Electron Collision Cross Sections Research Articles

A global model and two-dimensional simulation study of a low-pressure inductively coupled CF4 plasma considering non-Maxwellian EEDF

We analyze the discharge characteristics of a low-pressure inductively coupled CF4 plasma using a global model and a two-dimensional (2D) simulation. We first conducted a study comparing the experimental results with the global model, which makes it easier to compare the trend concerning external parameters and less computationally expensive, to validate the chemical reaction data, and then, compared the experimental results with the 2D simulation results. We then analyzed the discharge characteristics by comparing the 2D model results with the global model at various gas pressures and powers. The simulations were performed using COMSOL software, which is based on a fluid model. The electron energy distribution function (EEDF) was solved self-consistently using the Boltzmann equation solver, and then, coupled with the fluid model. The results were more consistent with the experimental results when the EEDF was calculated by solving the Boltzmann equation than for assuming the Maxwellian EEDF. Furthermore, the global model results were similar with the mean values obtained from the 2D model. This indicates that it is efficient to first validate the electron collision cross sections and reaction coefficients using the global model. Our approach is expected to be utilized in the analysis of new gases.

Cross Sections for Electron Collisions with the CO2 Molecule and CO2+ Molecular Ion

Electron collision cross section data are complied from the literature for electron collisions with the carbon dioxide molecule, CO2 and the CO2+ ion. Cross sections are collected and reviewed for total scattering, elastic scattering, momentum transfer, rotational excitation, vibrational excitation, electronic excitation, dissociative processes and ionization. The literature has been surveyed up to the end 2023. For each of these processes, the recommended values of the cross sections are presented with an estimated uncertainty.

Electron collision cross sections in tetrafluoropropene HFO1234ze(E) for gas mixtures in resistive plate chambers

Electron collision cross sections in tetrafluoropropene HFO1234ze(E) for gas mixtures in resistive plate chambers

Elastic cross section data for precursor molecules used in low-temperature plasmas: Sn(CH3)4 and Ga(CH3)3

Tetramethyltin [Sn(CH3)4] and trimethylgallium [Ga(CH3)3] are important source molecules of Sn and Ga atoms which are used in manufacturing techniques involving low-temperature plasmas. Accurate numerical modeling of plasma environments requires a comprehensive set of electron scattering cross sections by these precursor molecules. Here, we report the elastic integral, differential, and momentum transfer cross sections for electron collisions with Sn(CH3)4 and Ga(CH3)3 for energies ranging from 0 to 30 eV. Our calculations were carried out with the Schwinger multichannel method implemented with pseudopotentials and considered two levels of approximation in our calculations, namely static-exchange and static-exchange plus polarization. We identified three shape resonances for Sn(CH3)4 and one clear low-lying resonance for Ga(CH3)3. The low-energy behavior of the s-wave cross section and eigenphase was investigated and, for both molecules, we found evidence of a Ramsauer–Townsend (RT) minimum and a virtual state. Our results indicate that negative differential conductivity would occur in a gas composed of Sn(CH3)4. On the other hand, this effect would be suppressed in a gas of Ga(CH3)3 due to an overlap between the position of the RT minimum and the shape resonance in the momentum-transfer cross section.

Dichotomy of the description of the elastic and electronically inelastic scattering of electrons by methane

The interaction between electrons and methane is studied with a particular focus on describing the dynamics of elastic and electronic excitation processes under the influence of the multichannel coupling effects. Elastic and electronically inelastic integral and differential cross sections are reported. These cross sections were calculated with the Schwinger multichannel method implemented with norm-conserving pseudopotentials within the minimal orbital basis for single-configuration interaction approach with up to 181 open channels. While an excellent agreement with previously published data is found in the elastic channel, the comparisons involving electronic excitation cross sections reveal significant discrepancies. Furthermore, the lack of reliable experimental data regarding the electronically inelastic channels hampers a more detailed analysis of the theoretical results. Additionally, total ionization and total cross sections for electron collisions with methane are also presented. By highlighting the current theoretical challenges in dealing with electron-induced electronic excitation of molecules, we seek to contribute to a deeper understanding of this scattering process and, thus, pave the way for future research.

Elastic and electronically inelastic scattering of electrons by 2H-pyran and 4H-pyran molecules

We report on elastic and electronically inelastic integral and differential cross sections for electron collisions with the 2H-pyran and 4H-pyran molecules. The scattering calculations were performed with the Schwinger multichannel method and aimed to (i) investigate the formation of resonant states, (ii) assign and compare the resonance spectrum of these isomers, and (iii) evaluate the influence of multichannel coupling effects upon elastic and electronically inelastic scattering processes. In the elastic channel, calculations carried out at the static-exchange and static-exchange plus polarization levels of approximation revealed the presence of three shape resonances for each one of the pyran isomers. For the 2H-pyran molecule, we found two resonances related to the formation of long-lived π∗ anion states that are centered at 1.38 or 1.32 eV (π1∗) and 4.54 or 4.46 eV (π2∗), depending on the polarization model used in the calculations, and a broad resonance of σ∗ character located around 9.50–10.00 eV. The resonances observed in the case of the 4H-pyran molecule have the same character with centers located at 2.08 or 2.20 eV (π1∗), 3.92 or 3.94 eV (π2∗), and 9.24–10.00 or 9.50–10.00 eV (σ∗), depending on the polarization model used in the calculations. The difference in the position of the resonances when comparing the results for the 2HPY and 4HPY molecules is explained in terms of the inductive effect. The electronically inelastic calculations employed the minimal orbital basis for single configuration interactions strategy and considered up to 129 open channels for 2H-pyran and up to 249 open channels for 4H-pyran. According to these levels of channel coupling, we computed integral and differential cross sections for the excitation from the ground state to the 13A′, 23A′, 11A′′, and 21A′ electronic excited states of 2H-pyran and to the 13B2, 13A1, 11B1, and 11B2 electronic excited states of 4H-pyran. As a general trend, for both isomers, we observed that the magnitude of the cross sections is reduced as more channels are considered open in the scattering calculations. We also obtained the total ionization cross sections for 2H- and 4H-pyran using the binary-encounter-Bethe model, which next was summed to the elastic and electronically inelastic cross sections to estimate the total cross sections. As a whole, these results correspond to the first set of cross sections for these targets published to date. Such an effort is aimed at addressing the demand of different communities regarding the expansion of the cross section data set for electron collisions with molecules of technological, environmental, and biological relevance, a need that has been raised by several reviews on the subject.

Elastic and electronically inelastic scattering of electrons by the pyrazine molecule.

We report on elastic and electronically inelastic integral and differential cross sections as well as ionization and total cross sections for electron collisions with the pyrazine molecule. The Schwinger multichannel method is applied in calculations carried out according to the minimal orbital basis for single configuration interactions strategy from the 1-channel up to 139-channels close-coupling level of approximation. With these calculations we have obtained integral and differential cross sections as well as excitation functions for elastic electron scattering and, also, integral and differential cross sections for electronic excitation from the ground state to the 3B1u, 3B2u, 3B3u, 1B1u, 1B2u and 1B3u excited states of pyrazine by electron impact. By summing the total ionization cross section obtained by means of the binary-encounter-Bethe model to these elastic and electronically inelastic contributions, we provided an estimate for the total cross section describing the electron-pyrazine interaction process. The independent atom model with the screening-corrected additivity rule plus interference terms method was also used in the present study to determine elastic integral and differential as well as ionization and total cross sections for electron collisions from pyrazine. The present results were, whenever possible, critically compared to the experimental and theoretical data available in the literature. In general, the overall agreement between the present results and the experiment is quite encouraging.

Electron collision cross section data in plasma etching modeling

Semiconductor chips are the cornerstone of the information age, which play a vital role in the rapid development of emerging technologies such as big data, machine learning, and artificial intelligence. Driven by the growing demand for computing power, the chip manufacturing industry has been committed to pursuing higher level of integration and smaller device volumes. As a critical step in the chip manufacturing processes, the etching process therefore faces great challenges. Dry etching (or plasma etching) process based on the low-temperature plasma science and technology is the preferred solution for etching the high-precision circuit pattern. In the low-temperature plasma, electrons obtain energy from the external electromagnetic field and transfer the energy to other particles through collision process. After a series of complex physical and chemical reactions, a large number of active particles such as electrons, ions, atoms and molecules in excited states, and radicals are finally generated, providing the material conditions for etching the substrate. Dry etching chamber is a nonlinear system with multiple space-time dimensions, multiple reaction levels and high complexity. Facing such a complex system, only by fully understanding the basic physical and chemical reaction of the etching process can we optimize the process parameters and improve the etching conditions, so as to achieve precision machining of the semiconductor and meet the growing demand of the chip industry for etching rate and yield. In the early days, the process conditions of dry etching were determined through the trial-and-error method, which is characterized by high cost and low yield. However, with the help of plasma simulation, nowadays people have been able to narrow the scope of experiment to a large extent, and find out efficiently the optimal process conditions in a large number of parameters. In this review, we first introduce the basic theory of the mostly used models for plasma simulation including kinetic, fluid dynamic, hybrid and global models, in which the electron collision cross sections are the key input parameters. Since the formation of the low-temperature plasma is driven by the electron-heavy particle collision processes, and the active species for plasma etching are generated in the reactions induced by electron impact, the accuracy and completeness of the cross-section data greatly affect the reliability of the simulation results. Then, the theoretical and experimental methods of obtaining the cross-section data of etching gases are summarized. Finally, the research status of the electron collision cross sections of etching atoms and molecules is summarized, and the future research prospect is discussed.

Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters.

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

Theoretical study of a new molecular ion species BeN+: molecular states and cross sections for electronic excitation and dissociation.

We present here a theoretical study of a new molecular ion species BeN+, which has not been reported before. Using a good quality configuration interaction model, we first undertake a configuration interaction calculation of the molecular states to obtain the potential energy curves of several low lying states of BeN+ and the dipole and transition dipole moments of some of its states as a function of the internuclear distance. We find the ground state to be bound and of X 3Σ- character having a shallow minimum at Re = 2.9031a0 and several other closely spaced excited states some of which are repulsive. We have determined the spectroscopic parameters for some of these states by fitting the raw potential energy data to a 6-parameter analytical potential energy function. Subsequently, the R-matrix method is used to obtain electron collision cross sections for electronic excitation from the ground X 3Σ- state to several of its excited states at the equilibrium Re = 2.9031a0 and cross sections for electron impact dissociation. We have also reported many Feshbach resonances and their widths at the equilibrium Re = 2.9031a0, which may, in future studies, be extended to potential energy curves for neutral dissociative states. The states and cross sections obtained are of considerable significance for edge plasma chemistry in fusion devices operating with beryllium walls.

Temperature-Dependent Functions of the Electron–Neutral Momentum Transfer Collision Cross Sections of Selected Combustion Plasma Species

The collision cross sections (CCS), momentum transfer cross sections (MTCS), or scattering cross sections (SCS) of an electron–neutral pair are important components for computing the electric conductivity of a plasma gas. Larger collision cross sections for electrons moving freely within neutral particles (molecules or atoms) cause more scattering of these electrons by the neutral particles, which leads to degraded electron mobility, and thus reduced electric conductivity of the plasma gas that consists of electrons, neutral particles, and ions. The present work aimed to identify the level of disagreement between four different methods for describing how electron–neutral collision cross sections vary when they are treated as a function of electron temperature alone. These four methods are based on data or models previously reported in the literature. The analysis covered six selected gaseous species that are relevant to combustion plasma, which are as follows: carbon monoxide (CO), carbon dioxide (CO2), molecular hydrogen (H2), water vapor (H2O), potassium vapor (K), and molecular oxygen (O2). The temperature dependence of the collision cross sections for these species was investigated in the range from 2000 K to 3000 K, which is suitable for both conventional air–fuel combustion and elevated-temperature oxygen–fuel (oxy-fuel) combustion. The findings of the present study suggest that linear functions are enough to describe the variations in the collision cross sections of the considered species in the temperature range of interest for combustion plasma. Also, the values of the coefficient of variation (defined as the sample standard deviation divided by the mean) in the collision cross sections using the four methods were approximately 27% for CO, 42% for CO2, 13% for H2, 39% for H2O, 44% for K, and 19% for O2. The information provided herein can assist in simulating magnetohydrodynamic (MHD) power generators using computational fluid dynamics (CFD) models for combustion plasma flows.

Calculated cross sections for electron collisions with the BeN molecule

We report a low energy electron collision calculation with the BeN molecule in its X ground state using the molecular R-matrix method at a single geometry, namely, the equilibrium a 0 of the molecule. Using a suitable target model, we have calculated the elastic cross section and cross sections for electron impact excitation in several low-lying excited states of BeN. Cross sections for electron impact dissociation is derived from the electronic excitation cross sections. In addition, molecular data on bound sates of BeN and e-BeN negative ion resonances and widths at the target equilibrium Re that may be relevant for other studies are also provided.

Cross Sections for Electron Collisions with N2, N2*, and N2+

Electron collision cross section data are complied from the literature for electron collisions with the nitrogen molecules, N2, N2+, and N2*. Cross sections are collected and reviewed for total scattering, elastic scattering, momentum transfer, rotational excitation, vibrational excitation, electronic excitation, dissociative processes, and ionization. The literature has been surveyed up to the end of 2021. For each of these processes, the recommended values of the cross sections are presented.

Electron-neutral collision cross sections for H2O: II. Anisotropic scattering and assessment of the validity of the two-term approximation

This work proposes a complete and consistent set of cross sections (CS) for electron collisions with water gas molecules to be published in the IST-Lisbon database on LXCat. The set is validated by the electron swarm analysis technique. The anisotropic angular distribution of electrons in rotational collisions is considered by means of the Born approximation in a two-term Boltzmann solver (LisbOn KInetics two-term Boltzmann solver (LoKI-B)) and a Monte Carlo simulations code (LoKI-MC), both freely available as open-source codes. The inclusion of electron anisotropic scattering in rotational collisions significantly improves the agreement between calculations and measurements of the electron drift velocity, reduced mobility, characteristic energy, reduced Townsend ionisation coefficient, reduced effective Townsend coefficient and reduced attachment coefficient. The MC simulations are deemed more accurate and shown to yield similar results as LoKI-B with the proposed set. The use of LoKI-MC also validates the set of CSs against parameters that cannot be obtained by LoKI-B, such as the longitudinal diffusion coefficient or the bulk transport coefficients.

Extended reaction kinetics model for non-thermal argon plasmas and its test against experimental data

An extended reaction kinetics model (RKM) suitable for the analysis of weakly ionised, non-thermal argon plasmas with gas temperatures around 300 K at sub-atmospheric and atmospheric pressures is presented. It considers 23 different species including electrons as well as the ground state atom, an atomic and molecular ion, four excited molecular states, and 15 excited atomic states of argon, where all individual 1s and 2p states (in Paschen notation) are included as a separate species. This 23-species RKM involves 409 collision processes and radiative transitions and recent electron collision cross section data. It is evaluated by means of results of time- and space-dependent fluid modelling of argon discharges and their comparison with measured data for two different dielectric barrier discharge configurations as well as a micro-scaled atmospheric-pressure plasma jet setup. The results are also compared with those obtained by use of a previously established 15-species RKM involving only the two lumped 2p states 2p10…5 and . It is found that the 23-species RKM shows generally better agreement with experimental data and provides more options for direct comparison with measurements than the frequently used 15-species RKM.

Properties of Electron Swarm Parameters in Tetrahydrofuran

Reported electron collision cross sections data in the energy range ~ 0 to 300 eV from gaseous biomolecule Tetrahydrofuran (THF) have been used to calculate the electron energy distribution function (EEDF) and swarm parameters for electrically excited of THF, using a two-term solution of the Boltzmann equation. The electron swarm parameters namely (mean energy, drift velocity, diffusion coefficient, electron mobility, characteristic energy, attachment and ionization coefficient), at room temperature and atmospheric pressure are presented over a wide range of applied electric field strength E/N (E is the electric field and N is the gas number density) varying from 0.1 Td to 1000 Td (1Td = 10-17 Vcm2). The EEDF found to be non-Maxwellian. The electron swarm parameters are compared with those calculated using multi term kinetic theory and experimentally using the pulsed Townsend technique. The influence of inelastic cross section on the calculated transport parameters is also explained.

Elastic Electron Scattering by Diborane(6) and Diborane(4) Molecules

We present integral, differential, and momentum transfer cross sections for elastic electron collisions with the two most stable isomers of the B2H4 molecule, hereafter referred to as isomer I (C2v symmetry) and isomer II (D2d symmetry), and with the B2H6 molecule (D2h symmetry). The isomer I of B2H4 and the B2H6 molecule are known for their electrodeficiency in the "three-center two-electron" (3c-2e) bond, a region in which a hydrogen atom occupies a bridged position between two non-hydrogen atoms. The cross sections were computed by using the Schwinger multichannel method implemented with norm-conserving pseudopotentials, and the scattering calculations were carried out in the static-exchange and static-exchange plus polarization levels of approximation for energies from 0.1 to 50 eV. We discuss the presence of shape resonances in the scattering cross sections. We also made a direct comparison among the cross sections of these three targets.

Electron-neutral collision cross sections for H2O: I. Complete and consistent set

This work proposes a complete and consistent set of cross sections (CSs) for electron collisions with water molecules to be published in the IST-Lisbon database on LXCat. The set is validated from the comparison between experimental and computed electron swarm parameters. The former are collected from literature while the latter are calculated using a space-homogeneous two-term Boltzmann solver, assuming isotropic scattering in inelastic collisions. Rotational CSs, based on the Born approximation, are optimised by means of the electron swarm analysis technique. Superelastic rotational and vibrational collisions are accounted for in the calculations and found to be particularly important for low-energy electrons interacting with water molecules. The set can be used with codes assuming space-homogeneous conditions, in particular common two-term Boltzmann solvers, ensuring a good agreement with experiments. Therefore, it constitutes an important tool for fast calculations and modelling of complex plasma chemistries.

Low-Energy Electron Scattering from c-C4F8

Electron collision cross-sections of c-C4F8 were investigated at low energies by using the R-matrix method. The static exchange (SE), static exchange with polarization (SEP), and close-coupling (CC) models of the R-matrix method were used for the calculation of the scattering cross-section. The shape resonance was detected with all the models at around 3~4 eV, and a Feshbach resonance was detected with the SEP model at 7.73 eV, in good agreement with the previous theoretical calculation. The resonance detected was also associated with the experimental dissociative electron attachment of c-C4F8, which displayed the resonances at the same energy range. The cross-sections calculated are important for plasma modeling and applications.

Plasma diagnostics and modeling of lithium-containing plasmas

Thin-film deposition from chemically reactive multi-component plasmas is complex, and the lack of electron collision cross-sections for even the most common metalorganic precursors and their fragments complicates their modeling based on fundamental plasma physics. This study focuses on understanding the plasma physics and chemistry in argon (Ar) plasmas containing lithium bis (trimethylsilyl) amide used to deposit Li x Si y thin films. These films are emerging as potential solid electrolytes for lithium-ion batteries, and the Li-to-Si ratio is a crucial parameter to enhance their ionic conductivity. We deposited Li x Si y films in an axial flow-through plasma reactor and studied the factors that determine the variation of the Li-to-Si ratio in films deposited at various points on a substrate spanning the entire reactor axis. While the Li-to-Si ratio is 1:2 in the precursor, the Li-to-Si ratio is as high as 3:1 in films deposited near the plasma entrance and decreases to 1:1 for films deposited downstream. Optical emission from the plasma is dominated by Li emission near the entrance, but Li emission disappears downstream, which we attribute to the complete consumption of the precursor. We hypothesized that the axially decreasing precursor concentration affects the electron energy distribution function in a way that causes different dissociation efficiencies for the production of Li and Si. We used Li line intensities to estimate the local precursor concentration and Ar line ratios to estimate the local reduced electric field to test this hypothesis. This analysis suggests that the mean electron energy increases along the reactor axis with decreasing precursor concentration. The decreasing Li-to-Si ratio with axially decreasing precursor concentration may be explained by Li release from the precursor having lower threshold energy than Si release.