Numerical study on discharge characteristics influenced by secondary electron emission in capacitive RF argon glow discharges by fluid modeling

A one-dimensional(1D) fluid model of capacitive RF argon glow discharges between two parallel-plate electrodes at low pressure is employed. The influence of the secondary electron emission on the plasma characteristics in the discharges is investigated numerically by the model. The results show that as the secondary electron emission coefficient increases,the cycle-averaged electric field has almost no change; the cycle-averaged electron temperature in the bulk plasma almost does not change, but it increases in the two sheath regions; the cycle-averaged ionization rate, electron density, electron current density, ion current density, and total current density all increase. Also, the cycle-averaged secondary electron fluxes on the surfaces of the electrodes increase as the secondary electron emission coefficient increases. The evolutions of the electron flux, the secondary electron flux and the ion flux on the powered electrode increase as the secondary electron emission coefficient increases. The cycle-averaged electron pressure heating, electron Ohmic heating, electron heating, and ion heating in the two sheath regions increase as the secondary electron emission coefficient increases. The cycle-averaged electron energy loss increases with increasing secondary electron emission coefficient.     

Effect of driving frequency on electron heating in capacitively coupled RF argon glow discharges at low pressure

A one-dimensional(1D) fluid model on capacitively coupled radio frequency(RF) argon glow discharge between parallel-plates electrodes at low pressure is established to test the effect of the driving frequency on electron heating. The model is solved numerically by a finite difference method. The numerical results show that the discharge process may be divided into three stages: the growing rapidly stage, the growing slowly stage, and the steady stage. In the steady stage,the maximal electron density increases as the driving frequency increases. The results show that the discharge region has three parts: the powered electrode sheath region, the bulk plasma region and the grounded electrode sheath region. In the growing rapidly stage(at 18 μs), the results of the cycle-averaged electric field, electron temperature, electron density, and electric potentials for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are compared, respectively. Furthermore,the results of cycle-averaged electron pressure cooling, electron ohmic heating, electron heating, and electron energy loss for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are discussed, respectively. It is also found that the effect of the cycle-averaged electron pressure cooling on the electrons is to "cool" the electrons; the effect of the electron ohmic heating on the electrons is always to "heat" the electrons; the effect of the cycle-averaged electron ohmic heating on the electrons is stronger than the effect of the cycle-averaged electron pressure cooling on the electrons in the discharge region except in the regions near the electrodes. Therefore, the effect of the cycle-averaged electron heating on the electrons is to "heat" the electrons in the discharge region except in the regions near the electrodes. However, in the regions near the electrodes, the effect of the cycle-averaged electron heating on the electron is to "cool" the electrons. Finally, the space distributions of the electron pressure cooling the electron ohmic heating and the electron heating at 1/4 T, 2/4 T, 3/4 T, and 4/4 T in one RF-cycle are presented and compared.     

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.     

Simulation of radio-frequency atmospheric pressure glow discharge in γ mode

The existence of two diffe1：ent discharge modes has been verified in an rf （radio-frequency） atmospheric pressure glow discharge （APGD） by Shi [J. Appl. Phys. 97, 023306 （2005）]. In the first mode, referred to as a mode, the discharge current density is relatively low and the bulk plasma electrons acquire the energy due to the sheath expansion. In the second mode, termed γ mode, the discharge current density is relatively high, the secondary electrons emitted by cathodc under ion bombardment in the cathode sheath region play an important role in sustaining the discharge. In this paper, a one-dimensional self-consistent fluid model for rf APGDs is used to simulate the discharge mechanisms in the mode in helium discharge between two parallel metallic planar electrodes. The results show that as the applied voltage increases, the discharge current becomes greater and the plasma density correspondingly increases, consequentially the discharge transits from the a mode into the γ mode. The high collisionality of the APGD plasma results in significant drop of discharge potential across the sheath region, and the electron Joule heating and the electron collisional energy loss reach their maxima in the region. The validity of the simulation is checked with the available experimental and numerical data.     

电子回旋共振等离子体密度均匀性的数值研究

基于漂移扩散近似,在轴对称假设下,对电子回旋共振等离子体源腔室内的等离子体建立了二维流体模型.采用有限差分法对所建立的模型进行了自洽数值模拟,得到了等离子体密度均匀性随时间演化的数值结果.通过对数值结果的分析,研究了背景气体压强、微波功率和磁场线圈电流对等离子体密度均匀性的影响.研究表明,在电离初期,电子密度的均匀性好于离子密度的均匀性.在电离后期,离子密度的均匀性好于电子密度的均匀性.随着背景气体压强的增大,电子密度和离子密度的均匀性都在增加,且离子密度的均匀性增加的更快.随着微波功率的增大,电子密度和 关键词： 等离子体密度均匀性 背景气体压强 微波功率 磁场线圈电流     

Numerical Study on Characteristics of Argon Radio-Frequency Glow Discharge with Varying gas Pressure

A one-dimensional fluid simulation on argon rf glow discharge with varying linearly gas pressure from 1 Torr to 100 Tort is performed. The model based on mass conservation equations for electron and ion under diffusion and mobility approximation, and the electron energy conservation equation is solved numerically by finite volume method. The numerical results show that a uniform plasma with high density can be obtained from rf glow discharge with varying gas pressure, and the density of plasma becomes higher as the gas pressure varies from 1 Tort to 100 Tort. It is also shown that in the range of the gas pressure from 1 Tort to 100 Tort with the slower rate of varying gas pressure, higher density of plasma can be obtained.     

Driving frequency effects on the mode transition in capacitively coupled argon discharges

A one-dimensional fluid model is employed to investigate the discharge sustaining mechanisms in the capacitively coupled argon plasmas, by modulating the driving frequency in the range of 40 kHz-60 MHz. The model incorporates the density and flux balance of electron and ion, electron energy balance, as well as Poisson's equation. In our simulation, the discharge experiences mode transition as the driving frequency increases, from the γ regime in which the discharge is maintained by the secondary electrons emitted from the electrodes under ion bombardment, to the α regime in which sheath oscillation is responsible for most of the electron heating in the discharge sustaining. The electron density and electron temperature at the centre of the discharge, as well as the ion flux on the electrode are figured out as a function of the driving frequency, to confirm the two regimes and transition between them. The effects of gas pressure, secondary electron emission coefficient and applied voltage on the discharge are also discussed.     

大气压双频氦气放电等离子体特性的数值研究

用一维流体模型研究了大气压双频氦气放电等离子体的特性。数值模拟的结果表明,在单、双频放电中,随着应用电压的增加,电子密度和放电电流都增加。相对于单频放电,双频放电中低频源的耦合效应使得放电中的电流以及电子密度降低。随着低频源电压峰值的增加,电子密度降低,离子通量,电子损失能量以及电子吸收能量均降低;但电子温度和电势随着低频源电压峰值的增加而增加。在相同低频源电压下,随着高频源电压的增加离子流非线性增加。     

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Based on one dimensional fluid model, the characteristics of helium plasma discharge driven by dual frequency at atmospheric pressure were studied. The results show that the electron density and discharge current increase with power voltage both in single frequency discharge and dual frequency discharge. In comparison with single frequency discharge, the discharge current and electron density in dual frequency discharge are lowered due to the coupling of low frequency source. As the voltage of low frequency source increases, the electron density, ion flux, electron energy dissipation, as well as electron heating decrease, whereas electron temperature and potential increase. As the voltage of high frequency source increases, the ion flux nonlinearly increases at the same voltage of low frequency source.     

Effects of secondary electron emission on plasma characteristics in dual-frequency atmospheric pressure helium discharge by fluid modeling

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 He_2~+, metastable atoms of He*and metastable molecules of He*_2 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 sheath's 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.     

Numerical study on the characteristics of nitrogen discharge at high pressure with induced plasma

Based on the fluid theory of plasma, a model is built to study the characteristics of nitrogen discharge at high pressure with induced argon plasma. In the model, species such as electrons, N2+, N4+, Ar+, and two metastable states (N 2(A3∑u+), N2 (a1 ∑u-)) are taken into account. The model includes the particle continuity equation, the electron energy balance equation, and Poisson抯equation. The model is solved with a finite difference method. The numerical results are obtained and used to investigate the effect of time taken to add nitrogen gas and initially-induced argon plasma pressure. It is found that lower speeds of adding the nitrogen gas and varying the gas pressure can induce higher plasma density, and inversely lower electron temperature. At high-pressure discharge, the electron density increases when the proportion of nitrogen component is below 40%, while the electron density will keep constant as the nitrogen component further increases. It is also shown that with the increase of initially-induced argon plasma pressure, the density of charged particles increases, and the electron temperature as well as the electric field decreases.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

甚高频电容耦合氢等离子体特性研究

采用高H₂稀释的SiH₄等离子体放电, 特别是甚高频等离子体增强化学气相沉积技术是当前高速制备优质微晶硅薄膜的主流方法. 尽管在实验上取得了很大的突破, 但其沉积机理一直是研究的热点和难点. 本文通过建立二维时变的轴对称模型,在75 MHz放电频率下, 对与微晶硅沉积非常相关的甚高频电容耦合氢等离子体放电进行了数值模拟, 研究了沉积参数对等离子体特性的影响, 并与光发射谱(OES)在线监测结果进行了比较. 结果表明: 电子浓度 n_e在等离子体体层中间区域最大, 而电子温度 T_e及H_α与H_β的数密度在体层和鞘层界面附近取极大值; 当气压从1 Torr (1 Torr=133.322 Pa)增大至5 Torr时, 等离子体电势单调降低, 在体层中间区域 n_e先快速增大然后逐渐减小, T_e先下降后趋于稳定; 随着放电功率从30 W增大到70 W, 电子浓度 n_e及H_α与H_β的数密度均线性增大, 而电子温度 T_e基本保持不变; OES在线分析结果与模拟结果符合得很好.     

Importance of high local cathode spot pressure on the attachment ofthermal arcs on cold cathodes

The importance of having high local cathode spot pressures for the self-sustaining operation of a thermal arc plasma on a cold cathode is theoretically investigated. Applying a cathode sheath model to a Cu cathode, it is shown that cathode spot plasma pressures ranging 7.4-9.2 atm and 34.2-50 atm for electron temperatures of ~1 eV are needed to account for current densities of 10⁹ and 10¹⁰ A·m^-2, respectively. The study of the different contributions from the ions, the emission electrons, and the back-diffusing plasma electrons to the total current and heat transfer to the cathode spot has allowed us to show the following. 1) Due to the high metallic plasma densities, a strong heating of the cathode occurs and an important surface electric field is established at the cathode surface causing strong thermo-field emission of electrons. 2) Due to the presence of a high density of ions in the cathode vicinity, an important fraction of the total current is carried by the ions and the electron emission is enhanced. 3) The total current is only slightly reduced by the presence of back-diffusing plasma electrons in the cathode sheath. For a current density j_tot=10⁹ A·m^-2 , the current to the cathode surface is mainly transported by the ions (76-91% of j_tot while for a current density j_tot = 10¹⁰ A·m^-2, the thermo-field electrons become the main current carriers (61-72% of j_tot). It is shown that the cathode spot plasma parameters are those of a high pressure metallic gas where deviations from the ideal gas law and important lowering of the ionization potentials are observed     

Numerical study on characteristics of nitrogen discharge at high pressure with induced plasma

Based on the fluid theory of plasma, a model is built to study the characteristics of nitrogen discharge at high pressure with induced argon plasma. In the model, the spices such as electron, N₂⁺, N₄⁺, Ar⁺, and two metastable states (N₂ (A³∑_u⁺), N₂ (a¹∑_u^-)) are taken into account. The model includes particle's continuity equations, electron's energy balance equation, and Poisson equation. The model is solved with a finite difference method. The numerical results are obtained and used to investigate the effect of time taken to add nitrogen gas and initially-induced argon plasma pressure. It is found that lower speeds of adding the nitrogen gas and varying the gas pressure can induce higher plasma density, and inversely lower electron temperature. At high-pressure discharge, the electron density increases when the proportion of nitrogen component is below 40%, while the electron density will keep constant as the nitrogen component further increases. It is also shown that with the increase of initially-induced argon plasma pressure, the density of charged particles increases, and the electron temperature as well as the electric field decrease.     

大气压脉冲调制射频氩气放电等离子体特性的数值研究

基于等离子体流体理论,建立了大气压脉冲调制射频氩气放电的一维流体模型。通过数值模拟的方 法研究了放电参数(放电电极间距、射频频率)对氩等离子体特性的影响。研究结果表明：当电压固定时,随着电 极间距的增加,等离子体区逐渐增大,最大电子密度也增加,在 0.20cm 达到最大值后略有降低;放电电流密度 与输入功率密度随着电极间距的增加而增加;鞘层区电子温度随着电极间距的增加而降低;在脉冲开启前期,等 离子体区电子温度随着电极间距的增加而增加,但当脉冲开启后期,电极间距对等离子体区电子温度影响较小。 不同射频频率下最大电子密度随电极间隙的增加而减小,也具有一个最优值。      

高功率微波输出窗内侧击穿动力学的PIC/MCC模拟研究

高功率微波在受控热核聚变加热、微波高梯度加速器、高功率雷达、定向能武器、超级干扰机及冲击雷达等方面有着重要的应用.本文针对高功率微波输出窗内侧氩气放电击穿过程,建立了二次电子倍增和气体电离的一维空间分布、三维速度分布（1D3V）模型,并开发了相应的PIC/MC程序代码.研究了气压、微波频率、微波振幅对放电击穿的影响.结果表明：在真空情况下,介质窗放电击穿只存在二次电子倍增过程;在低气压和稍高气压时,二次电子倍增和气体电离共存;在极高气压时,气体电离占主导.给出了不同气压下电子、离子的密度和静电场的空间分布.此外还观察到,在500 mTorr时,随着微波振幅或微波频率的变化,气体电离出现的时刻和电离产生的等离子体峰值位置有较大差异,尤其是当微波频率（GHz）在数值上是微波振幅（MV/m）的2倍时,气体电离出现的较早.     

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采用Langmuir探针法结合发射光谱法对螺旋波诱导的低压氢等离子体进行诊断,根据Druyvesteyn 方法和日冕模型分析电子能量几率函数(EEPF)、有效电子温度(Teff)、电子密度(ne)及激发态氢原子密度(nH*)随实验参数的变化规律.结果表明:随射频功率(Prf)、气压(p)和约束磁场(B)的增大,EEPF峰位由高能向低能移动,Teff 下降;当Prf从25W增大至35W左右时,ne发生跳跃增长,而nH*始终随Prf增大线性增长;随p增大,ne和nH*都呈现先增加后减小的变化规律;随B增强,ne线性增长,而nH*先增大后减小.     

Power Absorption in High Power Microwave Discharges

Measurements on RF power absorption in microwave discharges at 2.45 GHz, at pressures from 1 to 30 Torr in N2 and from 1 to 500 Torr in Ar, are described. A linear slow-wave structure of the strapped-bar type was employed for coupling RF energy to the plasma. From measurements on the plasma volume and on the total power absorbed, the variation with gas pressure of the RF power density in the plasma was obtained. For an incident power of 1 kW, power densities as high as 2-3 W/cm3 over relatively large plasma volumes could be achieved. The experimental data were used to calculate the pressure dependence of the electron density in an argon plasma, for an incident power of 1 kW.