E/N values inelastic processes due to argon began to control the swarm energy thus leading this binary mixture act essentially like pure argon.

On the use of Monte Carlo simulations to model transport of positrons in gases and liquids

In this paper we make a parallel between the swarm method in physics of ionized gases and modeling of positrons in radiation therapy and diagnostics. The basic idea is to take advantage of the experience gained in the past with electron swarms and to use it in establishing procedures of modeling positron diagnostics and therapy based on the well-established experimental binary collision data. In doing so we discuss the application of Monte Carlo technique for positrons in the same manner as used previously for electron swarms, we discuss the role of complete cross section sets (complete in terms of number, momentum and energy balance and tested against measured swarm parameters), we discuss the role of benchmarks and how to choose benchmarks for electrons that may perhaps be a subject to experimental verification. Finally we show some samples of positron trajectories together with secondary electrons that were established solely on the basis of accurate binary cross sections and also how those may be used in modeling of both gas filled traps and living organisms.

Low-energy electron and positron transport in gases and soft-condensed systems of biological relevance

We present a study of electron and positron transport in water in both the gaseous and liquid states using a Boltzmann equation analysis and a Monte-Carlo simulation technique. We assess the importance of coherent scattering processes when considering transport of electrons/positrons in dense gases and liquids. We highlight the importance of electron and positron swarm studies and experiments as a test of the accuracy and completeness of cross-sections, as well as a technique for benchmarking Monte-Carlo simulations. The thermalization of low-energy positrons (<150eV) in water is discussed and the sensitivity of the profiles to the form of the cross-sections in this energy region, and assumptions in the microscopic processes, is considered.

Determination of Electron Swarm Parameters in Pure CHF3 and CF4 by a Time-Resolved Method

The density-normalized effective ionization coefficient (α − η)/N (α and η are the ionization and attachment coefficients respectively), the electron drift velocity Ve and density-normalized longitudinal diffusion coefficient NDL in trifluoromethane (CHF3) and carbon tetrafluoride (CF4) were measured using a pulsed Townsend technique over a wide E/N range. From the plots of (α − η)/N, we have derived the limiting field strength, (E/N)lim, which is valid for the analysis of insulation characteristics and applications to power equipment. Comparisons of the electron swarms parameters between CHF3 and CF4 have been performed, and the global warming potential (GWP) is also taken into account.