Numerical simulation of super-short pulsed discharge in Helium with particle-in-cell Monte--Carlo collisions technique

This paper reports that a simulation of glow discharge in pure helium gas at the pressure of 1.333×10³ Pa under a high-voltage nanosecond pulse is performed by using a one-dimensional particle-in-cell Monte Carlo collisions (PIC--MCC) model. Numerical modelling results show that the cathode sheath is much thicker than that of anode during the pulse discharge, and that there exists the phenomenon of field reversal at relative high pressures near the end of the pulse, which results from the cumulative positive charges due to their finite mobility during the cathode sheath expansion. Moreover, electron energy distribution function (EEDF) and ion energy distribution function (IEDF) have been also observed. In the early stage of the pulse, a large amount of electrons can be accelerated above the ionization threshold energy. However, in the second half of the pulse, as the field in bulk plasma decreases and thereafter the reverse field forms due to the excessive charges in cathode sheath, although the plasma density grows, the high energy part of EEDF decreases. It concludes that the large volume non-equilibrium plasmas can be obtained with high-voltage nanosecond pulse discharges.     

Electron temperature in a decaying krypton plasma in the presence of a low electric field

The influence of low electric fields on the average electron energy in an afterglow krypton plasma is studied by means of probe diagnostics and theoretical analysis. It is shown that, when the average electron energy is lower than the energy corresponding to the minimum scattering transport cross section, the degree of plasma ionization substantially affects the shape of the electron energy distribution function (EEDF). The nonequlibrium character of the EEDF results in the density dependence of the coefficient of ambipolar diffusion, which leads to a change in the radial profile of the charged particle density, an increase in the drop in the ambipolar potential across the plasma, and an increase in the rate of diffusive plasma decay. These effects substantially enhance the diffusive cooling of electrons, which is probably a decisive factor influencing the electron energy balance in high-Z noble gases.     

射频辉光放电CH4等离子体中电子的能量分布

通过求解Lorentz简化的玻尔兹曼方程,得到射频放电CH₄等离子体中电子的能量分布函数.求解过程中使用一个简化的射频电场模型代替泊松方程求解放电电场.共计包含6类环境气体及27种电子碰撞反应.通过EEDF对等离子体中的电子反应率系数、电子平均能量、电子的传输率系数等进行求解分析.结果表明,在等离子体鞘层区域电子能量具有Maxwell分布形式,在正柱区域具有Druyvesteyn分布形式.最高电子能量和最大反应率系数出现在鞘层区域.电子的迁移率系数和扩散率系数随射频周期的演化时空分布不均匀.     

Modeling of plasma-etch processes using well stirred reactorapproximations and including complex gas-phase and surfacereactions

A 0-D or well stirred reactor model determines spatially and time-averaged species composition in plasma-etch reactors, through solution of species, mass, and electron-energy balance equations. The use of well stirred reactor approximations reduces the computational expense of detailed kinetics calculations and allows investigation of the dependence of plasma chemistry on etch-process parameters. The reactor is characterized by a chamber volume, surface area, net mass flow or residence time, pressure, energy loss to surroundings, power deposition, and inlet-gas composition. The electron-energy equation includes a detailed power balance with losses to ions and electrons through the sheath, as well as inelastic and elastic collision losses. The model employs reaction-rate coefficients for electron-impact reactions, which require an assumption of the electron energy distribution function (EEDF). We compare model results using Maxwellian EEDF's, as well as reaction-rate coefficients determined as a function of average electron energy through solution of the Boltzmann equation, for chlorine chemistry. The Boltzmann rates are determined by time-lagging the equilibration of electrons with applied electric fields. The Maxwellian reaction rates give higher ionization fractions than the Boltzmann rates, affecting the predicted electronegativity and positive ion composition for chlorine plasmas. The model also shows a strong sensitivity of the plasma composition to the assumed surface-recombination probability of atomic chlorine     

两种温度电子对稳态等离子体鞘层的影响

建立包含冷热电子的无碰撞等离子体鞘层的流体模型,利用数值模拟研究含有两种温度电子时等离子体鞘层的产生.结果表明:对于含有两种不同温度电子的稳态等离子体,冷电子的温度越低或者冷电子的含量越多,鞘边离子的马赫数临界值就越小,鞘层的宽度就变得越窄,沉积器壁的离子动能流也就越少.此外,研究不同种类的等离子体(Ar、Ke、Xe),鞘层厚度和离子沉积器壁动能流受冷电子的影响.     

Effect of cold electron emission on diffusion plasma parameters and the sheath structure in a double plasma device

It is observed experimentally that by injecting cold electrons in the discharge region of a double plasma device, the plasma parameters and sheath structure can be controlled in the other region, which is devoid of any electrical discharge. The main discharge region is separated from the region under investigation by a grounded mesh grid. Both cold and hot ionizing electrons are emitted from separate sets of filaments in the discharge region. With an increase in the cold electron emission current, the plasma parameters in the discharge region get changed, which in turn alter the plasma parameters in the other region. Two important effects caused by cold electrons in the diffusion region are the increase in the plasma density and decrease in the plasma potential. The increase in the plasma density and decrease in the sheath potential drop therefore cause the contraction of the sheath.     

Effects of nonlocal electron kinetics and transition from αto γ regime in an RF capacitive discharge in nitrogen

The electron kinetics and regime of operation of asymmetrically coupled RF (27-MHz) nitrogen discharges in two vessels with different interelectrode gaps over the range of 0.20-0.35 torr gas pressure are studied in terms of the electron energy distribution function (EEDF). The latter is measured by means of a computer-controlled data acquisition system, a Langmuir probe with cross-modulation second derivative technique applied. The experiments are performed with an axial resolution along the RF electric field and accompanied with a measurement of electrical discharge characteristics. The effects of local and nonlocal plasma response are considered. The transition between α and γ discharge regimes is registered by measuring the EEDF and its moments' changes with the increase of the RF discharge current density     

The Impact of Direct Ionization by Beam Electrons on the Electron Kinetics of the Beam Discharge Plasma in Molecular Hydrogen

In a recent paper the stationary beam plasma discharge in partially dissociated hydrogen was investigated where the electron component was described by the Boltzmann equation for a mixture of atomic and molecular hydrogen and the main heavy charged and neutral particles by balance equations. It was assumed that, via the quasilinear beam plasma interaction, the electron beam produces only the turbulent electric field whilst an additional production of plasma electrons due to direct ionization by the beam and thus a direct influence on the balances of charge carriers were neglected. Now the additional production of plasma electrons due to direct ionization by the beam is studied on the basis of a generalized Boltzmann equation but for the simpler model of a purely molecular hydrogen plasma. For experimentally obtainable values of the turbulence energy density, beam energy, beam ionization degree and electron life time the calculation of the electron energy distribution function and of the direct beam contribution to the electron particle balance shows a marked influence of the direct beam ionization with increasing degree of beam ionization.     

Effect of Parallel-Plate Geometry on Mode Transition Behavior in Argon Microplasmas: Two-Dimensional Simulation

A two-dimensional self-consistent fluid model is employed to investigate radio-frequency process parameters on the plasma properties in Ar microdischarges. The neutral gas density and temperature balance equations are taken into account. We mainly investigate the effect of the electrode gap on the spatial distribution of the electron density and electron temperature profiles, due to a mode transition from the regime(secondary electrons emission is responsible for the significant ionization) to the regime(sheath oscillations and bulk electrons are responsible for sustaining discharge) induced by a sudden decrease of electron density and electron temperature.The pressure, radio-frequency sources frequency and voltage effects on the electron density are also elaborately investigated.     

Simulation study of the sheath region of a processing plasma with two-temperature electrons and charged nanoparticles

A four-fluid model is used to investigate the structure of a dusty plasma sheath with two species of electrons, i.e., cold and hot electrons. Numerical results show that, in the presence of hot electrons, regular fluctuations are developed in the spatial profiles of the sheath potential and number densities of the plasma and dust nanoparticles. The amplitude and spatial period of the fluctuations depend on the hot electron parameters. The sheath width shows a non-monotonic dependence on the temperature and number density of the hot electrons, as well as the density and Mach number of the nanoparticles.     

甚高频激发容性耦合氩等离子体的电子能量分布函数的演变

甚高频激发的容性耦合等离子体由于离子通量和能量的相对独立可控而受到人们的关注. 本文采用朗缪尔探针诊断技术测量了40.68 MHz激发的容性耦合Ar等离子体的特性(如电子能量概率分布、电子温度和密度等)随宏观参量的演变情况. 实验结果表明, 电子能量概率分布随着气压的增加从双麦克斯韦分布逐步转变为单麦克斯韦分布并最终演变为Druyvesteyn分布, 而射频激发功率的增加促进了低能电子布居数的增强; 在从等离子体放电中心移向边界的过程中, 低能电子的布居数显著下降, 而高能电子的布居则有所上升; 放电极板间距的变化直接导致了等离子体中电子加热模式的转变. 另外, 我们也对等离子体中的高低能电子密度和温度的分配情况进行了讨论.     

On the Kinetics of the Active Zone of the Stationary SF6 Beam Discharge Plasma

The paper deals with the impact of intensive electron attachment on the kinetics of the electrons in the active zone of the stationary band-like beam discharge plasma in SF₆ which is an alternative useful plasma medium for “dry etching”. The energy distribution of the electrons in this plasma was obtained by numerically solving the Boltzmann equation which includes apart from elastic collisions, different exciting collision processes, attachment in electron collisions, direct ionization, the ambipolar loss of electrons, Coulomb interaction between electrons and of electrons with ions and the power input to the electrons by the turbulent electric field. In particular, due to the needed fulfilment of the consistent electron particle balance, for an extended region of the turbulence energy density in this plasma a large impact on the electron kinetics of the intensive electron attachment, which is the prevailing electron loss process, was found enforcing independent of the turbulence energy density always a large power input to the electrons, smooth and only slowly decreasing energy distributions even in the energy region of direct ionization.     

Negative Ion Kinetics in RF Glow Discharges

Using temporally and spatially resolved laser spectroscopy, we have determined the identities, approximate concentrations, effects on the local field, and kinetics of formation and loss of negative ions in RF discharges. Cl- and BCl3- are the dominant negative ions found in low-frequency discharges through Cl2 and BCl3, respectively. The electron affinity for Cl is measured to be 3.6118 ± 0.0005 eV. Negative ion kinetics are strongly affected by application of the RF field. Formation of negative ions by attachment of slow electrons in RF discharges is governed by the extent and duration of electron energy relaxation. Similarly, destruction of negative ions by collisional detachment and field extraction is dependent upon ion energy modulation. Thus, at low frequency, the anion density peaks at the beginning of the anodic and cathodic half-cycles after electrons have attached but before detachment and extraction have had time to occur. At higher frequencies, electrons have insufficient time to attach before they are reheated and the instantaneous anion density in the sheath is greatly reduced. When the negative ion density is comparable to the positive ion density, the plasma potential is observed to lie below the anode potential, double layers form between sheath and plasma, and anions and electrons are accelerated by large sheath fields to electrode surfaces.     

Effect of Discharge Plasma Potential on Diffusion Plasma Parameters Controlled by a Mesh Grid in a Double Plasma Device

The plasma region under investigation is separated from the discharge region by a mesh grid. Plasma potential and electron number densities and electron temperatures under bi‐Maxwellian approximation for electron distribution function of the multi‐dipole argon plasma are measured. The cold electrons in the diffusion region are produced by local ionization. The hot electrons are the ionizing electrons behaving as Maxwellian. The electron trapping process in the discharge region is produced by potential well due to positive plasma potential with respect to the anode and by a repulsive grid. The dependence of ratios of the density of the hot to the cold electrons N_E (=N_eh/N_ec) and hot to cold electron temperature T(=T_eh/T_ec) in the diffusion region on the depth of the potential well has been investigated. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust particles in collisionless plasma sheath with arbitrary electron energy distribution function

Dust particles often appear in industrial plasmas as undesirable product of the plasma-wall interactions. Large particles of several micrometers in diameter are concentrated in a thin layer (the sheath) above the lower electrode of the rf driven parallel plate device, where the electric force is strong enough to compensate particle’s gravity. Experimental and theoretical uncertainties are significantly increased in the plasma sheath. Common models of dust charging in the plasma sheath suppose the Maxwellian electron energy distribution function (EEDF) in conjunction with a flux of cold ions satisfying classical Bohm criterion at the sheath edge. In this paper we generalize this model to arbitrary EEDF with adapted Bohm criterion. We limit our considerations to collisionless or slightly collisional plasma, where the EEDF inside the sheath is expressed through the EEDF in the plasma bulk. Derived theoretical formulas are incorporated into numerical model, describing collisionless radio frequency (rf) plasma sheath together with the electrical charge, various kinds of forces, balancing radius and oscillation frequency of particles.     

ICP等离子体鞘层附近区域发光光谱特性分析

为了独立控制鞘层附近区域离子密度和离子能最分布,采用光发射谱(OES)测量技术,对不同射频功率、放电气压和基底偏压下感应耦合等离子体鞘层附近区域辉光特性进行了研究.原子谱线和离子谱线特性分析表明,在鞘层附近区域感应耦合等离子体具有较高的离子密度和较低的电子温度.改变放电气压和射频功率,对得到的光谱特性分析表明,鞘层附近区域离子密度随射频功率的增大而线性增大,在低压下随气压的升高而增大.低激发电位原子谱线强度增加迅速,高激发电位原子谱线强度增加缓慢,而离子谱线强度增加很不明显.改变基底直流偏压,对得到的发射光谱强度变化分析表明,谱线强度随基底正偏压的增加而增大.随着基底负偏压的加入,谱线强度先减小而后增大;直流偏压为-30 V时,光谱强度最弱.快速离子和电子是引起Ar激发和电离过程的主要能量来源.     

射频低压等离子体电子能量分布函数的探针诊断

本文对于无内电极放电的射频低压等离子体,采用探针电流调制法,设计并建立了三探针诊断电子能量分布函数的测量系统,测量了压力在10^-3—10^-1Torr下氮气等离子体的电子能量分布函数。从理论和实验上研究了探针鞘层上射频干扰电压对测量电子能量分布函数的影响,给出了确定射频干扰值以及对射频干扰的影响进行修正的方法,并采用该方法对实验数据进行了修正,得到了正确的电子能量分布函数。根据所得到的电子能量分布函数计算的电子平均能量,与由探针伏安特性计算得到的电子平均能量相差不超过5％,该结果间接证明了本文实验测量系统的可靠性以及对射频干扰影响进行修正的正确性。     

Hysteresis transition between diffuse and constricted modes of dc discharge in argon

The results of theoretical studies of hysteresis transition between the diffuse and constricted modes of a dc glow discharge in argon are presented. It has been shown that the experimentally observed hysteresis of the current voltage characteristic (CVC) at the transition from the constricted to the diffuse mode is caused by the nonlocal formation of the electron energy distribution function (EEDF) while taking into account the heterogeneity of radial fields, namely, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region. The effect of the non-local formation of the EEDF has been described approximately by introducing the effective temperature of the high-energy part of the EEDF and solving the equation for the radial profile of the high-energy part of the EEDF.     

二次电子分布函数对绝缘壁面稳态鞘层特性的影响

由于缺乏详细的理论计算和实验结果,在研究绝缘壁面稳态流体鞘层特性时,通常假设壁面出射的总二次电子服从单能分布(0)、半Maxwellian分布等.在单能电子轰击壁面的详细二次电子发射模型基础上,采用Monte Carlo方法统计发现:当入射电子服从Maxwellian分布时,绝缘壁面发射的总二次电子服从三温Maxwellian分布.进而,采用一维稳态流体鞘层模型进行对比研究,结果表明:二次电子分布函数对鞘边离子能量、壁面电势、电势及电子/离子密度分布等均具有明显影响;总二次电子服从三温Maxwellian分布时,临界空间电荷饱和鞘层无解,表明随着壁面总二次电子发射系数的增加,鞘层直接从经典鞘层结构过渡到反鞘层结构.