Modeling of the nanoparticle coagulation in pulsed radio-frequency capacitively coupled C_2H_2 discharges

The role of pulse parameters on nanoparticle property is investigated self-consistently based on a couple of fluid model and aerosol dynamics model in a capacitively coupled parallel-plate acetylene(C2H2) discharge. In this model, the mass continuity equation, momentum balance equation, and energy balance equation for neutral gas are taken into account.Thus, the thermophoretic force arises when a gas temperature gradient exists. The typical results of this model are positive and negative ion densities, electron impact collisions rates, nanoparticle density, and charge distributions. The simulation is performed for duty ratio 0.4/0.7/1.0, as well as pulse modulation frequency from 40 k Hz to 2.7 MHz for pure C2H2 discharges at a pressure of 500 m Torr. We find that the pulse parameters, especially the duty ratio, have a great affect on the dissociative attachment coefficient and the negative density. More importantly, by decreasing the duty ratio, nanoparticles start to diffuse to the wall. Under the action of gas flow, nanoparticle density peak is created in front of the pulse electrode,where the gas temperature is smaller.     

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.     

信号在时变等离子体中的传播特性

高速飞行器等离子鞘套由于飞行姿态调整、湍流、非均匀烧蚀等因素的影响,使其等离子体参数存在时变特性,针对这种传输介质的快速时变特性引起的电波幅度、相位上的寄生调制效应,本文利用大面积辉光放电等离子体产生装置,搭建了等离子体中信号传输实验系统,进行了S频段的单频信号与调制信号传输实验,观测验证了调制效应的存在,且其调制频率与等离子体变化频率具有一致性,进一步分析了等离子参数与寄生调制效应的关系,理论和实验结果表明:即使当载波频率大于等离子频率时,时变等离子引起的寄生调制效应也会使传输信号的星座图发生旋转,造成其判决容差裕度变小,通信可靠性下降,并且载波频率越接近等离子频率时,其寄生调制效应越强烈。     

Simulation of nanoparticle coagulation in radio-frequency C_2H_2/Ar microdischarges

The nanoparticle coagulation is investigated by using a couple of fluid models and aerosol dynamics model in argon with a 5% molecular acetylene admixture rf microdischarges,with the total input gas flow rate of 400 sccm.It co-exists with a homogeneous,secondary electron-dominated low temperature γ-mode glow discharges.The heat transfer equation and flow equation for neutral gas are taken into account.We mainly focused on investigations of the nanoparticle properties in atmospheric pressure microdischarges,and discussed the influences of pressure,electrode spacing,and applied voltage on the plasma density and nanoparticle density profiles.The results show that the characteristics of microdischarges are quite different from those of low pressure radio-frequency discharges.First,the nanoparticle density in the bulk plasma in microdischarges is much larger than that of low pressure discharges.Second,the nanoparticle density of 10 nm experiences an exponential increase as soon as the applied voltage increases,especially in the presheath.Finally,as the electrode spacing increases,the nanoparticle density decreased instead of increasing.     

Fluid simulation of the pulsed bias effect on inductively coupled nitrogen discharges for low-voltage plasma immersion ion implantation

Planar radio frequency inductively coupled plasmas(ICP) are employed for low-voltage ion implantation processes,with capacitive pulse biasing of the substrate for modulation of the ion energy. In this work, a two-dimensional(2D) selfconsistent fluid model has been employed to investigate the influence of the pulsed bias power on the nitrogen plasmas for various bias voltages and pulse frequencies. The results indicate that the plasma density as well as the inductive power density increase significantly when the bias voltage varies from 0 V to-4000 V, due to the heating of the capacitive field caused by the bias power. The N+fraction increases rapidly to a maximum at the beginning of the power-on time, and then it decreases and reaches the steady state at the end of the glow period. Moreover, it increases with the bias voltage during the power-on time, whereas the N_2~+ fraction exhibits a reverse behavior. When the pulse frequency increases to 25 kHz and40 kHz, the plasma steady state cannot be obtained, and a rapid decrease of the ion density at the substrate surface at the beginning of the glow period is observed.     

Ion energy distribution in a radio frequency sheath of plasma with Kappa electron velocity distribution

A hybrid model consisting of a one-dimensional radio frequency sheath model and an equivalent circuit model is used to investigate the effect of the non-Maxwellian plasma with enhanced electron tails on ion energy distribution (IED) at the plasma–wall interface. With the assumption that electrons obey the Kappa distribution in which the parameter κ characterizes the deviation from Maxwellian distribution, the bimodal shape of the IED can always be found with the decrease of κ under the condition of current experimental advanced superconducting tokamak (EAST) discharges during the ion cyclotron range of frequency wave heating. However, the height of the low-energy peak of the IED decreases, while the high-energy peak does not change significantly. In addition, the IED shifts towards the higher-energy regime, and the width of the IED expands with the decrease of κ . It is also shown that frequency and amplitude of the disturbance current, bulk plasma density, and ion temperature are the crucial parameters for determining the shape of IED even in the presence of super-thermal electrons.     

Runaway Electron Beam Instability in Slide-Away Discharges in the HT-7 Tokamak

Slide-away discharges are achieved by decreasing the plasma density or ramping down the plasma current in runaway discharges in the HT-7 tokamak. In the case of plasma current ramp down, the ratio of the electron plasma frequency to the electron cyclotron frequency is higher than in the stationary pulses when the discharge goes into a slide-away regime. The instability regime is characterized by relaxations in the electron cyclotron emission due to relativistic anomalous Doppler effect which transfers energy from parallel to perpendicular motion. The triggering of relativistic anomalous Doppler effect at higher density by ramping down of plasma current may provide a alternative runaway energy control scenario.     

Anomalous capacitive sheath with deep radio-frequency electric-field penetration

A novel nonlinear effect of anomalously deep penetration of an external radio-frequency electric field into a plasma is described. A self-consistent kinetic treatment reveals a transition region between the sheath and the plasma. Because of the electron velocity modulation in the sheath, bunches in the energetic electron density are formed in the transition region adjacent to the sheath. The width of the region is of order V(T)/omega, where V(T) is the electron thermal velocity, and omega is the frequency of the electric field. The presence of the electric field in the transition region results in a collisionless cooling of the energetic electrons and an additional heating of the cold electrons.     

Positively Biased Probes in Magnetized Plasmas

Positively biased probes in magnetized plasmas can create several phenomena which are not described by standard probe theories. These include transient currents for pulsed electrodes in the regime of Electron MHD, relaxation oscillations induced by large probes and high frequency instabilities at the sheath‐plasma frequency. Although they may limit the use of probes for diagnostic purposes they also offer new applications and belong to the general knowledge of probes in plasmas (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear lumped model circuit of capacitively coupled plasmas at the intermediate radio-frequencies

The discharge dynamics in geometrically asymmetric capacitively coupled plasmas are investigated via a lumped model circuit. A realistic reactor configuration is assumed. A single and two separate RF voltage sources are considered. One of the driven frequencies (the higher frequency) has been adjusted to excite a plasma series resonance, while the second frequency (the lower frequency) is in the range of the ion plasma frequency. Increasing the plasma pressure in the low pressure regime ($\le 100\text{mTorr}$) is found to diminish the amplitude of the self-excited harmonics of the discharge current, however, the net result is enhancing the plasma heating. The modulation of the ion density with the lower driving frequency affect the plasma heating considerably. The net effect depends on the amplitude and the phase of the ion modulation.     

Nonlinear dynamics of radio frequency plasma processing reactorspowered by multifrequency sources

The source frequency has a strong influence on plasma characteristics in RF discharges. Multiple sources at widely different frequencies are often simultaneously used to separately optimize the magnitude and energy of ion fluxes to the substrate. In doing so, the sources are relatively independent of each other. These sources can, however, nonlinearly interact if the frequencies are sufficiently close. The resulting plasma and electrical characteristics can then be significantly different from those due to the sum of the individual sources. In this paper, a plasma equipment model is used to investigate the interaction of multiple frequency sources in capacitively and inductively coupled RF excited plasmas. In capacitively coupled systems, we confirmed that the plasma density increases with increasing frequency but also found that the magnitude of the DC bias and DC sheath voltage decreases. To produce a capacitively coupled discharge having a high plasma density with a large DC bias, we combined low and high frequency sources. The plasma density did increase using the dual frequency system as compared to the single low frequency source. The sources, however, nonlinearly interacted at the grounded wall sheath, thereby shifting both the plasma potential and DC bias. In inductively coupled plasmas (ICP), the frequency of the capacitive substrate bias does not have a significant effect on electron temperature and density. The DC bias and DC sheath voltage at the substrate were, however, found to strongly depend on source frequency. By using additional RF sources at alternate locations in ICP reactors, it was found that the DC bias at the substrate was varied without significantly changing other plasma parameters, such as the substrate sheath potential     

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.     

2D Simulations of Short‐Pulsed Dielectric Barrier Discharge Xenon Excimer Lamp

Self‐consistent two‐dimensional (2D) simulations of short‐pulsed dielectric barrier discharge (DBD) in pure xenon have been performed. It is shown that during short current pulse the traversal inhomogeneity of the plasma parameters can be important only at the end of the current pulse as an edge effect close to the side walls. During the current pulse, the gap voltage drops until the ionization wave reaches the cathode so the current in the cathode sheath is the displacement current. This means that almost all of the absorbed power is deposited into excitation of xenon atoms and not to the ion heating in the cathode sheath as in the traditional glow discharges. This fact is one of the reasons of high efficiency of short‐pulsed DBD. The developed model allows one to estimate the temporal position of the plasma‐sheath boundary. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the pressure dependence of DC bias voltage in asymmetric,capacitive RF sheaths

A semianalytical model for capacitively coupled radio frequency (RF) sheaths of asymmetric (unequal electrode area) systems has been developed. It can be applied in the high-frequency (ω > ω _pi) regime at different pressures. An analytical approximation to the pressure-dependent ion density profile is used. The time-varying electric field and potential within the sheath are obtained by solving Poisson's equation. The current balance and zero net DC current conditions are applied to solve for the RF sheath parameters and DC bias voltage. The DC voltage ratio between the powered and grounded electrode sheaths increases as the pressure decreases, which results in a larger DC bias voltage at lower pressures     

Excitation of the half-frequency of the input signal in theresponse of an antenna immersed in a plasma

The nonlinear response of a cylindrical monopole antenna immersed in a steady-state collisionless magnetic-field-free plasma and driven by a single-frequency RF source is investigated. The thickness of the ion sheath surrounding the antenna is controlled by a DC bias applied to the latter. It is found that at frequencies of the driving signal close to twice the frequency of a sheath wave resonance, the 1/2-subharmonic is excited, provided that the input power level is sufficiently high. The dependence of this process on the sheath thickness and on the electron plasma density is studied in the vicinity of several sheath wave resonances. This nonlinear effect is interpreted as a parametric excitation due to the periodic modulation of the sheath thickness, and hence its capacitance, by the applied RF signal. A similar effect can be obtained by replacing the antenna-sheath-plasma structure in the measuring circuit by a variable capacitance diode. A numerical analysis of the differential equation describing the current waveform in a microwave network modeling the antenna-sheath-plasma system is presented. It confirms the fact that a periodically modulated capacitance embedded in a linear circuit is responsible for the observed excitation of the half-frequency of the input signal     

碰撞对两种正离子的电负性磁鞘影响的数值研究

建立包括两种正离子的电负性磁鞘的流体模型,利用四阶龙格库塔法数值求解描述一维稳态等离子体鞘层的方程组,考察离子与中性粒子碰撞对一维稳态等离子体鞘层的影响.结果表明:鞘边Ar⁺与He⁺的含量比值与碰撞参数对离子马赫数的取值范围都有影响.鞘边负离子含量越少,碰撞对鞘层中带电粒子密度的影响越明显.并且随碰撞参数的加大,鞘层中电子、负离子的密度下降越快,两种正离子的密度则呈现不同的波动变化.鞘边负离子含量越多,碰撞对鞘层中两种正离子的速度影响就越明显.此外,碰撞参数越大对鞘边δ越大的鞘层中的带电粒子密度影响越大.     

Effects of gas pressure on plasma characteristics in dual frequency argon capacitive glow discharges at low pressure by a self-consistent fluid model

A self-consistent fluid model for dual radio frequency argon capacitive glow discharges at low pressure is established.Numerical results are obtained by using a finite difference method to solve the model numerically, and the results are analyzed to study the effect of gas pressure on the plasma characteristics. It shows that when the gas pressure increases from 0.3 Torr(1 Torr = 1.33322×10~2 Pa) to 1.5 Torr, the cycle-averaged plasma density and the ionization rate increase;the cycle-averaged ion current densities and ion energy densities on the electrodes electrode increase; the cycle-averaged electron temperature decreases. Also, the instantaneous electron density in the powered sheath region is presented and discussed. The cycle-averaged electric field has a complex behavior with the increasing of gas pressure, and its changes take place mainly in the two sheath regions. The cycle-averaged electron pressure heating, electron ohmic heating, electron heating, and electron energy loss are all influenced by the gas pressure. Two peaks of the electron heating appear in the sheath regions and the two peaks become larger and move to electrodes as the gas pressure increases.     

射频等离子体鞘层动力学模型

在流体力学方程的基础上建立了一种自洽的无碰撞射频等离子体鞘层动力学模型.这种自洽性包含两个方面:一方面,由于考虑了瞬时鞘层电场对离子运动的影响,因此该模型适用于描述任意频率段的射频鞘层演化过程;另一方面,在模型中采用等效电路方法来自洽地确定极板上的瞬时电位与瞬时鞘层厚度之间的关系.采用数值方法模拟出鞘层的瞬时厚度及极板的瞬时电位变化、鞘层内离子密度和电场强度等物理量的时空变化.结果表明,当射频场的频率小于或等于离子等离子体频率时,离子流密度明显地随时间变化 关键词： 射频 离子 鞘层 流体力学     

Sheath motion in a capacitively coupled radio frequency discharge

The sheath motion in a capacitively coupled RF discharge is highly nonlinear. The voltage waveform on a cylindrical probe placed in the sheath region is measured as a function of position and time. A circuit model of the probe-discharge system relates the observed probe voltage to the sheath motion. The equations derived from this circuit model are solved numerically with varying nonlinear sheath motions; the resulting waveforms are compared with the experimental observations to determine the actual sheath motion. The time-varying plasma potential is also determined, indirectly, from the comparison. The authors also report observation of oscillations related to the plasma frequency, whose peak harmonic component can be calculated from a single plasma model. These oscillations can be a useful plasma diagnostic for determining plasma density. The presence of these high-frequency oscillations may significantly enhance the rate of stochastic heating of electrons     

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在HL-2A装置上研制了用于测量等离子体密度分布的两套幅度调制微波反射仪。微波反射仪采用时间延迟法。这两套微波反射仪有不同的频率范围(26.5～40GHz和40～60GHz),它们所对应的密度测量范围是(0.84～1.98)×1019m-3和(1.98～4.47)×1019m-3。时间分辨率可达1ms,空间分辨率约为5mm。