Electronic Rate Research Articles

Secondary electron effect on sustaining capacitively coupled discharges: A hybrid modeling investigation of the ionization rate

A one-dimensional fluid/Monte Carlo hybrid model was used to quantitatively study the secondary electron effect on sustaining the discharge by examining the ionization induced by bulk electrons and secondary electrons under different external discharge parameters. The results indicate that as the voltage increases, secondary electrons gain more energy from the stronger electric field. Therefore, the ionization region induced by secondary electrons expands and the ionization rate becomes comparable to and even exceeds that of bulk electrons. As the pressure increases, secondary electrons collide with neutrals sufficiently, thus their contribution to the plasma generation becomes pronounced and eventually they dominate the discharge. Besides, the distribution of the secondary electron ionization rate varies from flat to saddle-shape, due to the energy loss at the discharge center at higher pressures. Finally, when the discharge gap expands, the electron density calculated in the case without secondary electrons increases linearly, whereas the value first increases and then decreases in the model with secondary electrons taken into account. The results obtained in this work are important for improving the high aspect ratio etching process by secondary electrons.

Effects of secondary electron emission on plasma characteristics in dual-frequency atmospheric pressure helium discharge by fluid modeling**Project supported by the National Natural Science Foundation of China (Grant No. 11505089).

A one-dimensional (1D) fluid simulation of dual frequency discharge in helium gas at atmospheric pressure is carried out to investigate the role of the secondary electron emission on the surfaces of the electrodes. In the simulation, electrons, ions of He+ and , metastable atoms of He* and metastable molecules of are included. It is found that the secondary electron emission coefficient significantly influences plasma density and electric field as well as electron heating mechanisms and ionization rate. The particle densities increase with increasing SEE coefficient from 0 to 0.3 as well as the sheathʼs electric field and electron source. Moreover, the SEE coefficient also influences the electron heating mechanism and electron power dissipation in the plasma and both of them increase with increasing SEE coefficient within the range from 0 to 0.3 as a result of increasing of electron density.

Effect of acoustic phonon scattering on impact ionization rate of electrons in monolayer graphene nanoribbons

In this paper, we have studied the behavior of impact ionization rate of electrons in monolayer graphene nanoribbons due to various scattering mechanisms. The effects have been analyzed using the comprehensive analytical expressions, which result from all the possible inelastic interactions before the ionizing collision inside the graphene nanoribbons structures. These interactions include scattering of electrons due to acoustic phonon, inter-carrier scattering and optical phonon. Also, the obtained results are compared with previously reported data. The overestimation in earlier data has been analyzed in detail through the developed analytical expression. In addition to this, the percentage change in electron ionization rate has been calculated by considering it with and without acoustic phonon scattering.

Diminution of impact ionization rate of charge carriers in semiconductors due to acoustic phonon scattering

The effects of acoustic phonon scattering on the impact ionization rate of charge carriers in a semiconductor have been studied in this paper. The inelastic interactions of charge carriers with both deformation and piezoelectric acoustic phonons have been considered. An analytical expression of impact ionization rate has been developed by considering all possible types of inelastic collision mechanisms such as acoustic phonon scattering, optical phonon scattering, and inter-carrier scattering prior to the ionizing collision. The said expression has been used to calculate the impact ionization rate of electrons and holes in 4H-SiC as functions of electric field and doping concentration at room temperature. Numerical results show that the ionization rate of charge carriers deteriorates significantly due to the interactions of those with acoustic phonons. This deterioration is found to be more pronounced in hot carriers. The numerical results calculated from the present model have been compared with the ionization rate data calculated numerically using an earlier developed analytical expression of ionization rates, which does not take into account the acoustic phonon-scattering events. The calculated results have also been compared with earlier reported experimental data. It is observed that the numerical results obtained from the present model are in better agreement with the experimental results.

Electron kinetics in capacitively coupled plasmas modulated by electron injection

The controlling effect of an electron injection on the electron energy distribution function (EEDF) and on the energetic electron flux, in a capacitive radio-frequency argon plasma, is studied using a one-dimensional particle-in-cell/Monte Carlo collisions model. The input power of the electron beam is as small as several tens of Watts with laboratory achievable emission currents and energies. With the electron injection, the electron temperature decreases but with a significant high energy tail. The electron density, electron temperature in the sheath, and electron heating rate increase with the increasing emission energy. This is attributed to the extra heating of the energetic electrons in the EEDF tail. The non-equilibrium EEDF is obtained for strong non-local distributions of the electric field, electron heating rate, excitation, and ionization rate, indicating the discharge has transited from a volume heating (α-mode dominated) into a sheath heating (γ-mode dominated) type. In addition, the electron injection not only modifies the self-bias voltage, but also enhances the electron flux that can reach the electrodes. Moreover, the relative population of energetic electrons significantly increases with the electron injection compared to that without the electron injection, relevant for modifying the gas and surface chemistry reactions.

Monitoring the electron dynamics of the excited state via higher-order spectral minimum

A pump-probe scheme for monitoring the electron dynamics of the excited state has been investigated by numerically solving the two-state time-dependent Schrödinger equation based on the non-Born-Oppenheimer approximation. By adjusting the delay time between a mid-infrared probe pulse and an ultra violet pump pulse, an obvious minimum can be seen in the higher-order harmonic region. With electron probability density distribution, ionization rate and classical simulation, the minimum can be ascribed to the electron localization around one nucleus at larger delay time and represents the electron dynamics of the excited state at the time of ionization. Moreover, the position of the minimum is much more sensitive to the nuclear motion.

Influence of oblique magnetic field on the impact ionization rate of charge carriers in semiconductors

In this paper, an analytical model has been presented to study the influence of magnetic field on the impact ionization rate of charge carriers in semiconductors. The magnetic field is supposed to be applied along the oblique direction with respect to the direction of applied electric field. Numerical calculations have been carried out by using the comprehensive analytic expression of ionization rate of charge carriers formulated by the authors, in order to study the effect of oblique magnetic field on the ionization rate of electrons and holes moving under a steady electric field in 4H-SiC. Results show that the application of nonzero steady magnetic field in oblique direction leads to significant reduction in ionization rates. Moreover, the above-mentioned magnetic field-induced reduction in ionization rates is found to be maximum when the steady magnetic field is applied along the normal direction with respect to the external electric field.

Kinetic theory of transport processes in partially ionized reactive plasma, II: Electron transport properties

Abstract The previously obtained in (Zhdanov and Stepanenko, 2016) general transport equations for partially ionized reactive plasma are employed for analysis of electron transport properties in molecular and atomic plasmas. We account for both elastic and inelastic interaction channels of electrons with atoms and molecules of plasma and also the processes of electron impact ionization of neutral particles and three-body ion–electron recombination. The system of scalar transport equations for electrons is discussed and the expressions for non-equilibrium corrections to electron ionization and recombination rates and the diagonal part of the electron pressure tensor are derived. Special attention is paid to analysis of electron energy relaxation during collisions with plasma particles having internal degrees of freedom and the expression for the electron coefficient of inelastic energy losses is deduced. We also derive the expressions for electron vector and tensorial transport fluxes and the corresponding transport coefficients for partially ionized reactive plasma, which represent a generalization of the well-known results obtained by Devoto (1967). The results of numerical evaluation of contribution from electron inelastic collisions with neutral particles to electron transport properties are presented for a series of molecular and atomic gases.

Impact Ionization Rate of Electrons in Monolayer Graphene Nanoribbons

ABSTRACTThe authors have proposed a comprehensive analytical model for evaluating the impact ionization rate of electrons in monolayer graphene nanoribbons (GNRs). The impact ionization phenomena have been viewed as a multistage scattering process. All possible combinations of optical phonon scattering and electron–electron collision events prior to the impact ionization have been taken into account in the model. The impact ionization rate of electrons in monolayer GNR has been calculated and results are compared with the numerical data obtained from an analytical model proposed earlier. The effects of temperature and sheet electron concentration on the ionization rate have also been studied.

Experimental and simulation study of a capacitively coupled oxygen discharge driven by tailored voltage waveforms

We report experimental and particle-based kinetic simulation studies of low-pressure capacitively coupled oxygen plasmas driven by tailored voltage waveforms that consist of up to four harmonics of base frequency 13.56 MHz. Experimentally determined values of DC self-bias and electrical power deposition, as well as flux density and flux-energy distribution of the positive ions at the grounded electrode are compared with simulation data for a wide range of operating conditions. Very good agreement is found for self-bias and flux-energy distribution of the positive ions at the electrodes, while a fair agreement is reached for discharge power and ion flux data. The simulated spatial and temporal behaviour of the electric field, electron density, electron power absorption, ionization rate and mean electron energy shows a transition between sheath expansion heating and drift-ambipolar discharge modes, induced by changing either the number of harmonics comprising the excitation waveform or the gas pressure. The simulations indicate that under our experimental conditions the plasma operates at high electronegativity, and also reveal the crucial role of singlet metastable molecules in establishing discharge behavior via the fast destruction of negative ions within the bulk plasma.

Additional confirmation of a generalized analytical model based on multistage scattering phenomena to evaluate the ionization rates of charge carriers in semiconductors

This paper contains additional validations of a comprehensive analytical model based on multistage scattering phenomena to evaluate the impact ionization rates of charge carriers in semiconductors which was proposed by the authors and reported earlier. The model has been used to evaluate the ionization rates of both electrons and holes in some potential wide bandgap (WBG) semiconductors such as Wurtzite-GaN (Wz-GaN), type-IIb diamond and 6H-SiC. The numerical results obtained from the analytical model within the respective electric field ranges under consideration have been compared with the ionization rate values calculated by using the empirical relations fitted from the experimentally measured data. The calculated values of impact ionization rates of electrons and holes in all the WBG semiconductors under consideration are found to be in close agreement with the experimental results.

Contribution of proton and electron precipitation to the observed electron concentration in October–November 2003 and September 2005

Abstract. Understanding the altitude distribution of particle precipitation forcing is vital for the assessment of its atmospheric and climate impacts. However, the proportion of electron and proton forcing around the mesopause region during solar proton events is not always clear due to uncertainties in satellite-based flux observations. Here we use electron concentration observations of the European Incoherent Scatter Scientific Association (EISCAT) incoherent scatter radars located at Tromsø (69.58° N, 19.23° E) to investigate the contribution of proton and electron precipitation to the changes taking place during two solar proton events. The EISCAT measurements are compared to the results from the Sodankylä Ion and Neutral Chemistry Model (SIC). The proton ionization rates are calculated by two different methods – a simple energy deposition calculation and the Atmospheric Ionization Model Osnabrück (AIMOS v1.2), the latter providing also the electron ionization rates. Our results show that in general the combination of AIMOS and SIC is able to reproduce the observed electron concentration within ± 50% when both electron and proton forcing is included. Electron contribution is dominant above 90 km, and can contribute significantly also in the upper mesosphere especially during low or moderate proton forcing. In the case of strong proton forcing, the AIMOS electron ionization rates seem to suffer from proton contamination of satellite-based flux data. This leads to overestimation of modelled electron concentrations by up to 90% between 75–90 km and up to 100–150% at 70–75 km. Above 90 km, the model bias varies significantly between the events. Although we cannot completely rule out EISCAT data issues, the difference is most likely a result of the spatio-temporal fine structure of electron precipitation during individual events that cannot be fully captured by sparse in situ flux (point) measurements, nor by the statistical AIMOS model which is based upon these observations.

Ionization and excitation of the excited hydrogen atom in strong circularly polarized laser fields

In the recent work of Herath et al. [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)] the first experimental observation of a dependence of strong-field ionization rate on the sign of the magnetic quantum number $m$ [of the initial bound state $(n,l,m)]$ was reported. The experiment with nearly circularly polarized light could not distinguish which sign of $m$ favors faster ionization. We perform ab initio calculations for the hydrogen atom initially in one of the four bound substates with the principal quantum number $n=2$, and irradiated by a short circularly polarized laser pulse of $800\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$. In the intensity range of ${10}^{12}\ensuremath{-}{10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$ excited bound states play a very important role, but also up to some ${10}^{15}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$ they cannot be neglected in a full description of the laser-atom interaction. We explore the region that with increasing intensity switches from multiphoton to over-the-barrier ionization and we find, unlike in tunneling-type theories, that the ratio of ionization rates for electrons initially counter-rotating and corotating (with respect to the laser field) may be higher or lower than 1.

Electron Transfer Reaction of Ion Pairs: 1. Surfactant Cobalt(III) Complexes by Fe(CN)6 4− in Microheterogeneous Media

Abstract The kinetic study of reduction of single chain surfactant octahedral cobalt(III) complexes, cis-[Co(en)2(4AMP)(DA)](ClO4)3 and cis-[Co(trien)(4CNP)(DA)](ClO4)3 (where en = ethylenediamine; trien = triethylenetetramine; 4AMP = 4-aminopyridine; 4CNP = 4-cyanopyridine; DA = dodecylamine) with [Fe(CN)6]4– has been carried out by spectrophotometric method under pseudo first order conditions using an excess of a reductant in different media namely, micelles, β-cyclodextrim (β-CD), liposome vesicles (DPPC) and ionic liquids ((BMIM)Br) at different temperatures in order to have deep insight into the molecular behavior during the electron transfer reaction. The analysis of kinetic results strongly suggests that the reduction reaction between the surfactant complex and [Fe(CN)6]4– occurs via a second order outer sphere electron transfer mechanism. The remarkable increase in the rate of electron transfer from the oxidant to reductant is observed in ionic liquid medium as compared to the rest of all other media studied in the present investigation. This can be ascribed due to the fact that the formation of aggregated and constrained geometry of the surfactant cobalt(III) complexes (oxidants) in ionic liquid medium renders the rate of one electron transfer from the oxidants to the reductant, [Fe(CN)6]4– to be higher. Furthermore, the rate constant value increases with increase in the concentration of micelles, however in the presence of β-cyclodextrin medium the rate of electron transfer substantially decreases due to the inclusion of long aliphatic chain of the surfactant cobalt(III) complexes into β-cyclodextrin. In liposome media, second order rate constant for this electron transfer reaction from both the oxidants was found to decrease with increase in the concentration of the liposome below the phase transfer temperature of DPPC. However, above the phase transition temperature the reaction was found to increase with increase in the concentration of the DPPC. The main driving force for this phenomenon is considered to be the intervesicular hydrophobic interaction between the surfactant complexes and vesicular surface. The activation parameters (ΔS‡ and ΔH‡) of this outer sphere electron transfer reaction have been calculated by varying temperatures and the analysis of the data corroborates the kinetics of the reaction.

Influence of the anisotropy on the performance of D-band SiC IMPATT diodes

Numerical simulation has been made to predict the RF performance of direction and < $$ 11\bar{2}0 $$ > direction p+/n/n−/n+ (single drift region) 4H silicon carbide (4H-SiC) impact-ionization-avalanche-transit-time (IMPATT) diodes for operation at D-band frequencies. We observed that the output performance of 4H-SiC IMPATT diode is sensitive to the crystal direction of the one-dimensional current flow. The simulation results show that direction 4H-SiC IMPATT diode provides larger breakdown voltage for its lower electron and hole ionization rates and higher dc-to-rf conversion efficiency (η) for its higher ratio of drift zone voltage drop (VD) to breakdown voltage (VB) compared with those for < $$ 11\bar{2}0 $$ > direction 4H-SiC IMPATT diode, which lead to higher-millimeter-wave power output for direction 4H-SiC IMPATT compared to < $$ 11\bar{2}0 $$ > direction. However, the quality factor Q for the < $$ 11\bar{2}0 $$ > direction 4H-SiC IMPATT diode is lower than that of direction, which implies that the < $$ 11\bar{2}0 $$ > direction 4H-SiC IMPATT diode exhibits better stability and higher growth rate of microwave oscillation compared with direction 4H-SiC IMPATT diode.

3-D Particle Modeling of Positive Streamer Inception From a Needle Electrode in Supercritical Nitrogen

Positive streamers need a source of free electrons ahead of them to propagate. Here we investigate a possible source of these electrons in high density media: field ionization. Zener's model is used to obtain the field ionization rate of free electrons from impurities. Including this effect, we simulate the inception of positive streamers in supercritical N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , in a needle-to-plane electrode geometry. Our 3-D particle simulation shows how the discharge branches into positive streamer channels around the electrode.

Possible modification of the cooling index of interstellar helium pickup ions by electron impact ionization in the inner heliosphere

AbstractInterstellar neutrals penetrating into the inner heliosphere are ionized by photoionization, charge exchange with solar wind ions, and electron impact ionization. These processes comprise the first step in the evolution of interstellar pickup ion (PUI) distributions. Typically, PUI distributions have been described in terms of velocity distribution functions that cool adiabatically under solar wind expansion, with a cooling index of 3/2. Recently, the cooling index has been determined experimentally in observations of He PUI distributions with Advanced Composition Explorer (ACE)/Solar Wind Ion Composition Spectrometer and found to vary substantially over the solar cycle. The experimental determination of the cooling index depends on the knowledge of the ionization rates and their spatial variation. Usually, ionization rates increase with 1/r2 as neutral particles approach the Sun, which is not exactly true for electron impact ionization, because the electron temperature increases with decreasing distance from the Sun due to the complexity of its distributions and different radial gradients in temperature. This different dependence on distance may become important in the study of the evolution of PUI distributions and is suspected as one of the potential reasons for the observed variation of the cooling index. Therefore, we investigate in this paper the impact of electron ionization on the variability of the cooling index. We find that the deviation of the electron ionization rate from the canonical 1/r2 behavior of other ionization processes plays only a minor role.

A generalized analytical model based on multistage scattering phenomena for estimating the impact ionization rate of charge carriers in semiconductors

A generalized analytical model based on multistage scattering phenomena has been developed in this paper for estimating the impact ionization rate of charge carriers in semiconductors. The probabilities of impact ionization initiated by electrons and holes have been calculated separately by taking into account all possible combinations of optical phonon scattering and carrier-carrier collisions prior to the impact ionization. Finally the analytical expressions of impact ionization rate of electrons and holes have been developed by using the aforementioned impact ionization probabilities. The impact ionization rates of electrons and holes in 4H-SiC have been calculated within the field range of $$2.5\times 10^{8}$$2.5×108---$$6.5\times 10^{8}\hbox { V m}^{-1}$$6.5×108Vm-1 by using the analytical expressions of those developed in the present paper. Those are also calculated by using the analytical expressions developed by some other researchers earlier without considering the multistage scattering phenomena. Finally the theoretical results obtained from the analytical model proposed in this paper and the analytical model developed by earlier researchers within the field range under consideration have been compared with the ionization rate values calculated by using the empirical relations fitted from the experimentally measured data. Closer agreement with the experimental data has been achieved when the impact ionization rate of charge carriers in 4H-SiC are calculated from the proposed model as compared to the earlier one.

Stimulated Compton Scattering in Two-Color Ionization of Hydrogen with keV Electromagnetic Fields

We present a theoretical study of two-color ionization of hydrogen with keV photons at intensities ranging from 1016 to 1018 W/cm2. We consider the atom in interaction with a superposition of two electromagnetic pulses centered around two frequencies that differ by a few atomic units and we present in detail the case of the frequencies 55 and 50a.u. We present the electron energy spectra, angular distributions, and ionization rates based on nonperturbative and perturbative calculations. Although the ejected electron energy distribution is dominated by one-photon ionization from each pulse, we are able to identify the contribution of stimulated Compton scattering, a process in which one photon is absorbed while the other is emitted, the photon energy difference being transferred to the electron. This leads to low-energy electrons, and we show in particular that it is of crucial importance to consider the retardation effects on the ionization rates and the electron angular distributions. The relative propagation direction of the two fields also plays an important role; in the case of counterpropagating fields, the ionization by stimulated Compton scattering is dominated by A2 and competes with one-photon ionization at high intensities.

Two-dimensional simulation of atmospheric pressure cold plasma jets in a needle-plane electrode configuration

The propagation mechanisms of atmospheric pressure cold plasma jets have recently attracted much attention. In this paper, by using a self-consistent two-dimensional plasma fluid model, we have investigated the propagation problems in the cold atmospheric pressure helium plasma jets that are surrounded by helium itself and thin dielectric tube, respectively. The spatio-temporal distributions of electron density, ionization rate, electrical field, and electron temperature were obtained. It is found that both the radius and the permittivity of dielectric tube have an impact on the discharge characteristics. A new method of improving the electron density and plasma jet size was also proposed.